please answer ASAP I will brainlist
Step-by-step explanation:
a) 23.6 (1.08)^x for 2016 x = 26 ('x' is the number of years past 1990)
23.6 (1.08)^(26) = 174.6 billion
b) 109 = 23.6 ( 1.08)^x
4.6186 = 1.08^x
x = log 4.6186 / log1.08 = 19.88 yrs
means 1990 + 19.88 yrs = year 2010
Akira has 3 cheeses to arrange on a cheese board. She would like to arrange them in a row. In how many different orders can she arrange them?
Answer:
Step-by-step explanation:
Akira has 3 cheeses to arrange on a cheese board. She would like to arrange them in a row
The number of permutations of n distinct objects is given by n! (n factorial). In this case, Akira has 3 cheeses to arrange in a row. Therefore, the number of different orders she can arrange them is 3! = 6¹⁴.
So Akira can arrange the 3 cheeses in 6 different ways.
what is the percentage of profit of $350 on a $1200 investment
The percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.
The percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:
Percentage of profit = (Profit / Investment) x 100
In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:
PercThe percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:
Percentage of profit = (Profit / Investment) x 100
In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:
Percentage of profit = (350 / 1200) x 100
Calculating this expression gives us:
Percentage of profit = 0.2917 x 100 = 29.17%
Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.
To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917. Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.entage of profit = (350 / 1200) x 100
Calculating this expression gives us:
Percentage of profit = 0.2917 x 100 = 29.17%
Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.
To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917.
Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.
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Part A: solve the equation---
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
but i have to use the values x= -4,0,5. can some one please help me? i'm am so confused!!!
Answer:
Step-by-step explanation:
I understand your confusion. Let's go through the steps together to solve the equation correctly:
Given equation: 5 + x - 12 = 2x - 7
Combine like terms on the left side and the right side of the equation:
x - 7 = 2x - 7
Now, let's isolate the variable x. Subtract x from both sides of the equation:
x - x - 7 = 2x - x - 7
Simplifying:
-7 = x - 7
Next, add 7 to both sides of the equation:
-7 + 7 = x - 7 + 7
Simplifying:
0 = x
Therefore, the solution to the equation is x = 0.
If you need to use the values x = -4, 0, and 5, you can substitute each value into the original equation to check if it satisfies the equation. Let's do that:
For x = -4:
5 + (-4) - 12 = 2(-4) - 7
-11 = -15 - 7
-11 = -22
The equation is not satisfied for x = -4.
For x = 0:
5 + 0 - 12 = 2(0) - 7
-7 = -7
The equation is satisfied for x = 0.
For x = 5:
5 + 5 - 12 = 2(5) - 7
-2 = 3
The equation is not satisfied for x = 5.
Therefore, the correct solution to the equation is x = 0. The values x = -4 and x = 5 do not satisfy the equation.
3. Your family is planning a road trip stretching from coast to coast for this summer. The route and the time frame are nearly set; now you need to plan out the finances. Your parents have decided that rental of an RV will be cheaper than staying in hotels, but they would like an estimate on the total cost. Can you help them?
a. To rent an RV, the following costs apply: $125 per day, plus 32 cents per mile. Additionally, to drop off the RV on the other side of the country, there is an extra fee of $2,500. Write an equation to describe the total cost of RV rental.
b. Your parents have two options for their road trip plans. The first option stretches over 3500 miles and includes fewer stops but more beautiful scenery. It will take about a week and a half (11 days). The second option stretches over just 3000 miles, but it includes more overnight stops and will therefore take two weeks (14 days). Which of these two options is cheaper?
c. Your little sister really wants to take the two-week trip, but your parents really want to keep the RV rental cost under $5,000. You can compromise by either taking a more direct route (lessening the miles) or by stopping for less overnight stays (lessening the days of the rental). What would the domains be for these two compromises? Justify why you think your domains are correct.
d. Write and solve equations to find how many miles or how many days you would have to eliminate in order to stay under the $5,000 budget. Explain each step as you solve your equations. Finally, make a recommendation to your parents about which compromise you think is best.
Answer:
Step-by-step explanation:
a. To write an equation describing the total cost of RV rental, we can use the given information:
Let x be the number of days of rental.
Let y be the number of miles driven.
The total cost of RV rental can be calculated as follows:
Total cost = (125 * x) + (0.32 * y) + 2500
b. To compare the cost of the two options, we need to calculate the total cost for each option.
Option 1:
x = 11 days
y = 3500 miles
Total cost = (125 * 11) + (0.32 * 3500) + 2500
Option 2:
x = 14 days
y = 3000 miles
Total cost = (125 * 14) + (0.32 * 3000) + 2500
Compare the total costs of both options to determine which one is cheaper.
c. To compromise and keep the rental cost under $5,000, we can adjust either the number of miles driven or the number of days of rental.
For the first compromise (lessening the miles), let's assume the new number of miles driven is y1.
The domain for the compromise in miles would be 0 ≤ y1 ≤ 3500, as you cannot drive more miles than the original option or negative miles.
For the second compromise (lessening the days of rental), let's assume the new number of days of rental is x1.
The domain for the compromise in days would be 0 ≤ x1 ≤ 14, as you cannot have more days of rental than the original option or negative days.
The justification for these domains is that they restrict the values within the range of the original options while allowing for adjustments in the desired direction.
d. To find out how many miles or how many days need to be eliminated to stay under the $5,000 budget, we can set up and solve equations.
For the compromise in miles (y1):
(125 * x) + (0.32 * y1) + 2500 ≤ 5000
For the compromise in days (x1):
(125 * x1) + (0.32 * y) + 2500 ≤ 5000
Solve each equation by isolating the variable to determine the maximum allowed value for y1 or x1, respectively.
Finally, after solving the equations, compare the maximum allowed values for y1 and x1 and consider other factors like practicality, time constraints, and preferences to make a recommendation to your parents about which compromise is best.
Ralph chase plans to sell a piece of property for $145000. He wants the money to be paid off in two ways-short term note at 10% interest and a long term note at 8% interest. Find the amount of each note if the total annual interest paid is $13100.
10%:
8%:
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the amount of money Ralph Chase will receive through the short-term note is represented by "x" and the amount through the long-term note is represented by "y".
According to the problem, the total amount Ralph plans to sell the property for is $145,000. Therefore, we have the equation:
[tex]\displaystyle x+y=145000[/tex] ...(1)
Now let's consider the interest paid annually. The interest paid on the short-term note at 10% is calculated as [tex]\displaystyle 0.10x[/tex], and the interest paid on the long-term note at 8% is [tex]\displaystyle 0.08y[/tex]. The total annual interest paid is given as $13,100. Therefore, we have the equation:
[tex]\displaystyle 0.10x+0.08y=13100[/tex] ...(2)
We now have a system of two equations (1) and (2). We can solve this system to find the values of "x" and "y".
Multiplying equation (2) by 100 to eliminate decimals, we get:
[tex]\displaystyle 10x+8y=1310000[/tex] ...(3)
Now we can solve equations (1) and (3) simultaneously using any method such as substitution or elimination.
Multiplying equation (1) by 10, we get:
[tex]\displaystyle 10x+10y=1450000[/tex] ...(4)
Subtracting equation (3) from equation (4), we can eliminate "x" and solve for "y":
[tex]\displaystyle 2y=140000[/tex]
Dividing both sides by 2, we find:
[tex]\displaystyle y=70000[/tex]
Now substituting the value of "y" back into equation (1), we can solve for "x":
[tex]\displaystyle x+70000=145000[/tex]
Subtracting 70000 from both sides, we have:
[tex]\displaystyle x=75000[/tex]
Therefore, the amount of money Ralph Chase will receive through the short-term note is 75,000 and through the long-term note is $70,000.
Solve this ASAP PLS HELP
Answer:
(2, -1)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=-2x+3\\y+9=4x\end{cases}[/tex]
To solve the given system of equations, we can use the method of substitution.
Substitute the first equation into the second equation to eliminate the y term:
[tex](-2x+3)+9=4x[/tex]
Solve for x:
[tex]-2x+3+9=4x[/tex]
[tex]-2x+12=4x[/tex]
[tex]-2x+12+2x=4x+2x[/tex]
[tex]12=6x[/tex]
[tex]\dfrac{12}{6}=\dfrac{6x}{6}[/tex]
[tex]2=x[/tex]
[tex]x=2[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]y=-2(2)+3[/tex]
[tex]y=-4+3[/tex]
[tex]y=-1[/tex]
Therefore, the solution to the system of equations is (2, -1).
To verify the solution by graphing the system, find two points on each line by substituting two values of x into each equation. Plot the points and draw a line through them. The solution is the point of intersection.
Graphing y = -2x + 3
[tex]\begin{aligned} x=0 \implies y&=-2(0)+3\\y&=0+3\\y&=3\end{aligned}[/tex] [tex]\begin{aligned} x=-2 \implies y&=-2(-2)+3\\y&=4+3\\y&=7\end{aligned}[/tex]
Plot points (0, 3) and (-2, 7) and draw a straight line through them.
Graphing y + 9 = 4x
[tex]\begin{aligned} x=0 \implies y+9&=4(0)\\y+9&=0\\y&=-9\end{aligned}[/tex] [tex]\begin{aligned} x=3 \implies y+9&=4(3)\\y+9&=12\\y&=3\end{aligned}[/tex]
Plot points (0, -9) and (3, 3) and draw a straight line through them.
The solution to the graphed system of equations is the point of intersection of the two lines: (2, 1).
1) (20) The temperature on a mountain forms a linear relationship with
the altitude at any given point of the mountain.
The temperature at 4800 feet is 79 degrees while the temperature at
6400 feet is 67 degrees.
=Find a linear model T(x) = mx + b Where x is the altitude.
a) Find the linear model. Show work!
b) What are the units of m, the slope of the line? Hint: Look at the units
of the x values and y values.
c) Find T(5800)
By analyzing the temperature-altitude relationship on a mountain, we can establish a linear model that describes how temperature changes with varying altitudes.
Step-by-step explanation:
a) Knowing the altitude and temperature data, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are two points on the line.
Using the altitude and temperature values provided:
(x1, y1) = (4800, 79) and (x2, y2) = (6400, 67),
we can calculate the slope:
m = (67 - 79) / (6400 - 4800)
= -12 / 1600
= -0.0075.
Now, to find the y-intercept (b), we can substitute one of the points (4800, 79) into the equation:
79 = (-0.0075)(4800) + b.
Solving for b, we have:
b = 79 + 0.0075(4800)
= 79 + 36
= 115.
Therefore, the linear model is T(x) = -0.0075x + 115.
b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.
c) To find T(5800), we can substitute x = 5800 into the linear model:
T(5800) = -0.0075(5800) + 115
= -43.5 + 115
= 71.5.
Answers:
a) T(x) = -0.0075x + 115.
b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.
c) 71.5 degrees.
Find the value of x
A. 16
B. 6
C. 4√5
8. √5
Colin and Paul have played 38 tennis matches.
Colin has won 20 times.
Paul won the rest.
a) Estimate the probability that Colin wins.
b) Estimate the probability that Paul wins.
Answer:
P(Colin) = 20/38
P(Paul) = 18/38
Step-by-step explanation:
Colin won 20 times out of 38, so the probability that he wins would be 20/38 (or 10/19 simplified).
Paul won 18 times out of 38, so the probability that he wins would be 18/38 (or 9/19 simplified).
Answer:
a) Probability of Colin winning = 10/19
b) Probability of Paul winning = 9/19
Step-by-step explanation:
Total number of matches = 38
Colin won 20,
Paul won the rest so, 38 - 20 = 18
Paul won 18 matches,
From this data, we calculate the probabilities of Colin or Paul winning,
a) Estimate the probability that Colin wins.
Colin won 20 out of 38 matches, so his probability of winning is,
20/38 = 10/19
Probability of Colin winning = 10/19
b) Estimate the probability that Paul wins
Paul won 18 out of 38 matches, so his probability of winning is,
18/38 = 9/19
Probability of Paul winning = 9/19
Simplify the expression to a polynomial in standard form (x^2+3x+3) (-2x^2-x+6)
The polynomial [tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex] simplifies to [tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18.[/tex]
A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is defined as a sum of terms, where each term consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.
The general form of a polynomial is:
P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a₀
To simplify the expression[tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex], we need to perform the multiplication and combine like terms.
First, we multiply each term in the first polynomial by each term in the second polynomial:
[tex](x^2 + 3x + 3) * (-2x^2 - x + 6) = x^2 * (-2x^2 - x + 6) + 3x * (-2x^2 - x + 6) + 3 * (-2x^2 - x + 6)[/tex]
Expanding each term, we get:
=[tex](-2x^4 - x^3 + 6x^2) + (-6x^3 - 3x^2 + 18x) + (-6x^2 - 3x + 18)[/tex]
Now, we combine like terms:
=[tex]-2x^4 + (-x^3 - 6x^3) + (6x^2 - 3x^2 - 6x^2) + (18x + 18x - 3x) + 18[/tex]
Simplifying further:
=[tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18[/tex]
The simplified expression in polynomial standard form is:
-2x^4 - 7x^3 - 3x^2 + 33x + 18
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In random sampling, the probability of selecting an item from the population is:
Select one:
a. Un-Known
b. One
c. known
d. undefined
e. Un-decided
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answer: c. known
Step-by-step explanation:
In random sampling, the probability of selecting an item from the population is known. This probability can be calculated based on the sampling method and the characteristics of the population being sampled. Random sampling ensures that each item in the population has an equal chance of being selected, making the probability of selection known and calculable.
below is the graph of a trigonometric function it has a maximum point at (-pi , 7.7) and a minimum point at (- 1/3 pi, -6.7)
what is the period of the function? give an exact value
The period of the trigonometric function is -2π/3.
What is the period of the function?To determine the period of the trigonometric function based on the given information, we need to consider the pattern of the graph and identify the interval over which it repeats.
Given that the maximum point is at (-π, 7.7) and the minimum point is at (-1/3π, -6.7), we can observe that the graph completes one full oscillation between these two points.
The distance between the maximum and minimum points corresponds to half of the period. Therefore, the full period of the function can be found by doubling this distance.
The distance between (-π, 7.7) and (-1/3π, -6.7) can be calculated as follows:
Δx = -1/3π - (-π) = π/3π - π = -π/3
Since the full period is twice this distance, we multiply by 2:
2 * (-π/3) = -2π/3
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can someone tell me which graph is right and how did we graph it?
The graph of the trigonometric function is the first one.
Which graph is the correct one?Here we have the trigonometric function:
y = 15*sin(x/2).
So, the amplitud if 15, thus, the distance between a maximum and a minimum must be of 15*2 = 30 units.
Also, for x =0 we have:
y = 15*sin(0/2) = 0
y = 0
So the fourth graph can be discarded.
Also, when x increases also does the function (near x = 0), so the third graph is discarded.
Finally, sin(pi) = 0, in this case when x = 2pi we will get:
15*sin(2pi/2) = 0
Then we have an x-intercept at 2pi, thus, the correct option is the first one.
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What kind of growth model (pattern) is shown in the table?
x
y
1
5
2
25
3
125
4
625
5
3,125
square root
linear
exponential
quadratic
Answer:
Option C is correct.
The kind of growth model is shown in the table is exponential
Step-by-step explanation:
Exponential growth function is in the form of : ......[1]; where a is the initial value and b> 0.
Consider any two point from the table:
(1 , 5) and ( 2 , 25)
Substitute these in the equation [1] we get;
......[2]
......[3]
Divide equation [3] by [2] we have;
Simplify:
Now substitute this value in equation [2] we get;
Divide both sides by 5 we get;
Simplify:
1=a or a = 1
Therefore, the table shown the exponential growth function y=5^x
Assume that each circle shown below represents one unit.express the shaded amount as a single fraction and as a mixed number
One fraction :
Mixed number:
The shape is represented as below
As one fraction = 9/4As a mixed number = 2 1/4How to represent the figure as a fractionThe figure is of three shapes, the firs two are whole numbers then the last is a fraction.
Adding them results to
shape 1 + shape 2 + shape 3
1 + 1 + 1/4
As one fraction
= 9/4
as a mixed number
= 2 1/4
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the value of tan80°×tan10°+sin70+sin 20
The value of tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276
What is Trigonometry?Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.
Given:
tan(80°) × tan(10°) + sin(70°) + sin(20°)
Using Trigonometric identity
sin (A · B) = sin A cos B - cos A sin B
So, tan(80°) × tan(10°) + sin(70°) + sin(20°)
[tex]\rightarrow \tan (80 \times 10)=1[/tex]
[tex]\rightarrow\sin(70^\circ+20^\circ)=1.28171276[/tex]
[tex]\rightarrow 1.28171276+1=\bold{2.28171276}[/tex]
Hence, tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276
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This Month
Quality
Productivity
Safety
Engagement
Last Month
Quality
Productivity
Safety
Engagement
ce Scores are based on 100 prant scale,
Great is 80 or stove for a categories
482324R
A
90
79
68
78
A
94
62
70
Group
B
2338-32N
70
58
84
88
B
74
86
76
72
33880*880
96
25
72
92
82
in which performance area are the
groups performing most
consistently compared to last
month?
Quality
Productivity
Associate Engagement
Group A is performing most consistently in terms of quality and associate engagement compared to last month.
To determine which performance area the groups are performing most consistently compared to last month, we need to compare the scores of each performance area between the two months.
Let's analyze each performance area:
Quality:
For Group A, the quality score increased from 90 to 94, indicating an improvement in quality performance. However, for Group B, the quality score decreased from 74 to 70, indicating a decline in quality performance. Therefore, Group A is performing more consistently in terms of quality compared to last month.
Productivity:
For Group A, the productivity score decreased from 79 to 62, showing a significant decline in productivity performance. Similarly, for Group B, the productivity score decreased from 86 to 58, indicating a notable decline as well. Both groups experienced a decrease in productivity performance, but Group A had a larger decline. Therefore, neither group is performing consistently in terms of productivity compared to last month.
Associate Engagement:
For Group A, the engagement score increased from 68 to 70, suggesting a slight improvement in associate engagement. Conversely, for Group B, the engagement score increased from 76 to 72, indicating a slight decline. Both groups had minor changes in engagement scores, but Group A had a smaller change. Therefore, Group A is performing more consistently in terms of associate engagement compared to last month.
Based on the analysis, Group A is performing most consistently in terms of quality and associate engagement compared to last month. However, neither group is performing consistently in terms of productivity. It is important to address the productivity decline and identify areas for improvement to ensure consistent performance across all categories.
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Find the center of the ellipse defined by the equation... 100 points
Answer:
(-4,4)
Step-by-step explanation:
You rewrite the terms:
(x + 4)^2 => [x - (-4)]^2
(y - 4)^2 => [y - (4)]^2
so h = -4 and k = 4
so center of ellipse is (h,k) or (-4,4)
Answer:
Center = (-4, 4)
Step-by-step explanation:
The standard form of the equation of an ellipse with center (h, k) is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
The given equation is:
[tex]\dfrac{(x+4)^2}{25}+\dfrac{(y-4)^2}{9}=1[/tex]
Comparing the given equation with the standard form, we can see that h = -4 and k = 4. Therefore, the center (h, k) of the ellipse is (-4, 4).
The cost of 2.5 litres of petrol in the United Kingdom is £1.70. The cost of 1 US gallon of petrol in the United States is $3.30. £1 = $1.42 1 litre = 0.26 US gallons Is petrol cheaper in the United Kingdom or United States?
The cost of 2.5 liters of petrol in the United Kingdom is £1.70. The cost of 1 US gallon of petrol in the United States is $3.30. £1 = $1.42 and 1 liter = 0.26 US gallons. So, is petrol cheaper in the United Kingdom or the United States.
Let's find out the cost of 2.5 liters of petrol in the United States dollars;Cost of 1 litre of petrol in the United Kingdom = £1.70/2.5 = £0.68Cost of 1 liter of petrol in the United States = $3.30/3.78 (as 1 US gallon = 3.78 liters) = $0.87We know that £1 = $1.42£0.68 = $0.68 x 1.42 = $0.96So, the cost of 1 liter of petrol in the United Kingdom is $0.96 (approximately)The cost of 1 liter of petrol in the United States is $0.87 (approximately)
Therefore, petrol is cheaper in the United States than the United Kingdom.
So, the answer is that petrol is cheaper in the United States than in the United Kingdom.
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¿Cuál es el costo de un plátano si el racimo de 22 plátanos cuesta $23.10?
The cost of a single unit is given as follows:
$1.05.
El costo de un plátano es el seguiente:
$1.05.
How to obtain the cost of a single unit?The cost of a single unit is obtained applying the proportions in the context of the problem.
The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:
23.1/22 = $1.05.
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graph the equation y = 2x + 2
Answer:
Step-by-step explanation:
When the equation is in the slope intercept form of y = mx + b, you know that the m is the slope and the b is the y-intercept (0, b)
By looking at the equation y=2x + 2, you can determine that the y-intercept will be at the point (0, 2) and the slope is 2.
To graph, start with the point of (0, 2) then go up 2 units and to the right 1 unit. So the next point will be at (1, 4)
You can also, substitute and number in for the x and calculate the y value. For example, if x is 3, then y=2(3)+2; y = 8 so the point (3, 8) is on the line.
In the diagram, mDGF = 62x+4. Find mDGF
O-210°
G
D
30x+5
F
E
The measure of the arc DGF which substends the angle DEF at the circumference of the circle is equal to 190°
What is angle subtended by an arc at the centerThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference.
Given that the arc DGF = (62x + 4)°
62x + 4 = 2(30x + 5)
62x + 4 = 60x + 10
62x - 60x = 10 - 4 {collect like terms}
2x = 6
x = 6/2
x = 3
arc DGF = 62(3) + 4 = 190°
Therefore, the measure of the arc DGF which substends the angle DEF at the circumference of the circle is equal to 190°
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Darla, Ellie, and Fran ate a whole container of ice cream. Darla ate half as much as Ellie ate, and Fran ate 5 times as much as Darla ate. If the container of ice cream cost $4.00, how much, in dollars, should each person pay?
pleasee help so disssicult
When going from left to right, the item goes up, it increases, and when it goes down, it decreases
What is the volume of this
figure?
A 774 cm³
B 3,546 cm³
C 843 cm3
D 2,250 cm³
Hello!
V
= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)
= 1,620cm³ + 630cm³
= 2,250cm³
On a piece of paper, graph y<-3/4x+2. Then determine which answer choice
matches the graph you drew.
The graph of the linear inequality is given by the image presented at the end of the answer.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The function for this problem is given as follows:
y = -3x/4 + 2.
Hence the graph crosses the y-axis at y = 2, and when x increases by 4, y decays by 3.
The inequality is given as follows:
y < -3x/4 + 2.
Meaning that points below the dashed line are the solution to the inequality.
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You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 25 by 26 ft brick patio installed.
Answer:
$4929
Step-by-step explanation:
I assume the cost is proportional to the area.
15 ft × 20 ft = 300 ft²
25 ft × 26 ft = 650 ft²
650/300 = x/$2275
300x = 650 × $2275
x = $4929
Answer: $4929
71)
Mia buys 4 calculators and 2 pens for $20.60
Heidi buys 5 calculators and 3 pens for $26.90.
Write down a pair of simultaneous equations and solve
cost of a pen.
Answer:
Therefore, the cost of a pen is $2.30.
Step-by-step explanation:
Let's assign variables to represent the cost of a calculator and the cost of a pen.
Let c represent the cost of a calculator.
Let p represent the cost of a pen.
Based on the given information, we can form the following pair of simultaneous equations:
Equation 1: 4c + 2p = 20.60 (Mia buys 4 calculators and 2 pens for $20.60)
Equation 2: 5c + 3p = 26.90 (Heidi buys 5 calculators and 3 pens for $26.90)
To solve for the cost of a pen, we'll eliminate the variable c by multiplying Equation 1 by 5 and Equation 2 by 4. Then we'll subtract Equation 1 from Equation 2:
5 * (4c + 2p) = 5 * 20.60
4 * (5c + 3p) = 4 * 26.90
20c + 10p = 103.00
20c + 12p = 107.60
Subtracting Equation 1 from Equation 2:
(20c + 12p) - (20c + 10p) = 107.60 - 103.00
20c - 20c + 12p - 10p = 4.60
2p = 4.60
p = 4.60 / 2
p = 2.30
Therefore, the cost of a pen is $2.30.
Answer:
Let's assume that the cost of a calculator is x and the cost of a pen is y. Then we can write the following pair of equations:
4x + 2y = 20.60 (equation 1)
5x + 3y = 26.90 (equation 2)
To solve for the cost of a pen, we need to eliminate x from the equations. We can do this by multiplying equation 1 by 5 and equation 2 by -4, and then adding them:
(5)(4x + 2y = 20.60) becomes 20x + 10y = 103 (equation 3)
(-4)(5x + 3y = 26.90) becomes -20x - 12y = -107.60 (equation 4)
Adding Equation 3 and Equation 4 gives:
-2y = -4.60
Divide both sides by -2:
y = 2.30
Therefore, the cost of a pen is $2.30.
Step-by-step explanation:
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The data below shows the money Paritosh spends on a weekend. What will be the central angles of each of these categories?with the numbers 40 100 50 50
The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.
To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:
Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.
Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).
Central angle for the first category: (40/240) * 360 = 60 degrees.
Central angle for the second category: (100/240) * 360 = 150 degrees.
Central angle for the third category: (50/240) * 360 = 75 degrees.
Central angle for the fourth category: (50/240) * 360 = 75 degrees.
The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.
These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.
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