f(x) = x2 – 4x – 21.

The correct answer is C. The samples are dependent because there is a natural pairing between the two samples (before and after their first year of college).

In this case, the weight measurements of each student are paired based on their individual progress over time.

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Given statements:Assuming that SAS is true, let us find whether the given statements are true or false.

(a) Triangle ABC is congruent to triangle ACBThe given statement is false since the given two triangles ABC and ACB have two equal sides, but the included angles are different.

Hence, they are not congruent.(b) Triangles ABC and ACB are congruentThe given statement is false since the given two triangles ABC and ACB have two equal sides, but the included angles are different. Hence, they are not congruent.

(c) If P is a point not on line I, then there is a unique line through P that is parallel to I.

The given statement is true since the parallel postulate states that a unique line can be drawn parallel to a given line that passes through a point not on the line.Hence, if P is a point not on line I, then there is a unique line through P that is parallel to I.

(d) AB + BC > AC if and only if A, B, and C are the vertices of a triangle.The given statement is true since the triangle inequality theorem states that the sum of the two sides of a triangle is always greater than the third side. Hence, if AB + BC > AC, then A, B, and C are the vertices of a triangle.

(e) In triangle ABC, if AB > AC, then angle B is larger than angle C.The given statement is false since the larger side of a triangle is opposite to the larger angle. Hence, if AB > AC, then angle C is larger than angle B.

(f) Given triangles ABC and DEF, if angles A and D are right angles, AB = DE, and BC = EF, then the triangles are congruent.The given statement is true since the RHS (Right Angle, Hypotenuse, Side) congruence criterion states that if two right-angled triangles have their hypotenuse and one side equal, then they are congruent. Hence, the given triangles ABC and DEF are congruent.

Therefore, the given statements are (a) false, (b) false, (c) true, (d) true, (e) false, and (f) true.

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Answer:

5/8, -5/8

Step-by-step explanation:

64x^2 = 25

divide both sides by 64

x^2 = 25/64

take the square root of both sides, and the negative square roots

Answer:

x = 5/8=0.625 and x = -5/8=−0.625

Step-by-step explanation:

f(x)=64x^2+6=31

Subtract 6 from both sides.

64x^2+6=31

Subtract 6 from 31 to get 25.

64x^2=25

Divide both sides by 64.

x^2=25/64

Take the square root of both sides of the equation.

x=5/8=0.625

x=-5/8=−0.625

Answer:

\(g=\frac{x-2}{3}\)

Step-by-step explanation:

\(x=3g+2\)

- Reverse it to take "\(g\)" on the left side

\(3g+2=x\)

- Take \(+2\) on the other side which will be \(-2\)

\(3g=x-2\)

- Take "\(3\)" on the other side

{remember: \(3\) is being multiplied by \(g\), so when you carry it on the other side it will be divided by the rest}

therefore:- \(g=\frac{x-2}{3}\)

Hope it helps.....

If the quadrilateral is a trapezoid , then the value of x is = (b) 5 .

We know that the Midsegment of a trapezoid is parallel to each of the base and it's length is one half the sum of the lengths of the bases.

From the figure , we can observe that ⇒ side lengths are  21 units, 27 units , and the sides are parallel to each other.

From the given diagram of the trapezoid , the below expression is true:

that means : ⇒ 5x-1 = (21 + 27)/2  ;

⇒ 2(5x - 1) = 21 + 27 ;

⇒ 10x = 48 + 2 ;

⇒ 10x = 50

On Divide both sides by 10 ;

we have ;

⇒ x = 50/10  ;

⇒ x = 5  .

Therefore , for the quadrilateral the value of x is = 5 .

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The given question is incomplete , the complete question is

The quadrilateral in the below figure is a trapezoid. What is the value of x ?

(a) 4

(b) 5

(c) 48

(d) 25

Answer:

\(\frac{2}{5} , \frac{1}{2} ,\frac{5}{8} ,\frac{2}{3}\)

from least to the greatest

Answer:

2/5, 1/2, 5/8, 2/3

Step-by-step explanation:

What we can do to order these fractions is make them have the same denominator:

75/120, 60/120, 80/120, 48/120
Now we can order these in order from least to greatest:

48/120, 60/120, 75/120, 80/120

Now we convert them back to what they originally were:

2/5, 1/2, 5/8, 2/3
This is our answer!

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

To compare the y-intercepts of two functions, we need to look at their equations and see which one has a larger constant term.

The constant term is the term that does not have any variable attached to it.

For example, if we have the functions:

f(x) = 2x + 5
g(x) = 3x + 2

Then, we can see that f(x) has a larger y-intercept because its constant term is 5, whereas the constant term of g(x) is 2.

This means that the graph of f(x) intersects the y-axis at the point (0, 5), which is higher than the point (0, 2) where g(x) intersects the y-axis.

Therefore, without knowing the specific functions, we cannot determine which one has a greater y-intercept. We would need to look at their equations or given values to make a comparison.

It's important to remember that the y-intercept represents the value of the function when x = 0, and it can be positive, negative, or zero depending on the function.

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Step-by-step explanation:

\( \huge \frac{3}{x} - \frac{x}{4} \\ \\ \huge= \frac{3 \times 4 - x \times x}{x \times 4} \\ \\ \huge = \frac{12 - {x}^{2} }{4x} \)

Answer:

filled in dot on -2 and shade the rest to the right (see below)

Step-by-step explanation:

This can also be read as "x is equal to or greater than -2." The "alligator" mouth, aka the inequality sign, is "eating" the x, meaning it's greater than the -2.

First graph the -2. Because it's also equal to, the dot on the -2 is filled in.

The inequality also acts as an arrow. It's pointing to the right, so the rest of the number line to the right is shaded.

This arrow method works only when the variable is on the left side so that is read "x is greater/less than a number."

Answer:

y=-3x-1

Step-by-step explanation:

Use point-slope form:

(y-2)=-3(x+1)

y-2=-3x-3

y=-3x-1

Answer:

x=7

Step-by-step explanation:

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

not B

Step-by-step explanation:

I took the test

The total time required to process all six jobs is 42 days.

The start time for Job 4 is 18 and the end time is 28.

Body of the Solution: Based on the provided processing times for each job, here's the Gantt chart showing the sequence of jobs 1, 2, 3, 4, 5, 6 and the corresponding time required to process each job:

Job: 1 |----|

Job: 2       |---------|

Job: 3                  |-----|

Job: 4                         |----------|

Job: 5                                       |-----|

Job: 6                                               |----|

Time 0 4    13     18      28     34      42

In the Gantt chart, each job is represented as a horizontal bar, and the length of the bar corresponds to the processing time for that job. The chart starts at time 0 and ends at the total processing time required for all the jobs.

To determine the total time required to process all six jobs, we can look at the end time of the last job, which is 42. Therefore, the total time required to process all six jobs is 42 days.

Thus, the total time required to process all six jobs is 42 days.

develop a gantt chart to determine the total time required to process all six jobs. use the following sequence of jobs: 1, 2, 3, 4, 5, 6;Where the processing times (days)are 4,9,5,10,6,8 respectively.

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Answer:

15.6 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula below, where \((x_1, y_1)\) is the first coordinate and \((x_2, y_2)\) is the second coordinate.

\(\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}\)

Using the distance formula above,

distance between A(-3, 1) and B(7, 13)

= \(\sqrt{(13-1)^{2} + [7-(-3)]^{2} } }}\)

= \(\sqrt{12^2+(7+3)^2}\)

= \(\sqrt{244}\)

= 15.6 units (3 s.f.)

Additional:

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As the angle increases from 0 to π/2, the value of sine increases, and the value of cosine decreases.

Trigonometry is a branch of mathematics that deals with the relationships between angles and sides of triangles.

Let us first understand the concept of sine and cosine. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle and the length of the hypotenuse. Similarly, the cosine of an angle is defined as the ratio of the length of the adjacent side and the length of the hypotenuse.

As the angle θ increases from 0 to π/2, the length of the opposite side (the numerator in sine) of the triangle increases, and the length of the hypotenuse (the denominator in sine) remains the same. Therefore, the value of sine increases as θ increases.

On the other hand, as the angle θ increases from 0 to π/2, the length of the adjacent side (the numerator in cosine) decreases and the length of the hypotenuse (the denominator in cosine) remains the same. Therefore, the value of cosine decreases as θ increases.

This behavior is consistent with the fact that sine is an increasing function, while cosine is a decreasing function within this range of angles.

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Complete Question:

If 0< θ <π/2, as Theta increases, the value of

cos(θ) [Decreases/Increases/Remains The Same]

and the value of sin(θ) [Decreases/Increases Remains The Same]​

Answer:

10/10 - 7/10 = 3/10

Step-by-step explanation:

Given:

Number of muffin made = 12

Number of muffin burned = 2

Number of muffin serve = 7 / 10

Find:

Equation for number of muffin remain

Computation:

Number of muffin remain = 12 / 2

Number of muffin remain = 10

Equation for number of muffin remain = Number of muffin remain  - Number of muffin serve

10/10 - 7/10 = 3/10

y = f(x) + k

The k on the function will translate the function up or down.

If k is positive, it will translate up.

If k is negative, it will translate down.

Answer:

1. The discount price of a T-shirt is  $14.40

2. The regular price of a hat is $22.50

3. The discount price is y = x(0.8)

Step-by-step explanation:

1.

20% = 0.2

18 times 0.2 = $3.60

18 - 3.60 = $14.40

So, the discount price of a T-shirt is $14.40

2.

100% - 20% = 80%

18 / 80 = 0.225

0.225 x 100 = $22.50

So, the regular price of a hat is $22.50

3.

Let's y represent the total cost

We have the equation

y = x(0.8)

The equation of the tangent line to the curve at the given point, y = 4ex cos(x), (0, 4) as calculated is y' = 0.

In order to find the equation we will have to differentiate y = 4ex cos(x)

On differentiating we get the differential as ,

y' = - 4eˣsin(x)

given the value of x as 0 and y as 4

y' = -4e⁰sin(0)

  = 0   because sin( 0 ) = 0

Therefore ,the required equation is , y' = 0.

Differentiation is a technique which is used to find the derivative of a  function . Differentiation is a mathematical procedure it determines the rate of change of a function based on one of its variables.

Other than differentiation calculus also has a branch known as integration.

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Answer:

Number of nickels = 17

Number of dimes = 23

Step-by-step explanation:

Let

x = number of nickels

y = number of dimes

x + y = 40 (1)

0.05x + 0.10y = 3.15 (2)

From (1)

x = 40 - y

Substitute x = 40 - y into (2)

0.05x + 0.10y = 3.15 (2)

0.05(40 - y) + 0.10y = 3.15

2 - 0.05y + 0.10y = 3.15

- 0.05y + 0.10y = 3.15 - 2

0.05y = 1.15

y = 1.15/0.05

y = 23

Substitute y = 23 into (1)

x + y = 40 (1)

x + 23 = 40

x = 40 - 23

x = 17

Number of nickels = 17

Number of dimes = 23

Answer: f-1(x) = 5x+3

Step-by-step explanation: just did the assignments

Answer:

25.08

Step-by-step explanation:

do 76 ÷ 100, and then multiply that by 33

Answer:

76/100*33

0.76*33

25.08

Answer:

12 in

Step-by-step explanation: