Find the greatest common factor of 12y4 and 7y3.

The equation that represents the horizontal parabola given on the graph is:

y² = -8x

The equation of a quadratic function, of vertex (h,k), is given by:

x = a(y - k)² + h

In which a = 1/p is the leading coefficient.

In this problem, the vertex is (0,0), hence h = k = 0, and:

ay² = x.

The directrix is at x = 2, and the parabola opens left, hence:

p = -4(2 - 0) = -8.

Hence the equation is:

y² = px = -8x.

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-5(y+2)=25

y+2=25 ÷(-5)

y+2= -5

y= -5-2

y=7

The total wages of Steve will be equal to W=$560 worked for 56 hours.

The amount of money charged by a worker for working for a particular company on an hourly or day basis is called the wages.

Here the time of the worker is given as . he worked 40 hours at a regular rate, 8 hours at a time and a half and 8 hours at double time and the earning per hour is $10.

The total time will be:-

40+8+(1÷2)x8x2=56

Now the total earnings will be given as:-

T=10x56=$560

Hence the total wages of Steve will be equal  W=$560 worked for 56 hours.

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Answer:

5 : 1

Step-by-step explanation:

Unit conversion (between cm and mm) : 1 cm = 10 mm

⇒ 4 cm : 8 mm

⇒ 4 x 10 mm : 8 mm

⇒ 40 mm : 8 mm

⇒ 5 : 1

The solution to the system of equations is (-3,4)

The equations are given as:

5x + 2y = 14

y = x – 7

Substitute y = x – 7 in the first equation

5x + 2(x - 7) = 14

Expand

5x + 2x - 14 = 14

Evaluate the like terms

7x = 28

Divide

x = 4

Substitute x = 4 in y = x – 7

y = 4 – 7

Evaluate

y = -3

Hence, the solution to the system of equations is (-3,4)

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Answer:

See below ~

Step-by-step explanation:

The true statements based on the graph :

Answer:

A.

Step-by-step explanation:

Because if she plays for a certain amount of time it would go up. And it she took a break it would be a straight line then go up the same line as the one at the bottom. Thus making your answer A.

The number of the combinations of 3 scoops of ice cream can Laura choose will be 20.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

Laura wants 3 scoops of ice cream.

She can choose from vanilla, chocolate, mint, raspberry, blueberry, and coffee flavors.

Then the number of the combinations of 3 scoops of ice cream can Laura choose will be given as

→ ⁿCₐ

The total number of the flavor will be

n = 6

Then the number of the chosen flavor will be

a = 3

Then we have

→ ⁶C₃

→ 20

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Based on the size of the pool that Mr. DelGrande wants to build, the ratio of the Olympic pool to the smaller pool is 2.5:1 and the area of an Olympic pool is 1,250 m².

The ratio of the pools is:

Olympic pool length : Mr. DelGrande pool

             50                 :              20

Simplest terms give:

50 / 20 : 20 / 20

2.5 : 1

Given the area of Mr. DelGrande's pool, the area of an Olympic pool is:

= Ratio ² x Area of Mr. DelGrande pool

= 2.5² x 200

= 1,250 m²

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Answer:

15.7 lbs (please mark brainliest)

Step-by-step explanation:

2.6+x+x=34

2x=31.4

x=15.7

Answer: 14.4

Step-by-step explanation: I took 34 and divided it by 2 then subtracted 2.6 from 17 which gave me 14.4. If it's wrong, sorry.

Answer:

35 ways

Step-by-step explanation:

[tex]_7C_4=\frac{7!}{4!(7-4)!}=\frac{7!}{4!*3!}=\frac{7*6*5}{3*2*1}=\frac{210}{6}=35[/tex]

Therefore, Dwight can arrange his schedule in 35 ways if he must pick 4 out of 7 courses to choose from.

Answer:

[tex]313.3333\%[/tex]

Step-by-step explanation:

Based on given conditions, formulate:

[tex] \frac{310 - 75}{75} [/tex]

Calculate the sum:

[tex] \frac{253}{75} [/tex]

Simplify it:

[tex] \frac{47}{15} [/tex]

Convert that to a decimal:

[tex]3.133333[/tex]

Multiply that:

[tex]3.133333 \times \frac{100}{100} [/tex]

Calculate that:

[tex] \frac{3.133333 \times 100}{100} [/tex]

Convert that:

[tex]313.3333\%[/tex]

Answer:

in 720 Possibles ways Ten runners can be arranged  as first, second, and third placers

Answer:

The peanut is 12.59 feet away from the base of the platform.

Step-by-step explanation:

When solving these equations, we can first start out by noticing that this requires a trigonometry function.

There are three types : cos, sin, and tan.  (cosine, sin, and tangent)

Cos is for finding and dealing with the adjacent and the hypotenuse.

Sin is for finding and dealing with the opposite and the hypotenuse.

Tan is for finding and dealing with the opposite and the adjacent.

The opposite is the bottom base, to the peanut.

The adjacent is the height from the bottom base, to the top.

The hypotenuse is the top, to the peanut.

27 feet would be the adjacent.

Since we don't know bottom base to the peanut, we would call this x. (opposite)

*Side note*  :   The degrees is always in between the adjacent and hypotenuse.

For this, we need the length between the peanut and the bottom base. This would be the adjacent and the opposite. Meaning we're using tangent. The equation for tangent is :

tan (degrees) = opposite/adjacent

So, now we simply put in the data.

tan 25 = x/27

We can now, first get x alone by multipling both sides by 27.

27 * tan 25 = x

Plug this into a scientific calculator :

27 * tan 25

We the answer to be 12.59

The peanut is 12.59 feet away from the base of the platform

The equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

The foci are given as:

(1, 7) and (1, -13)

The foci of a hyperbola are represented using: (m, n+p) and (m, n-p)

Where the center of the hyperbola is (n,p)

By comparison, we have:

m = 1

n + p = 7

n - p =13

Where n = ae

The solution to the above system of equations is

m = 1, n = 10 and p = -3

The directrix is given as:

y = 64/10

The directrix is represented as:

y = a/e

So, we have:

a/e = 64/10

Substitute n = ae in n = 10

ae = 10

Solving ae = 10 and a/e = 64/10, we have:

a = 8 and e = 10/8

To calculate b, we make use of:

[tex]b = a\sqrt{(e^2 - 1)[/tex]

So, we have:

[tex]b = 8\sqrt{(\frac{10}{8}^2 - 1)[/tex]

Evaluate

b = 8 * 0.75

b = 6

The equation of the hyperbola is then calculated using:

[tex]\frac{(y - p)^2}{a^2} -\frac{(x - m)^2}{b^2} = 1[/tex]

This gives

[tex]\frac{(y + 3)^2}{8^2} -\frac{(x - 1)^2}{6^2} = 1[/tex]

Evaluate

[tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]

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Answer:

The question asks, "find the slope".

9) -4/15

10) -1/14

11) -3/4

12) -1/4

13) 11/17

14) -18/13

15) 0

16) -30

17) -5

19) -1/5

21) 1/4

23) -1

25) -2/3

Answer:

the correct graph is attached

Step-by-step explanation:

x ≥ 1 means there is a closed dot at 1

and -x + 8 means there should be an y intercept at 8 with negative slope

so it could've only been the right side graphs than the first function is positive so the top right cant be right meaning the bottom right is the correct graph

The solution to the system of equation is (4.75, -11)

3.2x + 0.5y = 4.2

-1.6x -0.5y = 3.4

3.2x + 0.5y = 4.2

-1.6x -0.5y = 3.4

add equation(i) to equation(ii)

Therefore,

1.6x = 7.6

divide both sides by 1.6

x = 7.6 / 1.6

x = 4.75

Therefore,

3.2(4.75) + 0.5y = 4.2

0.5y = 4.2 - 15.2

0.5y = -11

y = - 11 / 0.5

y = - 22

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Answer:

The solution is x=4.75  and   y = -22

Step-by-step explanation:

To find the solution to the system of equations, we will follow the steps below:

3.2x + 0.5y = 4.2 --------------------------------------------------------------------------(1)

-1.6x -0.5y = 3.4 ----------------------------------------------------------------------------(2)

add equation (1) and equation (2)

1.6x =7.6

Divide both-side of the equation by 1.6 to get the value of x

1.6x /1.6 =7.6/1.6

x =4.75

substitute x = 4.75 into equation (1) and solve for y

3.2(4.75) + 0.5y = 4.2

15.2 + 0.5y = 4.2

subtract 15.2 from both-side of the equation

15.2 - 15.2 + 0.5y = 4.2-15.2

0.5y = -11

Divide both-side of the equation by 0.5

0.5y/0.5 = -11/0.5

y = -22

The solution is x=4.75  and   y = -22

Answer:

1 4979/9999

Step-by-step explanation:

1.497949794979....

= 1 4979/9999

Answer:

3rd option

Step-by-step explanation:

the ratio of b : c is the cos77° , that is

cos77° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{c}[/tex] ≈ 0.224951054.

Answer:

f(4) = 25

Step-by-step explanation:

substitute x = 4 into f(x)

f(4) = 2(4)² - 7 = 2(16) - 7 = 32 - 7 = 25

Answer:

160

Step-by-step explanation:

160 divided 8 =20

Answer:

The answer is 160

Step-by-step explanation:

Let the unknown number be x.

x/8=20

x and 8 are linked by a division so if 8 crossed the equality sign it becomes multiplication. So we'll have

x=20*8

x=160

Therefore x is equal to 160.

LET'S CHECK IF IT'S CORRECT

160/8=20

Answer:

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Based on the graph,

   2. f(4)

   3. x when f(x) = 5

   4. x when f(x) = -3

Answer:

40 meters

Step-by-step explanation:

x=4

3x-4=12-4

2x-3=8-3

12-4=8

8-3=5

8x5=40

Using the z-distribution, it is found that we reject the null hypothesis, which means that her claim is not validated.

At the null hypotheses, it is tested if the mean is of 110, that is:

[tex]H_0: \mu = 110[/tex].

At the alternative hypotheses, it is tested if the mean is less than 110, that is:

[tex]H_1: \mu < 110[/tex].

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

In this problem, we have that the parameters are given as follows:

[tex]\overline{x} = 105, \mu = 110, \sigma = 15, n = 50[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{105 - 110}{\frac{15}{\sqrt{50}}}[/tex]

z = -2.36.

Using a z-distribution calculator, z = -2.36 has a p-value that is less than the standard significance level of 0.05, hence we reject the null hypothesis, which means that her claim is not validated.

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Answer:

66.84 feet.

Step-by-step explanation:

Distance around = length of straight part + length of the semi-circle

= 2*13 + π*13

= 66.84 feet.