Answer:
Given:
Principal= $5,000
After 3 years, Amount= $7,100
After 8 years, Amount= $10,350
Step-by-step explanation:
Interest after 3 years= $7,100- $5,000
=$2,100
Interest in last 5 years= $10,350- $7,100
=$ 3,250
Difference between first 3 years and last 5 years= $3,250- $2,100
=$1,150
Amount= Principal*[tex](1+r/100)^{t}[/tex]
10,350=5000[tex](1+r/100)^{8}[/tex]
[tex]\frac{10350}{5000}[/tex]=[tex](1+r/100)^{8}[/tex]
2.07=[tex](1+r/100)^{8}[/tex]
[tex]2.07^{1/8}[/tex]=1+[tex]\frac{r}{100}[/tex]
1.095-1=[tex]\frac{r}{100}[/tex]
0.095*100=r
r=9.5%
Average rate=[tex]\frac{5000*9.5*1}{100}[/tex]
=$475
Answer:
drop down 1 a slower rate per year
drop down 2 670
Step-by-step explanation:
as in three years you get $7100
you take that and subtract it by your starting amount (5000)
7100-5000= 2100
then divide 2100 by the number of years (3)
to get your annual rate of 700$
then you take the 8 year total and subtract it from your 3 year total
10350-7100= 3250
Then divide that by 5 because that how many years it has been
to get the annual rate of 650
making the 5 year rate slower.
The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000
10350-5000= 5350
then take 5350 and divide it by the number of years (8)
you then get you average rate of 668.75
668.75=670
Hope this helps!
Solve for y
*show your work *
6. -6 + 2y= -x
7. 3y - 6x = 15
8. 2x + 4y = 8
9. 3x -3y = 3
10. 1/2y - 4x = 2
Answer: 1)2x=4 -> 4/2 = 2 so x=2
2) y=0
3) x=3
4) 2y + (3*3y) = -15
11y=-15
y = -15/11
5) 4x + 7x + 63 = 19
11x = -44
x = -4
Step-by-step explanation:
The local candle store marks up the price of its candles by 75% before selling them. If the store paid
the distributor $6.99 per candle, how much will a candle cost in the store?
Answer:
$12.23
Step-by-step explanation:
75/100 = 0.75
0.75 x 6.99 = 5.2425
6.99 + 5.2425 = 12.2325
1/4x+3/8 factored by the GCF
Given:
[tex]\dfrac{1}{4}x+\dfrac{3}{8}[/tex]
To find:
The factor form of given expression by the GCF.
Solution:
First we need to find the GCF of [tex]\dfrac{1}{4}[/tex] and [tex]\dfrac{3}{8}[/tex].
So, make denominators same.
[tex]\dfrac{1}{4}=\dfrac{1\times 2}{4\times 2}=\dfrac{2}{8}[/tex]
Now,
[tex]GCF\left(\dfrac{2}{8},\dfrac{3}{8}\right)=\dfrac{1}{8}[/tex]
[tex]GCF\left(\dfrac{1}{4},\dfrac{3}{8}\right)=\dfrac{1}{8}[/tex]
We have,
[tex]\dfrac{1}{4}x+\dfrac{3}{8}[/tex]
It can be written as
[tex]=\dfrac{2}{8}x+\dfrac{3}{8}[/tex]
Taking out the GCF [tex]\dfrac{1}{8}[/tex], we get
[tex]=\dfrac{1}{8}(2x+3)[/tex]
Therefore, the required factor form is [tex]\dfrac{1}{8}(2x+3)[/tex].
the length of a rectangle is one unit more than its width. if the area of the rectangle is 56 square units,find the dimensions of the rectangle
Given:
The length of a rectangle is one unit more than its width.
Area of rectangle = 56 units
To find:
The dimensions of the rectangle.
Solution:
Let, width of the rectangle be x.
Then, length of the rectangle = x+1
Area of a rectangle is
[tex]Area=length\times width[/tex]
[tex]56=(x+1)\times x[/tex]
[tex]56=x^2+x[/tex]
[tex]0=x^2+x-56[/tex]
By splitting the middle term, we get
[tex]x^2+8x-7x-56=0[/tex]
[tex]x(x+8)-7(x+8)=0[/tex]
[tex](x-7)(x+8)=0[/tex]
Using zero product property, we get
[tex]x-7=0[/tex] and [tex]x+8=0[/tex]
[tex]x=7[/tex] and [tex]x=-8[/tex]
Width cannot be negative. So, x=7.
Now,
Width = 7 units
Length = 7+1
= 8 units
Therefore, the length of the rectangle is 8 units and width is 7 units.
Answer:
7
Step-by-step explanation: POV: I got it right
(C)
A man, 1.4m tall, is inspecting the behavior of a bird sitting at the top of a pole of
the height 43.4m. If the man is standing 14√3m away from the bottom of the pole
on the horizontal level, at what angle is he looking at the bird?
60°
take (43.4-1.4)m to get the remaining height which Wii be you height ie.42m
base is the distance that the man stands away from the pole
using tan rule will be opposite/adjacent
16 children together weigh 480 kg 960 g . If weight of all the children are equal, find the weight of each child.
Answer:
30.06 kg
Step-by-step explanation:
480kg 960g = 480969g.
480960 / 16 = 3060g
30060g
30060g = 30.06kg.
Select the correct answer
Answer:
1/49
Step-by-step explanation:
multiplying two of these, as long as the bases are the same, which is true here, you can add the exponents
so the exponents would be
-5/6 + (-7/6)=-5/6-7/6=-12/6=-2
7^-2=1/49
Answer:
Step-by-step explanation:
1/49
Set up the following additional using a vertical format and find the sum of the given polynomials:
7b+3, -4b+5, and -3b+2
Answer:
Step-by-step explanation:
The Answer is 10
What is the solution?
Answer:
(2,3)
Step-by-step explanation:
it's the point of intersection
hope this helps, pls mark brainliest :D
Answer:
2,3 i believe 2 on the x axis and 3 on the y
Step-by-step explanation:
You throw a ball into the air from a height of 5 feet with an
initial vertical velocity of 32 feet per second. Use the vertical
motion model, h = –16t2 + vt + s, where v is the initial
velocity in feet per second and s is the height in feet, to
calculate the maximum height of the ball. Round your answer
to the nearest tenth if necessary.
Maximum height
11. Find the measure of each missing angle.
Help me pls!
Answer:
1=15?
Step-by-step explanation:
5*4=15 becuz lower angle=top 1 angle and stuff i hope this helps. im just a helpless 6th grader :)
I BET EVERYONE CAN GET THIS RIGHT BUT NOT ME
Writing Equations of Parallel Lines
y
10
What is the slope of the line that is parallel to the given
line and passes through the given point?
8
6
What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
given point?
4.
2
-10 -8 6 4
What is the y-intercept of the line that is parallel to the
given line and passes through the given point?
2
4.
6
8
10
-2
-2
4
-6
-8
-10
Answer:
The slope of the parallel line to the given line is [tex]-\frac{1}{4}[/tex]
The equation of the parallel line to the given line and passes through the given point is y + 4 = [tex]-\frac{1}{4}[/tex] (x + 2)
The y-intercept of the parallel line to the given line and passes through the given point is [tex]-\frac{9}{2}[/tex]
Step-by-step explanation:
The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]The point-slope form of the linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the lineThe slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-interceptParallel lines have the same slopes and different y-interceptsIn the given figure
∵ The given line passes through points (2, 6) and (-6, 8)
∴ x1 = 2 and y1 = 6
∴ x2 = -6 and y2 = 8
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{8-6}{-6-2}[/tex] = [tex]\frac{2}{-8}[/tex] = [tex]-\frac{1}{4}[/tex]
∴ The slope of the given line is [tex]-\frac{1}{4}[/tex]
∵ Parallel lines have the same slopes
∴ The slope of the parallel line to the given line is [tex]-\frac{1}{4}[/tex]
∵ The parallel line passes through the point (-2, -4)
∴ x1 = -2 and y1 = -4
∵ m = [tex]-\frac{1}{4}[/tex]
→ Substitute them in the point-slope form above
∵ y - (-4) = [tex]-\frac{1}{4}[/tex] (x - (-2))
∴ y + 4 = [tex]-\frac{1}{4}[/tex] (x + 2)
∴ The equation of the parallel line to the given line and passes through
the given point is y + 4 = [tex]-\frac{1}{4}[/tex] (x + 2)
∵ m = [tex]-\frac{1}{4}[/tex]
→ Substitute it in the slope-intercept form above
∴ y = [tex]-\frac{1}{4}[/tex] x + b
→ To find b substitute x by -2 and y by -4 (coordinates the given point)
∵ -4 = [tex]-\frac{1}{4}[/tex](-2) + b
∴ -4 = [tex]\frac{1}{2}[/tex] + b
→ Subtract [tex]\frac{1}{2}[/tex] from both sides
∴ [tex]-\frac{9}{2}[/tex] = b
∵ b is the y-intercept
∴ The y-intercept of the parallel line to the given line and passes
through the given point is [tex]-\frac{9}{2}[/tex]
Answer:
What is the slope of the line that is parallel to the given line and passes through the given point?
✔ –1/4
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?
✔ y + 4 = –1/4(x + 2)
What is the y-intercept of the line that is parallel to the given line and passes through the given point?
✔ –9/2
Step-by-step explanation:
6. Sharon divides a meatloaf into elevenths. How many elevenths equals the whole meatloaf?
Answer:
11 elevenths equal a whole meatloaf
11/11=1
Answer:
11 11ths
Step-by-step explanation:
11/11 = 1 whole
What is the simplified form of the expressions? a. −6a2b−1 b. 5/y−3
Given:
The expressions are
[tex]-6a^2b^{-1}[/tex]
[tex]\dfrac{5}{y^{-3}}[/tex]
To find:
The simplified form of each expression.
Solution:
We have,
[tex]-6a^2b^{-1}[/tex]
[tex]=-6a^2(\dfrac{1}{b})[/tex] [tex][\because x^{-n}=\dfrac{1}{x^n}][/tex]
[tex]=-\dfrac{6a^2}{b}[/tex]
Therefore, the simplified form of [tex]-6a^2b^{-1}[/tex] is [tex]-\dfrac{6a^2}{b}[/tex].
We have,
[tex]\dfrac{5}{y^{-3}}[/tex]
[tex]=\dfrac{5}{\dfrac{1}{y^3}}[/tex] [tex][\because x^{-n}=\dfrac{1}{x^n}][/tex]
[tex]=5\times \dfrac{y^3}{1}[/tex]
[tex]=5y^3[/tex]
Therefore, the simplified form of [tex]\dfrac{5}{y^{-3}}[/tex] is [tex]5y^3[/tex].
Helplsieedgoodgradeplspls
Answer:
He would need to walk the dog 6 more times because 8 times 11 is 88 and if he has already walked the dog 5 times you would subtract that from 11 to get 6. So the answer would be 6
Step-by-step explanation:
8·11= 88
11-5= 6
HELP ASAP
1. A group of numbers, variables, and/or operation symbols that represent a mathematical relationship. is called?
2. A known number, a variable, or the product of a known number and a variable; separated by plus (+) and minus (-) symbols. is called?
Answer:
1. polynomial
2. equation
I hope it will be useful.
Write 1.417x10^2 in standard notation please hurry .thank you
Answer:
The standard notation would be 141.7
Step-by-step explanation:
Can someone help me please
Answer: B
Step-by-step explanation:
It has to be B. None of the other answers make sense.
help please..... I cant find the answe
Answer:
[tex]6^{30}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] ⇔ [tex]a^{mn}[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]
Given
[tex]\frac{(6^-4)^{-9} }{6^6}[/tex]
= [tex]\frac{6^{36} }{6^{6} }[/tex]
= [tex]6^{(36-6)}[/tex]
= [tex]6^{30}[/tex]
70% of 350 is what number?
Answer:
245
Step-by-step explanation:
What is 70 percent (calculated percentage %) of number 350? Answer: 245.
5713065981 if your this guy text me
Answer:
imagine she doesn't find him
*grins with werid intantions*
Which set represents a function?
{(1, 3), (4, 5), (4, 9), (6, 19)}
{(-5, 6), (-3, 13), (-14, 30)}
{(12, 12), (12, 13), (12, 14)}
Answer: {(-5, 6), (-3, 13), (-14, 30)} is a function
{(12, 12), (12, 13), (12, 14)} and {(1, 3), (4, 5), (4, 9), (6, 19)} are not a function
Answer:
the second set
Step-by-step explanation:
You cannot have the same number in your domain twice.
How do I solve 1.5 to the -2 power or 1.5^-2 (its an exponent) I have had to repost this like 3 times IF YOU ARE NOT SURE THEN DONT ANSWER the answer is .4 repeating if your explanation does not get that move along
Answer:
see explanation
Step-by-step explanation:
Using the rule of exponents
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex] , then
[tex]1.5^{-2}[/tex]
= [tex]\frac{1}{1.5^{2} }[/tex]
= [tex]\frac{1}{2.25}[/tex]
= 0.4444.....
Please help ASAP I am so confused
Here are the steps, hope it helps!
Scarlet deposited $500 in a savings account with simple interest. One year later she had earned $30 in interest. What was the interest rate?
Answer:
6%
Step-by-step explanation:
Interest = Principal x Rate x Time (in years)
30 = 500r
r = 3/50 or 6/100 which is 6%
For the function F(x) = }, which of these could be a value of F(x) when xis
close to zero?
Given:
The graph of the function [tex]f(x)=\dfrac{1}{x}[/tex].
To find:
The value of the function f(x), when x is close to zero.
Solution:
From the given graph it is clear that, f(x) approaches towards infinity and negative infinity as x approaches towards 0.
[tex]f(x)\to \infty[/tex] as [tex]x\to 0^+[/tex]
[tex]f(x)\to -\infty[/tex] as [tex]x\to 0^-[/tex]
In means, the value of must be very large positive value or very large negative if x is close to zero.
From the given options -10,000 is very large negative value.
So, the possible value of f(x) could be -10000 if x is close to 0.
Therefore, the correct option is A.
I need help thank you
Answer:
x is greater than or equal to 8.75 or 8 3/4
Step-by-step explanation:
So we first write the inequality 3 + 1.2c "is greater than or equal to sign" 13.5. Then we subtract 3, then divide both sides by 1.2 to isolate c. We get x "is greater than or equal to" 8.75.
math please help me
answer choice
This system has no solutions.
(5/8, 14)
This system has infinitely many solutions.
(−5/8, 4)
Answer:
What do you mean? It could be both, in different ways.
The list of all factors for 21 is 1, 3, 7, and 21.
True or False
plz i need help
Answer:
true
Step-by-step explanation:
hope you have a wonderful new year