On a school trip the ratio of teachers to students is 2:5.
There are 60 students on the trip.
Work out the total number of people in the trip

You can see all answers in the picture

Answer:

1) The polynomial in standard form is f(x) = x³ - 9·x² + 23·x - 15

2) The polynomial in standard form is f(x) = x³ - (2 - 2·i)·x² + 4·i·x

3) The polynomial in standard form is f(x) = x² + (3·i - 3)·x + 2 - 6·i

4) The polynomial in standard form is f(x) = x² - (5 + √5)·x + 6 + 3·√5

Step-by-step explanation:

Given that that the polynomial is of least degree, we have;

The standard form is the form, f(x) = a·xⁿ + b·xⁿ⁻¹ +...+ c

1) The zeros of the polynomial are x = 5, 3, 1

Which gives the polynomial in factored form as_f(x) = (x - 5)·(x - 3)·(x - 1)

From which we have;

f(x) = (x - 5)·(x - 3)·(x - 1) = (x - 5)·(x² - 4·x + 3) = x³ - 4·x² + 3·x - 5·x² + 20·x - 15

f(x) = x³ - 9·x² + 23·x - 15

The polynomial in standard form is therefore f(x) = x³ - 9·x² + 23·x - 15

2) The zeros of the polynomial are x = 2, 0, 2·i

Which gives the polynomial in factored form as_f(x) = (x - 2)·(x)·(x - 2·i)

From which we have;

f(x) = (x - 2)·x·(x - 2·i) = (x² - 2·x)·(x - 2·i) = x³ - 2·i·x² + 2·x² + 4·ix

The polynomial in standard form is therefore f(x) = x³ - (2 - 2·i)·x² + 4·i·x

3) The zeros of the polynomial are x = 2, 1 - 3·i

Which gives the polynomial in factored form as_f(x) = (x - 2)·(x - 1 - 3·i)

From which we have;

f(x) = (x - 2)·(x - (1 - 3·i)) = x² - x + 3·i·x - 2·x + 2 -6·i = x² + 3·i·x - 3·x + 2 - 6·i

The polynomial in standard form is therefore f(x) = x² + (3·i - 3)·x + 2 - 6·i

4) The zeros of the polynomial are x = 3, 2 + √5

Which gives the polynomial in factored form as_f(x) = (x - 3)·(x - (2 + √5))

From which we have;

f(x) = (x - 3)·(x - (2 + √5)) = x² - 2·x - x·√5 - 3·x + 6 + 3·√5

f(x) = x² - 5·x - x·√5 + 6 + 3·√5 = x² - (5 + √5)·x + 6 + 3·√5

The polynomial in standard form is therefore f(x) = x² - (5 + √5)·x + 6 + 3·√5.

Answer:

m=1

c=7

I hope it will be useful.

Answer:

y = 7

Step-by-step explanation:

Given

4y - 6 = 2y + 8 ( subtract 2y from both sides )

2y - 6 = 8 ( add 6 to both sides )

2y = 14 ( divide both sides by 2 )

y = 7

Answer:

9 books each

Step-by-step explanation:

Answer:

D. 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Set Up Equation

3x + 3x + 10 + 2x + 10 = 180

Step 2: Solve for x

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. Anna earns $20 for every 400 envelopes. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

Jason has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

[tex]y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table of Anna and Jason we can see that Anna makes more stuffing than Jason for the same number of envelopes.

c) Anna has a savings of $100 initially. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]

Therefore from the graph there is a y intercept at 100. That is the earnings starts initially is $100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value of y at x = 0)

For the first graph, the slope is 1/20 with an initial value of 0 while for the second graph the slope is 1/15 with an initial value of 100

D) The trend line pass through the points (10, 10) and (100, 40), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]

Answer:

a and c are correct

Step-by-step explanation:

i hoped this helped

Answer:

The nonlinear system of equations has 4 solutions ⇒ B

Step-by-step explanation:

The number of solutions of a system of equations equal to the number of points of intersection of the graphs of the equations of the system

Let us use this note to solve the question

From the given figure

∵ The nonlinear system of equations represented by two curves and a circle

∵ Each curve intersects the circle into two points

∴ The number of the points of intersection is 4

→ By using the note above

∵ The number of intersection points equal to the number of solutions

∴ The number of solutions is 4

∴ The nonlinear system of equations has 4 solutions

Answer:

10.8 kg

Step-by-step explanation:

w = 80 + 5.4t

At time 0, when he starts the diet, his initial weight is

w = 80 + 5.4(0)

w = 80

80 kg.

After 2 months, t = 2. His weight is

w = 80 + 5.4t

w = 80 + 5.4(2)

w = 80 + 10.8

w = 90.8

90.8 kg.

His gain in 2 months was 90.8 kg - 80 kg = 10.8 kg

Answer: 10.8 kg

The wrestler gains 10.8 kg every 2 months.

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

We have been given an equation that models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for t months.

w = 80 + 5.4t

We need to find his weight after 2 months.

At time t = 0, when he starts the diet, the wrestler's initial weight would be,

⇒ w = 80 + 5.4(0)

⇒ w = 80 kg

After 2 months, t = 2 the wrestler's weight  weight would be,

⇒ w = 80 + 5.4(2)

⇒ w = 80 + 10.8

⇒ w = 90.8 kg

We need to find the weight gain in 2 months.

90.8 - 80 = 10.8 kg

Therefore, the wrestler gains 10.8 kg every 2 months.

Learn more about an equation here:

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Answer:

Function.

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

If we apply the Vertical Line Test to the graph, we can see that each x-value has it's own y-value. Therefore, the graph is a function and not a relation.

Answer:

s = 6 inches

Step-by-step explanation:

Given:

r = 53 inches,

∠S = 6°

∠T = 58°.

Required:

Length of s

Solution:

Use Sine Rule

Thus:

[tex] \frac{s}{Sin(S)} = \frac{r}{Sin(R)} [/tex]

<R = 180 - (58 + 6)

<R = 116°

r = 53 inches,

∠S = 6°

s = ?

Plug in the values

[tex] \frac{s}{Sin(6)} = \frac{53}{Sin(116)} [/tex]

Multiply both sides by Sin(6)

[tex] \frac{s}{Sin(6)} \times Sin(6) = \frac{53}{Sin(116)} \times Sin(6) [/tex]

[tex] s = \frac{53 \times Sin(6)}{Sin(116)} [/tex]

[tex] s = 6 inches [/tex] (nearest inch)

Answer:

Step-by-step explanation:

The correct question is shown in the image attached below.

Recall that: the line m is parallel to line n. In addition to that, [tex]m \angle 1 = 50^0[/tex] and [tex]m \angle 2 = 48^0[/tex], and [tex]\angle ABC[/tex] is bisected by line s.

At this moment, by the angle addition postulate, angle DEF i.e.

∠DEF [tex]= m \angle 1 + m \angle 2[/tex]

∠DEF = 50° + 48°

∠DEF = 98°

Similarly, using the rule of the alternate exterior angle ∠DEF = ∠ABC (∵ alternate exterior angles exhibit congruency).

Furthermore, By the definition of a bisector, angles 4 and 5 are congruent due to the fact that the line of a bisector splits the angle into two equal parts.

m∠4 = m∠5

∴

98/2 = 49°

Finally;

from the diagram, angle 3 and 4 are vertical angles

Thus, m∠3 = 49 by substitution property of equality ( because vertical angles are congruent angles).

Answer:

Distance xy = 11.66 unit (Approx)

Step-by-step explanation:

Given:

x(-7,10)

y(3,4)

Find:

Distance xy

Computation:

Distance = √(x2-x1)²+(y2-y1)²

Distance xy = √(3+7)²+(4-10)²

Distance xy = √ 100 + 36

Distance xy = 11.66 unit (Approx)

Answer:

This is because the object on the 1st scale weighs (more) than the object on second scale, each pound of error results in a (lesser) percent error. The first scale was (10) pounds off the second scale,was (3) pounds off, so 1st scale was (10)% off 2nd scale was (12)% off.

Answer:

Because the object on Scale 1 weighs more than the object on Scale 2, each pound of error results in a lesser percent error. Scale 1 was 10 pounds off and Scale 2 was 3 pounds off, so Scale 1 was 10% off and Scale 2 was 12% off.

Step-by-step explanation:

Got it right on TTM so yeah! :)

Answer:

30

Step-by-step explanation:

I asked the my math tutor lol

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

We have,

Amount = 1102

Percentage increase = 2%

Another percentage increase = 1%

Now,

The final amount.

= 101% of 102% of 1102

This can be written as,

= 101/100 x 102/100 x 1102

= (101 x 102 x 1102) / 10000

= 1135.28

Thus,

The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.

Learn more about percentages here:

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Answer:

g(x) = 1/2x² is the correction option.

Hence, option B is true.

Step-by-step explanation:

Please check the attached graph.

It means when we multiply the parent function by a number 'b' which is less than 1, then the parent function f(x) = x² is vertically compressed by b.

Here, the graph is vertically compressed by 1/2, therefore we conclude that g(x) = 1/2x² is the result of vertical compression of the parent function by 1/2.

Therefore, g(x) = 1/2x² is the correction option.

Hence, option B is true.

The total area of a circle is pi * radius^2

The total area of the circle is pi x 5^2 = 25pi sq. cm.

2/5 of this is success, so the answer is 2/5 * 25pi = 10 pi sq. cm.

Answer:

2.333

Step-by-step explanation:

Given that:

Conceded goals: 0,1,2,3,4

Frequency:2,8,4,10,6

Mean(m) = Σ(fx) / Σf

Σfx = (0*2) + (1*8) + (2*4) + (3*10) + (4*6) = 70

Σf = (2 + 8 + 4 + 10 + 6) = 30

Hence,

Mean = 70 / 30

Mean = 2.333

Answer:

c

Step-by-step explanation:

c Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?

y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.

y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.

y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.

y less-than one-half x. y less-than-or-equal-to negative one-half x + 2v

The system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

The solution set is given as:

[tex](x,y) = (2,1)[/tex]

The above solution set is true for x + 2y ≤ 4 and 2x - y > 0, and the proof is as follows:

Substitute 2 for x and 1 for y in x + 2y ≤ 4 and 2x - y > 0.

So, we have:

[tex]\mathbf{2 + 2\times1 \le 4 }[/tex]

[tex]\mathbf{2 + 2\le 4 }[/tex]

[tex]\mathbf{4\le 4 }[/tex] --- this is true, because 4 is less than or equal to 4

Also, we have:

[tex]\mathbf{2x - y > 0}[/tex]

[tex]\mathbf{2 \times 2 - 1 > 0}[/tex]

[tex]\mathbf{4 - 1 > 0}[/tex]

[tex]\mathbf{3> 0}[/tex] --- this is also true, because 3 is greater than 0

Hence, the system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

Read more about inequalities at:

https://brainly.com/question/11702933

Final Answer: [tex]x = 3 + \sqrt{2}, 3 - \sqrt{2}[/tex]

Steps/Reasons/Explanation:

Question: Solve by using the quadratic formula:  [tex]x^{2} - 6x + 7 = 0[/tex].

Step 1: Use the Quadratic Formula.

[tex]x = \frac{6 + \sqrt[2]{2} }{2}, \frac{6 - \sqrt[2]{2} }{2}[/tex]

Step 2: Simplify solutions.

[tex]x = 3 + \sqrt{2}, 3 - \sqrt{2}[/tex]

~I hope I helped you :)~ The quadratic formulaic is attached in an image.

Answer:

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

Step-by-step explanation:

We have a ratio of

Red Jolly Ranchers : Green Jolly Ranchers

3:7

Sum of the proportion = 3 + 7 = 10

Hence:

Let the total number of jolly ranchers = x

7/10 of x = 42 Green Jolly Ranchers

Hence:

7/10 × x = 42

7x /10 = 42

Cross Multiply

7x = 420

x = 420/7

x = 60 Jolly Ranchers

The total amount of Jolly Ranchers in the container is 60 Jolly Ranchers

1. f(x) = x² + x + 4

f(x) = 0

0 = x² + x + 4

-4 = x² + x

2. linear equation

one solution

Answers:

plus all rounded so i don't cuffuse anyone

Answer:

1/4n - 16 =

1/4(n - 64)

Step-by-step explanation:

Two expression are said to be equivalent, if after substituting the value of variable by any constant the numerical value of both original expression and equivalent expression are same.

Answer:

C. 42 is 6 times as many as 252

Step-by-step explanation:

because 42×6 = 252