Given the graph below. What is the axis of symmetry (vertex)of the parabola?

The third member of the Pythagorean triple is 28 and this can be determined by using the Pythagorean theorem.

Given :

21 and 35 are two members of a Pythagorean triple.

The following steps can be used in order to determine the third member of the Pythagorean triple:

Step 1 - The Pythagorean theorem can be used in order to determine the third member of the Pythagorean triple.

[tex]H^2 = P^2+B^2[/tex]

where the hypotenuse is H, the perpendicular is P, and the base is B of the right-angle triangle.

Step 2 - Now, substitute the value of H and P in the above expression in order to determine the value of 'B'.

[tex]35^2 = 21^2+B^2[/tex]

Step 3 - Simplify the above expression.

[tex]B^2= 784[/tex]

[tex]B = 28[/tex]

So, the third member of the Pythagorean triple is 28.

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Answer:

y=1/2x+3

Step-by-step explanation:

grabbing two points in this case (0,3) and (2,4)

we use the rise over run formula meaning it rises 1 and runs 2 so our slope is 1/2

to get the y intercept just look at where the line touches the y line in this case at 3

using the equation y=mx+b and m is slope and b is y interecpt we plug in the numbers

so we get y=1/2x+3

Answer:

Second Graph.

Explanation:

It's the only graph that is concave down and the slope is decreasing.

She saved 20%.

The price of the table was 250 and she bought it for 200, meaning 1/5 of the original price was marked off. 1/5 = 20% which means it was 20% off the original price.

Answer:

See answer below.

Step-by-step explanation:

P(v) = -4v³ + 12v² - 9v

Point (-5, -845) is not a point on the graph

P(-5) = -4(-5)³ + 12(-5)² - 9(-5)

P(-5) = 500 + 300 + 45

P(-5) = 800 + 45

P(-5) = 845                     point (-5, 845) is a solution

Answer:

[tex]\frac{\pi}{6}[/tex] radians

[tex]cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

A reference angle is an acute angle between the terminal arm/terminal side and the x-axis. In this case, the reference angle is [tex]\frac{7\pi}{6}-\pi=\frac{\pi}{6}[/tex].

As for [tex]cos(\frac{7\pi}{6})[/tex], we can identify the value of it using the unit circle as attached below. Recall that points on the unit circle are defined as [tex](cos(\theta),sin(\theta))[/tex], so [tex]cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}[/tex].

Answer:

no

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

start with brackets

-5-3 = -8

2(-8)

= -16

Answer:

1. Becky, 2. No one, 3. Brian and Carol, 4. Tom, 5. Jake

Step-by-step explanation:

The order has to be Brian, Tom, Jake, Becky, and Carol.

1. Becky

2. No one

3. Brian and Carol

4. Tom

5. Jake

Answer:

7

Step-by-step explanation:

y=kx is the general formula for direct proportion where k is the constant. In your equation instead of k there is 7 so 7 is the constant.

Answer:

the image was not clear....hope the values are correct

Answer is in the attached file.

Answer:

-8

Step-by-step explanation:

Answer:

p = - [tex]\frac{2}{3}[/tex] , p = 2

Step-by-step explanation:

Using the discriminant to solve for p

Δ = b² - 4ac

The condition on the discriminant for 2 eeal and equal roots is

b² - 4ac = 0

Given

p²x² - (p + 2)x + 1 = 0

with a = p² , b = - (p + 2) , c = 1 , then

(- (p + 2) )² - 4p² = 0

(p + 2)² - 4p² = 0

p² + 4p + 4 - 4p² = 0

- 3p² + 4p + 4 = 0 ( multiply through by - 1 )

3p² - 4p - 4 = 0 ← in standard form

(3p + 2)(p - 2) = 0 ← in factored form

Equate each factor to zero and solve for p

3p + 2 = 0 ⇒ 3p = - 2 ⇒ p = - [tex]\frac{2}{3}[/tex]

p - 2 = 0 ⇒ p = 2

Answer:

2$ compatible numbers are 200 and 100

Step-by-step explanation:

Answer:

C=31.41592654

Step-by-step explanation:

C=2πr

r=5

C=2π(5)

Therefore C= 10π or C=31.41592654

Answer:

C = 31.4

Step-by-step explanation:

Answer:

  y = -x +2

Step-by-step explanation:

The slope can be found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (6 -5)/(-4 -(-3)) = 1/-1 = -1

The y-intercept can be found from ...

  b = y -mx

  b = 5 -(-1)(-3) = 2

The slope-intercept equation for the line is ...

  y = mx +b

  y = -x +2 . . . . use the values of m and b we found

Answer:

y=-1/2x-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=-1/2(x-(-6))

y+5=-1/2(x+6)

y=-1/2x-6/2-5

y=-1/2x-3-5

y=-1/2x-8

Answer:

x=6

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Answer:

im pretty sure that the answer is -50.5 feet.

Step-by-step explanation:

The equivalent value of the expression 1, point, 86, divided by, 2 is given by A = 0.93.

Given data:

Let the expression be represented as A.

Now, the value of A is

A = 1, point, 86, divided by, 2.

Substituting the values in the equation:

[tex]A=\frac{1.86}{2}[/tex]

On simplifying the equation:

[tex]A=0.93[/tex]

Therefore, the value of A is 0.93

Hence, the equation is A = 0.93

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The complete question is attached below:

Find the equivalent value of the expression "1, point, 86, divided by, 2".

Answer:

7.8 or 8

Step-by-step explanation: To get the hypotenuse of a right triangle we must square each part.

5^2 is 25 and 6^2 is 36

Now you add the two squared parts, which equals 61. 61 squared isn't a perfectly squared. This means the answer is 7.8 or rounded to the nearest tenth the answer will be 8.

Answer:

a: -1/2

b: 15

Step-by-step explanation:

A system that has infinite solutions is the same line on top of itself.

Hope that helps

Answer:

125

Step-by-step explanation:

because 3125 divided 25 equals 125.

how do you want me to show you how i divided?

Answer:

125 is the answer, you can check this by simply multiplying 125 by 25, which will give you 3125.

Step-by-step explanation:

The correlation coefficients off both the scatter plots are mentioned above.

        [tex]${\displaystyle {\begin{aligned}r_{xy}&={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{ns'_{x}s'_{y}}}\\[5pt]&={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-(\sum x_{i})^{2}}}~{\sqrt {n\sum y_{i}^{2}-(\sum y_{i})^{2}}}}}.\end{aligned}}}[/tex]

       where [tex]{\displaystyle s'_{x}}[/tex] and [tex]{\displaystyle s'_{y}}[/tex] are the uncorrected sample standard deviations of        

       X and Y.

Given are the scatter plot graphs as shown.

For the graph {1}, the correlation coefficient is positive and is in range of between 0.7 to 0.8

For the graph {2}, the correlation coefficient is negative and is in range of between -0.4 to 0.45

Therefore, the correlation coefficients off both the scatter plots are mentioned above.

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Hope you could get an idea from here.

Doubt clarification - use comment section.

The equation [tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex] has been proved to be true

The equation is given as:

[tex]\frac pq = \frac qr[/tex]

Cross multiply

[tex]pr = q^2[/tex]

Rewrite as:

[tex]q^2 = pr[/tex]

Also, we have:

[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex]

Substitute [tex]q^2 = pr[/tex]

[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3[/tex]

Expand

[tex]p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3[/tex]

Simplify

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3[/tex]

Rewrite as:

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3[/tex]

Substitute [tex]pr = q^2[/tex]

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3[/tex]

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3[/tex]

Divide q^6 by q^3

[tex]p3+q3+r3=r^3 +q^3 + p^3[/tex]

Rewrite the equation as:

[tex]p3+q3+r3=p^3 +q^3 + r^3[/tex]

Hence, the equation has been proved

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