Find the measures of <1 and <2 if <3 = 78^0 and <4 = 102^0.
Assume the lines are parallel.









Figure is not drawn to scale.
Angle 78 102 12
<1
<2

5242880 insects would be present in 20 days.

The correct answer is an option (c)

"[tex]f(x)=ab^x[/tex],

where a is the initial value

b is the growth rate

x is time. "

For given question,

Suppose the function for the population growth is,

[tex]A(t)=A_0\times b^t[/tex]                    

A colony of insects doubles every day.

⇒ b = 2

The colony has 5 insects today.

⇒ [tex]A_0=5[/tex]

So, the exponential growth function would be,

[tex]A(t)=5\times 2^t[/tex]                   ...........(1)

We need to find the number of insects after 20 days,

From equation (1),

[tex]\Rightarrow A(20)=5\times 2^{20}\\\\\Rightarrow A(20)=5\times 1048576\\\\\Rightarrow A(20)=5242880[/tex]

Therefore, 5242880 insects would be present in 20 days.

The correct answer is an option (c)

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The base of the given expression will be 4.

Here, we are given that 4 is multiplied by itself 7 times, that is-

4 x 4 x 4 x 4 x 4 x 4 x 4

As anything raised to the power 1 is the number itself, the given expression can also be written as follows-

[tex]4^{1} * 4^{1} *4^{1} *4^{1} * 4^{1} *4^{1} *4^{1}[/tex]

Now, we know that when we need to find the product of 2 numbers whose bases are same, we can simply add the powers. Mathematically this can be represented as follows-

[tex]a^{n}a^{m} =a^{n+m}[/tex]

Thus, the given expression will become-

[tex]4^{1} * 4^{1} *4^{1} *4^{1} * 4^{1} *4^{1} *4^{1}[/tex] = [tex]4^{1+1+1+1+1+1+1}[/tex]

= [tex]4^{7}[/tex]

Thus, we see that when 4 is multiplied 7 times, the base comes out to be 4 only.

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answer:

The correct answers are choices B, C, and D. Here is an explanation for each choice: B. All congruent figures are exactly the same size and shape. This is what makes one figure congruent to another. C. If the figures are the same size and shape, then the corresponding sides will also be congruent. D.If the figures are the same size and shape, then the corresponding angles will also be congruent.

Therefore, the slope of a line on a standard XY-plane that passes through points (1, 3) and (4,-3) is -2.

So, option (c) is correct.

Given two points are (1, 3) and (4, -3)

We need to find the slope of a line

The slope of a line (m) :

m = y₂ - y₁ / x₂ - x₁

Given (x₁, y₁) =  (1, 3) and (x₂, y₂) =  (4, -3)

Slope (m) =  y₂ - y₁ / x₂ - x₁

                = -3 - 3 / 4 - 1

                = -6 / 3

                = -2

Therefore, the slope of a line on a standard XY-plane that passes through points (1, 3) and (4,-3) is -2.

So, option (c) is correct.

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Answer:

C I think. Sorry if it's incorrect but I pretty sure it isn't.

Answer:

i think it is c

Step-by-step explanation:

Answer:

A. 3x+6= 0

Step-by-step explanation:

When you divide - 3 with -x, you will get a positive value and same goes for - 3 and - 2

So that is how you get the answer 3x+6= 0

Answer:

1h 20m

Step-by-step explanation:

Let the total amount of work be x.

Shannon:

2h = x

1h = [tex]\frac{1}{2}[/tex]x

So basically Shannon does  [tex]\frac{1}{2}[/tex]x work per hour.

Sarah:

4h = x

1h = [tex]\frac{1}{4}[/tex]x

So basically Sarah does [tex]\frac{1}{4}[/tex]x work per hour.

Together:

1h = [tex]\frac{1}{2}[/tex]x + [tex]\frac{1}{4}[/tex]x

    = [tex]\frac{2}{4}[/tex]x + [tex]\frac{1}{4}[/tex]x

    = [tex]\frac{3}{4}[/tex]x

Amount of time spent = [tex]\frac{4}{4}[/tex]x ÷ [tex]\frac{3}{4}[/tex]x

                                     = [tex]\frac{4}{4}[/tex]x × [tex]\frac{4}{3}[/tex]x

                                     = [tex]\frac{16}{12}[/tex]h

                                     = 1[tex]\frac{4}{12}[/tex]h

                                     = 1h 20m

Answer:

4/3 hours

Step-by-step explanation:

For every hour that Sarah mows, Shannon mows twice as much. Because of this, Sarah is going to mow two times as much of the field as Shannon. You can set up an equation where x is the fraction of lawn mowed. This equation should be:

2x + x = 1 -> 3x = 1

The reason the equation is set up like this is because there is 1 whole lawn that the fraction of the lawn that Shannon mows (2x) plus the fraction of the lawn that Sarah mows (x) adds up to. You can use this equation to solve for x, which will be 1/3.

Since you know x, you can find what fraction of the lawn Shannon and Sarah mow. Since Shannon mows a fraction of 2x of the lawn, the fraction she mows will be 2*1/3 = 2/3. The fraction that Sarah mows will be x = 1/3.

Now that you know the fraction of the whole lawn that both Saran and Shannon mow, you can multiply their respective fraction by the amount of time it takes for them to mow a whole lawn. To do this for Shannon, you multiply 2/3 of the lawn by 2 hours, which gives you 4/3 hours. To do this for Sarah, you multiply 1/3 of the lawn by 4 hours, which also gives you 4/3 hours.

Answer:

28.32552

Step-by-step explanation:

multiply

Answer:

28.32552

Step-by-step explanation:

39.331 × 0.72= 28.32552

Answer:

True

True

False

Step-by-step explanation:

Rate of Change is slope. There is no change in slope as the line is straight.

Using the slope formula:

[tex]m=\frac{x_{2}-x_{1} }{y_{2}-y_{1}} \\m=\frac{4-0}{1-0}\\m=4[/tex]

Where m is slope

Since gold beads are on the x-axis, that means there are 4 black beads per gold bead

Answer:

Is it B

Step-by-step explanation:

Answer:

Step-by-step explanation:

B test!

Answer:

The first one!

Step-by-step explanation:

The sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.

Answer:

The answer is C.

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:1 1/4

Step-by-step explanation: If it is 5/4 it makes one whole leaving an extra

Answer:

Isosceles

Step-by-step explanation:

The triangle has two equal sides of 16 cm. Isosceles triangles are classified to have either two of the same sides or two of the same angles.

Answer:

ad=DC is your answer.....

Answer:

c

Step-by-step explanation:

16-30i

The complete sequence is 24, 30, 36, 42, 48, 54, 60

The nth term of an arithmetic progression is expressed according to the equation;

Tn = a + (n-1)d

where

a is the first term

n is the number of terms

d is the common difference

Determine the common difference

d = 42-b = b - 30

-b-b = -30-42

-2b = -72

b = 36

d = 36-30

d = 6

For the first term;

d = 30 - a

6 = 30 - a

a = 24

For the value of c

c = 42 + 6

c = 48

For the value of d

d = 48 + 6

d = 54

For the value of e

e = 54 + 6

e = 60

Hence the complete sequence is 24, 30, 36, 42, 48, 54, 60

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Answer:

ax + by = c

<=> ax = c - by

<=> x = [tex]\frac{c-by}{a}[/tex]

Step-by-step explanation:

Answer:

0.48173

Step-by-step explanation:

Given that :

Mean (m) = 2.24

Standard deviation (s) = 1.38

Sample size (n) = 40

P(x ≥ 2.55)

Z = (x - m) / (s/sqrt(n))

Z = (2.55 - 2.24) / (1.38 / sqrt(40))

Z = 0.01 / 0.2181971

Z = 0.0458301

P(Z ≥ 0.0458) = 0.48173 ( Z probability calculator)

Answer:

Ok

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Okay.

A negative exponent means we want to "flip" the term.

so we get

(1/-c^2)^1/3

When we get a fraction exponent, we want to "root" the term by that

so we get

[tex]\sqrt[3]{\frac{1}{-c^2} }[/tex]

Which simplifies to

[tex]\frac{\sqrt[3]{1} }{\sqrt[3]{-c^2} }[/tex]

Which becomes[tex]1/\sqrt[3]{-c^2}[/tex]

Answer:

12.50x less than or equal to $200

Step-by-step explanation:

Answer:

It's not A or D it has to be B or C.

Step-by-step explanation: i just took the quiz on edge and it wasn't  A or D.

Answer:

Its B

Step-by-step explanation:

Answer:

168 miles

Step-by-step explanation:

d = rt

d = 42 × 4

d = 168

Answer:

d = rt

d = 42×4

d = 168

Step-by-step explanation:

That is the distance between the towns.

You have to multiply the amount of miles by the time it took.

Answer:

height of the vessel should be 50 cm I guess

Answer:

30 4/5 or 30.8

Step-by-step explanation:

Take intercepts from the graph:

Calculate the intercepts

Points are: (3, 0) and (0, - 9)

Ordered pairs given:

Take intercepts from the graph:

Calculate the intercepts:

Points are: (- 2, 0) and (0, - 4)