What is the slope of the line passing through the points (1, 7) and (4, -1)? Leave your answer as a fraction

The average rate of change for the interval from x = 7 to x = 8 will be 15. Then the correct option is D.

We have,

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

Average rate = (y₂ - y₁) / (x₂ - x₁)

The quadratic equation with the vertex is given as

y = (x -  0)² - 1

y = x² - 1

Then the average rate of change for the interval from x = 7 to x = 8 will be

Average rate = [y(8) - y(7)] / (8 -7)

Then we have

Average rate = (64 -1 - 49 + 1) / 1

Average rate = 15

Thus, the correct option is D.

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The area of the shaded region round your answer to the nearest hundredth is 301.59 square units.

We are given that;

The radius of outer circle is 16 and inner circle is 8

Now,

we need to find the area of the outer circle. The formula for the area of a circle is A = pir2, where r is the radius. The radius of the outer circle is 16, so the area is A = pi162 = 256pi.

Next, we need to find the area of the inner circle. The radius of the inner circle is 8, so the area is A = pi*82 = 64pi.

Then, we need to subtract the area of the inner circle from the area of the outer circle. This gives us 256pi - 64pi = 192pi.

Finally, we need to divide the result by 2, since the shaded region is half of the area between the two circles. This gives us 192pi/2 = 96pi.

The final answer is 96pi square units. Rounding to the nearest hundredth, we get 301.59 square units.

Therefore, by the area answer will be 301.59 square units.

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Step 01:

Data

total math problems = 60

problems solved = 1/4

problems

Step 02:

The number of ways of 3 volumes chosen at random is 455.

The number of ways that will include volume 1 and volume 2 is 13 and

The number of ways that will include volume 1 but not volume 2 is 156

Permutation and combination

In Mathematics, Permutation and combination are the ways of representing a group of objects by selecting from a set and forming subsets. These define the different types of ways to arrange a certain group of data.

When we select objects from a group, it is said to be permutations, whereas the combination is a way of selecting items, here the order of selection does not matter.

The formula for the combination of x things from a set of n things without replacement is given by

Here we have,

Number of volumes of  an encyclopedia = 15

Number volumes were chosen at a time = 3

From above formula

The number of ways of 3 volumes is chosen at random is

¹⁵C₃ = 15!/3!(15 - 3)!  

= 15!/3!(12)!  

= 15 × 14 × 13 × 12! / 6 (12!)

= 455  

(b) Including volume 1 and volume 2

To Include volume 1 and volume 2 in the set, first, we choose volume 1 and volume 2, and then we must choose the 3rd volume from the remaining volumes from 3 to 15 volumes [total 13 volumes].

Therefore the number of ways that will include volume 1 and volume 2

= 1 × 1 × 13 = 13  

(c) Including volume 1 but not volume 2

Here we are including volume 1 but not volume 2, for that in the first place we chose volume 1, for the second and third place we must choose from the remaining volumes 3 to 15 [total 13 volumes except 2 ]

The number of ways that will include volume 1 but not volume 2

= 1 × 13 × 12

= 156

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Can you explain more? if your looking for the slope of both it is 5/9 for the fist one and 2/3 for the second. If your looking for y and x -intercept for the first one x intercepts at (-2,0) and y intercepts at (0, 4/3) and, for the second one x intercepts at ( -13/5, 0) and y intercepts at (0, 13/9)

Answer:

$18.67

Step-by-step explanation:

First, convert the percentage to a decimal.

1.45% = 0.0145

Then, multiply the gross pay by the decimal.

$1287.50 × 0.0145 = $18.67

The Social Security Tax will be $18.67.

the distance from point P = (3, -2) to the line passing through points A = (3, -5) and B = (4, 5) is 3 / √101.

To find the distance from point P = (3, -2) to the line passing through points A = (3, -5) and B = (4, 5), we can use the formula for the distance between a point and a line.

The formula for the distance between a point (x₁, y₁) and a line Ax + By + C = 0 is given by:

distance = |Ax₁ + By₁ + C| / √(A² + B²)

First, let's find the equation of the line passing through points A and B.

The slope of the line can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-5)) / (4 - 3) = 10

Since the line passes through point A (3, -5), the equation of the line can be found using the point-slope form:

y - y₁ = m(x - x₁)

y - (-5) = 10(x - 3)

y + 5 = 10x - 30

10x - y - 35 = 0

Now we have the equation of the line in the form Ax + By + C = 0, where A = 10, B = -1, and C = -35.

Substituting the coordinates of point P (3, -2) into the formula, we can calculate the distance:

distance = |10(3) + (-1)(-2) + (-35)| / √(10² + (-1)²)

distance = |30 + 2 - 35| / √(100 + 1)

distance = |-3| / √101

distance = 3 / √101

Therefore, the distance from point P = (3, -2) to the line passing through points A = (3, -5) and B = (4, 5) is 3 / √101.

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Answer:

Step-by-step explanation:

Answer:

x = 15\(\sqrt{3}\) , y = 15

Step-by-step explanation:

Using the sine and cosine ratios in the right triangle and the exact values

sin60° = \(\frac{\sqrt{3} }{2}\) , cos60° = \(\frac{1}{2}\) , then

sin60° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{30}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2x = 30\(\sqrt{3}\) ( divide both sides by 2 )

x = 15\(\sqrt{3}\)

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

cos60° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{y}{30}\) = \(\frac{1}{2}\) ( cross- multiply )

2y = 30 ( divide both sides by 2 )

y = 15

The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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Answer:

3 Ducks

Step-by-step explanation:

Two ducks are in front of the last duck; the first duck has two

ducks behind; one duck is between the other two

Hence , there are 3 ducks

Hope it is correct

Answer: I think 7

Step-by-step explanation: Sorry if its wrong.

First, we are going to calculate the total distance that Cody runs in a week as:

Because he runs 4 times a week and every time runs 3/6 of a mile.

It means that he runs 2 miles a week

Now, we need to calculate how many times Arianna runs to cover 2 miles.

So, we need to divide 2 by 4/6 of a mile as:

Therefore, she needs to run 3 times a week to cover 2 miles.

Answer: 3 times

The area of rhombus KLMN is 287.3 in²

A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

Given:

Since, the diagonals of a rhombus bisects each other at a right angle,

Let they bisect at O,

so, KM = 2MO = 2KO = 2×11.4 = 22.8 in

Thus, Δ KON is a right triangle,

Using Pythagoras theorem,

KN² = KO² + ON²

ON = √17²-11.4²

ON = 12.611 in

LN = 2×12.611

LN = 25.22 in

Then, Area of a rhombus = 1/2 × diagonal 1 × diagonal 2

Area = 1/2 × 25.22 × 22.8

        = 287.3 in²

Hence, the area of rhombus KLMN is 287.3 in²

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Answer:

\(y=11x-3\)

Step-by-step explanation:

Given ordered pairs:

(1, 8)  (2, 19)  (3, 30)  (4, 41)

As the y is directly proportional to x (y values increase +11 for every +1 increase for the x-values) then the equation will be linear.

Point-slope form of a linear equation:  \(y-y_1=m(x-x_1)\)

(where \(m\) is the slope and \((x_1,y_1)\) is a point on the line)

\(\textsf{slope }m=\dfrac{y_2-y_1}{x_2-x_1}\)

Let:

\(\implies \textsf{slope }m=\dfrac{19-8}{2-1}=11\)

Using point-slope equation with m = 11 and point (1, 8):

      \(y-y_1=m(x-x_1)\)

\(\implies y-8=11(x-1)\)

\(\implies y=11x-3\)

The equation of a line on a point (-2,2) is y = -2x-2. That option A is correct.

Here we have to find the equation of a line.

The given data:

Point = ( -2, 2)

Slope(m) = -2

Equation of a line:

y = mx + c

Now putting the values as

y = 2

x = -2

m = -2

We will get the y-intercept.

So we have:

2 = -2 × -2 + c

c = 2 - 4

  = -2

So, y = -2x -2

Therefore we get the equation of line as y = -2x -2.

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Answer:

Solve each set of parentheses so they equal 0:

(X-2) = 0 add 2 to both sides : x = 2

(X + 7) = 0 subtract 7 from both sides: x = -7

The zeros are 2 and -7

Answer:

Value of x could be = 2 or -7

Step-by-step explanation:

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Answer:

he must run 30 miles to burn 1200 calories

Step-by-step explanation:

8 miles = 320 calories

Answer: A and E

Step-by-step explanation: they both appear to be 3 units tall and 2 units wide. Two objects are congruent if they are similar but in different places or if they have the same ratio 3:2 but at different sizes: like 6:4 for example

Hope this helps! :)

Answer:

1. 12x - 6

2. -2x + 17

Step-by-step explanation:

1.

2.

Answer:

\(\boxed{\sf 12x-6}\)

\(\boxed{\sf -2x+17}\)

Step-by-step explanation:

\(\sf 1)\: 8x - 2(3 - 2x)\)

Apply Distributive Property to multiply -2 by (3-2x):

→ \(\sf 8x-6+4x\)

Combine like terms:

→ \(\sf (8x+4x)\)

\(\boxed{\sf 12x-6}\)

______________________________

\(\sf 2)\: 4x + 5-3(2x - 4)\)

Apply Distributive property:

Multiply -3 by (2x-4):

\(\sf 4x+5-6x+12\)

Combine like terms:

→\(\sf (4x+(-6x))\)

→ \(\sf (5+12)\)

\(\boxed{\sf -2x+17}\)

_____________________________

The given vectors are:(5,2), (-2,11), (7,-3), and (-8,-14).

The direction angle of a vector is the angle between the vector and the positive x-axis measured counterclockwise. Therefore, the direction angle of vector v = (x,y) is given by θ = tan⁻¹(y/x).a. For vector (5,2), direction angle is given by:θ = tan⁻¹(2/5) = 21.801 degrees (rounded to 3 decimal places)b.

For vector (-2,11), direction angle is given by:θ = tan⁻¹(11/-2) = 101.31 degrees (rounded to 3 decimal places)c. For vector (7,-3), direction angle is given by:θ = tan⁻¹(-3/7) = -23.198 degrees (rounded to 3 decimal places)Note that the direction angle here is negative because the vector points towards the negative x-axis.d.

For vector (-8,-14), direction angle is given by:θ = tan⁻¹(-14/-8) = 60.26 degrees (rounded to 3 decimal places)

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Answer:

  20.3 ft

Step-by-step explanation:

You want to know the height of a building if a 33 ft ladder reaches from the top of the building to a point 26 ft from the bottom of the building.

The geometry can be modeled by a right triangle with hypotenuse 33 ft and one leg of 26 ft. The other leg length (the building height) is found using the Pythagorean theorem.

  26² + h² = 33²

  h = √(33² -26²) ≈ 20.3 . . . . ft

The building is about 20.3 feet high.

__

Additional comment

This ladder makes an angle of about 38° with the ground. For ladder safety, an angle around 70° is usually recommended.

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The element that orients readers by previewing the structure of the report is "Organization."

Organizing a report effectively helps readers understand the flow of information and the logical structure of the content. By providing an overview of the organization, readers can anticipate the main sections, their sequence, and the connections between them.

The organization element typically includes headings, subheadings, and a clear hierarchy of information. It outlines the main sections and subsections of the report, indicating how they are related and how they contribute to the overall message or argument.

In addition to the organization element, the other options listed—Definitions of key terms and Sources and methods—also play important roles in a report. Definitions of key terms clarify terminology and provide a common understanding, while Sources and methods explain the sources of information and the methods used in the report's research or analysis. However, in the context of previewing the structure, the Organization element specifically serves this purpose.

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Answer:

-5

Step-by-step explanation:

the answer, please give brainliest if u can

The floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be A. 2.3e^7.

It should be noted that scientific notation simply means. way that's used to express numbers that are either too large or too small to be written in decimal form.

Therefore, it should be noted that the floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be:

= 2.3 × 20^7

= 2.3 × e^7

= 2.3e7

The correct option is A.

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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?

a. 2.3e^7

b. 2.3 × 10e^7

c. 2.3e × 10^7

d. 2.3 × e^7

Answer:

A.

Step-by-step explanation:

'The difference' means minus or subtraction. 'plus' and 'increased' are both for addition.

Brainliest please!

Answer: The equivalent expression is:

new price = s*0.8

Step-by-step explanation:

When the original price of something is A, and we have X% off, the new price if that object will be:

New price = A - (X%/100%)*A

Like in this case, the original price is s, and the discount is 20%

Then the new price can be written as:

new price = s - (20%/100%)*s = s - 0.2*s = s*(1 - 0.2) = s*0.8

This is the equivalent expression we wanted to get.

Answer:

new price = s*0.8

Step-by-step explanation:

Answer:

y = -3x + 2

Step-by-step explanation:

To find the slope of an equation you can do (y2-y1)/(x2-x1). Plug the values in from the equation and you get (-1+7)/(1-3), or 6/-2. This means the slope is -3. Then you plug the values of y and x into an equation y = -3x + b, and you get -1 = (-3)1 + b. Solve for b. -1 = -3 + b, (add 3 to each side) 2 = b. Then plug b back into your equation and you get y = -3x + 2

Answer:

-3x+2=y

Step-by-step explanation:

u need to find the slope intercept formula which mx+b=y

m=slope

b=y-intercept

first u should find the slope which is y2-y1/x2-x1

point 1:(1,-1)

point 2:(3,-7)

-7+1/3-1=-6/2=-3

m=-3

now replace the variables

-3(1)+b=-1

-3 times 1=-3

-3+b=-1

add 3 to both sides

b=2

now the equation is -3x+2=y