Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(0) = 2 C. g(7) = -1 D. g(-13) = 20

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The Rate of plane in still air and rate of wind is 738 , 100 respectively .

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one

Given ,

An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time.

Let speed of plane be Vp and Va

Now,

Vp - Va  = 4466 / 7

Vp+Va = 5866 / 7

So, Evaluating the equations,

we get,

2Vp = (4466+5866) / 7

Vp = 1476 / 2

Vp = 738

So substitute Vp =738 in Vp-Va = 4466/7

738 - Va = 638

Va = 738 - 638

Va = 100.

Hence, The Rate of plane in still air and rate of wind is 738 , 100 respectively .

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Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

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The input (x) that satisfies the condition of being multiplied by 6 and then Subtracted by 80 to give the same value as the output is 16.

The input as "x." According to the given information, the input (x) is multiplied by 6 and then subtracted by 80, resulting in the output. In mathematical terms, this can be expressed as:

Output = (6 * x) - 80

The problem states that the input and output are the same. Therefore, we can set up the equation:

x = (6 * x) - 80

To solve for x, we'll rearrange the equation and isolate the variable:

x - 6 * x = -80

Combine like terms:

-5 * x = -80

Divide both sides by -5:

x = (-80) / (-5)

Simplifying the division:

x = 16

Hence, the input (x) that satisfies the condition of being multiplied by 6 and then subtracted by 80 to give the same value as the output is 16.

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Answer:

C. 10–15, 15–20, 20–25, 25–30, 30–35

Step-by-step explanation:

Answer:

Non-linear equations:

\(y=x^2 +2x-3\)

\(3y=2^x\)

Step-by-step explanation:

Linear equation: y = mx + b

Therefore, a linear equation has 2 variables that have no exponents.

So the non-linear equations are:

\(y=x^2 +2x-3\)  (this is a quadratic equation - polynomial with degree 2)

\(3y=2^x\) (this is an exponential equation)

Answer: B

Step-by-step explanation:

Answer:

B. (3, 2)

Step-by-step explanation:

When looking for a solution to an inequality you have to look for a point that is located in the shaded part of the inequality when graphed. B.) (3,2) is the only point that is located in the shaded part meaning that, that is a solution to the inequality

Answer:

Ruby: £18

Edward: £24

Claire: £27

David: £42

Emma: £45

Step-by-step explanation:

6 + 8 + 9 + 14 + 15 = 52

Each one receives the following fraction of the total:

Ruby: 6/52

Edward: 8/52

Claire: 9/52

David: 14/52

Emma: 15/52

Ruby: 6/52 × £156 = £18

Edward: 8/52 × £156 = £24

Claire: 9/52 × £156 = £27

David: 14/52 × £156 = £42

Emma: 15/52 × £156 = £45

Answer:

Ruby: £18

Edward: £24

Claire: £27

David: £42

Emma: £45

Answer:

Ruby=18, Edward=24, Charlie=27, David=42, Emma=45

Step-by-step explanation:

sum of ratios is 52

for each one write the ratio over the sum of ratio multiplied by total amount

\(\frac{6}{52} *156\)=18

\(\frac{8}{52} *156\)=24

\(\frac{9}{52} * 156\)=27

\(\frac{14}{52} * 156\)=42

\(\frac{15}{52} * 156\)=45

and to check add all of them and they give 156 pounds

In a parallelogram ABCD, if point C lies on the line x = −1, then the y-value of C is option C: 0.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

Since ABCD is a parallelogram, it is known know that opposite sides are parallel.

Therefore, the slope of side AB is the same as the slope of side CD, and the slope of side BC is the same as the slope of side AD.

The points B and C both lie on the line x = -1.

Therefore, the x-coordinate of point C is also -1.

Use the slope of side BC to find the y-coordinate of point C.

The slope of side BC can be found as -

slope of BC = (y-coordinate of C - y-coordinate of B) / (-1 - 1)

slope of BC = (y-coordinate of C - 2) / (-2)

Since side AD is parallel to side BC, it has the same slope.

The slope of side AD can be found as -

slope of AD = (y-coordinate of D - y-coordinate of A) / (-1 - 1)

slope of AD = (2 - 4) / (-2) = 1

Since the slopes of two parallel lines are equal so -

slope of AD = slope of BC

Therefore, equate the two slopes and solve for the y-coordinate of point C -

1 = (y-coordinate of C - 2) / (-2)

Multiplying both sides by -2 -

-2 = y-coordinate of C - 2

Adding 2 to both sides -

y-coordinate of C = 0

Therefore, the y-coordinate of point C is 0.

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Figure ABCD is a parallelogram. If point C lies on the line x = −1, what is the y-value of point C?

Answer:

3x12 36x1 4x9 18x2 6x6

Step-by-step explanation:

In a logarithmic equation, the variable is in the argument of the logarithm.

As with other types of equations, the goal in solving is to isolate the variable on one side of the equation.

---------

Example: Solve \(4\log_2(20-x) = 12\) for x.

\(\begin{array}{|c|c|} \cline{1-2} & \\\text{Isolate the log expression.} & \log_2(20-x) = 3\\ & \\\cline{1-2} & \\\text{Rewrite in exponential form.} & 2^3 = 20-x\\ & \\\cline{1-2} &\\\text{Simplify the exponent.} & 8 = 20-x\\ & \\\cline{1-2}\text{Solve for x.} & -12 = -x\\ & \\& 12 = x\\\cline{1-2}\end{array}\)

Let's check the answer.

\(4\log_2(20-x) = 12\\\\4\log_2(20-12) =12\\\\4\log_2(8) = 12\\\\4*\frac{\log(8)}{\log(2)} = 12\\\\4*\frac{0.90308998699194}{0.30102999566399} \approx 12\\\\4*2.9999999999999 \approx 12\\\\11.9999999999996\approx 12\)

We have rounding error. This is why we don't land exactly on 12, but we get really close.

---------

Or we could check the answer this way

\(4\log_2(20-x) = 12\\\\\log_2(20-x) = 3\\\\\log_2(20-12) = 3\\\\\log_2(8) = 3\\\\8 = 2^3\\\\8 = 8 \ \ \ \checkmark\\\\\)

The answer is confirmed.

Step-by-step explanation:

x = 3

y = - 2

z = 6

\(7xyz\)

Solution,

= 7 × 3 ( - 2 ) × 6

= 21 ( - 2 ) × 6

= - 42 × 6

= - 252

hence the answer is - 252....

The distance of a rock after three seconds will be 144 feet.

A function is an assertion, concept, or principle that establishes an association between two variables.

Let's use the formula for direct variation, which is:

d = kt²

64 = k(2²)

64 = 4k

k = 16

Now we can use this value of k to find the distance when t = 3:

d = 16 × (3²)

d = 16(9)

d = 144

Therefore, the rock will fall 144 feet in 3 seconds.

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The complete question is given below.

The distance, d, that a rock falls when dropped from a cliff varies directly as the square of time, t, the rock is falling. If a rock falls 64 feet in 2 seconds, how far will it fall in 3 seconds?

The given information:

% mark up = 40

Reduced = $144

Markdown = ?

The formula for percentage markup is given as

Let the actual price be x

Hence,

Reduced price = 60% of actual price

Solving for x

Therefore, actual price = $240

Inserting these values into the %markup formula gives

Solve for markup

Threefore, markup = $96

Answer:

12-28

Step-by-step explanation:

Answer:

l _ to the cinema at least a week

The flight time from Athens to Berlin is 50 minutes as per the given data.

Local time refers to the time in a specific location or time zone. It is the time that is used and observed by people in a particular region or city.

To find the flight time from Athens to Berlin, we need to calculate the time difference between the two cities and subtract it from the elapsed time between the departure and arrival times.

Athens is one hour ahead of Berlin when it is 9:00 AM in Athens, it is 8:00 AM in Berlin. This means that when the plane leaves Athens at 13:15 local time, it is 12:15 in Berlin.

The elapsed time between the departure time (13:15) and the arrival time (15:05) is 1 hour and 50 minutes.

However, we need to account for the time difference between the two cities. Since Berlin is one hour behind Athens, we need to subtract one hour from the elapsed time:

1 hour and 50 minutes - 1 hour = 50 minutes

Therefore, the flight time from Athens to Berlin is 50 minutes.

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The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Answer: the Dorians were far less advanced then the Mycenaean Greeks; economy collasped and trade stopped

Answer:

4 cups of flour is needed and 4/3 cups of sugar

Step-by-step explanation:

Given

2 dozen Muffins; 3 cups of flour and 1 cup of sugar

Required

Determine the cups of flour if 18 muffins is used

First, we have to determine the proportion of the number of muffins used previously and now;

Represent this with p;

\(p = \frac{2\ dozen}{18}\)

\(p = \frac{2 * 12}{18}\)

\(p = \frac{24}{18}\)

\(p = \frac{4}{3}\)

Multiply this to the previous cups of flours and sugars;

Cups of flour = p * previous cups of flour

\(Cups\ of\ flour = \frac{4}{3} * 3\)

\(Cups\ of\ flour = 4\)

Cups of Sugar = p * previous cups of sugar

\(Cups\ of\ sugar= \frac{4}{3} * 1\)

\(Cups\ of\ sugar= \frac{4}{3}\)

Hence, 4 cups of flour is needed and 4/3 cups of sugar

Answer:

1) Gathering the data:

Jonah and his 3 friends = 4 people

Bill = $86 (no tax)

Tip = 18% of $86 (1.18)

Sales Tax = 6%

Total amount =?

2) Let's calculate the Tip (18% over the Cost)

1.18 x 86=101.48

3) Let's calculate how much they'll pay with tax

101.48 x 1.06=107.57 (rounding up)

Dividing by 4 : 107.57 : 4 = $26.89

4) Expression:

Answer:

$448

Step-by-step explanation:

This can be solved simply by using multiplication:

28 (chairs) x 16 (dollars per each chair) = 448 (dollars total)

Hope it helps! :)

The correct option is B. The students knew whether or not music was playing while they were taking the exam

Given,

The class was split into two groups.

The first group took the midterm exam while background music was playing, and the second group took the exam without any background music.

In a blind experiment, any information that might affect the subjects is kept secret until the experiment is over. The pupils in this instance are aware of their group membership.

In order to answer this question, an experiment is carried out to see how music affects learning. One group of students studies while background music is playing, while the other group does not.

However, because of the background music playing here, the pupils are aware of which group they belong to. The experiment's outcomes are impacted by this.

Therefore the correct option is B. The students knew whether or not music was playing while they were taking the exam.

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Answer:

hola :]

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

3x - 6 = 12

3x = 18

x = \(\frac{18}{3}\)

x = 6

Answer:

\(Perimeter = 38.6\)

Step-by-step explanation:

Given

\(A\ B = 13\)

\(B\ F = 9\)

\(F\ C = 5.6\)

Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

\(Perimeter = A B + B\ C + A\ C\)

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

\(B\ C^2 = B\ F^2 + F\ C^2\)

Substitute values for BF and FC;

\(B\ C^2 = 9^2 + 5.6^2\)

\(B\ C^2 = 81 + 31.36\)

\(B\ C^2 = 112.36\)

\(B\ C^2= \sqrt{112.36\)

\(B\ C = 10.6\)

Next, we calculate A C.

To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

\(A\ B^2 = B\ F^2 + A\ F^2\)

Substitute values for B F and A B;

\(13^2 = 9^2 + A\ F^2\)

\(169= 81 + A\ F^2\)

\(A\ F^2 = 169 - 81\)

\(A\ F^2 = 88\)

\(A\ F = \sqrt{88\)

\(A\ F = 9.4\)

Since F lies on line A C:

\(A\ C = A\ F + F\ C\)

\(A\ C = 9.4 + 5.6\)

\(A\ C = 15.0\)

Recall that:

\(Perimeter = A\ B + B\ C + A\ C\)

\(Perimeter = 13 + 10.6 + 15.0\)

\(Perimeter = 38.6\)

Hence, the perimeter is 38.6

Given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:

Recall:

Given that P is the orthocenter of triangle ABC, where,

Perimeter of △ABC = AB + BC + AC

First, we need to find BC and AC.

△BFC is a right triangle, apply Pythagorean theorem to find BC:

\(BC = \sqrt{BF^2 + FC^2}\)

\(BC = \sqrt{9^2 + 5.6^2}\\\\\mathbf{BC = 10.6}\)

△BFA is a right triangle, apply Pythagorean theorem to find FA:

\(FA = \sqrt{AB^2 - BF^2}\)

\(FA = \sqrt{13^2 - 9^2}\\\\\mathbf{FA = 9.4}\)

AC = FA + FC

AC = 9.4 + 5.6

AC = 15

Perimeter of △ABC = AB + BC + AC

Perimeter of △ABC = 13 + 10.6 + 15

Perimeter of △ABC = 38.6 units

Therefore, given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:

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A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

\(x=8\)

\(y=24\)

Step-by-step explanation:

3x+2y=72

If y=3x, we plug it into our equation and get:

3x+2×3x=72

3x+6x=72

9x=72

Divide both sides by 9

x=8

Answer:

x = 8

Step-by-step explanation:

3x + 2y = 72

Put y as (3x), and solve for x.

3x + 2(3x) = 72

Multiply 2(3x).

3x + 6x = 72

Add like terms 3x and 6x.

9x = 72

Divide 9 into both sides and isolate x.

x = 72/9

x = 8

The value of x is 8.

For each statement for triangle SQP and SQR, Q is the midpoint of PR: No, ∠P ≅ ∠R: No, ∠PSQ ≅ ∠RSQ: Yes, m∠P = 33°, m∠RSQ = 57°: No, ∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes.

What is triangle?

A triangle is a geometric shape that consists of three line segments connected end-to-end to form a closed shape. Triangles are one of the basic shapes studied in geometry and are used in a wide range of applications, from construction to computer graphics.

Here are the answers to whether each statement provides enough information to prove that △SQP ≅ △SQR:

Q is the midpoint of PR: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the angles or sides.

∠P ≅ ∠R: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠SQP is a right angle, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-side (AAS) congruence criterion.

∠SQP is a right angle, m∠P = 33°, m∠RSQ = 57°: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-angle (AAA) congruence criterion.

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