Calculate the slope of the line shown on the graph at right?

Answer:

x = 7, x = 5

Step-by-step explanation:

\(\frac{3x+3}{8}\) = 2x - 11 ( multiply both sides by 8 to clear the fraction )

3x + 3 = 16x - 88 ( subtract 3x from both sides )

3 = 13x - 88 ( add 88 to both sides )

91 = 13x ( divide both sides by 13 )

7 = x

--------------------------------------------------------------

\(\frac{4x-6}{7}\) = 2 ( multiply both sides by 7 )

4x - 6 = 14 ( add 6 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

3x + 3 / 8 = 2x - 11

Multiply both sides by 8

8 × ( 3x + 3 / 8 ) = 8 × ( 2x - 11 )

3x + 3 = 16x - 88

Add both sides 88

3x + 3 + 88 = 16x - 88 + 88

3x + 91 = 16x

Subtract both sides 3x

3x - 3x + 91 = 16x - 3x

91 = 13x

Divide both sides by 13

91 ÷ 13 = 13x ÷ 13

7 = x

x = 7

_________________________________

4x - 6 / 7 = 2

Multiply both sides by 7

( 4x - 6 / 7 ) × 7 = 2 × 7

4x - 6 = 14

Add both sides 6

4x - 6 + 6 = 14 + 6

4x = 20

Divide both sides by 4

4x ÷ 4 = 20 ÷ 4

x = 5

negative; The inverse function will have a slope that is the negative reciprocal of the original function.

A linear function is a function that can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. A linear function with a negative slope will have an inverse function. The inverse function will have a slope that is the negative reciprocal of the original function. For example, if the original linear function has a slope of -2, the inverse function will have a slope of 1/2. The inverse function will also have a y-intercept that is the negative reciprocal of the original function's y-intercept. The inverse function will be of the same form, y = mx + b, but with a different m and b than the original function. The inverse function will have the same x-intercept as the original function. Knowing the slope and y-intercept of the original linear function allows us to calculate the slope and y-intercept of the inverse function.

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Answer:

X=437 over 100

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

It is simple

As the slope is represented by m,

And the equation of line is

y=mx+c

Therefore, here m=17, which is the slope of the given eq.

The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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If the area of rectangle abcd is 16in² and the area of the rectangle a’b’c’d’ is 64in², the scale factor used to dilate the rectangle was 2.

When a rectangle is dilated, its dimensions are multiplied by a common factor known as the scale factor. The scale factor is the ratio of the corresponding sides of the original rectangle and the dilated rectangle.

Let the scale factor be represented by k. The area of the original rectangle is 16 in², so we can write:

length x width = 16

Let L and W represent the length and width of the original rectangle, respectively. Therefore, we have:

LW = 16

After dilation, the area of the new rectangle is 64 in². The length and width of the new rectangle are kL and kW, respectively. Therefore, we can write:

(kL)(kW) = 64

Simplifying the above equation, we get:

k²LW = 64

Substituting the value of LW from the first equation, we get:

k²(16) = 64

Solving for k, we get:

k = √4 = 2

This means that the length and width of the new rectangle are twice the length and width of the original rectangle.

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Answer:

Step-by-step explanation:

8*2= 2>answer

Answer:

see image

Step-by-step explanation:

The Venn diagram will have two intersecting circles and space outside of both circles.

Let one circle be France-travellers. The other Germany. The intersection is both. Outside both circles are the stay-at-home people.

Fill in the intersection first. Subtract 12 - 5 to find out how many to put in France-only. Subtract 9-5 to find out how many go in Germany only.

Put the 6 stay-at-homers outside both circles. See image.

The lengths of the ladders can be found by solving the equations x^2 + y^2 = 24^2 and (x+1)^2 + (y+3)^2 = 24^2 using the Pythagorean theorem.

To find the lengths of the ladders, let's break down the information given in the problem:
1. Both ladders are placed against a vertical wall.
2. The upper end of each ladder is 24 feet above the ground.
3. One ladder is one foot longer than the other.
4. The lower end of the longer ladder is 3 feet farther from the wall than the lower end of the other ladder.

Let's assign variables to the lengths of the ladders. Let's say the length of the shorter ladder is "x" feet. Since the longer ladder is one foot longer, its length would be "x+1" feet.

Now, let's consider the distance of the lower ends of the ladders from the wall. The lower end of the shorter ladder is closer to the wall, so we'll consider that distance as "y" feet. Since the lower end of the longer ladder is 3 feet farther, its distance from the wall would be "y+3" feet.
To solve for the lengths of the ladders, we can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse (the length of a ladder) is equal to the sum of the squares of the other two sides.

For the shorter ladder:
x^2 + y^2 = 24^2
For the longer ladder:
(x+1)^2 + (y+3)^2 = 24^2
Simplifying these equations will give us the lengths of the ladders.

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She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

To make the recipe,

3/4 quart of lemonade and 3 cups of cranberry juice

The ratio of cranberry juice to a quart of lemonade

⇒ 3/(3/4) = 4

To make the same recipe with 1(2/5) quarts of lemonade the ratio of cranberry juice to a quart of lemonade must be maintained.

So,

4 = cranberry juice / 1(2/5)

(5/7) × cranberry juice = 4

Cranberry juice = 28/5 ⇒ 5 (3/5).

Hence "She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade".

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Answer:

It will take about half an hour more for maria to finish his/her project than Juan.

Step-by-step explanation:

9/10 > 2/6

=> 54/60 > 20/60

=> 34/60

Therefore, it will take about half an hour more for maria to finish his/her project than Juan.

Hoped this helped.

Answer:

50min estimate 3/4h

Step-by-step explanation:

find 9/10h

60 : 10 * 9 = 54 min

find 2/6h

60 : 6 * 2 = 4 min

54 - 4 = 50 min

The derivative of the given integral is: f'(x) = 2x(ex⁶)

First we are given a definite integral going from a constant to a function of x. The function is:

f(x)= (2, x²) ∫ex³dx  

g(x) = (2,x) ∫ex³dx (same except that the bounds are now from a constant to x which allows the first fundamental theorem to be used)

Defining a similar function were the upper bound is just x then allows us to say f(x) = g(x²) which allows us to say that:

f'(x) = g'(x²) = g'(x²) * 2x (by the chain rule) and g(x) is written so that we can easily take its derivative using the theorem that the derivative of an integral from a constant to x is equal the the inside of the integral

g'(x) = ex³

g'(x²) = e(x²)³

= ex⁶

We know f'(x) = g'(x²)*2x

Thus:

f'(x) = 2x(ex⁶)

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The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4.

A box plot, also known as a box-and-whisker plot, is a graphical representation of numerical data that displays the distribution of a dataset. It provides a visual summary of the minimum, first quartile, median, third quartile, and maximum values, as well as any outliers that may be present.

To construct a box plot from the given data (diameters of cans in an assembly line: 5.7, 5.6, 5.1, 5.4, 5.2, 5.6, 5.7, 5.3, 5.8, 5.2), follow these steps:

1. Sort the data in ascending order: 5.1, 5.2, 5.2, 5.3, 5.4, 5.6, 5.6, 5.7, 5.7, 5.8.

2. Find the median (middle value) of the dataset, which is 5.4.

3. Determine the first quartile (Q1), which is the median of the lower half of the data. In this case, it is the median of the numbers below 5.4: 5.2.

4. Find the third quartile (Q3), which is the median of the upper half of the data. In this case, it is the median of the numbers above 5.4: 5.7.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 5.7 - 5.2 = 0.5.

6. Identify any outliers in the dataset. Outliers are values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. In this case, there are no outliers.

7. Construct the box plot using a number line. Draw a box from Q1 to Q3, with a line inside representing the median. Add whiskers (lines) extending from the box to the minimum value (5.1) and the maximum value (5.8).

The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4. The whiskers would extend from 5.1 to 5.8. This visual representation provides an overview of the distribution and key statistical measures of the diameters of cans in the assembly line.

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The quadratic regression equation that best fits the data set is \(y = -1.62x^2 + 34.89x - 5.57.\)

To determine which quadratic regression equation best fits the data set, we can use a graphing calculator or other technology to perform a quadratic regression analysis on the given data.

Using a graphing calculator, we can enter the data set as follows:

Press the STAT button.

Press ENTER to select 1:Edit.

Enter the x-values in L1 and the y-values in L2.

Press STAT again and choose CALC.

Choose option 5:QuadReg.

Press ENTER to select the regression equation.

The calculator will display the quadratic regression equation in the form y = \(ax^2 + bx + c.\)

After performing the quadratic regression analysis, we get the following equation:

y = \(-1.62x^2 + 34.89x - 5.57\)

Therefore, the quadratic regression equation that best fits the data set is \(y = -1.62x^2 + 34.89x - 5.57.\)

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Full Question: Use a graphing calculator or other technology to answer the question. 4.5 122 Which quadratic regression equation best fits the data set? 6.2 145 7.0 155 8.9 189 O Û = 1.62x2 + 34.89x +5.57 10.1 171 © = -5.5722 + 34.89x – 1.62 14.8 170 O Û = -1.62x2 + 34.89x 15.7 133 © y = -1.62x2 + 34.893 – 5.57

Answer:

I think it's 3,600

Step-by-step explanation:

multiplication

Answer:

Ez *puts link epicly* B^)

Answer: 5.628975

Step-by-step explanation:

Add everything up to get $68.23

Answer:

9:50

Step-by-step explanation:

To get the ratio, we can just simplify a fraction down to 1.

Since there's 18 dimes, and 100 coins in total, we'll start with the fraction

18/100

Put 18/100 in simplest form

9/50

Then Turn the fraction into a ratio

9/50 -> 9:50

For every 9 dimes there's 50 coins.

I hope this helped.

(Simplified to 1, is 1/5.56 or 1:5.56)

Answer:

3

Step-by-step explanation:

First, we can start by multiplying the equation 2x - 3y = 12 by six to see where that gets us,

2x - 3y = 12 --> 12x - 18y = 72

12x - 18y = 72

5x + 6y = 18 (other equation)

We can notice that eliminating the y term would be the easiest to go about, so we want to find the number that we can multiply 6 by to get 18. That number is 3, so the factor is 3.

You can use the fact that non of 2 times 6 doesn't include 5 as factor.

There are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.

Those values of the factor are \(3\)   (for elimination of y) or \(-\dfrac{12}{5}\) (for elimination of x)

Our aim in doing so is to make the coefficients of same variable equal and with opposite signs so that when we add the equations, that variable gets eliminated because of coefficient becoming zero.

For example, take the given equations and the factor by which Yumiko multiplied the second equation.

5x + 6y = 18

2x – 3y = 12 => 12x - 18y = 72   (since she multiplied this with 6)

Let she multiply the first equation with factor "p"

Then we will have the system as;

\(p \times 5x + p \times 6y = p \times 18\\12x - 18y = 72\)

Adding both the equations, we get:

\((5p + 12)x + (6p - 18)y = 18p + 72\)

Since there are two variables and since any one of them can be eliminated depending on the value of p, thus we have two cases:

Then we have coefficient of x = 0

or

\(5p + 12 = 0\\5p = -12\\p = -\dfrac{12}{5}\\\)

Then we have coefficient of y = 0

or

\(6p - 18 = 0\\6p = 18\\p = \dfrac{18}{6} = 3\)

Thus, there are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.

Those values of the factor are \(3\)  or \(-\dfrac{12}{5}\)

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To prove that for every integer n, n² - 2 is not divisible by 4, a direct proof will be used. To prove the statement, we will employ a direct proof, showing that for any arbitrary integer n, n² - 2 cannot be divisible by 4.

Assume that n is an arbitrary integer. We will consider two cases: when n is even and when n is odd.

Case 1: n is even (n = 2k, where k is an integer)

In this case, n² is also even since the square of an even number is even. Therefore, n² - 2 = 2m, where m is an integer. However, 2m is divisible by 2 but not by 4, so n² - 2 is not divisible by 4.

Case 2: n is odd (n = 2k + 1, where k is an integer)

In this case, n² is odd since the square of an odd number is odd. Therefore, n² - 2 = 2m + 1 - 2 = 2m - 1, where m is an integer. 2m - 1 is not divisible by 4 as it leaves a remainder of either 1 or 3 when divided by 4.

In both cases, we have shown that n² - 2 is not divisible by 4. Since these cases cover all possible integers, the statement holds true for all values of n.

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To prove that for every integer n, n² - 2 is not divisible by 4, a direct proof will be used. To prove the statement, we will employ a direct proof, showing that for any arbitrary integer n, n² - 2 cannot be divisible by 4.

Assume that n is an arbitrary integer. We will consider two cases: when n is even and when n is odd.

Case 1: n is even (n = 2k, where k is an integer)

In this case, n² is also even since the square of an even number is even. Therefore, n² - 2 = 2m, where m is an integer. However, 2m is divisible by 2 but not by 4, so n² - 2 is not divisible by 4.

Case 2: n is odd (n = 2k + 1, where k is an integer)

In this case, n² is odd since the square of an odd number is odd. Therefore, n² - 2 = 2m + 1 - 2 = 2m - 1, where m is an integer. 2m - 1 is not divisible by 4 as it leaves a remainder of either 1 or 3 when divided by 4.

In both cases, we have shown that n² - 2 is not divisible by 4. Since these cases cover all possible integers, the statement holds true for all values of n.

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The coffee costs per pound which cost more between Carry's and Ken's is Ken's coffee at $11.25 per pound

Given:

Carry:

Cost of coffee = $37.10

Number of pounds = 3 1/2 pounds

Unit cost per pound = Cost of coffee / Number of pounds

= 37.10 / 3½

= 37.10 ÷ 7/2

= 37.10 ÷ 3.5

= $10.6 per pound

Ken:

Cost of coffee = $60

Number of pounds = 5 1/3 pounds

Unit cost per pound = Cost of coffee / Number of pounds

= 60 ÷ 5 1/3

= 60 ÷ 16/3

= 60 × 3/16

= (60×3)/16

= 180/16

= $11.25 per pound

Therefore, the difference per pound in the cost is

Ken - Carry

= $11.25 : $10.6

= $0.65

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The only possible answer is that Amar's speed is (10/7)th of Akbar's speed, which is option d.

Let's assume Amar's speed as 'a', Antony's speed as 'x', and Akbar's speed as 'y'.

According to the given information:

Antony completes the race 14m ahead of Amar, so we have: x = a + 14.

Akbar finishes 20m ahead of Antony, so we have: y = x + 20.

Akbar finishes 32m ahead of Amar, so we have: y = a + 32.

We can substitute the value of x from the first equation into the second equation: y = (a + 14) + 20 = a + 34.

Equating the expressions for y from the second and third equations, we have: a + 34 = a + 32.

Simplifying, we get: 34 = 32, which is not possible.

Hence, the only possible answer is that Amar's speed is (10/7)th of Akbar's speed, which is option d.

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Answer:

90,000

Step-by-step explanation:

First you want to know how much money Angel plans to earn so you multiply 10,000 * 45 and that is 450,000. Then you find the 20% discount that Walmart negotiated so you turn 20% into a decimal. 20% as a decimal is 0.20 or 0.2. You then multiply 0.2 * 450,000 to get 90,000 which is the amount Walmart is discounting off. And if you need to find how much Angel is getting after the discount, subtract 90,000 from 450,000! :D I hope this helps!!

Answer:

1. $27.84

Step-by-step explanation:

Question 1

Trail mix is 2.32 pounds and it costs 3.50 dollars per pound. Hence the total cost for Trail mix is 2.32 X 3.50= $ 8.12

He bought twice as many ponds of dried fruit.....2.32 X 2 = 4.64 pounds

the cost of dried fruit will be 4.64 X $ 4.25 = $19.72

The total cost is therefore $8.12 + $19.72 = $27.84

Question 2

Yes, she bought enough dried nuts and mixed fruits for the party.

a. You identify the things she bought

b. You find out whether the money she paid was enough for the quantity she was to buy

c. You now calculate to see if it was enough. that is

she wants a total of 6 pounds of dried fruit and mixed nuts.

she pays $21.60 for mixed nuts and and it is sold at $6.75 per pound

21.6÷ 6.75 = 3.2 pounds of mixed nuts

she pays $11.90 for dried fruit and it is sold at $4.25 per pound

$11.90÷$4.25 = 2.8 pounds

when we add the total quantity of items she bought: 3.2 + 2.8 = 6 pounds. thus she bought enough.

Answer:

x=2 or x=−6

Step-by-step explanation:

The value of x and y in the triangle are calculated to be

The point o f intersection of the perpendicular lines is called the circumcenter.

Applying the property of the circumcenter

4x - 1 = 6x - 5

4x - 6x = -5 + 1

-2x = -4

x = 2

plugging x into 6x - 5

6 * 2 - 5 = 7

sin 33 = 7 / hypotenuse

hypotenuse = 7 / sin 33 = 12.85

also sin (4y + 1) = 7 / 12.85

4y + 1 = arc sin (7/12.85)

4y + 1 = 33

4y = 32

y = 8

Hence x is 2 and y is 8

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-4

Step-by-step explanation:x=5-3+6/1x7

Answer: x = > 6

explanation:

Hope this helps.?

We can determine whether two lines are parallel, perpendicular, or neither using the slopes of the lines.

Two lines are parallel when both of the lines have the same slope, for example:

Two lines are perpendicular to each other when the product between the lines is equal to -1, for example:

if none of the conditions stated before the lines are neither parallel nor perpendicular.

In the given exercise:

both lines have different slopes, then they are not parallel.

Find the product between the slopes,

Answer:

The lines shown are perpendicular to each other because the product between the slopes is equal to -1.

Answer:

w=7

Step-by-step explanation:

A parallelogram is defined as a four-sided plane rectilinear figure with opposite sides parallel. This means that GH and FE must be equivalent, and HE and GF must be equivalent. Now, we just use those equations to solve.
16w-63=7w
9w-63=0

9w=63

w=7!!!
and we can double check.

16w-81=15w-74
16w=15w+7
w=7