Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.

Step 1:
Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches.

Step 2:
Substitute the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.

Step 3:
Combine like terms: (18 + 24) squared = 30 squared.

Step 4:
Evaluate each side: 1764 not-equals 900.

Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?
The triangle is actually a right triangle. In step 2, Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is not a right triangle, but in step 2 Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The triangle is not a right triangle, but in step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.

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

Answer:

The third one

Step-by-step explanation:

Median - Middle number in terms of value

Mode - outcome that appears the most

Mean - average ( add the numbers together and divide that by the amount of numbers )

Data without Kevins score

13, 21, 28, 9, 31

First let's find the mean

To find the mean we simply add the numbers up and divide that by the total amount of numbers ( there are 5 numbers )

13 + 21 + 28 + 9 + 31 = 102

102/5=20.4

So the mean without Kevins score is 20.4

Next let's find the mode

The mode is the number that appears the most

Looking at the data no number appears more than once so there is no mode

Finally let's find the median.

To make it easier to find let's list the numbers in order from least to greatest

9, 13 , 21 , 28, 31

We then go to the middle number ( which would be 21 )

The mode is 21

So for data without Kevins score the mean would be 20.4, the median would be 21 and the mode would be none

Now let's add in Kevin's score and repeat this process

Data with Kevin's score

13, 21, 28, 9, 31, 9

First let's find the mean

( Note that there is 6 numbers this time )

13 + 21 + 28 + 9 + 31 + 9 = 111

111/6 = 18.5

So mean with Kevin's score = 18.5

Next let's find the mode

The number 9 appears the most so the mode is 9

Finally let's find the mean

Once again let's list the numbers from least to greatest

9, 9, 13 , 21 , 28, 31

Because there is an even amount of numbers we will take the sum of the two middle numbers and divide that by 2

The two middle numbers would be 21 and 13

21 + 13 = 34

34/2=17

So median = 17

In the end we get the following

Without Kevins score

Mean = 20.4

Median = 21

Mode = none

With Kevin's score

Mean = 18.5

Median = 17

Mode = 9

This information corresponds with the third table

Answer:

find X in X with x if you find X with x in with x you got a formula

Answer:

Where 0 < x < 3

The location of the local minimum, is (2, 0)

The location of the local maximum is at (0, 16)

Step-by-step explanation:

The given function is f(x) = (x + 2)⁴

The range of the minimum = 0 < x < 3

At a local minimum/maximum values, we have;

[tex]f'(x) = \dfrac{(-x + 2)^4}{dx} = -4 \cdot (-x + 2)^3 = 0[/tex]

∴ (-x + 2)³ = 0

x = 2

[tex]f''(x) = \dfrac{ -4 \cdot (-x + 2)^3}{dx} = -12 \cdot (-x + 2)^2[/tex]

When x = 2, f''(2) = -12×(-2 + 2)² = 0 which gives a local minimum at x = 2

We have, f(2) = (-2 + 2)⁴ = 0

The location of the local minimum, is (2, 0)

Given that the minimum of the function is at x = 2, and the function is (-x + 2)⁴, the absolute local maximum will be at the maximum value of (-x + 2) for 0 < x < 3

When x = 0, -x + 2 = 0 + 2 = 2

Similarly, we have;

-x + 2 = 1, when x = 1

-x + 2 = 0, when x = 2

-x + 2 = -1, when x = 3

Therefore, the maximum value of -x + 2, is at x = 0 and the maximum value of the function where 0 < x < 3, is (0 + 2)⁴ = 16

The location of the local maximum is at (0, 16).

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

Answer:

X^2+7x+4

Step-by-step explanation:

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

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

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

Answer:

The answer is 11.8 m

Step-by-step explanation:

Hey Mate,

the volume of a cuboid is = whl....so the volume of it is the capacity of the tank

so 3 x 1.8 x 2.2 = 11.88 m is the answer

Answer:

it literally says +10

Step-by-step explanation:

scammer

Answer:

Step-by-step explanation:

6,7,8

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?

Answer:

1,2, and 5

Step-by-step explanation:

y=2*(3+x)  

y=3x-2

3x-y=2

Part (A)

(1 cm)/(20 cm) = (6 cm)/(x cm)

1/20 = 6/x

1*x = 20*6

x = 120

120 cm = 120/100 = 1.2 m

=========================================================

Part (B)

2.2 m = 2.2*100 = 220 cm

(1 cm)/(20 cm) = (x cm)/(220 cm)

1/20 = x/220

1*220 = 20*x

20x = 220

x = 220/20

x = 11

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.

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°.

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

For this question, we will need to know that when we divide two numbers with the same base but different exponents, we must subtract the exponents.

[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]

[tex]\dfrac{9^5}{9^3}[/tex]

Subtract the exponents:

[tex]9^2[/tex]

[tex]9^2[/tex]

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]

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

Answer:

C) 2

Step-by-step explanation:

Answer:

N-8

Step-by-step explanation:

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"

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]

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]

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]