if f(x) = 5x-2 and g (x) = 2x + 1 find (f-g) (x)

Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

Answer:

x = -12

Step-by-step explanation:

-10x+1+7x=37

Combine like terms

-3x+1 = 37

Subtract 1 from each side

-3x+1-1 = 37-1

-3x = 36

Divide by -3

-3x/-3 = 36/-3

x = -12

Given the information provided, we can determine the probability by dividing the number of firms with $1 million or more in income after taxes by the total number of firms in the sample.

Out of the 400 computer service firms surveyed, the number of firms with $1 million or more in income after taxes is given as 138. To calculate the probability, we divide this number by the total number of firms in the sample (400):

Probability = Number of firms with $1 million or more in income after taxes / Total number of firms

Probability = \(\frac{138}{400}\)

Simplifying the division, we find:

Probability = 0.345

Therefore, the probability that a particular firm selected has $1 million or more in income after taxes is 0.345 or 34.5%.

Based on the given options, the closest probability to 0.345 is 0.46, which is the best choice for the probability value.

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The estimated equation for these data is: Y= 6.47 + 1.013x

When x = 6, the estimated value of y is approximately 12.55.

To compute the estimated regression equation and predict the value of y when x = 6, we'll follow these steps:

Given data:

xi: 2, 6, 9, 13, 20

yi: 7, 18, 9, 26, 23

a. Compute b0 and b1 and develop the estimated equation for these data.

Step 1: Calculate the means of x and y:

x = (2 + 6 + 9 + 13 + 20) / 5 = 10

y = (7 + 18 + 9 + 26 + 23) / 5 = 16.6

Step 2: Calculate the deviations from the means:

xi - x: -8, -4, -1, 3, 10

yi - y: -9.6, 1.4, -7.6, 9.4, 6.4

Step 3: Calculate the sum of squared deviations:

Σ(xi - x): 180

Σ(yi - y)²: 316.8

Step 4: Calculate the sum of cross-products:

Σ(xi - x)(yi - y): 182.4

Step 5: Calculate the slope (b1):

b1 = Σ(xi - x)(yi - y) / Σ(xi - x)² = 182.4 / 180 ≈ 1.013

Step 6: Calculate the intercept (b0):

b0 = y - b1 * x = 16.6 - 1.013 * 10 ≈ 6.47

Therefore, the estimated equation for these data is:

Y = 6.47 + 1.013x

b. Use the estimated regression equation to predict the value of y when x = 6.

To predict the value of y when x = 6, substitute x = 6 into the estimated equation:

y = 6.47 + 1.013 * 6

y ≈ 6.47 + 6.078

y ≈ 12.55

Thus, when x = 6, the estimated value of y is approximately 12.55.

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Answer:

The difference between the Ranges in the dot plots is 2.

I've included a figure with the two-dot plots explained for easier comprehension.

The value on the far left of the numbered line that contains at least one point is the minimum value for students in Class A, and the maximum value is three (the value to the extreme right of the numbered line that contains, at least, one point).

Range = 3 - 0 = 3

The value to the far left of the numbered line that has at least one point is the minimum value for students in Class B, and the maximum value is 5. (the value to the extreme right of the numbered line that contains, at least, one point).

Range = 5 - 0 = 5

The dot plots' range differences are 5 - 3 = 2, which is a difference of two.

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Using the properties of similar triangles and ratio and proportion we get the vale of x as 2.8 units.

In the given figure the triangle ΔKFG and ΔFJH

KG is parallel to JH

Hence ΔKFG is similar to ΔFJH

Now using the property of similarity and proportion we can say that:

FG/FH = KF/JF

putting the values in the above proportion we get:

7 /(7+x) = 5/ 7

or, 49 = 35 +5 x

or, 14 = 5x

or, x =14/5

or, x = 2.8

The majority of ratio and percentage explanations involve using fractions.

A proportion states that two variables are equal, whereas a ratio is a fraction that is written as a:b. The two ratios given are equal to one another, as demonstrated by the proportional equation.

Hence the value of x is 2.8 units.

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The problem describes a scenario in which two objects, A and B, start moving towards each other from different locations and speeds. Object A starts from point A, which is 60 miles away from object B, at a speed of 20 mph, while object B starts from point B at a speed of 25 mph.

To solve this problem, we can use the formula Distance = Speed x Time. We know that the total distance between A and B is 60 miles and we want to find the time at which they meet. Let's call that time "t". Let's also assume that they meet at some point "x" miles away from A. Then, the distance that A travels is 60 - x and the distance that B travels is x. Using the formula, we can set up an equation:

Distance A + Distance B = Total Distance

(60 - x) + x = 60

Simplifying this equation, we get:

60 - x + x = 60

60 = 60

This equation is always true, so it doesn't give us any information about when A and B will meet. However, we can use the formula Distance = Speed x Time to set up another equation that relates the distance and speeds of A and B to the time they travel before meeting:

Distance A = Speed A x Time

Distance B = Speed B x Time

Substituting the distances and speeds we know, we get:

(60 - x) = 20t

x = 25t

We can use either equation to solve for t, but let's use the second equation. Substituting x = 25t, we get:

(60 - 25t) = 20t

Simplifying and solving for t, we get:

60 = 45t

t = 4/3

Therefore, A and B will meet after traveling for 4/3 hours, or 1 hour and 20 minutes.

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Step-by-step explanation:

Q.1

6×sqrt(27) + 11×sqrt(75) =

= 6×sqrt(3×9) + 11×sqrt(3×25) =

= 3×6×sqrt(3) + 5×11×sqrt(3) =

= 18×sqrt(3) + 55×sqrt(3) = 73×sqrt(3)

Q.2

53×sqrt(5) × (-103×sqrt(50)) =

= 53×-103 × sqrt(5)×sqrt(50) =

= -5459 × sqrt(5×50) = -5459 × sqrt(250) =

= -5459 × sqrt(10×25) = -5459 × 5×sqrt(10) =

= -27,295 × sqrt(10)

Q.3

1/4 + 1/2 rational (as both terms are rational)

sqrt3 + 4 irrational (as sqrt(3) is not rational)

sqrt4 + 7 rational (sqrt(4) = 2, 2+7 = 9)

2 x sqrt9 rational (sqrt(9) = 3, 2×3 = 6)

7 x sqrt6 irrational (sqrt(6) is not rational)

4x2sqrt3 irrational (sqrt(3) is not rational)

3. 7 x (1/3) rational (all terms are rational)

7 x sqrt81 rational (sqrt(81) = 9, 7×9 = 63)

The system of inequality y < 4x - 2 is represented by option B

An inequality graph represents the graphical representation of an inequality on a coordinate plane.

It visually represents the set of points that satisfy the given inequality. In the graph, the shaded region indicates the solution set of the inequality.

In the equation we watch out for dotted lines which is used to represent a less than of greater than without "equal to"

The graph is attached

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Answer: The man was worse off than in 2005

Step-by-step explanation:

Assume the man's salary in 2005 was $4,500.

In 2006 therefore, his salary goes to:

= 4,500 * (1 + 10%)

= $4,950

In 2007, this drops by 10%:

= 4,950 * ( 1 - 10%)

= $4,455

The man was worse off than in 2005 because the 10% reduction was based on the larger 2006 salary but the 10% increase was based on the smaller 2005 salary.

The specific name of the quadrilateral is kite

The measures of the missing angles are 75 degrees each

To determine the measure of the angle, we need to know the different properties of a kite.

The properties of a kite includes;

Since the adjacent angles are equal, we have that;

105+ x = 180

collect the like terms, we have;

x = 180 - 105

x = 75 degrees

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The quadrilateral is a kite and the missing angles are 105° and 45°

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

A kite has a pair of equal angle and the diagonals of a kite meets at 90°.

In a kite , there are two pairs of congruent or equal sides.

This means that the missing angles are

The opposite angle to 105 is also 105°

The fourth angle is calculated as;

105+105+105+x = 360

= 315 +x = 360

x = 360- 315

x = 45°

Therefore the quadrilateral is a kite and the missing angles are 105° and 45°

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The most appropriate choice for percentage will be given by-

14 categories can be carried

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Total area of selling space = \(2500 ft^2\)

Percentage of space used for isles = \(30\) %

Area of space used for isles = \(\frac{30}{100} \times 2500\)

                                               = \(750 ft^2\)

Area of space left = \(2500 - 750\)

                              = \(1750 ft^2\)

Area of space reserved for each category =  \(125 ft^2\)

No of categories = \(\frac{1750}{125}\)

                            = \(14\)

14 categories can be carried

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A discrete data random variable is a random variable that can only take on a finite or countable number of values.

Out of the options given, the number of cars finished in a factory each day is a discrete data random variable. This is because the number of cars finished can only take on a finite number of values, such as 0, 1, 2, 3, and so on. It cannot take on any value between these integers, and there are only a finite number of possible values.

In contrast, a person's height and weight are continuous data random variables, as they can take on any value within a certain range (for example, a person's height can take on any value between 4 feet and 7 feet).

Similarly, the volume of water in a swimming pool can take on any value within a certain range, and is also a continuous data random variable.

Therefore, the only discrete data random variable out of the options given is the number of cars finished in a factory each day.

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Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the rules of logarithms

logx + logy = log(xy)

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

Given

\(log_{x}\) 5 + \(log_{x}\) 12 = 7 , then

\(log_{x}\) (5 × 12) = 7 , that is

\(log_{x}\) 60 = 7 , thus

\(x^{7}\) = 60 → B

Answer:

Step-by-step explanation:

D the situation shows correlation with causation

Answer:

the situation shows correlation with caution

Answer:

361/1000

Step-by-step explanation:

this should be the answer

Use the limit definition to find the slope of the tangent line to the graph of f at the given point. f(x) = 14 − x2, (3, 5)

The slope of the tangent line to the graph of f at (3, 5) is -6.

The slope of the tangent line to the graph of f at (3, 5) can be found using the limit definition of the slope. The slope of the tangent line can be calculated as the limit of the average rate of change of the function f(x) between two points as the distance between the points approaches zero. The formula is given by: lim _(h → 0) [f(x + h) - f(x)] / h

where h is the change in x, which is the difference between the x-value of the point in question and the x-value of another point on the tangent line. The given function is f(x) = 14 - x². To find the slope of the tangent line at x = 3, we need to calculate the limit of the average rate of change of f(x) as x approaches 3.

Using the formula,

lim_(h → 0) [f(x + h) - f(x)] / h

= lim_(h → 0) [(14 - (x + h)²) - (14 - x²)] / h

= lim_(h → 0) [14 - x² - 2xh - h² - 14 + x²] / h

= lim_(h → 0) [-2xh - h²] / h

= lim_(h → 0) [-h(2x + h)] / h

= lim_(h → 0) [-2x - h] = -2x

When x = 3, the slope of the tangent line is -2(3) = -6.

Therefore, the slope of the tangent line to the graph of f at (3, 5) is -6.

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Answer: In a parallelogram, opposite angles are congruent, which means they have the same measure. So, if angle g has a measure of (4x - 16)°, then angle h also has a measure of (4x - 16)°. Therefore, the measure of angle h is (4x - 16)°.

So, the answer is 88°.

Step-by-step explanation:

Answer:

6a + (6 x 3) = 60

or

6a + 18 = 60

Step-by-step explanation:

You have 6 students who are assigned an unknown amount of problems. We can write it as 6x. Then each is given 3 more problems, so now we have 6x + (6 x 3). We also know that in all they have 60 problems.

Therefore, the equation is:

6x + 18 = 60

Then just solve

6x + 18 = 60

     - 18   -18

6x = 42

x = 7

The solution to the equation is - 6  

The mathematical statements which are formed by numbers and variables are known as equations. To solve an equation we can add or subtract the same integer from both sides.

Similarly, we can multiply or divide by the same integer on both sides. Here adding or subtracting, multiplying, or dividing doesn't change the condition of the equation.

Here we have

15 (negative 42 x + 40) = 15 (negative 8 x + 244)  

This can rewrite as follows

=> 15 (-42x + 40) = 15 (-8x + 244)

Divide by 15 into both sides

=> 15 (-42x + 40)/15 = 15 (-8x + 244)/15  

=>  (- 42x + 40) = ( -8x + 244)  

Add 8x on both sides

=>  - 42x + 40 + 8x =  -8x + 244 + 8x

=>  - 34x + 40 = 244

Subtract 40 from both sides

=> - 34x + 40 - 40 = 244 - 40

=> - 34x = 204

Divide by - 34 on both sides

=> - 34x/-34 = 204/-34

=>  x = - 6

Hence,

The solution to the equation is - 6  

Substitute x = - 6 in 15 (-42x + 40) = 15 (-8x + 244)  

=>  (-42(-6) + 40) =  (-8(-6) + 244)  

=>  252 + 40 = 292  [ Which is true ]

Hence, It is verified that x = -6

Hence,

The solution to the equation is - 6  

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Answer:

Paulina is reading a book with 677pages total. If she has already read 345 and plans to read 23 pages a day, how many days, x, will she nees to read at that pace until she finishes the entire book?

Step-by-step explanation:

\(345 + 23x = 677\)

23x=677-345

x=677-345/23

x=332/23

x= 14.43 days

The integral \(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx\) when evaluated is 72π

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

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx\)

Expand

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = \int\limits^6_{-6} {[x\sqrt{36 - x^2} + 4\sqrt{36 - x^2}}] \, dx\)

So, we have

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = \int\limits^6_{-6} {[x\sqrt{36 - x^2} dx+ 4\int\limits^6_{-6}\sqrt{36 - x^2}}] \, dx\)

Let u = 36 - x² and du = -2x

So, we have:

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = [-\frac{(36 - x^2)^\frac 32}{3}]|\limits^6_{-6} + 4\int\limits^6_{-6}\sqrt{36 - x^2}}] \, dx\)

Next, we have

x = 6sin(u), where \(u = \sin^{-1}(\frac x6})\)

This gives

dx = 6cos(u)du

So, we have

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = [-\frac{(36 - x^2)^\frac 32}{3}]|\limits^6_{-6} + 4\int\limits^6_{-6} 6\cos(u) \sqrt{36 - 36\sin^2(u)}}] \, du\)

Factor out √36

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = [-\frac{(36 - x^2)^\frac 32}{3}]|\limits^6_{-6} + 4\int\limits^6_{-6} 6\cos(u) * 6\sqrt{1 - \sin^2(u)}}] \, du\)

Rewrite as

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = [-\frac{(36 - x^2)^\frac 32}{3}]|\limits^6_{-6} + 4\int\limits^6_{-6} 6\cos(u) * 6\sqrt{\cos^2(u)}}] \, du\)

So, we have

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = [-\frac{(36 - x^2)^\frac 32}{3}]|\limits^6_{-6} + 4\int\limits^6_{-6} 6\cos(u) * 6\cos(u)}] \, du\)

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = [-\frac{(36 - x^2)^\frac 32}{3}]|\limits^6_{-6} + 4\int\limits^6_{-6} 36\cos^2(u)}] \, du\)

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = [-\frac{(36 - x^2)^\frac 32}{3}]|\limits^6_{-6} + 144\int\limits^6_{-6} \cos^2(u)} \, du\)

When integrated, we have

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = -\frac{(36 - x^2)^\frac23}{3} + 2x\sqrt{36 - x^2} + 72\sin^{-1}(\frac{x}{6})\)

Substitute in the boundaries and evaluate

So, we have

\(\int\limits^6_{-6} {(x + 4)\sqrt{36 - x^2}} \, dx = 72\pi\)

Hence, the solution is 72π

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To find the slope of the tangent line to the polar curve r = 6cosθ at the point (6 / √2 , π/4), we need to convert the polar coordinates to Cartesian coordinates and then differentiate to find the slope.

Given:

r = 6cosθ

Point in polar coordinates: (r, θ) = (6 / √2, π/4)

Converting to Cartesian coordinates:

x = r * cos(θ)

y = r * sin(θ)

Substituting the given values:

x = (6 / √2) * cos(π/4)

y = (6 / √2) * sin(π/4)

Simplifying:

x = 6 / 2 = 3

y = 6 / 2 = 3

So, the Cartesian coordinates of the point are (3, 3).

To find the slope of the tangent line, we need to differentiate the polar equation with respect to θ and then evaluate it at the given point.

Differentiating r = 6cosθ with respect to θ:

dr/dθ = -6sinθ

Now, evaluate dr/dθ at θ = π/4:

dr/dθ = -6sin(π/4) = -6 / √2 = -3√2

The slope of the tangent line is equal to the derivative dr/dθ evaluated at the given point, which is -3√2.

Therefore, the slope of the tangent line to the polar curve r = 6cosθ at the point (6 / √2, π/4) is -3√2.

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The slope of the tangent line to the polar curve r = 6cosθ at the point (6/√2, π/4) can be summarized as follows:

The slope of the tangent line is √2/2.

In the explanation, we can provide the steps to find the slope of the tangent line:

To find the slope of the tangent line to a polar curve, we need to express the curve in polar coordinates. Using the conversion formulas r = √(x^2 + y^2) and θ = arctan(y/x), we can rewrite the given polar curve r = 6cosθ as √(x^2 + y^2) = 6cos(arctan(y/x)).

Simplifying this equation, we get x^2 + y^2 = 6xcos(arctan(y/x)). Substituting the given point (6/√2, π/4) into this equation, we can find the corresponding values of x and y. Plugging these values into the equation, we obtain (6/√2)^2 + y^2 = 6(6/√2)cos(arctan(y/(6/√2))). Simplifying further, we have 18 + y^2 = 18cos(arctan(y/(6/√2))). By solving this equation, we find that y = 3. Finally, to calculate the slope of the tangent line at the point (6/√2, π/4), we take the derivative of the Cartesian equation and substitute the values of x and y. The resulting slope is √2/2, which represents the slope of the tangent line at the given point.

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Answer:

plug in the solutions into both equations for all three and you'll get the answer they have to work for both for it to be a solution when u plug it in just solve normally

Answer:

x = 85°

y = 45°

Step-by-step explanation:

For x, a line measures 180°, so subtract 95° from 180° to get 85°.

For y, all the angles in a triangle measure to 180°, and since we know x, add it to 50° and subtract it from 180°. 85° + 50° = 135°, and 180° - 135° = 45°

Answer:

x = 85

y = 45

Step-by-step explanation:

for x, angles on a straight line add up to 180 so 95 + x = 180 then evaluate for x

for y, angle in a triangle add up to 180 so 50+85 (as evaluated for x) +y= 180 and evaluate for y

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Given that ▱FGHI and ▱TUVW are similar figures, the scale factor from ▱TUVW to ▱FGHI  is 8/9.

The value of x is 32.

Therefore, the scale factor from TUVW to FGHI would be:

√64/√81 = 8/9

Find the value of x:

x/36 = 8/9

x = 32

Thus, given that ▱FGHI and ▱TUVW are similar figures, the scale factor from ▱TUVW to ▱FGHI  is 8/9.

The value of x is 32.

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Answer:

$4/baseball .

Step-by-step explanation:

Here we are given that $24 is paid for 6 baseballs and we need to find out the unit rate of the baseballs . This can be found by using the Unitary Method , as ;

Rate of 6 baseballs is $24

Rate of 1 baseball will be $24/6 = $4

Answer:

The area of the shaded part of the rectangle is 28 m².

Step-by-step explanation:

The area of the shaded part of the rectangle can be calculated by subtracting the areas of the two unshaded triangles from the area of the rectangle.

The area of a rectangle is the product of its width and length.

From inspection of the given diagram, the width of the rectangle is 4 m and the length is 14 m. Therefore, the area of the rectangle is:

\(\begin{aligned}\textsf{Area of the rectangle}&=4\cdot 14\\&=56\; \sf m^2\end{aligned}\)

The area of a triangle is half the product of its base and height.

The bases of the two unshaded triangles are congruent (denoted by the double tick marks) and are 7 m.

The height of both triangles is the height of the rectangle, 4 m.

Therefore, the two triangles have the same area.

\(\begin{aligned}\textsf{Area of 2 unshaded triangles}&=2 \cdot \dfrac{1}{2} \cdot 7 \cdot 4\\&=1 \cdot 7 \cdot 4\\&=7 \cdot 4\\&=28\; \sf m^2\end{aligned}\)

To calculate the area of the shaded part of the rectangle, subtract the area of the 2 unshaded triangles from the area of the rectangle:

\(\begin{aligned}\textsf{Area of the shaded part}&=\sf Area_{rectangle}-Area_{triangles}\\&=56-28\\&=28\; \sf m^2\end{aligned}\)

Therefore, the area of the shaded part of the rectangle is 28 m².