Select the reason that best supports Statement 7 in the given proof.

Using the given function, it is found that the projectile hits the ground after 20 seconds.

It hits the ground when it's height, given by h(t), is equals to zero.

In this problem, the function that models it's height is given by:

h(t) = -4.9t^2 + 98t.

Then:

h(t) = 0

-4.9t^2 + 98t = 0.

-4.9t(t - 20) = 0

t - 20 = 0 -> t = 20.

The projectile hits the ground after 20 seconds.

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Answer:

14

Step-by-step explanation:

2x((5-3)+(7-2)) = 14

Area :-

[tex]\\ \rm\rightarrowtail side^2[/tex]

[tex]\\ \rm\rightarrowtail 13^2[/tex]

[tex]\\ \rm\rightarrowtail 169[/tex]

Square root:-

Answer:

Step-by-step explanation:

Answer:

8 and yes

Step-by-step explanation:

c² - b² = a²

100 - 36 = a²

64 = a²

a = 8

the three sides form a sequence, 6, 8, 10, which is the pythagorean triple.

Answer:

Step-by-step explanation:

Hailey paid 80% of the regular price.

We have Hailey who paid 40$ for a jacket whose regular price was 50$.

Assume that she paid [x]% of the regular price.

Then, we can write -

40 = x% of 50

40 = (x/100) x 50

x = (4000/50)

x = 80%

Therefore, Hailey paid 80% of the regular price.

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[tex]-5+x = -2\\\\\implies x = -2 +5 = 3[/tex]

Answer:

x=3

Step-by-step explanation:

−5 + x = −2

Add 5 to each side

−5+5 + x = −2+5

x = 3

When trapezoidal prism undergoes a dilation, the size of the prism changes

The height of the image is 52.2 meters

The given parameters are:

A1 = 35 m²

A2 = 315 m²

H1 = 5.8 m

To calculate the height of the image, we make use of the following equivalent ratio

A1 : H1 = A2 : H2

So, we have:

35 : 5.8 = 315 : H

Express as fractions

35/5.8 = 315/H

Make H the subject

H = 315 * 5.8/35

Evaluate the product

H = 52.2

Hence, the height of the image is 52.2 meters

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Answer:

17.4

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

because the hypotenus is the longest of all the other sizes

Answer:

Step-by-step explanation:

Put the values of x to the equation y = 2x + 2 and calculate the value of y:

x = 2

y = 2 · 2 + 2 = 4 + 2 = 6

x = 5

y = 2 · 5 + 2 = 10 + 2 = 12

x = 6

y = 2 · 6 + 2 = 12 + 2 = 14

x = 8

y = 2 · 8 + 2 = 16 + 2 = 18

Answer:

No, no, no, yes, yes.

Step-by-step explanation:

A integer is a whole number, 1, 2, 3, etc.

The time it will take Carley's dad to mow the lawn is 3.3 hours.

Rate is the ratio between two related quantities in different units. Therefore,

The rate Carley do the  lawn = 1 / 5

When they work together they do it the 1 / 2 rate.

Therefore,

let

the hours it takes Carley dad = x hours . Therefore,

1 / 5 + 1 / x  = 1 / 2

x + 5/ 5x = 1 / 2

cross multiply

2(x + 5) = 5x

2x + 10 = 5x

10 = 5x - 2x

10 = 3x

x = 10 / 3

x = 3.3 hours

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Answer:

C

Step-by-step explanation:

To find A you have to divide 3/5 by 4 so that would not work.

To find B you have to subtract 1/4 from 3/5 and that doesn't match the problem.

To find C you do divide 3/5 by 1/4 which matches the problem.

And lastly for D you would divide 1/4 by 3/5 which is the opposite of what the question is asking for.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

The given equations are :

[tex]\qquad \sf  \dashrightarrow \:x + y = 32[/tex]

and

[tex]\qquad \sf  \dashrightarrow \:y = 7x[/tex]

Now, plug in the value of y from equation 2 into equation 1 to find out the value of x ~

[tex]\qquad \sf  \dashrightarrow \:x + y = 32[/tex]

[tex]\qquad \sf  \dashrightarrow \:x + 7x = 32[/tex]

[tex]\qquad \sf  \dashrightarrow \:8x = 32[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 32 \div 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 4[/tex]

Now, plug the value of x in equation 2 to find y

[tex]\qquad \sf  \dashrightarrow \:y = 7x[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 7 \times 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 28[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Answer:

665

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Answer:

665

Step-by-step explanation:

350 - 30( - 14 + 3.5) ← evaluate the parenthesis

= 350 - 30( - 10.5) ← distribute parenthesis by - 30

= 350 + 315

= 665

Step-by-step explanation:

-4-(3)=-7

step two

3+(-5)=-2

step three

4+6=10

step four

-5-9=-14

step five

-4+(-9)=-13

Answer:

a) -4 - ( 3) = - 7

b) 3 + ( -5) = 3 - 5 = -2

c) 4 + 6 = 10

d) -5 -9 = - 14

e) -4 + ( -9) = -4 -9 = - 13...

Answer:

$26.42

Step-by-step explanation:

P = 30 * 0.82 * 1.074 = 26.42

After x half-lifes, the amount of the isotope is:

A(x*T) = 90mg*e{-x*ln(2)}

And after 70 days, there are 5.628 mg

We define the half-life as the time such that the inital amount of a given substance reduces to half of it.

If the half-life is T, the amount of the substance can be written as:

A(t) = a*e^{-λ*t}

Where λ = ln(2)/T.

and a is the initial amount.

In this case, T = 17.5 days, then:

λ = ln(2)/17.5 days = 0.0396 / day

And we also have a = 90mg

Then the exponential equation is:

A(t) = 90mg*e^{-t*0.0396 / day}

After x half-lifes, the amount of the isotope left is:

A(x*T) = 90mg*e^{-x*T*ln(2)/T} = 90mg*e^{-x*ln(2)}

And after 70 days the amount is:

A(70 days) = 90mg*e^{-70 days*0.0396 / day} = 5.628 mg

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Answer:

Y=90mg(0.5)^5

1.86 after 70 days

Step-by-step explanation:

Answer: Statements 3, 4, 5

Step-by-step explanation:

Statement (3) is true because an interior angle and its exterior angle are supplementary.

Statement (4) is true by the exterior angle theorem.

Statement (5) because the sum of the angles of a triangle is 180 degrees.

Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.

If a function has a line of symmetry at x = x₀, then we know that:

f(x₀ + x) = f(x₀ - x).

So we have symmetry around that line.

Then, if the line of symmetry is at x = 5 and we know that:

f(8) = f(5 + 3) = -7

We also must have:

f(2) = f(5 - 3) = -7

Then the point (2, - 7) must be on the graph.

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The answer is A. Springsville has several different activities.

Answer: Division Property of equality

Step-by-step explanation:

5d= 75

1. Isolate the variable and remember, if the number is next to the letter, it means to multiply.

2. Reverse PEMDAS so instead of multiplying, divide instead.

3. 75/ 5 equals 15.

d=15

Answer: d=. 15

Step-by-step explanation:

Answer:

667.2

Step-by-step explanation:

aP/2 apothem is 13.9, perimeter is 16(6)= 96

multiply apothem and perimeter then divide by 2.

Answer:

x = - 3, y = - 1

Step-by-step explanation:

y = 7x + 20 -----> equation 1

4x - y = - 11

4x - ( 7x + 20 ) = - 11

4x - 7x - 20 = - 11

- 3x = - 11 + 20

- 3x = 9

x = 9 / - 3

x = - 3

Substitute x = - 3 in equation 1,

y = 7 ( - 3 ) + 20

  = - 21 + 20

y = - 1

Hence,

x = - 3

y = - 1

Answer:

Explanation:

y = 7x + 20 __ equation 1

4x - y = -11

y = 11 + 4x __ equation 2

using substitution method,

11 + 4x = 7x + 20

4x - 7x = 20 - 11

-3x = 9

x = -3

Find y,

y = 7x + 20

y = 7(-3) + 20

y = -1

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 99% confidence interval for the true mean number of visitors on summer days is given by:

c. 92.664 to 103.940 visitors

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 30 - 1 = 29 df, is t = 2.756.

The other parameters are given as follows:

[tex]\overline{x} = 98.3, s = 11.2, n = 30[/tex].

Hence, the bounds of the interval are given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 98.3 - 2.756\frac{11.2}{\sqrt{30}} = 92.664[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 98.3 + 2.756\frac{11.2}{\sqrt{30}} = 103.94[/tex]

Hence option c is correct.

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Answer:

Step-by-step explanation:

First, we have to find 14% of 56

14% of 56 is = 56 x 14/100

                  = 7.84

Now we have to increase the number 56 by 14%, which means we have to add 14% of 56 (7.84) to the given number (56)  

56 + (14% of 56)

= 56 + 7.84

= £63.84

Answer:

D. 16 square cm

Step-by-step explanation:

To solve this problem, we will have to look at the Scale factor.

1 : 8 =  1 cm (in the scale drawing) = 8cm (in the real object)

Since the area of the scale drawing is 2 cm, the equation will be 2 x 8 = 16.

Therefore, 16 will be the area of the real object.

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