14. Which of the following is true about given APQR given in Figure 7.82 to the right? a. p²+q²=² b. q²+r²=p² c. (p+q)²=r² d. p²+r²=q² Q P R T 9 Figure 7.82 P​

Answer: 10+17

Step-by-step explanation:

Distribute:

3(2+6)+4−1

6+18+4−1

Subtract the numbers:

6+18+4−1

6+17+4

Combine like terms:

6+17+4

10+17

solution:

10+17

Answer:

[tex]7 \frac{2}{9} [/tex]

Step-by-step explanation:

here is your answer

Calculation steps:

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex] = (14 - 4) + ( \frac{6}{9} - \frac{4}{9} )[/tex]

[tex] = 7 + \frac{6 - 4}{9} [/tex]

[tex] = 7 + \frac{2}{9} [/tex]

[tex]7 \frac{2}{9} [/tex]

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex] = \frac{35}{3} - \frac{40}{9} [/tex]

[tex] = \frac{(35 \times 9) - (40 \times 30)}{3 \times 9} [/tex]

[tex] = \frac{315 - 120}{27} [/tex]

[tex] = \frac{195}{27} [/tex]

[tex] = 7 \frac{2}{9} [/tex]

Answer:

10.

Step-by-step explanation:

median means the "middle" number in a set of numbers.

(I always the meaning of median by remembering "middle" because they rhyme).

NOTE: to find the median of a set of numbers you have to arrange that set of numbers in either ascending order (smallest to biggest value) or descending order (biggest to smallest value) .

sooo....

we were given :

11, 17, 7, 4, 15, 19

let's arrange in ascending order

4, 7, 11, 15, 17 , 19

now you can cancel them out ( cancel left number, right number)

i mean....

cancel out 4, cancel out 19

cancel out 7, cancel out 17

and we are left with 2 numbers which are11 and 15.

NOTE; (when you have two numbers or values remaining instead of one number, add those two numbers and divide by 2).

soooo...

11 + 15 = 20

20/2 = 10

median of the set of numbers is equal to 10.

Hope this helps.

Good luck ✅.

answer is: Notice that if the population doubles every 12 years, it quadruples (4 times) in 24, multiplies by 8 in 36, and multiplies by 16 in 48 years.

So values are

The rule is

Explicit formula

Equation here is

Answer:

[tex]f(x)=4^x[/tex] grows at a faster rate than the given quadratic function.

Step-by-step explanation:

Given table:

[tex]\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}[/tex]

First Differences in y-values:

[tex]0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27[/tex]

Second Differences in y-values:

[tex]3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15[/tex]

As the second differences are the same, the function is quadratic.

The coefficient of [tex]x^2[/tex] is always half of the second difference.

Therefore, the quadratic function is:

[tex]f(x)=3x^2[/tex]

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Therefore, the average rate of change for [tex]f(x)=3x^2[/tex] over the interval
0 ≤ x ≤ 3 is:

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9[/tex]

An exponential function that grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3  is [tex]f(x)=4^x[/tex]

[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}[/tex]

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21[/tex]

As 21 > 9, [tex]f(x)=4^x[/tex] grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3.

Answer:

The volume is 452 square inches.

Step-by-step explanation:

Volume=area of base*height

just plug in the values

Answer:

12

Step-by-step explanation:

6 X 2

the 6 sides of the spinner and the two faces of the coin

Answer: 36

Step-by-step explanation:

I just took the test on Edge :)

Answer:

1.

3.5 days

2.

6.75 minutes, 6 minutes 45 seconds, 6.8 minutes to 1 dp

Step-by-step explanation:

1.

With double the amount of tractors it will take half the time.

7 divided by 2 is 3.5

2.

This is an example of inverse proportion. The job that has to be done to to prepare the vegetables, That stays the same.

However, the more people there are to do the work, the quicker it will get done.

There is a constant to be found:

x multiplied by y equals k

3 x 45 = 135

For 20 people:

20 x y = 135

135 divided by 20 is:

6.75, or 6.8

Answer:

Relative frequency for each discount :

10% - 0.4925, 20% - 0.3325, 40% - 0.175

Since only 33.25% of customers got 20% discount, it is not an appropriate method.

Step-by-step explanation:

relative frequency = number of frequency/total number of frequency

you can find out relative frequency for each number and add them up to get relative frequencies of discounts.

Answer:

Associative Property of Addition

Step-by-step explanation:

Associative Property of Addition:

For any real numbers a, b, and c, (a + b) + c = a + (b + c).

Answer:

Commutative Property of Addition

Step-by-step explanation:

Answer:

c) 5

Step-by-step explanation:

we know that,

alpha + beta = -b/a

here, we are given that alpha is L and beta is M (roots of the quadratic equation)

therefore,

L+M = -b/a

L+M = -(-40)/8

L+M = 40/8

L+M = 5

HOPE IT HELPS!!

PLEASE MARK BRAINLIEST... ♡

Answer:

L + M are 5.122 and -0.122 so I am assuming the answer you want is 5 or c.

Step-by-step explanation:

SOME OF THIS I NEEDED TO RESEARCH BECAUSE I FEEL LIKE THIS IS OUT OF MY DEPTH BUT I GUESS HERE YOU GO

STEP

1

:

Equation at the end of step 1

 (23x2 -  40x) -  5  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  8x2-40x-5

The first term is,  8x2  its coefficient is  8 .

The middle term is,  -40x  its coefficient is  -40 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   8 • -5 = -40

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   -40 .

     -40    +    1    =    -39

     -20    +    2    =    -18

     -10    +    4    =    -6

     -8    +    5    =    -3

     -5    +    8    =    3

     -4    +    10    =    6

     -2    +    20    =    18

     -1    +    40    =    39

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 8x2 - 40x - 5  = 0

STEP

3

:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = 8x2-40x-5

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 8 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C ,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.5000  

Plugging into the parabola formula   2.5000  for  x  we can calculate the  y -coordinate :

 y = 8.0 * 2.50 * 2.50 - 40.0 * 2.50 - 5.0

or   y = -55.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 8x2-40x-5

Axis of Symmetry (dashed)  {x}={ 2.50}

Vertex at  {x,y} = { 2.50,-55.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-0.12, 0.00}

Root 2 at  {x,y} = { 5.12, 0.00}

Solve Quadratic Equation by Completing The Square

3.2     Solving   8x2-40x-5 = 0 by Completing The Square .

Divide both sides of the equation by  8  to have 1 as the coefficient of the first term :

  x2-5x-(5/8) = 0

Add  5/8  to both side of the equation :

  x2-5x = 5/8

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  5/8  +  25/4   The common denominator of the two fractions is  8   Adding  (5/8)+(50/8)  gives  55/8

 So adding to both sides we finally get :

  x2-5x+(25/4) = 55/8

Adding  25/4  has completed the left hand side into a perfect square :

  x2-5x+(25/4)  =

  (x-(5/2)) • (x-(5/2))  =

 (x-(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2-5x+(25/4) = 55/8 and

  x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

  (x-(5/2))2 = 55/8

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(5/2))2   is

  (x-(5/2))2/2 =

 (x-(5/2))1 =

  x-(5/2)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(5/2) = √ 55/8

Add  5/2  to both sides to obtain:

  x = 5/2 + √ 55/8

Since a square root has two values, one positive and the other negative

  x2 - 5x - (5/8) = 0

  has two solutions:

 x = 5/2 + √ 55/8

  or

 x = 5/2 - √ 55/8

Note that  √ 55/8 can be written as

 √ 55  / √ 8

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    8x2-40x-5 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     8

                     B   =   -40

                     C   =   -5

Accordingly,  B2  -  4AC   =

                    1600 - (-160) =

                    1760

Applying the quadratic formula :

              40 ± √ 1760

  x  =    ——————

                     16

Can  √ 1760 be simplified ?

Yes!   The prime factorization of  1760   is

  2•2•2•2•2•5•11

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 1760   =  √ 2•2•2•2•2•5•11   =2•2•√ 110   =

               ±  4 • √ 110

 √ 110   , rounded to 4 decimal digits, is  10.4881

So now we are looking at:

          x  =  ( 40 ± 4 •  10.488 ) / 16

Two real solutions:

x =(40+√1760)/16=5/2+1/4√ 110 = 5.122

or:

x =(40-√1760)/16=5/2-1/4√ 110 = -0.122

Answer:

G its G

Step-by-step explanation:

Answer:

5 seconds and 488 ft

Step-by-step explanation:

(a)

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 ), then

the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = - 16x² + 160x + 88 ← is in standard form

with a = - 16 and b = 160 then

[tex]x_{vertex}[/tex] = - [tex]\frac{160}{-32}[/tex] = 5

the maximum height is at the vertex, the turning point on the graph

then it takes 5 second to reach its maximum height

(b)

to find the maximum height substitute x = 5 into the equation

y = - 16(5)² + 160(5) + 88

  = - 16(25) + 800 + 88

 = - 400 + 888

 = 488

maximum height is 488 ft

The series of transformations that moves quadrilateral ABCD onto quadrilateral A'B'C'D' is C. reflection, translation.

It should be noted that transformation simply means the movement of object in a coordinate plane.

The common type of transformation in mathematics include translation, rotation, reflection, and dilation.

Here, the series of transformations that moves quadrilateral ABCD onto quadrilateral A'B'C'D' is reflection, and translation. Reflection is flipping the pre image and producing the mirror image while translation is movement of the pre image

Learn more about transformation on:

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Answer:

A

Step-by-step explanation:

Answer:

(-3, 13)

Step-by-step explanation:

The transformation that moves a point 4 left and 8 up is ...

 (x, y) ⇒ (x -4, y +8)

The transformation that reflects a point across the y-axis is ...

 (x, y) ⇒ (-x, y)

Applied after the translation, the transformation of ∆ABC becomes ...

 (x, y) ⇒ (-(x -4), y +8) = (4 -x, y +8)

Then point A gets moved to ...

 A(7, 5) ⇒ A'(4 -7, 5 +8) = (-3, 13)

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

the given expression can be solved as follows ~

[tex] \frac{x}{13} - 1 = \frac{5x}{2} + \frac{1}{2} \\ [/tex]

taking LCM both the sides ,

[tex] \frac{x - 13}{13} = \frac{5x + 1}{2} \\ [/tex]

on cross multiplying ,

[tex](x - 13)2 = (5x + 1)13 \\ \\ \implies \: 2x - 26 = 65x + 13[/tex]

let's now gather the like terms at either sides of the equation ~

[tex]65x - 2x = - 26 - 13 \\ \\ \implies \: 63x = - 39 \\ \\ \implies \: x = \frac{\cancel{ - 39}}{\cancel{63}} [/tex]

on simplifying the equation ,

[tex] \implies \frac{-13}{21}\\[/tex]

hope helpful ~

Answer:

11

Step-by-step explanation:

11x=121

11x/11 = 121/11

x = 11

So, 11*11 = 121

Hey there!

Do PEMDAS to solve.

PEMDAS simply means.

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtract

Some people use this method to make PEMDAS easier to understand

• Please
• Excuse
• My
• Dear
• Aunt
• Sally

4 + 4(5 + 2^2)

= 4 + 4(5 + 2 * 2)

= 4 + 4(5 + 4)

= 4 + 4(9)

= 4 + 36

= 40

Therefore, the answer should be: 40

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Amelias salary increase by $12,000 every year so 12*20 = $240,000 salary in 20th year.

Answer:

y = -x – 2

Step-by-step explanation:

Slope is ΔY/ΔX =  -1

plug this into the equation:

1=-(-3) +b

= -2=b

so we get; y = -x – 2

Answer: y = -x - 2

Step-by-step explanation:

     I will be writing this equation in slope-intercept form.

     First, we will find our m value, also known as the slope.

        [tex]\displaystyle \frac{\text{change in y}}{\text{change in x}} =\frac{1--4}{-3-2} =\frac{5}{-5}=-1[/tex]

     Now, we will find our b value, or the y-intercept.

-> The line intercepts the y-axis at (0, -2), so our y-intercept is -2.

     Lastly, we will write our equation.

y = mx + b

y = -x - 2

Read more about writing slope-intercept equations here:

https://brainly.com/question/15143525

Answer:

Step-by-step explanation:

The area of a square is 49 cm2. What is the perimeter, in cm, of the square?

first we use the inverse formula to find the side (√49 = 7), then multiply the side by 4 (7 x 4 = 28)

or you can use an expression

4 * √49 = 28

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the gradient (slope) m using the slope formula

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

with (x₁, y₁ ) = O (0, 0 ) and (x₂, y₂ ) = A (- 5, 2 )

[tex]m_{OA}[/tex] = [tex]\frac{2-0}{-5-0}[/tex] = [tex]\frac{2}{-5}[/tex] = - [tex]\frac{2}{5}[/tex]

(b)

the angle between a tangent and a radius at the point of contact is 90°

given a line with slope m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex]

(c)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{5}{2}[/tex] , then

y = [tex]\frac{5}{2}[/tex] x + c ← is the partial equation

to find c substitute A (- 5, 2 ) into the partial equation

2 = - [tex]\frac{25}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{25}{2}[/tex] = [tex]\frac{29}{2}[/tex]

y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{29}{2}[/tex] ← equation of tangent

Using sampling concepts, it is found that the correct statement is given by:

c. the sample is 85 people. the population is 2,534 people.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

In this problem, a group of 85 people, which is the sample, is taken from the entire population of 2,534 people, hence option c is correct.

More can be learned about sampling concepts at https://brainly.com/question/25122507

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Answer:

The answer would be C, Both I and II.

Step-by-step explanation:

You can find an attached file which shows the scenarios incase your confused.

I believe it is 312, hope this helps, sorry if it doesn't!:)

Answer:

The solution is in the image