Answer:
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The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid a(b) = 14 * (b + 5)/2 Which equation below represents the inverse function b(a) , which takes the trapezoid's area as input and returns as output the length of the other base? N(c) = (c + 15)/20; n(c) = (c + 20)/15; n(c) = (c - 20)/15; n(G) = (Q - 15)/20
Answer:
[tex]b(a) = \frac{a}{7} -5[/tex]
Step-by-step explanation:
Given
[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]
Required
The inverse function
We have:
[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]
[tex]a(b) = 7(b + 5)[/tex]
Rewrite as:
[tex]a = 7(b + 5)[/tex]
Divide by 7
[tex]\frac{a}{7} =b + 5[/tex]
Subtract 5
[tex]b = \frac{a}{7} -5[/tex]
Express as:
[tex]b(a) = \frac{a}{7} -5[/tex] --- the inverse function
Triangle ABC is an equilateral triangle with vertices at A(-2,2), B(1,5), and C(-3,6) (Round your answers to the nearest hundredth, 2 decimal places) . a) (2 pts) Determine the length of a side of the triangle. b) (2 pts) Calculate the perimeter of the triangle. c) (2 pts) Now increase the triangle by a scale factor of 4. How long is each side now? d) (2 pts) What is the perimeter of the new triangle? e) (2 pts) What is the area of the original triangle?
Answer:
The answer is below
Step-by-step explanation:
The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate is:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\[/tex]
An equilateral triangle is a triangle with three equal sides (all sides are equal).
a) Given vertices at A(-2,2), B(1,5), and C(-3,6):
[tex]AC=\sqrt{(-3-(-2))^2+(6-2)^2}=\sqrt{1+16}=\sqrt{17}=4.12\ unit\\\\AB=BC=AC=4.12\ unit[/tex]
b) Perimeter = AB + BC + AC = 3 * AC = 3 * 4.12 = 12.36 unit
c) If the scale factor is increased by 4, all the sides would also increase by 4. Hence the new length would be:
A'B' = B'C' = A'C' = 4 * AC = 4 * 4.12 = 16.48 unit
d) Perimeter = A'B' + B'C' + A'C' = 3 * A'C' = 3 * 16.48 = 49.44 unit
e) Area = [tex]\frac{\sqrt{3} }{4}*AC^2=\frac{\sqrt{3} }{4} *4.12^2=7.35\ unit^2[/tex]
PLEASE HELP MEE!! 50 POINTS
URGENT
The function y= x^2-10x+31 has a _____ (minimum, maximum) value of __ (5, 10, 31, 6)
Answer:
minimum value of 6
Step-by-step explanation:
Given
y = x² - 10x + 31
with a = 1, b = - 10
Since a > 0 then the function has a minimum value
The minimum value is the y- coordinate of the vertex.
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{-10}{2}[/tex] = 5
Substitute x = 5 into the function for y- coordinate of vertex
y = 5² - 10(5) + 31 = 25 - 50 + 31 = 6
The function has a minimum value of 6
1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.
9514 1404 393
Answer:
p = 3/4n +3
Step-by-step explanation:
Expressing the given equation in terms of powers of 3, we have ...
(27^(n+3))/(81^(p-1)) = 3
(3^3)^(n+3)/(3^4)^(p-1) = 3^1 . . . . as powers of 3
3(n +3) -4(p -1) = 1 . . . . . . . . . . . . log base 3 (or, equate exponents)
3n +9 -4p +4 = 1 . . . . . . . . . . . . . eliminate parentheses
3n +12 = 4p . . . . . . . . . . . . . . . . add 4p -1
p = 3/4n +3 . . . . . . . . . . divide by 4
Simplify (3x2 + 2x - 3) (x + 5)
Answer:
3(x)^3 + 2(x)^2 + 22x - 15
Step-by-step explanation:
(3(x)^2 + 2x - 3) (x + 5)
=>(3(x)^2 + 2x - 3) (x) + (3(x)^2 + 2x - 3) (5)
=>3(x)^3 + 2(x)^2 - 3x + 15x + 10x - 15
=>3(x)^3 + 2(x)^2 + 22x - 15
A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller number. If y represents the larger number and x represents the smaller number, which equations model the situation? Check all that apply.
y=3x-2
3x-y=2
3x-y=-2
y=2-3x
y=2(x+3)
Answer:
1,2, and 5
Step-by-step explanation:
y=2*(3+x)
y=3x-2
3x-y=2
HELP!!! I'm struggling in this class could you please help a person out?
Answer:
Options (2) and (3)
Step-by-step explanation:
Rigid transformation like translation, rotation or reflection form the image with no change in the area or shape.
By applying dilation, area of the image shape gets dilated by the scale factor 'k'.
If k > 1, area of the image will be greater than the original shape.
If 0 < k < 1, are of the image will be smaller than the original.
Option (1),
There is a dilation by a scale factor of [tex]\frac{2}{3}[/tex] and [tex]0<\frac{2}{3}<1[/tex],
Therefore, image will be smaller than the original.
Option (2)
There are two dilations.
First dilation is by a scale factor of 2 and the second is by a scale factor of [tex]\frac{2}{3}[/tex].
By first dilation area of the image will get doubled.
Followed by the dilation by a scale factor of [tex]\frac{2}{3}[/tex], area of the image will be dilated by the scale factor = [tex]2\times \frac{2}{3}[/tex]
= [tex]\frac{4}{3}[/tex]
Since, [tex]\frac{4}{3}>1[/tex], image will be greater than the original.
Option (3)
In this option polygon is dilated by a scale factor [tex]\frac{3}{2}[/tex].
Since, [tex]\frac{3}{2}>1[/tex]
Image will have the greater area than the original.
Option (4)
In this option polygon is dilated by a scale factor [tex]\frac{1}{2}[/tex].
Therefore, area of the image will be less than the area of the original.
Options (2) and (3) will be the correct options.
if a number is divided by three and then two is added,the answer is twenty-nine.what is the number
Answer:
81
Step-by-step explanation:
the answer is 81, just out this in the solution
Answer:
81
Step-by-step explanation:
29-2=27
27*3=81
if we divide 81 by 3 we get 27 and 27 plus 2 is 29 so it is 81
Congruent angle pairs : find value of x and the value of y
Can somebody help plz help me with this?
Answer:
N-8
Step-by-step explanation:
can someone please help me in this question
Answer:
a. 26 cm²
b. 55 cm²
c. 78 cm²
d. 89.27 cm²
Step-by-step explanation:
a. The shape can be decomposed into two rectangles
Area of the larger rectangle = L*W
L = 7 cm
W = 2 cm
Area of the larger rectangle = 7*2 = 14 cm²
Area of the smaller rectangle = L*W
L = 4 cm
W = 5 - 2 = 3 cm
Area of the larger rectangle = 4*3 = 12 cm²
Area of the compound shape = 14 + 12 = 26 cm²
b. The shape can be decomposed into a rectangle and a triangle.
Area of the compound shape = area of rectangle + area of triangle
= L*W + ½*b*h
L = 8 cm
W = 5 cm
b = 5 cm
h = 14 - 8 = 6 cm
Plug in the values
Area = 8*5 + ½*5*6
Area = 40 + 15
= 55 cm²
c. The shape can be decomposed into a rectangle and a trapezoid
Area of the compound shape = area of the rectangle + area of the trapezoid
= L*W + ½(a + b)h
L = 12 cm
W = 3 cm
a = 12 cm
b = 9 cm
h = 4 cm
Plug in the values
Area = 12*3 + ½(12 + 9)4
Area = 36 + 42
Area = 78 cm²
d. The shape can be decomposed into a rectangle and a semicircle
Area of the compound shape = area of the rectangle + area of the semicircle
= L*W + ½(πr²)
L = 10 cm
W = 5 cm
r = ½(10) = 5 cm
Plug in the values
Area = 10*5 + ½(π*5²)
Area = 50 + 39.27
Area = 89.27 cm²
Solve: -8.8 > 2.3
I don't understand this- can someone help?
Well you can't really solve it but it's false.
It's should be -8.8 < 2.3
> means "is greater than"
< means "is less than"
4x-10+1.5x-4x+11=8.5-6
Answer:
x=1
Step-by-step explanation:
4x-10+1.5x-4x+11=8.5-6
Combine like terms
1.5x+1=2.5
Subtract 1 from each side
1.5x+1-1=2.5-1
1.5x = 1.5
Divide by 1.5
1.5x/1.5 = 1.5/1.5
x=1
Answer:
x=1
Step-by-step explanation:
Given :
4x-10+1.5x-4x+11=8.5-6
4x+1.5x-4x=8.5-6-11+10
1.5x=1.5
x=1
Value of x=1
Question 27(Multiple Choice Worth 1 points)
(07.03 LC)
How many solutions does the equation 4y - 4y - 12 = 14-2 have?
One
None
Two
Infinite
Answer:
none
Step-by-step explanation:
any value on y cancel 4y and then we will have -12=12 which is not true.
Write an equation that represent the value of an 8700 investment that has 9.1% interest rate compounded yearly y=a(b)^x
Answer:
future value = $8700(1.091)^x
Step-by-step explanation:
The formula for calculating future value:
FV = P (1 + r) n
FV = Future value
P = Present value = 8700
R = interest rate = 9.1%
N = number of years = x
future value = $8700(1.091)^x
Find the volume of each shape.
Step-by-step explanation:
1. length ×breadth ×height
12× 6 ×3= 216
2. A is the area of the base, h is the height
18×16=288
3.10×14×5=700
Answer:
21. 216m^3
22. 4071.5m^3
23. 700m^3
Step-by-step explanation:
21. V = L*W*H
V = 3*6*12
V = 216
22. V = [tex]\pi r^{2} h[/tex]
The diameter is 18 so the radius is 9
V = [tex]\pi[/tex](9^2)(16)
V= 4071.50408
23. V = L*W*H
V= 10*5*14
V=700
A cubical reservoir has capacity of 480000 l itters of liquid. If ifs length and breadth are 10m and 8m respectively, find the hight of the reservoir.
Answer:
Height = 6000 m
Step-by-step explanation:
[tex]Volume = length \times breadth \times height \\\\480000 = 10 \times 8 \times height\\\\480000 = 80 \times height\\\\height = \frac{480000}{80} = 6000 \ m[/tex]
Age of car = 8 years. Original cost = $18,000. The cost of maintenance and repairs is $
From the graph it seems to be around the area of 10%.
So,
18,000 * 0.10 = $1,800
look at the image for the question
Answer:
Answer is y = 6
Step-by-step explanation:
Solve for y.
Answer:
Y=6 I think but I’m not positive.
sorry if I’m wrong.
haha
get it? POSITIVE?
In 2014, a town's population was 795 people. By 2020, the population had grown to 1262 people. a. Create an exponential equation for the town's population "n" years from 2014. Round your multiplier to the nearest hundredth (2 decimal places).
Answer: [tex]P=795(1.84)^n[/tex]
Step-by-step explanation:
Given
Initial population was [tex]795[/tex] people
By 2020, it becomes [tex]1262[/tex] people
Suppose the population follows the trend [tex]P=P_oa^{n}[/tex]
where, [tex]n[/tex] is the number of years after 2014
For year 2020 it is 6. Insert the values
[tex]\Rightarrow 1262=795a^{6}\\\\\Rightarrow 1.587=a^{6}\\\\\text{Taking log both sides}\\\\\Rightarrow \log (1.587)=6\log (a)\\\Rightarrow \log (a)=0.2645\\\\\Rightarrow a=10^{0.2645}\\\Rightarrow a=1.84[/tex]
Thus, the exponential population trend is [tex]P=795(1.84)^n[/tex]
what is the measure of each exterior angle of a regular dodecagon?
Answer:
30°
Hope this answer is right!
Step-by-step explanation:
to go around the shape, you make a complete circle: 360°. So, divide 360° by the dodecagon's twelve exterior angles. Each exterior angle is 30°.
(5^-4/4^-6) multiplied by 5^3
Step-by-step explanation:
(5^-4/4^-6) multiplied by 5^3
4⁶×5³/5⁴
4⁶/5
819.2
Answer:
[tex]{ \tt{ (\frac{ {5}^{ - 4} }{ {4}^{ - 6} } ) \times {5}^{3} }} \\ \\ = { \tt{ \frac{ {5}^{ - 4} . {5}^{3} }{ {4}^{ - 6} } }} \\ \\ { \tt{ = \frac{ {5}^{ - 1} }{ {4}^{ - 6} } }} \\ { \tt{ = \frac{ {4}^{6} }{ {5}^{1} } }} \\ = { \tt{ \frac{4096}{5} }} \\ \\ = 819.2[/tex]
how do i do this, please explain....
Answer:
this is from a angle I think you want to write perimeter and area of this ×+1= and you want see that
Given the formula below, solve for x.
Answer:
find X in X with x if you find X with x in with x you got a formula
20 points for this make sure u explain
Answer:
it literally says +10
Step-by-step explanation:
scammer
Answer:
Step-by-step explanation:
6,7,8
PLEASE I NEED HELP!!!!
Q. Determine if the rates are equilvalent. Explain your reasoning. 25 hours in 5 days; 8 hours in 2 days. . .
[tex] \dashrightarrow [/tex] No!, as, we have 25 hours in 5 dyas is the equals to 5. While, 8 hours in 2 days is equals to 4.
Here, is a difference of 1 in 5 and 4.
Given the system of equations.
{-4x+y = 3
{2x - y = 12
Which of the options represents the resulting equation after an equivalent expression for y ls substituted into the
second equation.
2x - (4 X+3) = 12
-4(4y+)+y=3
2 (4x+3) - y
-4x+4 x-3=3
Answer:
A. 2x - (4x + 3) = 12
Step-by-step explanation:
A. 2x - (4x + 3) = 12
B. -4(4y+)+y=3
C. 2 (4x+3) - y
D. -4x+4 x-3=3
Given equation:
-4x+y = 3. (1)
2x - y = 12. (2)
From (1)
y = 3 + 4x
Substitute y = 3 + 4x into (2)
2x - y = 12 (2)
2x - (3 + 4x) = 12
Or
2x - (4x + 3) = 12
2x - 4x - 3 = 12
- 2x = 12 + 3
- 2x = 15
x = 15/-2
x = -7.5
Substitute x = -7.5 into (1)
-4x+y = 3 (1)
-4(-7.5) + y = 3
30 + y = 3
y = 3 - 30
y = -27
What is the slope of the line shown below?
10
O A-4
5
B. -2
ရှိ မရှိ ။
(2,4)
C. 2
10
15
45
O D. 4
10
Answer:
C) 2
Step-by-step explanation:
In parallelogram EFGH if m∡GHE=160 find ∡m∡EFG
Answer:
160°
Step-by-step explanation:
since it is a parallelogram it's opposite angles must be equal . So,
angle GHE = angle EFG
160 degree = angle EFG
What is the recursive formula for this geometric sequence?
-3, -21, -147, -1029, ...