If f(x) = 3x + 1 and g(x) = x − 3, find the quantity f divided by g of 8.
A. 125
B. 25
C. 20
D. 5

Answer:

Assuming that the figure is a rectangle:

x=12

angle GJH=22 degrees

Step-by-step explanation:

angle GHJ=angle IJH

5x+8=7x-16

simplify

2x=24

x=12

angle IJH=7x-16

substituting for x

IJH=7(12)-16=84-16=68 degrees

angle GJH=90-IJH

angle GJH=22 degrees

Answer:

answer is 38 yd

Step-by-step explanation:

area of square =1444 yd^2

z^2=1444 yd^2

z=\(\sqrt{1444\)yd^2

z=38 yd

Hope this helps u!!

Answer:

A and C

Step-by-step explanation:

42/200 = .21

76/200 = .38

Answer:

Apples and Pears

Step-by-step explanation:

21 % = Apples

41 % = Oranges

38 % = Pears

Probablity of less than 40% = pears and apples

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

The Cartesian to Polar equations can be defined as a set of equations that convert the coordinates of a point from Cartesian coordinates to Polar coordinates. We can define the Cartesian coordinates (x,y) in terms of the polar coordinates (r,θ) as follows:

Here, x is the horizontal coordinate, y is the vertical coordinate, r is the radial coordinate, and θ is the angular coordinate. We can use these relationships to convert the Cartesian equations to Polar equations.53. \( x=7 \)In polar coordinates, x = rcosθ.

Therefore, rcosθ = 7. We can write this as r = 7/cosθ.54. \( y=1 \)In polar coordinates, y = rsinθ. Therefore, rsinθ = 1. We can write this as r = 1/sinθ.55. \( x=y \)In polar coordinates, x = rcosθ and y = rsinθ.

Therefore, rcosθ = rsinθ. Dividing by r, we get tanθ = 1. Therefore, θ = π/4 or 5π/4.56. \( x-y=3 \)We can write this as y = x - 3. In polar coordinates, x = rcosθ and y = rsinθ. Therefore, rsinθ = rcosθ - 3.

Dividing by cosθ, we get tanθ = sinθ/cosθ = 1 - 3/cosθ. Therefore, cosθ = 3/(1 - tanθ). We can substitute this expression for cosθ in the equation rcosθ = x to get the polar equation in terms of r and θ.57. \( x^{2}+y^{2}=4 \)In polar coordinates, x = rcosθ and y = rsinθ.

Therefore, r^{2}cos^{2}θ + r^{2}sin^{2}θ = 4. Simplifying, we get r^{2} = 4 or r = ±2. Therefore, the polar equation is r = 2 or r = -2.58. \( y = x^{2} \)In polar coordinates, x = rcosθ and y = rsinθ. Therefore, rsinθ = r^{2}cos^{2}θ. Dividing by rcos^{2}θ, we get tanθ = r*sinθ/cos^{3}θ. Therefore, r = tanθ/cos^{3}θ.

The Cartesian to Polar equations can be defined as a set of equations that convert the coordinates of a point from Cartesian coordinates to Polar coordinates. We can define the Cartesian coordinates (x,y) in terms of the polar coordinates (r,θ) as follows:Here, x is the horizontal coordinate, y is the vertical coordinate, r is the radial coordinate, and θ is the angular coordinate. We can use these relationships to convert the Cartesian equations to Polar equations.53. \( x=7 \).

In polar coordinates, x = rcosθ. Therefore, rcosθ = 7. We can write this as r = 7/cosθ.54. \( y=1 \)In polar coordinates, y = rsinθ. Therefore, rsinθ = 1. We can write this as r = 1/sinθ.55. \( x=y \)In polar coordinates, x = rcosθ and y = rsinθ. Therefore, rcosθ = rsinθ.

Dividing by r, we get tanθ = 1. Therefore, θ = π/4 or 5π/4.56. \( x-y=3 \)We can write this as y = x - 3. In polar coordinates, x = rcosθ and y = rsinθ. Therefore, rsinθ = rcosθ - 3. Dividing by cosθ, we get tanθ = sinθ/cosθ = 1 - 3/cosθ. Therefore, cosθ = 3/(1 - tanθ).

We can substitute this expression for cosθ in the equation rcosθ = x to get the polar equation in terms of r and

\(θ.57. \( x^{2}+y^{2}=4 \)\)In polar coordinates, x = rcosθ and y = rsinθ. Therefore,\(r^{2}cos^{2}θ + r^{2}sin^{2}θ = 4\). Simplifying, we get r^{2} = 4 or r = ±2.

Therefore, the polar equation is r = 2 or r = -2.58. \( y = x^{2} \)In polar coordinates, x = rcosθ and y = rsinθ. Therefore, \(rsinθ = r^{2}cos^{2}θ\). Dividing by rcos^{2}θ, we get tanθ = r*sinθ/cos^{3}θ. Therefore, r = tanθ/cos^{3}θ.

Thus, these are the Polar equations that are equivalent to the given Cartesian equations.

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The value of y when x is 1 is -2

Linear also interpretes as straight and a graph is a diagram which shows a connection or relation between two or more quantity.

We can also define straight graph which is drawn on a plane connecting the points on x and y coordinates. It is a graph of a linear equation.

To calculate any value of x or y we can use the graph to determine the value of x if y is given and the value of y if x is given

Therefore from the graph;

when x is 1 , the reading of y to the straight line is -2. Therefore the value of y is -2.

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Answer:

32,29

Step-by-step explanation:

Answer:

(x,y) = (-3,-6)

Step-by-step explanation:

gm gn cgmcgmxgmgnx

Answer:

The area of the shaded region is, \(24mm^{2}\)

Step-by-step explanation:

First we have to calculate the area of ΔABC and ΔXYZ.

Area of ΔABC = \(\frac{1}2}\)×\(Base\)×\(Height\)

Area of ΔABC = \(\frac{1}{2}\)×\(5mm\)×\(12mm\)

Area of ΔABC =\(30mm^{2}\)

and,

Area of ΔXYZ = \(\frac{1}{2}\)×\(Base\)×\(Height\)

Area of ΔXYZ = \(\frac{1}{2} X3mmX4mm\)

Area of ΔXYZ = \(6mm^{2}\)

Now we have to calculate the area of the shaded region.

Area of the shaded region = Area of ΔABC - Area of ΔXYZ

Area of the shaded region = \(30mm^{2} - 6mm^{2}\)

Area of the shaded region = \(24mm^{2}\)

Therefore, the area of the shaded region is, \(24mm^{2}\)

Answer:

138

Step-by-step explanation:

120 x .15 = 18

120 + 18 = 138

Answer:

Step-by-step explanation:

\(120+15\%\times120=120+0.15\times120=120+18=138\)

Solution:

Consider the following graph:

For the point (x, y) to be a solution of the line above, the point (x, y) must belong to the function of this line, that is, it must be on the graph of the line. According to this, note that the point

(x,y)=(0,4) is on the line.

So that, we can conclude that the correct answer is:

A) (0,4)

Step-by-step explanation:

The root is

-sqr root of 5.

First, we put these roots in the forn of

\((x - a)\)

where a is the root

So we have

\((x - ( - 2))(x - \sqrt{5} )(x - \frac{10}{3} )\)

\((x + 2)(x - \sqrt{5} )(3x - 10)\)

\((3 {x}^{2} - 4x - 20)(x - \sqrt{5} )\)

To get rid of that square root, let have another root that js the conjugate posive root of 5.

\((3 {x}^{2} - 4x - 20)(x - \sqrt{5} )(x + \sqrt{5} )\)

\((3 {x}^{2} - 4x - 20)(x {}^{2} + 5)\)

Which will gives us a rational coeffeicent of degree 4.

Why we didn't do

\((x - \sqrt{5} )\)

?

Because

\((x - \sqrt{5} ) {}^{2} = {x}^{2} - 2 \sqrt{5} + 5\)

If we foiled out we will still have a irrational coeffceint.

Answer:

C.  f(x) = (x - 3)² + 4

Step-by-step explanation:

Given parent function:

\(f(x)=x^2\)

When a graph is translated "a" units right, subtract "a" from the x-value of the function.

Therefore, the translation of the parent function 3 units right is:

\(\implies f(x-3)=(x-3)^2\)

When a graph is translated "a" units up, add "a" to the function.

Therefore, the translation of the function 4 units up is:

\(\implies f(x-3)+4=(x-3)^2+4\)

The differential equations for the given families of curves are 07. y' = -5\(Ae^(-5x)\)- \(Bxe^(-5x)\), and 08. y' = 7\(Ae^(7x)\) - 8\(Be^(-8x)\).

To form the differential equations for the given families of curves, we need to differentiate the given expressions with respect to x.

For the first family of curves, y = \(Ae^(-5x)\) + \(Be^(bx)\), differentiating both sides with respect to x gives:

y' = -5\(Ae^(-5x)\) - \(Bxe^(-5x)\)

Therefore, the differential equation for the first family of curves is y' = -5\(Ae^(-5x)\) - \(Bxe^(-5x)\).

For the second family of curves, y =\(Ae^(7x)\)+ \(Be^(-8x)\), differentiating both sides with respect to x gives:

y' = 7\(Ae^(7x)\) - 8\(Be^(-8x)\)

Therefore, the differential equation for the second family of curves is y' = 7\(Ae^(7x)\)- 8\(Be^(-8x)\).

These differential equations describe the relationship between the rate of change of y (y') and the variables x, A, and B for the respective families of curves.

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The quotient of the given division operation is -343. and The correct option is the first option -343.

According to the statement

We have to find that the value of the quotient.

So, For this purpose, we know that the

Quotient can be defined as the result of the division of a number by any divisor.

In other words, The result of the division is the quotient.

From the given information:

we are to determine the quotient of the given division operation

And

The statement become is:

\(\frac{-7^{2} }{-7^{-1} }\)

Then we have to solve this

Then

\(\frac{49}{-7^{-1} }\)

Then

49*-7

-343.

the quotient of the given division operation is -343.

So, The quotient of the given division operation is -343. and The correct option is the first option -343.

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Answer:

-343

Step-by-step explanation:

Edge

There are 28 relations on set A.

To determine the number of relations on set A, we need to understand the concept of a relation. A relation between two sets A and B is a set of ordered pairs (a, b) where a is from set A and b is from set B. In this case, both sets A and B are the same, so we are looking for relations within set A.

In a relation on set A, each element of A can be related to any other element of A, including itself. This means that for each pair of elements in set A, we have two possibilities: either they are related or they are not.

Since there are 8 distinct elements in set A, for each pair, we have two choices: either they are related or not related. Therefore, for each pair of elements, we have 2 possibilities.

Now, the total number of relations on set A can be calculated by multiplying the number of possibilities for each pair of elements. Since there are 8 distinct elements in set A, there are (8 choose 2) pairs of elements in total.

Using the binomial coefficient formula, (n choose k) = n! / (k!(n-k)!), we can calculate (8 choose 2):

(8 choose 2) = 8! / (2!(8-2)!)

            = (8 * 7) / (2 * 1)

            = 28

Therefore, there are 28 different relations on set A.

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The ratio of nickels to dimes in the spare change on the dresser is 9:8. This means that for every 9 nickels, there are 8 dimes in the spare change on the dresser.

Let's start by assigning variables to the number of pennies, nickels, and dimes. We can represent the number of pennies as 2x, where x is a positive integer. According to the given ratio of pennies to nickels (2:3), the number of nickels would be 3/2 times the number of pennies, which is 3x. Similarly, according to the ratio of pennies to dimes (3:4), the number of dimes would be 4/3 times the number of pennies, which is 8x/3.

To find the ratio of nickels to dimes, we need to compare their quantities. The number of nickels is 3x, and the number of dimes is 8x/3. To make the comparison easier, we can multiply both quantities by 3 to eliminate the fractions. This gives us 9x nickels and 8x dimes.

Therefore, the ratio of nickels to dimes is 9:8. This means that for every 9 nickels, there are 8 dimes in the spare change on the dresser.

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Answer:

I believe number 9 is the middle answer

Step-by-step explanation:

please correct me if I'm wrong

Answer:

The answer is \(\frac{5}{11}\\\) = 0.45; rounded up(to the nearest tenth) is 0.5

Step-by-step explanation:

The angle measure of a circle in radians is 2\(\pi\).

First, find the circumference of the circle in terms of \(\pi\).

The formula for the circumference of a circle is 2\(\pi\)r (2 × \(\pi\) × radius)

Then find the ratio of the arc length of the central angle to the circumference.

Arc length of the central angle = 5.

Circumference = 22\(\pi\)

The ratio of the arc length of the central angle to the circumference is equal to  \(\frac{5}{22\pi }\)

Now use that ratio to find the central angle in radians by multiplying it by the angle measure of the circle in radians.

\(\frac{5}{22\pi }\) × 2\(\pi\) = 5/11

Round to the nearest tenth:

\(\frac{5}{11}\) ≈ 0.4545 = 0.5

Answer:

D (6, 21)

Step-by-step explanation:

Since the ratio of the corresponding values of x and y given in the table is 2 : 7

So, 6/ 21 = 2/7 = 2: 7

Thus, D (6, 21) is the correct answer.

Answer:

D

Step-by-step explanation:

Based on the above, the total cost of refurbishing the community hall would be £1,032

To calculate the value of the materials required to remodel the community hall we must carry out the following procedure:

Find the area of the living room walls:

According to the above, the total area of the walls would be 330m². To know the number of cans of paint we need would be:

On the other hand, to calculate the value of the floor tiles we must carry out the following procedure:

Calculate the floor area:

Finally, to know the total value we must add both values:

Note: This question is incomplete. Here is the complete information:

Attached image

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Answer:

15000+1250x

Step-by-step explanation:

Since the initial population is 15,000, we want to know how many people are going to Jonesville each year.  Assuming that in 2001 and in 2002, each year adds 1,250 people and that it is constant.  The equation is 15000+1250x in which 15,000 represents the initial number and 1250 is the amount of people added each year followed by x which is the number in years.

The value of a5 is 8.

Given that,

a₁ = 4

aₙ = aₙ₋₁ + 1

So, we can find the second term a₂ using the equation of nth term,

a₂ = a₍₂₋₁₎ + 1

a₂ = a₁ + 1

Applying the value of a₁,

a₂ = 4 + 1

a₂ = 5

So, finding the value of a₃,

a₃ = a₍₃₋₁₎ + 1

a₃ = a₂ + 1

a₃ = 5 + 1

a₃ = 6

So, the value of a₄ will be,

a₄ = a₃ + 1 = 6 + 1

a₄ = 7

Therefore,

a₅ = a₄ + 1 = 7 + 1

a₅ = 8

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If we are given the equation ax - b = cy and the value of "a" is zero (a = 0), we can solve for "x". The answer will be that x can take any value.

Start with the equation: ax - b = cy

Since "a" is zero, we have: 0x - b = cy

Simplifying further, we have: -b = cy

To isolate "x", we can divide both sides of the equation by "c":

(-b)/c = (cy)/c

Simplifying, we get: (-b)/c = y

Therefore, when "a" is zero, the equation ax - b = cy does not have a unique solution for "x". The value of "x" is indeterminate or undefined in this case.

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Answer:

∠ 2 = 34°

Step-by-step explanation:

∠ 1 + ∠ 2 = ∠ WXY , that is

37° + ∠ 2 = 71° ( subtract 37° from both sides )

∠ 2 = 34°

The constant of proportionality, k, is approximately -0.0042. Using this value, it will take approximately 36.97 minutes for the coffee to reach 160 degrees.

To solve the given problem, we can use the differential equation for Newton's Law of Cooling:

dT/dt = k(T - A)

Given that the initial temperature of the coffee is 186 degrees, the ambient temperature is 65 degrees, and after 11 minutes the temperature decreases to 176 degrees, we can plug these values into the equation:

176 - 65 = (186 - 65) * e^(11k)

Simplifying the equation:

111 = 121 * e^(11k)

Dividing both sides by 121:

111/121 = e^(11k)

To solve for k, we can take the natural logarithm (ln) of both sides:

ln(111/121) = 11k

Now we can calculate the value of k:

k = ln(111/121) / 11

k ≈ -0.0042 (rounded to four decimal places)

Now, let's use this value of k in the differential equation to find the time it takes for the coffee to reach 160 degrees:

160 - 65 = (186 - 65) * e^(-0.0042t)

95 = 121 * e^(-0.0042t)

Dividing both sides by 121:

95/121 = e^(-0.0042t)

Taking the natural logarithm of both sides:

ln(95/121) = -0.0042t

Solving for t:

t = ln(95/121) / (-0.0042)

t ≈ 36.97 minutes (rounded to two decimal places)

Therefore, it will take approximately 36.97 minutes for the coffee to reach 160 degrees.

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The complete question is:

Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dT/dt=k(T−A), where T is the temperature of the object after t units of time have passed, A is the ambient temperature of the object's surroundings, and k is a constant of proportionality.

Suppose that a cup of coffee begins at 186 degrees and, after sitting in room temperature of 65 degrees for 11 minutes, the coffee reaches 176 degrees. How long will it take before the coffee reaches 160 degrees?Include at least 2 decimal places in your answer.______ minutes

1) A conversion factor is a ratio that relates two different units of measurement and is used to convert between them.

2) The conversion factor for s/min (seconds per minute) is 60 s/min. This means that there are 60 seconds in one minute.

3) To determine the conversion factor for min²/s² (minutes squared per second squared), we need to analyze Equation 2.2-3. Since the units of the left-hand side of the equation are in minutes squared per second squared, we can equate it to the right-hand side of the equation and derive the conversion factor.

Equation 2.2-3: 1 min²/s² = (60 s/min)² / (1 s)²

Simplifying the equation:

1 min²/s² = (60² s² / s²)

Therefore, the conversion factor for min²/s² is 3600.

4) The conversion factor for m³/cm³ (cubic meters per cubic centimeter) can be derived by analyzing the relationship between the two units. Since there are 100 centimeters in 1 meter, the conversion factor is determined by cubing this ratio.

Conversion factor for m³/cm³ = (100 cm / 1 m)³

Simplifying the equation:

Conversion factor for m³/cm³ = (100³ cm³ / 1³ m³)

Therefore, the conversion factor for m³/cm³ is 1,000,000.

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The median number of emails sent per day in the given survey is 23.

To find the median, we first need to arrange the data in order from smallest to largest

20 20 20 21 22 22 22 23 23 24 24 25 26 26 27 27 27 27 27 27

The median is the middle value in the ordered list. Since there are 20 observations, we can find the median as follows

The 10th observation is 24, which is the first value greater than or equal to the median.

The 9th observation is 23, which is the last value less than or equal to the median.

Therefore, the median number of E-mails sent per day is 23.

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None of the descriptive alternatives are correct.

What is the null hypothesis?

In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

Here, we have

Given:  if obtained from an experiment, would lead to rejecting the null hypothesis if a = .01.

for 1st choice ; p-value =fdist(5,3,18)= 0.0107

for 2nd choice : p-value =fdist(4.08,3,8)=0.0496

for 3rd choice : p-value =fdist(150,1,1)=0.052

since none of the choices have p value less than 0.01; none of these would lead to a rejected null hypothesis.

Hence, none of the descriptive alternatives are correct.

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Slope-intercept form: y = mx + b

m = the slope

b = y-intercept.

In this problem,

m = 3/5

b = ?

So far y = 3/5x + b

Let's plug the point (-3, -1) into our slope equation.

-1 = 3/5(-3) + b

Simplify the right side.

-1 = -9/5 + b

Add 9/5 to both sides.

4/5 = b

The equation is: y = 3/5x + 4/5

Answer choice A is correct.