Natalie can hop 24 times in 8 minutes at a constant rate. How many times can she hop in 7 minutes?

Answer:

[tex]x_1=2; x_2=-1[/tex]

Step-by-step explanation:

The square term is [tex]x^2[/tex] so we expect the complete square to be of the form [tex](x-a) ^2=x^2+2ax+a^2[/tex].

Let's compare the first degree terms now: we have [tex]2ax[/tex] on one side and [tex]-1x[/tex] on the other. That would make [tex]a=- \frac12[/tex]. At this point we have still the second squared term, so we add and subtract [tex]\frac14 = (\frac12)^2[/tex]

Our equation becomes:

[tex]x^2-x+\frac14 -\frac14-2 =0\\(x-\frac12)^2-\frac94=0[/tex]

(the [tex]\frac94[/tex] term comes from rewriting [tex]2= \frac84[/tex] and adding the terms out of the bracket).

At this point it's just solving the equation:

[tex](x-\frac12)^2 = \frac94 \rightarrow x-\frac12=\pm\frac32\\x=\frac12\pm\frac32\\x_1=\frac42 = 2; x_2=\fra-\frac22=-1[/tex]

Answer:

You need to find what X= then put the answer in the box to the left

Step-by-step explanation:

Answer:

118

Step-by-step explanation:

62+x=180

x=180-62

x=118

Answer:

27

Step-by-step explanation:

Width = w

length = l

w=1/3 * l

or, l=3w

perimeter=2l+2w=24

2(l+w)=24

2(3w+w)=24

2*4w=24

8w=24

w=3

l=9

Area=3*9=27

Answer:

When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

Step-by-step explanation:

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Here you go, your equation should look a lot like this:

x²-16 -----> (x+4)(x-4).

Answer:

x = 4/5.

Step-by-step explanation:

7x - 1 = 2x + 3

Move one to the other side.

7x = 2x + 4

Subtract the 2x to the other side

5x = 4

Divide both sides by 5

x = 4/5.

Answer:

x = 0.8

Step-by-step explanation:

To find x, we need to isolate the constants on one side and the variables on the other. Simply subtract 2x both sides and add 1 both sides.

⇒ [tex]7x - 1= 2x + 3[/tex]

⇒ [tex]7x - 1 - 2x + 1 = 2x + 3 + 1 - 2x[/tex]

⇒ [tex]5x = 2x + 3 + 1 - 2x[/tex]

⇒ [tex]5x = 3 + 1[/tex]

Now, simplify the RHS.

⇒ [tex]5x = 3 + 1[/tex]

⇒ [tex]5x = 4[/tex]

Finally, divide 5 both sides to isolate the x variable.

⇒ [tex]\frac{5x}{5} = \frac{4}{5}[/tex]

⇒ [tex]x = \frac{4}{5} = 0.8[/tex]

As the histogram is skewed to the right because there is less data on the right side. So, she is correct that is option D.

A histogram graph is a graphical representation of given data. It is a bar graph that represents a frequency distribution by rectangles separated from each other with equal spaces.

A graph shows several dogs labeled 0 to 2 on the horizontal axis and frequency on the vertical axis.

here, we can see from a given data that as the number of dogs increases the frequency on the vertical axis decreases. At 0 dogs the frequency is 20, at 1 dog the frequency is 15, At 2 dogs the frequency is 12.

The histogram is skewed to the right because there is less data on the right side as the frequency decreases.

Therefore, the histogram is skewed to the right because there is less data on the right side. So, she is correct that is option D.

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Answer:

d

Step-by-step explanation:

The value of sin-1(1) is negative startfraction pi over 2 endfraction, startfraction -pi over 2 endfraction.

The value of sin (π/2) is equal to the number 1. The value of the sin-1(1) has to be find out.

Suppose the value of this function is x. Thus,

[tex]x=\sin^{-1}(1)[/tex]

Solve it further,

[tex]\sin(x)=(1)[/tex]              ......1

The value of sin (π/2) and -sin (-π/2) is equal to 1 such that,

[tex]\sin\dfrac{\pi}{2}=-\sin\left(-\dfrac{\pi}{2}\right)=1[/tex]

Put this value in the equation 1,

[tex]\sin(x)=\sin\left(\dfrac{\pi}{2}\right)=-\sin\left(-\dfrac{\pi}{2}\right)[/tex]

Thus, the range will be,

[tex]\left(\dfrac{\pi}{2},-\dfrac{\pi}{2}\right)[/tex]

Thus, the value of sin-1(1) is negative startfraction pi over 2 endfraction, startfraction -pi over 2 endfraction.

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Answer: C

Step-by-step explanation:

edge

Answer:

Step-by-step explanation:

Here 8 and 10 are the like terms (both are constants)

-3k -(-8) + 2 = -3k + 8 +2

                    = -3k + 10

Answer:

total - given, 360 -139 = 221

Answer:

30 tons of concrete

There are 2000 pounds in 1 ton

So 2000 pounds * 30 tons

30 * 2000 = 60000

60,000 pounds

Answer:

(a) Kaylee earns $19.50 per hour.

(b) Kaylee earns more per hour.

Step-by-step explanation:

a)

[tex]m[/tex] = $ per hour

[tex]y = mx[/tex]

[tex](39) = m(2)[/tex]

[tex](39 = m(2)) = 19.50 = m[/tex]

b) Kaylee earns more per hour

Kaylee earns $19.50 per hour and Joey earns $16.50 per hour.

Answer:  x = -4 + y

Step-by-step explanation:

Subtract y from both sides y- x - y = 4 - y

Simplify -x = 4 - y

Divide by -1

-x ÷ -1,

4 ÷ -1,

y ÷ -1,

Simplify x = -4 + y

Answer:

Step-by-step explanation:

Answer:

Option b is the answer.

Step-by-step explanation:

As you can see in the image you have given, the x values that are less than or equal to 4.5 are the elements of the solution set.

The Castillo family made a monthly payment of $270.83 and they owed the utility company $516

An equation is an expression that shows the relationship between two or more numbers and variables.

Two years ago the Castillo family used $3,250 worth of electricity. During last year, they actually used $3,766 of electricity, hence:

Monthly payment = $3250 / 12 = $270.83

Money owed = $3,766 - $3,250 = $516

The Castillo family made a monthly payment of $270.83 and they owed the utility company $516

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In the case of multiplication in exponents, if the numbers are the same, their exponents are added.

7 + 8 is written to the power of x, and 3 + 2 is written to the power of y.

Step-by-step explanation:

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[tex]===================================[/tex]

Step 1:

Use the Distributive Property:

[tex]\hookrightarrow\sf{-(3w+1)=-3w-1}[/tex]

Hence, the equation is

[tex]\hookrightarrow\sf{6-3w-1=8w-2}[/tex]

Move 8w to the left side

[tex]\hookrightarrow\sf{6-3w-1-8w=-2}[/tex]

Combine Like Terms

[tex]\hookrightarrow\sf{6-3w-8w-1=-2}[/tex]

Simplify

[tex]\hookrightarrow\sf{6-11w-1=-2}[/tex]

Move 6 and 1 to the right

[tex]\hookrightarrow\sf{-11w=-2+1-6}[/tex]

[tex]\hookrightarrow\sf{-11w=-7[/tex]

Divide both sides by -11

[tex]\hookrightarrow\sf{w=7/11}\\=============================[/tex]

Answer:

4.04

Step-by-step explanation:

I like to turn my fractions into decimals when I do this. Volume is found by length*width*height. In this case, it would be 3.5*1.75*4.66

The volume would be about    [tex]4ft^2[/tex]

Answer:

the correct answer is the second

Answer:

Solution:

The length of the arc part:

365 -60/360

x2x2x15=5/6 x2x2x15=252

Two segments: 2x15 = 30

All perimeter: (252 + 30) m

{divide into two parts?

Step-by-step explanation:

Is this what you wanted?

Answer:

See below.

Step-by-step explanation:

23,492,349

            /\

This is the hundreds place.

The place after it has a 4, so normally, we would round down. But, there is a 9 after the 4, so we round up the 4 to 5, and we round up again to the 3.

23,492,400

-hope it helps

Answer:

(A) QS = 8

(B) PS = 15

(C) SR = 6

(D) PQ = 17

(E) QR = 10

Step-by-step explanation:

i did it and got it correct! :D

All the distances are;

(A) QS = 8

(B) PS = 15

(C) SR = 6

(D) PQ = 17

(E) QR = 10

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}

Given:

The three points P(1,2), Q(16,10), and R(22,2) are on the coordinate plane.

To find the lengths of the different line segments in the given figure, we can use the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

(A) To find the length of QS, we need to find the difference between the y-coordinates of Q and S:

QS = |10 - 2| = 8

Therefore, QS has a length of 8 units.

(B) To find the length of PS, we need to find the difference between the x-coordinates of P and S:

PS = |16 - 1| = 15

Therefore, PS has a length of 15 units.

(C) To find the length of SR, we need to find the difference between the x-coordinates of S and R:

SR = |22 - 16| = 6

Therefore, SR has a length of 6 units.

(D) To find the length of PQ, we need to find the difference between the x-coordinates of P and Q:

PQ = √[1 - 16)² + (2 - 10)²]

Therefore, PQ has a length of 17 units.

(E) To find the length of QR, we need to use the distance formula:

QR = √[(22 - 16)² + (2 - 10)²]

= √[36 + 64]

= √100

= 10

Therefore, QR has a length of 10 units.

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The conclusion about the detergents in the sampling is D.Inferences cannot be made about the population of fabric from which the pieces were chosen.

Sampling is the selection of a subset of individuals that are gotten from a statistical population in order to estimate the characteristics of the whole population.

In this case, inferences cannot be made about the population of fabric from which the pieces were chosen. The conclusion cannot be made that detergent A cleans better than detergent B for the fabric from these bolts.

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Answer:

its cost 25 cents

in so will cost 275 cent so 2.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of LM is 24√(3)

the short leg is 24

the hypotenuse is 24*2 = 48