Select "equivalent" or "not equivalent" for each pair of expressions.
Expressions
equivalent or not equivalent?
5x - 7+ 3x and 3x - 7+ 5x equivalent not equivalent
4y+9+ 3y and 3y+9+ 4y equivalent not equivalent
6z - 2z + 4 and 4 + 22 - 6z equivalent not equivalent

Base on the similarity principle of triangles, the distance d across the lake as shown is 90 ft.

Two triangles are similar if they are only difference in size but have the same shape.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, let's create a proportion from the triangles since they are similar.

40 / d = 20 / 45

cross multiply

45 × 40 = 20d

1800 = 20d

divide both sides by 20

1800 / 20 = 20d / 20

d = 90 ft

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Answer:

1. B

2. E

3. D

4. B

5. C

6. B

7. E

8. D

9. D

10.D

11. E

Answer:

x*x=64

x= 8

Step-by-step explanation:

this means that the area is 64 in more than 2

Answer:

<3 ~= <5 - Alternate Interior Angles Theorem

<3 ~= <7 - Corresponding Angles Theorem

<5 ~= <7 - Vertical Angles Theorem

line I || line m - Transitive Property

Answer:

-20z + 2

Step-by-step explanation:

4(-5z + 2) + (-6) =

= -20z + 8 - 6

= -20z + 2

A city starts with a population of 500,000 people in 2007. Its population declines according to the equation

P(t) = 500,000e -0.099t

where P is the population in t years later. Approximately when will the population be half the initial amount?

Answer:

2014

Step-by-step explanation:

Given the exponential growth function :

P(t) = 500,000e^-0.099t

Where P is population in t years later

When the population will 1/2 the initial amount

1/2 the initial amount = 1/2 * 500,000 = 250,000

P(t) = 250,000

250,000 = 500000e^-0.099t

250,000/500000 = e^-0.099t

In(0.5) = - 0.099t

t = −0.69314 / - 0.099

t = 7.0014

t = 7

Year which population = 500,000 = 2007

Hence, half the population will be attained on (2007 + 7) = 2014

After 7 years population of the city will be half of the initial amount.

Population function:

[tex]P(t) = 500000 e^{-0.099t}[/tex]

Initial population means population at t=0

P(0) = 500000

Half of initial population = 250000

So, we need to calculate the time t when the population will be half of the initial amount.

[tex]250000= 500000 e^{-0.099t}\\\\e^{-0.099t} = \frac{1}{2}[/tex]

Taking log both sides

-0.099t (log e)= log (1/2)

The logarithm of e is 1 when considering the base of the log as e.

So, -0.099 t= -0.693

t=7

Therefore, After 7 years population of the city will be half of the initial amount.

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Answer:

0

Step-by-step explanation:

The points on a number line are called coordinates. The zero point is called the origin. The numbers to the right of the origin are positive numbers; the numbers to the left of the origin are negative numbers.

Answer:

0

Step-by-step explanation:

Answer: where is the graph

Step-by-step explanation:

i cant help if there is no graph

Answer:

See below.

Step-by-step explanation:

Question 1

a = -2 and x = -6

| a + x | / 2 - | a - x | / 2

| -2 + -6 | / 2 - | -2 + 6 | / 2

| -8 | / 2 - | 4 | / 2

8/2 - 4/2

= 4/2

= 2

Question 2

a = -5, b = 4, c = 1, d = -3

| a - b | - | c + d |

| -5 - 4 | - | 1 - 3 |

| -9 | - | -2 |

= 9 - 2

= 7

Answer:

A,B,E

Step-by-step explanation:

Answer:

8 = x

Step-by-step explanation:

100 - 4x = 20 + 6x

100 = 20 + 10x

80 = 10x

8 = x

Answer:

the third one is the correct answer

Answer: Suppose y varies directly with x. Write a direct variation equation that relates x and y.

Step-by-step explanation:

Answer is y = -5x

The equation for y varies directly with x is, y = - 5x.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, y varies directly with x.

Therefore,

y ∝ x.

y = kx, where k is the proportionality constant.

At y = - 10 when x = 2.

- 10 = 2k.

k = - 5.

So, y = - 5x.

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Answer:??????

Step-by-step explanation:

Answer:

d (3,11)

Step-by-step explanation:

Answer:

x is 10 and y is 20

Step-by-step explanation:

Answer:

1 yard = 3 feet

3 × 4 = 12 feet of fabric

12 - 4 = 8

8 - 6 = 2

they will have 2 feet of fabric left over

Answer:

16 signatures

Step-by-step explanation:

48/3 = 16

16 x 2 = 32

One-third of 48 is 16. So if Felix collected one-third and Andrea collected two-thirds, then Felix had 16 signatures and Andrea had 32 signatures.

Answer:

16

Step-by-step explanation:

48/3 = 16

16 x 2 = 32

1/3 of 48 is 16. if Felix collected 1/3 and Andrea collected 2/3, then Felix got 16 signatures

Answer:

Step-by-step explanation:

In this problem, we are expected to solve for the total area covered by water,   by addition of scientific notation

Given data

Area covered by salt water=  352,000,000 km2

Area covered by fresh water= 9 × 10^6 km2=9,000,000

Earth's surface is covered by water= 352,000,000 +9,000,000

Earth's surface is covered by water= 361000000

In scientific notation it is 3.61x10^8km^2

Answer:

560 is 40% of 1,400

Step-by-step explanation:

40 x 1400/ 100  = 560

560/1400 = 40%

Answer:3

Step-by-step explanation:

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The value of g(3) is 3

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

We need to find the value of g(3).

From the question, we have

g(x)= x-1,  -2≤x<-1

g(x)= 2x+3, -1≤x<3

g(x)= 6-x,     x≥3

The value 3 is in the function g(x)=6-x

When x is 3

g(3)=6-3

Subtract 3 from 6.

g(3)=3

Therefore value of function g(3) is 3.

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Answer:

18.75

Step-by-step explanation:

[tex]\\ \rm\Rrightarrow 18\dfrac{3}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{75}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{75(25)}{100}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1875}{100}[/tex]

[tex]\\ \rm\Rrightarrow 18.75[/tex]

Answer: 17 pages

Step-by-step explanation:

One eighth of 136:

136 divided by 8 = 17

Answer:

17 pages

Step-by-step explanation:

1/8 x 136 = 17

Answer:

a number line or something like this

Answer:

D

Step-by-step explanation:

4x5+4×12+12×6×2=212

Answer:

I think the answer may be option C

Answer:

the first gets =90birr

the second gets =120birr

the third gets =150birr

90+120+150=360birr

I hope you got your answer.