Which statement best explains whether the table represents a linear or nonlinear function?
A.) It is a linear function because there is a constant rate of change in both the input and output values.
B.) It is a nonlinear function because there is a constant rate of change in both the input and output values.
C.) It is a linear function because the input values are decreasing.
D.) It is a nonlinear function because the input values are increasing
​

Answer:

523.6 cm^3

Step-by-step explanation:

Volume of a sphere:

\( \frac{4}{3} \pi {r}^{3} \)

The diagram shows the diameter of the sphere is 10cm.

Radius (r) = 1/2 diameter

So r = 5 cm

Plug that into the formula above to get

\( \frac{4}{3} \pi \times{5}^{3} \)

= 523.6 cm^3

Answer:

120.8 feet

Step-by-step explanation:

Answer: 2,435

Step-by-step explanation:

trust

The equation of the line tangent to the graph of g at the point where x = 1 y + 10x + 44 =0.

What is line tangent?

A line that touches a curve at one point is said to be tangent. A point of tangency is the location where a curve and a line intersect. Y = mx + b is the slope-intercept formula for a line, where m is the line's slope. The straight line that "just touches" the curve at a particular location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

Given g(x)=f(2x)

Differentiate it on both side with respect to x.

\(\begin{aligned}& \frac{d g(x)}{d x}=2 * \frac{d f(2 x)}{d x} \\& \frac{d g(-1)}{d x}=2 * \frac{d f(-8)}{d x}=-5^* 2=-10\end{aligned}\)

Slope =-10

Here x coordinate = -4

g(-4)=f(-8)=-4 = y coordinate

Thus point of tangency on function g is (-4,-4)

Thus equation of tangent is

y + 4= -10(x+4)

y + 10x + 44 =0

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Answer:

  y = 8x -11

Step-by-step explanation:

You want the equation of the line tangent to g(x) = f(2x-6) at x=1, where f is a differentiable function with f(1) = 2, f(-4) = -3, f'(1) = 3, f'(-4) = 4.

The equation of the tangent line at x=1 can be written ...

  y = g'(1)(x -1) +g(1)

The necessary function values are ...

  g(1) = f(2·1 -6) = f(-4) = -3

and

  g'(x) = f'(2x -6)·(2x -6)' = 2f'(2x -6)

  g'(1) = 2f'(2·1 -6) = 2f'(-4) = 8

Then the equation of the line is ...

  y = 8(x -1) +(-3) = 8x -8 -3

  y = 8x -11 . . . . . . tangent to g(x) at x=1

__

Additional comment

The minimum polynomial function f(x) that can have the desired values and derivatives is a cubic. The attached graph shows g(x) and the tangent at x=1 using that cubic for f(x).

Answer: 10 years

Step-by-step explanation:

1720=960(1+0.061/12)

Answer:

Step-by-step explanation:

76

The rule that describes the composition transformation that maps ABCD to A''B''C''D'' is;

''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

The given coordinates of parallelogram ABCD are;

⇒ (3, 5), (6, 5), (4, 1), (1, 1)

The coordinates of the parallelogram A'B'C'D' are;

⇒ A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)

The coordinates of the parallelogram A''B''C''D'' are;

⇒ D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)

The image of the point (x, y), following a reflection about the x-axis is the point (x, -y).

And, The difference in the coordinates of the parallelogram ABCD and A'B'C'D' is the change in the sign of the y-coordinates

Therefore, the transformation that gives the parallelogram A'B'C'D' from the parallelogram ABCD is a reflection about the x-axis

Thus, The difference between the coordinates of the vertices of the parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the x-value by (-6), and a change in the y-value by (+1)

Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation of 1 unit, x in the y-direction.

Which gives;

The composition transformation that maps the pre-image ABCD to the final image A''B''C''D'', (given that in a composition transformation, the transformation to the right is done first) are; which is the option;

''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.

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Answer:

3p - q = 3(2-5) - (8x3) = -9 - 24 = -33. Therefore, 3p-q=-33.

The amount of water at the end of the fourth hour is 27000 gallons.

Given that :

A water tank is emptied at a constant rate.

Let x be the amount of water at first.

Amount of water at the end of first hour = 36000 gallons

Amount of water after the sixth hour = 21000 gallons.

The relation will be linear since the rate is constant.

Rate = (21000-36000) / (6 - 1)

       = -3000

Amount of water after fourth hour = 36000 + (-3000×3)

                                                         = 27000 gallons

Hence the amount of water after the fourth hour is 27000 gallons.

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a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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The probability of the coin showing heads is 1/2.

The probability of the spinner landing on purple is 1/4.

The probability of the cube showing a 1, 2, 3, or 5 is 2/3.

The probability of all three events happening is = 1/12.

Therefore, the probability that Jennifer will flip a heads, spin the spinner on purple, and roll a 1, 2, 3, or 5 is 1/12.

Here is a breakdown of the calculation:

Probability of coin showing heads: 1/2

Probability of spinner landing on purple: 1/4

Probability of cube showing 1, 2, 3, or 5: 2/3

Probability of all three events happening: 1/2 * 1/4 * 2/3 = 1/12

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Answer:

Approximately 33,510.7 cubic millimeters.

Step-by-step explanation:

The volume of a sphere can be calculated using the formula: V = 4/3 * π * r^3, where r is the radius of the sphere.

The diameter of the table tennis ball is 40 mm, so the radius is r = 40/2 = 20 mm.

To convert millimeters to cubic millimeters we have to cube the value of radius, so in this case, 20mm20mm20mm.

So, the volume of the table tennis ball in cubic millimeters is:

V = 4/3 * π * 20^3 = 4/3 * π * 8000 = approximately 33,510.7 cubic millimeters.

numbers:

2, 4, and 5

I am so sorry if i'm wrong!!! :|

Answer:

The slope is -3/2

The arc MQ in circle R is a semicircle, and its measure is 45 degrees or π/4 radians.

To determine the nature of the arc MQ in circle R, we need to consider the relationship between the length of the arc and the circumference of the circle. If the arc is less than half the circumference of the circle, it is a minor arc. If it is exactly half the circumference, it is a semicircle. If it is greater than half the circumference, it is a major arc.

Since PM is a diameter of circle R, the arc MQ is essentially one-half of the circumference of the circle, making it a **semicircle**.

To find the measure of the semicircular arc MQ, we need to calculate the measure of the corresponding angle at the center of the circle. This angle can be determined using the property that the angle at the center of a circle is twice the angle formed by any chord intersecting the circumference of the circle.

Since PM is a diameter, the angle at the center formed by PM is a right angle (90 degrees or π/2 radians). Therefore, the measure of angle PMQ (or angle QMP) is half of that, which is 45 degrees or π/4 radians.

Since the measure of the angle at the center of the circle corresponds to the measure of the arc it intercepts, the measure of arc MQ is also **45 degrees or π/4 radians**.

In summary, the arc MQ in circle R is a semicircle, and its measure is 45 degrees or π/4 radians.

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Answer:

Complex numbers

Step-by-step explanation:

Given

5 + i and 5 - i

Required

What are they called?

In numbering system,

Complex numbers are of the form:

\(a + bi\)

Comparing the given numbers to the form of complex number, we'll see that there's a perfect match between the two

i.e.

\(a + bi = 5 + i\)

\(a + bi = 5 - i\)

Hence, they are referred to as complex numbers

If one angle in an isosceles triangle is 90 degrees then the measure of each angle of an isosceles triangle will be 45 degrees

What is an isosceles triangle ?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that have the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.

As we know that in an isosceles triangle set of two angles are equal

And

we also know that sum of all the angles of a triangle is 180 degrees

So, According to the question

90 degrees + other angles =180 degrees

other angles = 90 degrees

one angle = 90/2

one angle = 45 degree  

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The equation showing the relation between shorter and longer skirt is 3s+4t = 140.

Given that the Scottish dance team used 140 yards of tartan to make dancing skirts.

The skirt pattern for the shorter members is 3- yards of fabric, and the skirt pattern for the taller members is 4 yards of fabric.

So, we need to find the equation represents the relationship between the number of short skirts and the number of long skirts that were made,

So, if there are s short skirts and t long skirts,

So,

The relation will be =

3s + 4t = 140

Hence the equation showing the relation between shorter and longer skirt is 3s+4t = 140.

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Um maybe try it out then ask for help from the teacher

Answer:

-6 and -5 (There are many more combinations of numbers that can equal to -11 but this is just one of the many possibilities.

Step-by-step explanation:

-6 and -5

See you can write it like this,

-6+ (-5)

= -6-5

=-11

Answer: The GCF of 7, 15, & 21 is 1

Step-by-step explanation: the greatest number that divides all three numbers is 1

The margin on the discounted bread is $2.33

Given,

In the question:

Your store cost on a loaf of bread is $0. 75,

and your retail price is $3. 85.

You are having a promotion which discounts the bread 20%.

To find the margin on the discounted bread.

Now, According to the question:

Given store cost on a loaf of bread is $0.75 and retail price is $3.85.

Discount is always given on retail price.

The amount of discount is 20%

Discount given on $3.85 = 20% of 3.85= .20(3.85)= 0.77.

Cost of bread after discount =3.85-0.77= 3.08

The discounted bread costs $3.08.

The difference in store cost and discounted cost = 3.08-0.75=$2.33

Hence, the margin on the discounted bread is $2.33

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Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer: (3,-5) minimum

Step-by-step explanation:

the vertex is at the bottom so it is a minimum

Answer:

I think the answer is OP=PQ

The correct equation will be OP = PQ.

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Given that, there is a line segment, OQ, and the point P is the midpoint of the line segment,

We need to determine the relation between OP and PQ,

So, according to the definition of midpoint, the midpoint divides the segment into two equal halves,

Therefore,

OP = PQ

Hence the correct equation will be OP = PQ.

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Answer:

7

hope it helps..........

Answer:

divide both sides by 2

Step-by-step explanation:

divide both sides by 2 then simplify and get x = 9 over 32

Answer:

Transposing square to rhs,it becomes root

Step-by-step explanation:

\(x^{2} =9/16\)

\(x=\)\(\sqrt{9}/\sqrt{16\\\) (transposing square to rhs,it becomes root)

\(x= 3/4\)

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Maryam answered 26 questions correctly and got 4 questions wrong on the test with 30 questions.

To find how many questions Maryam got wrong, we need to first determine how many questions she got right. Since she scored 86.7%, we can multiply the total number of questions by the percentage to get the number of questions she answered correctly.

86.7% of 30 questions is (86.7/100) * 30 = 26.01 questions.

Since Maryam cannot have answered a fractional number of questions correctly, we round down to the nearest whole number. Thus, she answered 26 questions correctly.

To find out how many questions she got wrong, we can simply subtract the number of questions she got right from the total number of questions. Therefore, Maryam got 30 - 26 = 4 questions wrong.

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Answer:

2(5+2)

Step-by-step explanation:

The greatest common factor would be 7. So now 35/7 is 5 and 14/7 is 2. Now put it in distributive property! GCF on the outside and the new numbers we just got in the inside. There's your answer! Have a great day! :)