The points (-3, r) and (4, -24) lie on a line with slope -4. Find the missing coordinate r=

The equation of the line is y = -0.35x – 3.55

Given,

The gradient of the line between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).

Since the line passes through the points (7,-6) and (3,8),  

• (x₁, y₁) = (7,-6) and

• (x₂, y₂) = (3,8).

So, substituting the values of the variables into the equation, we have

m = (y₂ - y₁)/(x₂ - x₁).

m = (8 - (-6))/(3 - 7).

m = (8 + 6)/ -4

m = 14/-4

m = -3.5

The equation of the line passing through the point (x₁, y₁) in point-slope form is given by

y - y₁ = m(x - x₁) where

• m = gradient =- 0.35 and

• (x₁, y₁) = (7, -6)

So, substituting the values of the variables into the equation, we have

y - y₁ = m(x - x₁)

y - (-6) = -0.35(x - 7)

y + 6 =-0.35 (x - 7)

y = (-0.35x + 2.45 – 6)

y = -0.35x – 3.55

So, the equation of the line is y = -0.35x – 3.55

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Options (1), (3), (4), (7) and (8) are rational numbers.

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

1) 1/4 + 1/2 = 1/4 + 2/4

= 3/4

3/4 is the rational number

2) √3 + 4 is an irrational number

3) √4 + 7

2 + 7 = 9

9 is the rational number

4) 2·√9

= 2·3

= 6

6 is the rational number

5) 7·√6 is an irrational number

6) 4·2√3 = 8√3

8√3 is an irrational number

7) 3·7·(1/3) = 7

7 is the rational number

8) 7·√81

=7·9 = 63

63 is the rational number

Therefore, options (1), (3), (4), (7) and (8) are rational numbers.

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Answer:

3 should be the answer to your question

the town's population at the beginning of 2000 was 74,500.Then the population in 2010 will be 96206.97

In 2000, the population of a town = 74500

Every year, it increase by 2.59%

To find the equation P(t) which represents the population of this town t years from 2000 to  2010.

Formula

If a be the original population of a town and it increases by r% every year, after t year the population will be

A = P ( 1+r/100)^t

Now,

Taking, P =74500, r = 2.59% we get,

A = 74500( 1+0.0259)^10

A= 74500(1.0259)^10

A= 96206.97

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If adana is going on vacation with her family in2 hours they travel 90.5 miles. they travel the same speed, The  equation that represents how far they will travel, d, in h hours is: r = d / t, D = r × t.

Given data;

Travels time : 2 hours in 90.5 miles

Formula for speed  is:

r = d / t

Where,

r = Speed

d = Distance

t = Time

Hence,

Speed = 90.5 / 2

Speed =45.25miles per hour

Since they travels d distance in h hour with the same speed let find the distance

D = r × t

Distance = Speed × Time

Distance = 45.25 × h

Distance = 45.25h miles

Therefore  r = d / t, D = r × t is the equation that represent the distance they travel.

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​5.8×10^-10 in standard form is: 0.00000000058.

Standard form can be defined as the way of written a number of digit in a simple form for easy understanding.

Given data:

​5.8 × 10 ^ -10

Now let ​this scientific notation 5.8 × 10 ^-10 into a standard form.

We know that  5.8×10^-10  can be re-written as :

5.8 ÷ 10 ^-10

= 5.8 × 10×10×10×10×10×10×10×10×10×10

= 5.8 ÷ 10000000000

= 0.00000000058

Hence,

​5.8×10^-10 = 0.00000000058

Therefore we can conclude that 0.00000000058 is the standard form of ​5.8  ×10 ^-10.

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Regarding the situation described, we have that:

a. The ball travels 21.4 feet.

b. The assumption is that the ball was served at an angle of 90º.

c. The Pythagorean Theorem was used to solve this problem.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, it is found that:

Assuming that the ball was served at an angle of 90º, the distance traveled by the ball is the hypotenuse of a right triangle of legs 7.5 feet and 20 feet, hence:

d² = 7.5² + 20².

d = sqrt(20² + 7.5²)

d = 21.4 feet. (which is Justin's estimate).

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Step-by-step explanation:

come on, this is really simple.

you need to put the given values of x into the places, where x appears in the functional expression.

which expression to be used ? that depends on the given value.

x = -1

is -1 >= 0 (to use the case for x >= 0) ? no, it is not.

-1 < 0, so we need to use the expression for x < 0.

y = -1 - 2 = -3

x = 0

is 0 >= 0 ? yes, it is.

so, we need to use the expression for x >= 0.

y = 3×0 + 1 = 0 + 1 = 1

x = 1

is 1 >= 0 ? yes, it is.

so, we need to use the expression for x >= 0.

y = 3×1 + 1 = 3 + 1 = 4

x = 2

is 2 >= 0 ? yes, it is.

so, we need to use the expression for x >= 0.

y = 3×2 + 1 = 6 + 1 = 7

Answer: y = 3x - 5

Step-by-step explanation:

3 is the reciprocal of -1/3 and by plugging in (1,-2) in to y=3x+b you get -2 = 3(1) + b which makes b = -5

a)

The x-intercept can be found as:

Therefore, the x-intercept is: (-2,0)

The y-intercept can be found evaluating the function for x = 0, so:

b) The parent function for this is given by:

c)

1st: A reflection over y-axis:

2nd: A horizontal compression:

3rd: A horizontal translation 8 units to the left:

4th: A reflection over y-axis:

5th: A vertical compression:

6th: A vertical translation 1 unit up:

d)

Where the blue graph is the parent function:

And the red graph is the function after the transformations:

e)

The domain and the range are:

Answer:

8

Step-by-step explanation:

See attached image.

Answer:

my best answer is C) angle 7. But there is not much context so i'm not 100% sure

Step-by-step explanation:

The 2lb candy cost the owner $8 and the 3lb candy cost the owner $4.5

The total weight of the candy is

[tex]3 + 2 = 5[/tex]

Let's write equation for this.

[tex]3(1.50) + 2x = 2.5(5)\\4.5 + 2x = 12.5\\12.5 - 4.5 = 2x \\8 = 2x\\x = 4[/tex]

The cost of the 2 pound candy is $4 per unit and the store owner spent $8 in the 2lb candy.

The cost of 3 pound candy was $4.5

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There are 100 groups of 10 milliliters in 1 liter

From the question, the given parameters are

Volume 1 = 10 milliliters

Volume 2 = 1 liter

The number of groups of the first group in the second is calculated as

Groups = Volume 2/Volume 1

Substitute the known values in the above equation

So, we have the following equation

Groups = 1 liter/10 milliliters

Evaluate the quotient

Groups = 100

Hence, the  number of groups is 100

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Answer:

[tex]x = - 3 + - \sqrt{13} [/tex]

Step-by-step explanation:

formula is x=-b+-sqrt b^2-4ac/2a

By the concept of unitary method she can run 320 yards  in 2 minutes at the same rate.

The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach might be helpful for answering questions on ratio and proportion, algebra, and other subjects. "It is a method where we get the value of a single unit from the value of many units and the value of multiple units from the value of a single unit." bra, geometry, etc. Before determining the value of additional or less items, we must first determine the value of one item by dividing it. There are two categories of unitary approaches.

720 yards = 4.5 minutes

1 minute = 720/4.5

= 160 yards

2 min = 160(2)

= 320 yards

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Answer: x = − 116/3

Step-by-step explanation:

Evaluate 5/3​x + 1/3 = 13/1/3 +8/3​x

Multiply the numbers 5x/3 + 1/3 = 13/1/3 + 8/3x

Simplify 5x/3 + 1/3 ​= 39 + 8x/3

Multiply both sides  5x/3 ​× 3 + 1/3 × 3 = 39 × 3+ 8/3x ​× 3

Simplify the expression 5x+1=117+8x

Move the variable to the left side 5x+1−8x=117

Subtract the terms −3x+1=117

Move the constant to the right side −3x=117−1

Subtract the terms −3x=116

Divide both sides −3x/-3 ​ = 116/-3

Simplify −3x/-3 ​ = 116/-3

Solution  ​x = − 116/3

A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.

B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.

Leah runs M miles everyday during the week except for Wednesday or Sunday.

We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.

We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.

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The things that can lead to bias include:

The question uses an inaccurate tool.

Some subgroups may be at a disadvantage due to prior experiences.

A medical research study assigns the healthier patients to the group using the new treatment and the sicker patients to the group using the traditional treatment.

It should be noted that bias simply means anything that leads to a systematic difference between the true parameter.

It should be noted that in a situation where the question uses an inaccurate tool. This will lead to bias and bring about inaccuracy.

Also, using different tools for the patients can lead to bias.

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answers are in the photo

goodluck

The value of f(x) + h(x) when f(x) = 2x - 1 and h(x) = x² + 1 is x² + 2x.

Addition of linear functions:
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as:
c(x) = a(x) + b(x) = (a+b)(x) – (i)
The addition of the functions strictly restricts to simple linear addition without any pre-defined constraints.

Given, f(x) = 2x - 1, g(x) = 3x and h(x) = x² + 1
Using the available formula in (i), we get
f(x) + h(x) = (f + h)(x) = (2x - 1) + (x² + 1) = x² + 2x = x(x + 2), which is a quadratic equation.
Thus, the required value of f(x) + h(x) is x² + 2x.

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Let's begin by listing out the information given to us:

The 99% confidence interval for the population proportion p is 0.833< p < 0.863.

Given that,

x = 3059

n = 3604

Point estimate = sample proportion = x / n =3059/3604=0.848

[tex]1 - \hat p[/tex]  = [tex]1-0.848 =0.152[/tex]

At 99% confidence level the z is ,

[tex]\alpha[/tex] = 1 - 99% = 1 - 0.99 = 0.01

[tex]\alpha[/tex]/ 2 = 0.01 / 2 = 0.005

[tex]Z\alpha[/tex]/2 = [tex]Z*0.005[/tex] = 2.576  (  Using z table   )

Margin of error = E = [tex]Z\alpha / 2 * (\sqrt(((\hat p * (1 - \hat p)) / n)[/tex]

                              = [tex]2.576* (\sqrt((0.848*0.152) /3604 )[/tex]

                               =0.015

A 99% confidence interval for population proportion p is ,

[tex]\hat p - E < p < \hat p + E[/tex]

0.848-0.015< p <0.848+ 0.015

0.833< p < 0.863

Hence, the 99% confidence interval for the population proportion p is 0.833< p < 0.863.

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Answer:

I not to sure but I think it is b+w=h(hours)

Step-by-step explanation:

Answer:

31.4

Step-by-step explanation:

C=2πr=2·π·5≈31.41593in

We can conclude that (A) yes, the table shows the constant of proportionality of 1/5.

So, the constant of proportionality of the given table:

Formula: k = y/x

So, substitute the values in the formula as follows:

So, yes, the table shows the constant of proportionality of 1/5.

Therefore, we can conclude that (A) yes, the table shows the constant of proportionality of 1/5.

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Based on the calculations, the final velocity of this car is equal to 85.0 mi/hr.

In order to determine the final velocity of this car, we would first calculate its acceleration based on the parameters provided. Mathematically, the acceleration of an object can be calculated by using this formula:

a = (V - U)/t

Where:  

Substituting the given parameters into the formula, we have:

a = (70.0 - 0)/10

a = 70.0/10

Acceleration, a = 7.0 mi/hr².

Now, we can determine the final velocity of this car as follows:

V = U + at

V = 50.0 + (7.0)(5)

V = 50.0 + 35.0

Final velocity, V = 85.0 mi/hr.

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Complete Question:

If a car can go from 0.0 mi/hr to 70.0 mi/hr in 10.0 seconds, what would be its final velocity after 5.0 seconds if its starting velocity was 50.0 mi/hr

Using the triangle sum theorem, x = 7 and y = 18.

The theorem that says that all the interior angles of a triangle will be equal to 180 degrees is referred to as the triangle sum theorem.

In the diagram given, since vertical angles are congruent, therefore:

(11x - 9) + (6x - 2) + 72 = 180 [triangle sum theorem]

Solve for x

11x - 9 + 6x - 2 + 72 = 180

17x + 61 = 180

17x = 180 - 61

17x = 119

x = 7

Also,

(5y - 8) + (11x - 9) + 30 = 180 [triangle sum theorem]

5y - 8 + 11x - 9 + 30 = 180

5y + 13 + 11x = 180

Plug in the value of x

5y + 13 + 11(7) = 180

5y + 13 + 77 = 180

5y + 90 = 180

5y = 180 - 90

5y = 90

y = 90/5

y = 18

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Answer:31%

Step-by-step explanation: