Triangle ABC has vertices A (-2, 2), B (2, 4) and C (3, -1).  What are the coordinates of A' after a dilation by a scale factor of 2.5?​

Answer:

136 mm²

Step-by-step explanation:

[tex]A=a^{2} +2a\sqrt{\frac{a^{2} }{4} } +h^{2}[/tex]

[tex]A=6^{2} +2(6)\sqrt{\frac{6^{2} }{4} } +8^{2}[/tex]

[tex]A=36 +12\sqrt{\frac{36 }{4} } +64[/tex]

[tex]A=36 +12\sqrt{9 } +64[/tex]

[tex]A=36 +12(3)+64[/tex]

[tex]A=36 +36+64[/tex]

A = 136

Step-by-step explanation:

The sides with the variables are the same length, so make them equal.

x+2=2x-3

Get x alone on one side.

5=3x

Simplify.

5/3 = x

Answer:

5

Step-by-step explanation:

x+2 = 2x-3

+3 +3

x+5 = 2x

-x -x

x=5

Hope this helps! :)

Answer:

2y - 9

Step-by-step explanation:

number = y

2 × y - 9

2 × y can be simplified to 2y.

2y - 9

Answer:

it should be 314.16, so I would choose 314

Answer:

c. -x + 3x + 7  = 2x+7

Step-by-step explanation:

f(x) = 3x +1 and g(x) = x - 6

f-g = 3x +1 - ( x - 6)

Distribute the minus sign

     = 3x+1 - x+6

     = 2x +7

answer is

(Y)=-23,-14, -5,4,13

hope this will help you

Answer:

OK

Step-by-step explanation:

The first screenshot is for #7 and the second screenshot is for #8

Answer:

6/8

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

4x - 2 = 3x + 14

4x - 2 + 2 = 3x + 14 + 2

4x = 3x + 16

4x - 3x = 3x - 3x + 16

x = 16

Answer:

4x+8

Step-by-step explanation:

X + 3( x + 2) + 2

Distribute

x +3x+6+2

Combine like terms

4x+8

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]4x + 8[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying the expression:}}\\\\\underline{x+3(x+2)+2}\\\\\rightarrow x + 3x + 6 + 2\\\\\rightarrow 4x + 6 + 2\\\\\rightarrow \boxed{4x + 8}[/tex]

⸻⸻⸻⸻  

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

84 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the length of the base and h is the height

A = 1/2 ( 5+9) * 12

A = 1/2 (14) * 12

A =84

Answer:

It is a sequence topic.

The general term of the sequence is 25+3(n-1) where n is the number of the term (here it is the row no.)

So the 20th term is the term with n=20. Substitute n=20 into the above general term, we will get 25+3(20-1) .

Please go on by yourself to work out the answer.

Answer:

16.2 cm

Step-by-step explanation:

use the pythagoran theorem

a² + b² = c²

15² + 6² = c²

225 + 36 = c²

261 = c²

Take the square root of both sides

16.1554944214 = c

Rounded

16.2 cm

Answer:

Sylvia=16

brother=8

Step-by-step explanation:

8+7=15

16-1=15

Answer:

consist of either a single capital letter or a capital letter and a small letter.

Step-by-step explanation:

A chemical reaction can be defined as a reaction in which two or more atoms of a chemical element react to form a chemical compound.

In Chemistry, a chemical element can be defined as any pure substance that is typically made up of only atoms and cannot be broken down into simpler substances through chemical processes. Thus, the atomic number (the number of protons in the nuclei of an atom) of a particular chemical element distinguishes from other chemical elements.

Generally, all chemical elements are denoted or represented by a symbol, which may either be single capital letter or a capital letter and a small letter.

This ultimately implies that, the symbols for elements with accepted names consist of either a single capital letter or a capital letter and a small letter. For example, the symbol for sodium is Na, copper is Cu, carbon is C, oxygen is O, iron is Fe, nitrogen is N, magnesium is Mg, potassium is K, argon is Ag, hydrogen is H, helium is He, phosphorus is P, etc.

Answer:

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 7.5 hours

This means that [tex]\mu = 7.5[/tex]

Standard deviation 27 minutes.

An hour has 60 minutes, which means that [tex]\sigma = \frac{27}{60} = 0.45[/tex]

What is the probability that the battery life is at least 8.1 hours?

This is 1 subtracted by the p-value of Z when X = 8.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8.1 - 7.5}{0.45}[/tex]

[tex]Z = 1.33[/tex]

[tex]Z = 1.33[/tex] has a p-value of 0.9082.

1 - 0.9082 = 0.0918

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.

Answer:

The predicted final exam grade is 83

Step-by-step explanation:

Given

[tex]\bar x = 75[/tex] -- midterm mean

[tex]\sigma_x = 10[/tex] --- midterm standard deviation

[tex]\mu =75[/tex] --- final mean

[tex]\sigma = 10[/tex] --- final standard deviation

[tex]r = 0.8[/tex]

Required

The predicted final grade of student who score 85 in midterm

The prediction is represented as:

[tex]y = \alpha + \beta x[/tex]

Where:

[tex]\beta = r * \frac{\sigma}{\sigma_x}[/tex]

[tex]\beta = 0.8 * \frac{10}{10}[/tex]

[tex]\beta = 0.8 * 1[/tex]

[tex]\beta = 0.8[/tex]

and

[tex]\alpha = \mu - r * \bar x[/tex]

[tex]\alpha = 75- 0.8 * 75[/tex]

[tex]\alpha = 75- 60[/tex]

[tex]\alpha = 15[/tex]

So:

[tex]y = \alpha + \beta x[/tex]

[tex]y = 15 + 0.8x[/tex]

For a student who gets 85, the prediction is:

[tex]y = 15 + 0.8*85[/tex]

[tex]y = 15 + 68[/tex]

[tex]y = 83[/tex]

Answer:

b open down and have a maximum

Step-by-step explanation:

A negative value for a will make the quadratic function open down

A downward facing parabola will have a maximum

Answer:

We can write sin x in terms of tan x/2 using the formula:

⇒ sin x = (2 tan (x/2)) / (1 + tan2(x/2))

Therefore, using the above formula, we can find the values of tan x/2 by putting the value of sin x.

⇒ -4/5 = (2 tan (x/2)) / (1 + tan2(x/2))

Now, if we replace tan (x/2) by y, we get a quadratic equation:

⇒ 0.8y2 + 2y + 0.8 = 0

⇒ 2y2 + 5y + 2 = 0

By using the quadratic formula, we get y = -0.5, -2

Hence, the value of tan (x/2) = -0.5, -2

Now, we have two solutions of tan (x/2).

Now, let's check for the ideal solution using the formula tan x = (2 tan (x/2)) / (1 - tan2(x/2)).

For tan (x/2) = -0.5:

⇒ tan x = 2(-0.5) / 1 - (-0.5)2 = -4/3

It is also given that x lies in the third quadrant. We know that tan is positive in the third quadrant, and here we get tan x = -4/3 which is negative.

Hence, we can say that tan (x/2) = -0.5 is not a correct solution. Hence it is rejected.

Now let's check for tan (x/2) = -2.

⇒ tan x = 2(-2) / 1 - (-2)2 = 4/3

Here, we get tan x = 4/3 which is positive.

Hence, we can say that tan (x/2) = -2 is a correct solution.

Answer:

Step-by-step explanation:

let one angle=a°

second angle=(90-a)°

tan a=7/10=0.7

a=tan^{-1}(0.7)≈35.0°

other angle=90-35=55.0°

Answer:

5328.78

Step-by-step explanation:

formula:

[tex]P(1+\frac{i}{n})^{n*t}\\2600(1+\frac{.08}{12})^{12*9}\\\\2600(1.006667)^{108}=5328.77861305[/tex]

this rounds to 5328.78

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

2 = 2 × 1

6 = 2 × 3

GCF = 2

[tex]\frac{2 /2 }{6/2} =\frac{1}{3}[/tex]

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\boxed{\frac{1}{3}}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplify:}}\\\\\frac{2}{6}\\\\\boxed{\text{Finding the Factors:}}\\\\2: 2\\6 : 2,3\\\\\boxed{\text{The GCF would be 2.}}\\\\\frac{2}{6} =\frac{2/2}{6/2}=\boxed{\frac{1}{3}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

You didn't attach an image, can't exactly help. sorry!

Answer:

Option 3 (C)

Step-by-step explanation:

It is the only one that changes the same amount every time ( times 2 )

Answer:

D. V=314.2cm³

Step-by-step explanation:

The volume of the cone is:

V=pi×r²×h/3=pi×5²×12/3=100×pi=314.2cm³

Answer: D) 314.2 [tex]cm^3[/tex]

Step-by-step explanation:

The formula for finding the volume of a right cone is [tex]V=\pi r^2\frac{h}{3}[/tex]

r is the radius and h is the height/altitude.

We can sub these values in and solve

[tex]V=\pi (5^2)(\frac{12}{3} )\\V=\pi (25)(4)\\V=100\pi[/tex]

Let's sub in 3.14 for [tex]\pi[/tex] since that is a close estimate

[tex]V=(100)(3.14)\\V=314[/tex]

The volume is about 314.

Our closest answer to that is D so that is the correct choice.

Answer:

197.34

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

x = -75.9

y = 2.6

-xy

Step 2: Evaluate