(A) Find the slope of the line that passes through the given points_
(B) Find the point-slope form of the equation of the line.
(C) Find the slope-intercept form of the equation of the line.
(D) Find the standard form of the equation of the line.
(4,2) and (11,8)

Answers

Answer 1

a) The slope of the line is 6 / 7.

b) The point-slope form of the equation of the line is y - 2 = (6 / 7) · (x - 4).

c) The slope-intercept form of the equation of the line is y = (6 / 7) · x - 17 / 7.

d) The point-slope form of the equation of the line is - 6 · x + 7 · y + 17 = 0.

How to find the equation of the line in three different forms

There are three different forms of the equation of the line:

Point-slope

y - y' = m · (x - x')                     (1)

Slope-intercept

y = m · x + k                             (2)

Standard

a · x + b · x + c = 0                   (3)

Where:

m - Slopek - y-Intercept

a) The slope that passes through the two given points is found by secant line formula:

m = [8 - 2] / [11 - 4]

m = 6 / 7

b) The point-slope form of the equation of the line is:

y - 2 = (6 / 7) · (x - 4)

c) The slope-intercept form of the equation of the line is:

y - 2 = (6 / 7) · x - 24 / 7

y = (6 / 7) · x - 17 / 7

d) The standard form of the equation of the line is:

7 · y = 6 · x - 17

- 6 · x + 7 · y + 17 = 0

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Related Questions

Erika's toy is valued at €450. Its value increased by 10% then decreases by 10% the year after. What is the value of Erika's toy after these two changes?

Answers

Answer:

€445.50

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

Initial value of the toy is €450.

After 10% increase the value is:

€450 + 10% = €450*1.1 = €495

After further 10% decrease the value becomes:

€495 - 10% = €495*0.9 = €445.50

The final value of the toy is €445.50.

What is the value of x when y equals 66?

y=0.985897x+0.194185

Answers

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

a box contains 14 chocolates 2 ith nuts 3 milk chocolate 4 truffles 3 dark chocolates 2 with coconut , Find the probability that you pick one with that does not have coconut

Answers

Answer:

6/7

Step-by-step explanation:

probability = #of cases / total

# cases is 14 - 2 coconuts = 12 without coconuts

total is 14

probability = 12/14 = 6/7

Write an expression for the following. "The sum of a number and 12 times 4

Answers

Answer:

4(x + 12)

Step-by-step explanation:

The sum of a number and 12 indicates addition. Then, it says that this sum will be multiplied by 4. So, we can use x to represent this random number.

URGENT A bakery wanted to make their muffins more uniform in size. They reworked their equipment to do so. To test the changes, they made 25 muffins then measured each one. Which of the following should they use to determine whether or not the equipment changes worked?

Select one:

a.
mean

b.
mode

c.
range

d.
interquartile range

Answers

The bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

To determine whether the equipment changes made by the bakery have resulted in more uniform-sized muffins, they should use the measure of variability. The most suitable measure, in this case, would be the range.

The range is calculated by finding the difference between the maximum and minimum values in a data set. In this scenario, the bakery made 25 muffins and measured each one. By finding the range of the measurements, they can assess the spread of sizes among the muffins.

Here's how they can use the range to evaluate the effectiveness of the equipment changes:

Collect the measurements of all 25 muffins.

Determine the maximum and minimum measurements.

Calculate the range by subtracting the minimum measurement from the maximum measurement.

If the range of the muffin sizes is smaller compared to the range before the equipment changes, it suggests that the modifications have resulted in more uniform-sized muffins. Conversely, if the range remains similar or larger, it indicates that the changes might not have effectively improved the uniformity of muffin sizes.

Therefore, the bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

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What is the perimeter?

What is the perimeter?

Answers

Answer:

26 (I think) :)

Step-by-step explanation:

i don’t know how to…

Answer:

26

Step-by-step explanation:

I think.

Given the following table of values for the function f(x), determine f^-1(4)

Given the following table of values for the function f(x), determine f^-1(4)

Answers

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

What is the inverse of a function?

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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I need helpppp fasttt ​

I need helpppp fasttt

Answers

Answer: the first opion is correct

as pentagon is concave so one angle mist be greater than 180°

Step-by-step explanation:

The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?

Answers

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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In science class, Polly learned that trees help make the oxygen that people breathe. One tree makes about 250 pounds of oxygen each year. Polly wonders how much oxygen the trees on her street make. When she gets home, she counts 32 trees on her street. How many tons of oxygen do they make in a year?

Answers

Answer:

They make 4 approximately tons of oxygen each year.

Step-by-step explanation:

( 250lbs × 32 ) ÷ 2000 = 4t

250 pounds because each tree makes about 250 pounds of oxygen a year.

× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.

÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.

Carlos read 150 words in one minute. He
read 5 times as many words as his younger
brother. How many words did his younger brother
read in one minute?

Answers

Answer:

30

Step-by-step explanation:

150/5 = 30

Answer: 30

Step-by-step explanation:

Grandparents want to make a gift of $100,000 for their grandchild’s 20th birthday. How much would have to be invested on the day of their grandchild’s birth if their investment could earn: (a) 10.5% compounded continuously? (b) 11% compounded continuously? (c) Describe the effect that this slight change in the interest rate makes over the 20 years of this investment

Answers

Answer:

20

Step-by-step explanation:

20 yenara they hain aahe aahe

my answer is 20 i guess........

two primes that add to 24

Answers

Answer:

11+13

Step-by-step explanation:

because of math boom

Help me please. Best answer gets brainliest.

Help me please. Best answer gets brainliest.

Answers

Answer:

3 for problem

Step-by-step explanation:

The height of a right triangular prism is 1 5/6 inches each side of the triangular base measures 10 inches and the height of the bases eight2 over 3 inches the triangular prism is place to top of cube whose side measures 10 inches so that one of the triangular prisms bases lies completely on one side of the cube what is the surface area of the solid formed

Answers

The surface area of the solid formed is approximately, 598.3 in².

What is the Surface Area of a Right Triangular Prism?

Surface area of the solid is the area covered by the solid all round.

The given parameters are:

Height of the prism (L) = 1 5/6 = 1.83 in.Side of base (s1) = 10 in.Side of base (s2) = 10 in.Side of base (s3) = 8 2/3  = 8.67 in.base (b) = 10Height (h) =  8.67 in.a = 10 in.

Surface area of the solid formed = 5(10×10) + (0.5×10×8.67) + 3(10×1.83) = 598.3 in²

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please answer correctly. Thank you​

please answer correctly. Thank you

Answers

Answer:

wag po lagi umasa sa brainly

What is the equation of the function
shown in the graph, given that the
equation of the parent function is
f(x) = (1/3)^x

A. g(x) = (1/3)^x + 2
B. g(x) = (1/3)^x – 2
C. g(x) = (1/3)^x + 1
D. g(x) = (1/3)^x - 1

Answers

Answer:

a is the same answer to this topic is the best way

Find f(a), f(a + h), and the difference quotient f(a + h) − f(a) h , where h ≠ 0.
f(x) = 2 − 4x

Answers

Answer:

-4

Step-by-step explanation:

(f(a+h)-f(a))/h=(2-4(a+h)-2+4a))/h=-4h/h=-4

PLEASEEEEEEEEEEEEE HELPPPP

PLEASEEEEEEEEEEEEE HELPPPP

Answers

The total area of the regions between the curves is 4.5 square units

The graph is attached

Calculating the total area of the regions between the curves

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

y = x² - 6x + 9 and y = x - 1

With the use of graphs, the curves intersect at

x = 2 and x = 5

So, the area of the regions between the curves is

Area = ∫x² - 6x + 9 - x + 1

This gives

Area = ∫x² - 7x + 10

Integrate

Area =  x³/3 - 7x²/2 + 10x

Recall that x = 2 and x = 5

So, we have

Area = [2³/3 - 7(2)²/2 + 10(2)] - [5³/3 - 7(5)²/2 + 10(5)]

Evaluate

Area = 4.5

Hence, the total area of the regions between the curves is 4.5 square units

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PLEASEEEEEEEEEEEEE HELPPPP

given that log c3 = 0.914
PLEASE HELP MATH

given that log c3 = 0.914PLEASE HELP MATH

Answers

Answer:

≈ 0.153

Step-by-step explanation:

using the rules of logarithms

log x - log y ⇔ log (\(\frac{x}{y}\) )

\(log_{b}\) b = 1

then

\(log_{c}\) ( \(\frac{4}{c}\) )

= \(log_{c}\) 4 - \(log_{c}\) c

= 1.153 - 1

= 0.153

Help me plzzz i need help.

Help me plzzz i need help.

Answers

Answer:

Perimeter: 7.8Area: 3.1

Step-by-step explanation:

Perimeter = all sides added up together2.8 + 2.8 + 1.1 + 1.1 = 7.8Area = L × W2.8 × 1.1 = 3.08Round 3.08 to the nearest tenth: 3.08 → 3.1

I hope this helps!

Few families can survive on a single salary.
Please select the best answer from the choices provided
T
F

Answers

Few families can survive on a single salary is true statement

Many families rely on dual incomes to make ends meet, especially in areas with high living costs.

However, there are still many families that rely on a single salary to support themselves.

While it may be challenging to make ends meet on a single salary, it is still possible for families to survive and even thrive in these circumstances.

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Help with all these? pls

Help with all these? pls

Answers

1. 76.56.

2. 96

3. The largest solution to the equation x²+16x+28=138 is 6.71.

4. The smallest solution to the equation x²+14x+14=145 is 5.96.

What is an equation?

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result (19/2)² = 76.56.

2. This is calculated by taking the coefficient of x (30) and dividing it by two (30/2) and then squaring the result (30/2)² = 96.

3. This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (16) plus or minus the square root of the coefficient of x squared (16²) minus 4 times the coefficient of the x term (4x16) minus the constant (28) divided by 2 times the coefficient of the x term (2x16).

4.  This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (14) plus or minus the square root of the coefficient of x squared (14²) minus 4 times the coefficient of the x term (4x14) minus the constant (14) divided by 2 times the coefficient of the x term (2x14).

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1.  For the given equation, c need to be 90.25 to complete the square.

2. 225

3. The largest solution to the equation x²+16x+28=138 is 6.

4. The smallest solution to the equation x²+14x+14=145 is -14.

What is an equation?

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result

(19/2)² = 90.25.

2. This is calculated by taking the coefficient of x (30) and dividing it by two which is (30/2) and then squaring the result

(30/2)² = 225.

3. The largest solution to the equation x²+16x+28=138 is 6.

This can be calculated by using the quadratic formula to solve the equation.

(a=1, b=16, c=28)

x = -8 ± √((16)² - 4(1)(28))/2(1).

x = -8 ± √(240)/2

x = 6 or -14.

Since 6 is the larger solution, it is the largest solution to the equation.

4.  The smallest solution for x2+14x+14=145 can be determined by using the Quadratic Formula.

a=1, b=14, and c=14

x = [-14 ± √(142-4(1)(14))]/(2(1))

x = [-14 ± √(196)]/2

x = [-28/2] or [14/2]

x = -14 or 7

Therefore, the smallest solution for x2+14x+14=145 is x=-14.

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Can I get help with Number 4?

Can I get help with Number 4?

Answers

Answer:

210 marchers

Step-by-step explanation:

five sevenths times 294 is 210

What is the lateral surface area of the triangular prism?



Round to the hundredths place.

What is the lateral surface area of the triangular prism?Round to the hundredths place.

Answers

Answer:

A triangular prism is a three-dimensional shape having two triangular bases and three rectangular sides.

Order these numbers from least to greatest.
5.772 , 11/2, 5 6/11, 5.77

Answers

Answer:

6/11, 11/2, 5.77, 5.772

Step-by-step explanation:

Consider the expression below.
9+ 4(x + 2) - 3x
Select the term that best describes "3" in the given expression.
A. exponent
B. coefficient
c. constant
D. variable

Answers

Answer:

es D

Step-by-step explanation:

es una variable porque lleva una letra o un símbolo en esa caso representa una cantidad esa letra

the answer is d have a great day :)))

Amy is building a cardboard box in the shape of a triangular prism. The dimensions of the box are shown in the diagram. 2 cm 1.5 cm What is the total surface area of ​​this box in square centimeters? 33 cm? 37.5 cm2 A B31.5 cm2 D 7.5 cm? Please help

Amy is building a cardboard box in the shape of a triangular prism. The dimensions of the box are shown

Answers

Answer:

37.5

Step-by-step explanation:

you have to multiply all the dimensions

Answer:

TSA=Ph+2B

(2+1.5+2.5)5+2(1/2*1.5*2)

6(5)+2(1.5)

30+3

33

Step-by-step explanation:

Please help! In a tidal river, the time between high and low tide is 5.8 hours. At high tide, the depth of water is 17.2 feet, while at low tide the depth is 4.6 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine).

Write an equation for the depth () of the tide (in feet) hours after 12:00 noon.

Answers

Answer:

Step-by-step explanation:

mean tide is (17.2 + 4.6)/ 2 = 10.9 ft

Amplitude of tide is (17.2 - 4.6)/ 2 = 6.3 ft

The full tide cycle is 2(5.8) = 11.6 hrs

As we are not told the tide condition at 12:00 noon,

I will ASSUME that the tide is high and use the cosine function

D = 10.9 + 6.3cos(2π(t/11.6)) ft

where t is in hours after noon high tide.

make sure your calculator is set to radians.

If you want to use degrees, the equation becomes

D = 10.9 + 6.3cos(360(t/11.6)) ft

Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95

Answers

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

How much cheaper is the car washes Malcolm orders than the car washes Martha's order?

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
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