What are the zeros of the function y = (x − 4)(x2 − 12x + 36)?

A.
-6, 4, and 6
B.
4 and 6
C.
-6 and -4
D.
0, 4, and 6

The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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The maximum height of the ball is at 18.0625 feet which occurs at 0.9375 s

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

Let h represent the height of the ball after t seconds, hence:

h(t) = 4 + 30t - 16t²

The maximum height is at h'(t) = 0, hence:

h'(t) = 30 - 32t

-32t + 30 = 0

t = 0.9375 s

h(0.9375) = 4 + 30(0.9375) - 16(0.9375)² = 18.0625 feet

The maximum height of the ball is at 18.0625 feet which occurs at 0.9375 s

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The equations will be solved by putting the values of the variables in the bracket.

1. (b + a) = 4; use a = 1 and b = 3

( 1 + 3) = 4

2) c(b + b); use b = 1 and c = 5

5(1 + 1)

= 5 × 2 = 10

3) 4+ pm; use m = 4 and p =3

= 4 + (4 × 3)

= 4 + 12

= 16

4) 5+ pm; use m = 4 and p = 2

= 5 + (2 × 4)

= 5 + 8

= 13

5) m(p + 2); use m = 5 and p = 2

= 5(2 + 2)

= 5 × 4

= 20

6) h+j²; use h = 1 and j = 4

= 1 + 4²

= 17

7) y-(x - 5); use x = 5 and y = 6

= 6 - (5 - 5)

= 6 - 0

= 6

8) 4xy; use x = 5 and y = 2

= 4 × 5 × 2

= 40

9) n(p + 3); use n = 2 and p = 2

= 2(2 + 3)

= 10

10) y +x+x; use x = 3 and y=5

= 5 + 3 + 3

= 11

11) 6+ a-b; use a = 4 and b = 4

= 6 + 4 - 4

= 6

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Pamela Demars computer printer allows for optimal settings with a panel of three on off switches in a row. 13 different settings can she select if no two adjacent switches can both be on.

The term "offset" in computer science refers to a piece of data's position in relation to another place. For instance, when a programme accesses a bytes array, the fifth byte is four bytes away from the start of the array. A set is an abstract data type in computer science that may contain distinct items without regard to order. A finite set is a mathematics idea that has been computerized.

There are 5 switches with each switch either in On or Off state.

Thus, total no of settings = 2⁵ = 32

Let 0 represent Off state and

1 represent On state

The different settings are:

00000, 00001, 00010, 00011, 00100, 00101, 00110, 00111, 01000, 01001, 01010, 01011, 01100, 01101, 01110, 01111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111

Settings in which no two adjacent switch is both On

00000, 00001, 01010, 00100, 00101, 01000, 01001, 01010, 10000, 10001, 10010, 10100, 10101

No. of settings in which no two adjacent settings is both On =  13

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The scalar triple product is 0.

If v = 4i - j and w = 6i + 7j - 4k, then their cross product is

v × w = (4i - j) × (6i + 7j - 4k)

v × w = 24 (i × i) + 28 (i × j) - 16 (i × k) - 6 (j × i) - 7 (j × j) + 4 (j × k)

v × w = 28k - 16 (-j) - 6 (-k) + 4i

v × w = 4i + 16j + 34k

and

u • (v × w) = (i + 4j - 2k) • (4i + 16j + 34k)

u • (v × w) = 4 + 64 - 68

u • (v × w) = 0

Yes, they are coplanar.

The vectors v and w together span a plane. v × w is a vector that is perpendicular to this plane. Since the dot product of u with this vector is 0, this means u is perpendicular to v × w, which in turn means that u is in the same plane as v and w.

The constant of the proportionality is 2/3

From the question, we have the following parameters that can be used in our computation:

x  y

3  2

The constant of the proportionality is calculated as

k = y/x

substitute the known values in the above equation, so, we have the following representation

k = 2/3

Hence, the proportionality constant is 2/3

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Answer:

$39

Step-by-step explanation:

First, let's get the values of each number by rounding them off to the nearest dollar before adding them.

1. $2.69 = $3

2. $14.45 = $14

3. $8.05 = $8

4. $13.95 = $14

Now that you have the rounded off numbers, you may add them.

Let's solve.

The estimated total is $39.

Answer:

No

Step-by-step explanation:

If you have a repeating decimal it doesn't matter who many decimal digits there are. Most repeating decimals I have encountered end up converting into a fraction that has a denominator of 9.

Hope This Helps :)

Answer:

It depends

Step-by-step explanation:

It depends on what the repeating decimal is. For instance if the decimal is a repeating 8 then you only have to use one digit. If, however, it is something like .673673673 going on forever you just need however many until it loops again. In this case you would need three, because that is how long the loop is.

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

The probability of randomly removing a yellow bead is 0.8 or 80% if the bag contains 15 beads that are either red or yellow the probability of randomly removing a red bead is 20%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

We have the probability P(R) of randomly removing a red bead is 20%.

Let's suppose the number of red beads is n(R)

\(\rm P(R) = 20\% \Rightarrow 0.20\\\\\rm \frac{n(R)}{15} = 0.20\)

n(R) = 15×0.20

n(R) = 3

Number of yellow beads = 15 -3 = 12

The probability randomly removing a yellow bead:

\(=\rm \frac{12}{15}\)

= 0.8 or 80%

Thus, the probability of randomly removing a yellow bead is 0.8 or 80% if the bag contains 15 beads that are either red or yellow the probability of randomly removing a red bead is 20%.

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we can conclude that 2/3 is not equal to 4/5.

To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.

To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.

For 2/3 and 4/5, we have:

2 * 5 = 10

3 * 4 = 12

Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.

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Answer: (0,10)

Step-by-step explanation: y=mx+b

y=12.5x+10

0=12.5x+10

10 is y because its on the outside

Answer:

15:25 or 15 brownies

Step-by-step explanation:

25 / 5 = 5 (scale factor)

3 * 5 = 15

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Answer:

C

Step-by-step explanation:

in the triangle with respect to the 50° angle, the side opposite is c and the adjacent side is 14.

thus using the tangent ratio in the right triangle

tan50° = \(\frac{opposite}{adjacent}\) = \(\frac{c}{14}\) ( multiply both sides by 14 )

14 × tan50° = c , then

c ≈ 16.7  ( to 1 decimal place )

In this problem, the cosine function is used to solve for the length of side C in a right-angled triangle, because the angle and the adjacent side are known. According to trigonometry, the cosine for an angle is the length of the adjacent side divided by the hypotenuse.

In the given right-angled triangle, since the length of side C (hypotenuse) is unknown and one of the acute angles (50 degrees) is known, you should use the cosine function to solve for the length of side C. According to Trigonometry, cosine of an angle (in a right-angled triangle) is equal to the adjacent side divided by the hypotenuse. Hence, cos(50) = 14 / C. You could solve this equation for C.

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The average T2, T7, T6, T4, and T10 in Processor 1

T8, T9, T3, T1, and T5 on Processor 2.

Work on tasks t2, t7, t6, t4, and t10 will be done by processor 1. The first task to be finished is task t2, followed by tasks t7, t6, t4, and lastly t10. Work on tasks t8, t9, t3, t1, and t5 will be done by processor 2. The first work to be finished is task t8, followed by t9, t3, t1, and ultimately t5. In order to finish the job quickly, both processors will cooperate, with Processor 1 concentrating on the early tasks and Processor 2 concentrating on the later duties. This guarantees that the project is finished on schedule and that all the tasks are carried out in the proper order.

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Answer:

C = 2 x 4.5 x π

Step-by-step explanation:

The equation to find the circumference of the circle is

C = 2π · r

r = 4.5 in

Looking at the options, the answer is C = 2 x 4.5 x π

Answer:

Below

Step-by-step explanation:

radius = 4.5       diameter = 2 x 4.5  in

the circumference of a circle is given by the formula   p * d

  substitute in the underlined equation for 'diameter')

          circumference = 2 * 4.5 * pi    inches

The correct statement regarding the minimum value of the quadratic functions is given as follows:

D) The graphed function has a lower minimum value.

From the graph, the minimum value of the quadratic function is given as follows:

y = -8.

The algebraic function is defined as follows:

f(x) = 0.25x² - 2x.

Hence the coefficients are given as follows:

a = 0.25 and b = -2.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 2/0.5

x = 4.

Then the y-coordinate of the vertex, representing the minimum value, is given as follows:

f(4) = 0.25(4)² - 2(4)

f(4) = -4 -> meaning that the graphed function has a lower minimum value.

The graph is given by the image presented at the end of the answer.

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Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40

We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

The test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.

In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:

The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

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ANSWER IS B 30

Step-by-step explanation:

The function's graph is parallel to this line is 3x.

The general equation of a straight line is y = mx + c, where m is the gradient or slope, and y = c is the value where the line cuts the y-axis. This number c is called as intercept.

From the question,

Parallel lines have same slope.

The slope given, m =3.

The function's graph is parallel to this line is 3x.

Hence the required answer is f(x)= 3x.

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The required probability would be 9.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is the measure of the likelihood or chance that a particular event will occur.

If the theoretical probability of rolling a sum greater than 10 is 3/36, then the experimental probability is also 3/36 or 1/12 since the die is fair

If the experiment is repeated 108 times, the expected number of times rolling a sum greater than 10 is given by:

Expected number = probability x number of trials

Expected number = (1/12) x 108

Expected number = 9

Therefore, we can predict that the rolls will result in a sum greater than 10 9 times if the experiment is repeated 108 times.

Hence, the required probability would be 9.

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Answer:

Step-by-step explanation:

Exact form: x = -22/5

Decimal form: x = -4.4

Mixed number form: x = -4 2/5

Answer:

44ft

Step-by-step explanation:

P= 2(L+W)

P= 2(12+10)

P= 2(22)

P=44ft

The solution of the equation  -22 = q + 7(2q - 1) is as follows:

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Let's solve the equations as follows:

-22 = q + 7(2q - 1)

The variable in the equation is q. A variable is an letter use to represent number in an equation.

-22 = q + 7(2q - 1)

-22 = q + 14q - 7

-22 = 15q - 7

add 7 to both sides of the equation

-22 + 7 = 15q - 7 + 7

-15 = 15q

divide both sides by 15

q = -15 / 15

q = -1

Therefore,

q = -1

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Answer:

-22 = q + 7(2q - 1)

-22 = q + 14q - 7

-22 = 15q - 7

add 7 to both sides of the equation

-22 + 7 = 15q - 7 + 7

-15 = 15q

divide both sides by 15

q = -15 / 15

q = -1

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

The prism shown is a rectangular prism with a height of 3 in a length of 5 in and a width of 8 in

The volume of a rectangular prism can easily be calculated by multiplying the height by the length by the width

So V = 3 * 5 * 8

3 * 5 = 15

15 * 8 = 120

V = 120

Therefore your answer is 120

The missing vertex is (12, 6) with an area of 112 in².

A vertex is a point where two or more lines, edges, or curves meet in a geometric shape. In a two-dimensional shape, such as a triangle or quadrilateral, a vertex is where two sides meet.

Given vertices of rectangular design:

(5, 6), (12, −10), and (5, −10).

the length of the side connecting (5, 6) and (5, -10), which is 6 - (-10) = 16.

by adding this length to the y-coordinate of the vertex (5, 6), which gives us (5, 6+16) = (5, 22).

Similarly, we can find the length of the side connecting (5, 6) and (12, -10), which is 12 - 5 = 7.

We can add this length to the x-coordinate of the vertex (5, 6), which gives us (5+7, 6) = (12, 6).

Therefore, the missing vertex is (12, 22 - 10) = (12, 12).

To find the area of the rectangle, we can use the formula

A = length x width.

Using Distance formula between (5, 6) and (12, 6),

length=√(12-5)²+(6-6)²

length=√7²

Length=7 in

Using Distance formula between (5, -10) and (5, 12),

length=√(5-5)²+(12+10)²

length=√22²

Length=22 in

the area of the rectangle is;

A = 7 x 22 = 154 square inches.

Therefore, the correct answer is A: The missing vertex is (12, 6) with an area of 112 in²

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Answer: Option a will be right i took the test

Step-by-step explanation:

Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

Answer: \(f^{-1}(x)=2x-6\)

Step-by-step explanation:

To find the inverse, we want to switch the y with x and x with y. Once we do that, we solve for y.

\(y=\frac{1}{2}x+3\)        [switch x and y]

\(x=\frac{1}{2}y+3\)        [subtract both sides by 3]

\(x-3=\frac{1}{2} y\)        [multiply both sides by 2]

\(y=2x-6\)

Now, we know that  \(f^{-1}(x)=2x-6\).