Choose an equation in slope-intercept form for the line that passes through (0,7) and is parallel to the y=4x-19
a. y= (1/4)x - 7
b. y= (1/4)x + 9
c. y = 4x + 3
d. y = 4x + 7

Check the picture below.

let's take a looksie at that, notice, if we split the circle into 6 even pieces, we end up with six 60° angles at the center, namely six equilateral triangles as you see there.

now, if we run a dashed line as you see from a corner to the other to make the flatter triangle which is shaded, we end up cutting the equilateral triangle into two equal halves, each with 30° and 30° angles, because the dashed line intercepts the green line at 90°.

well, the flatter triangle from corner to corner, is spanning over two equilateral triangles, if it's owning half of one, it must be also owning half of the other.  What the dickens does that mean?  well, it means the area of the flatter triangle that's shaded, is really the same area as a "whole" of one of those equilateral triangles.

so hmmm we have three of those flatter triangles shaded hmm, so let's simply get the area of three of those equilateral triangles and sum them up.

[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\large area of the shaded region}}{36\sqrt{3}~~ + ~~36\sqrt{3}~~ + ~~36\sqrt{3}}\implies 108\sqrt{3}\qquad \approx\qquad \text{\LARGE 187.1}[/tex]

f\mathopen{}\mathclose{\left(6\right)}f(6)​ = (6-6)(something) + 22​ = 0(something) + 22​ = 22 which has a remainder of 22 when divided by x-6x-6​. f\mathopen{}\mathclose{\left(6\right)}f(6)​ = \boxed{22}.

The remainder theorem states that when a polynomial is divided by a linear term, the remainder equals the value of the polynomial at the root of the linear term. This theorem may be used to determine the roots of a polynomial by dividing it by a linear term and solving for the remainder. For instance, when the polynomial x3+x2-5x+6 is divided by (x2), the result is identical to the polynomial's value at x=2. After finding the remainder, we may determine that the polynomial's root is 2, which we can do by solving for the remainder. This theorem may also be used to discover the roots of higher degree polynomials by combining linear terms.

How to solve?

f\mathopen{}\mathclose{\left(x\right)}f(x)​ can be written as (x-6)(something) + 22​.  

f\mathopen{}\mathclose{\left(6\right)}f(6)​ = (6-6)(something) + 22​ = 0(something) + 22​ = 22​.

Therefore, f\mathopen{}\mathclose{\left(6\right)}f(6)​ = \boxed{22}.

To learn more about the remainder theorem, visit:

https://brainly.com/question/9160275

#SPJ1

Answer:

Slope- y=1/4x-6

Y intercept= (0,-6)

Hope this helps!

The side lengths of the triangle are 89 ft, 132 ft and 159 ft

The given parameters are

Angle, A = 34 degrees

Hypotenuse = 159 ft

The length BC is calculated as

sin(A) = BC/Hypotenuse

So, we have

BC = Hypotenuse * sin(A)

This gives

BC = 159 * sin(34 degrees)

Evaluate

BC = 89 ft

The length AC is calculated as

cos(A) = AC/Hypotenuse

So, we have

AC = Hypotenuse * cos(A)

This gives

AC = 159 * cos(34 degrees)

Evaluate

AC = 132 ft

Here, we have

Angle, A = 34 degrees

Because the triangle is a right triangle, we have

Angle, C = 90 degrees

The sum of angles in a triangle is 180

So, we have

Angle B = 180 - 90 - 34

Angle B = 56

This is calculated as

Area = 0.5 * BC * AC

So, we have

Area = 0.5 * 89 * 132

Evaluate

Area = 5874

Hence, the area is 5874 square units

Read more about right triangles at

https://brainly.com/question/2437195

#SPJ1

let's go like the crab, go backwards, start at the last

if you don't have a Unit Circle, this is a good time to get one, there are many online.

Check the picture below.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +6}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{midpoint}{(-5~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +6}{2}=-5\implies x+6=-10\implies \boxed{x=-16} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-5\implies y+7=-10\implies \boxed{y=-17}[/tex]

Answer:

X+1>12/3

X+1>4

X>4-1

X>3

Answer:

Step-by-step explanation:

24

Answer: 24!

Step-by-step explanation:

hope this help

Answer:

7

Step-by-step explanation:

seven is the value e you would get

Answer: The answer is 2

Step-by-step explanation:

3j + 4 = 10  J = 2

3x2=6

6+4= 10

Answer:

(1, -2)

Step-by-step explanation:

The line is tangent to the parabola, so it intersects in only 1 point.

Answer: (1, -2)

Part A: Probability that one of 400-page novels will have exactly one error-free page is 24.06%.

Part B.) No more than three pages contain errors: 40.06%.

The given data in the question-

The following is the probability mass function (PMF) for X:

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

Part A.) One of 400-page novels will have exactly one error-free page.

P(x = 1)  = ⁿCₓ . pˣ . qⁿ⁻ˣ

n = 400, x = 1

P(x = 1)  = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹

P(x = 1)  =  0.2706

Thus,  probability that one of 400-page novels will have exactly one error-free page is 24.06%.

Part B.) No more than three pages contain errors.

P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

P(x = 0)  = ¹⁰⁰C₀ . (0.005)⁰ . (0.995)¹⁰⁰ ⁻ ⁰

P(x = 0)  = 0.01346

P(x = 1)  = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹

P(x = 1)  = 0.0270

P(x = 2)  = ¹⁰⁰C₂ . (0.005)² . (0.995)¹⁰⁰ ⁻ ²

P(x = 2)  = 0.00068

P(x = 3)  = ¹⁰⁰C₃ . (0.005)³ . (0.995)¹⁰⁰ ⁻ ³

P(x = 3)  = 0.0000027

Thus, P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

P(x ≤ 3) =  0.01346 + 0.00068 + 0.00068 + 0.0000027

P(x ≤ 3) =  0.4060021

Consequently, the likelihood of at maximum three pages having typographical errors is 40.06%.

To know more about the binomial distribution, here

https://brainly.com/question/15557838

#SPJ4

The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say that number is x,

Quotients of 20 and x will be given as 20/x

20/x - 4 = 0

20/x = 4

x = 20/4 = 5

Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".

For more about the equation,

https://brainly.com/question/10413253

#SPJ1

Answer:

k = 7

Step-by-step explanation:

given y varies jointly with x and w then the equation relating them is

y = kxw ← k is the constant of variation

to find k use the condition when y = - 42, x = 2 and w = - 3 , then

- 42 = k × 2 × - 3

- 42 = - 6k ( divide both sides by - 6 )

7 = k

constant of variation is k = 7

Answer:

C.)

Step-by-step explanation:

1.) Since she does 8 vases in 2 hours, she would do 4 vases in 1 hour.

2.) By using this, we divide 50/4 to figure out the amount of hours. This is equal to 25/2, which is equal to 12.5.

3.) Now, check the options. C.) fits this situation the best. Therefore, C.) is the answer.

Answer: 54

Step-by-step explanation: 3 x 30seconds = 90 seconds (1 1/2)

3 x 18 = 54

Answer:

Option 2 —› (56 - 42) / 7 = 2

Step-by-step explanation:

First you use PEMDAS to check.

P- parentheses

E- Exponents

M- Multiplication (can be switched with D)

D- Division (can be switched for M)

A- Addition

S- Subtraction

Now you need to solve each problem.

Option 1: INCORRECT

(56 - 42) / 7 = 5

(14) / 7 = 5

2 = 5

Option 2: CORRECT

(56 - 42) / 7 = 2

(14) / 7 = 2

2 / 2

I'll do the rest, so you can see how to solve.

Option 3: INCORRECT

56 - (42 / 7) = 2

56 - 6 = 2

50 = 2

Option 4: INCORRECT

(56 - 7) / 42 = 5

(49) / 42 = 5

1 1/6 = 5

Answer:

On (3,7) and (-2,7)

Step-by-step explanation:

The perimeter of the image of the triangle is approximately equal to 87 units.

In this problem we find the coordinates of the vertices of a triangle: A(x, y) = (- 4, 3), B(x, y) = (4, 3), C(x, y) = (- 4, - 6), of which we must determine the perimeter of its image, which is the result of a scale factor of 3. The perimeter is the sum of the lengths of the triangle. The length of each side of the image of the triangle can be found by Pythagorean theorem and definition of dilation:

l = √[(Δx)² + (Δy)²]

Where:

And the perimeter of the image of the triangle is described below:

p = k · (AB + BC + AC)

Where k is the scale factor.

First, determine the lengths of sides AB, BC and AC:

Side AB

AB = √[[4 - (- 4)]² + (3 - 3)²]

AB = 8

Side BC

BC = √[(- 4 - 4)² + (- 6 - 3)²]

BC = √[(- 8)² + (- 9)²]

BC = √145

Side AC

AC = √[(- 4 - 4)² + (- 6 - 3)²]

AC = 9

Second, determine the perimeter of the image:

p = 3 · (8 + √145 + 9)

p = 3 · (17 + √145)

p = 51 + 3√145

p ≈ 87.125

To learn more on perimeters: https://brainly.com/question/9369181

#SPJ1

Answer:

Step-by-step explanation:

P = 2(L + W)

P = 34

L = W + 5

34 = 2(W + 5 + W)

34 = 2(2W + 5)

34 = 4W + 10

34 - 10 = 4W

24 = 4W

24/4 = W

6 = W <=== 6 meters wide

L = W + 5

L = 6 + 5

L = 11 <=== 11 meters long

The solution to probability problem is the expected value for a person that buys one ticket is -$2.32

Probability is a measure of the likelihood or chance that a specific event will occur, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

According to the given information:

To find the expected value, you need to multiply each possible outcome by its probability and then add them together.

In this case, there are two possible outcomes: either the person wins the laptop computer (with a probability 1/1500), or they don't win anything (with a probability 1499/1500).

So, the expected value can be calculated as:

E(x) = (1/1500)($1000) + (1499/1500)(-$3)

E(x) = $0.67 - $2.99

E(x) = -$2.32

So the expected value for a person that buys one ticket is -$2.32.

To know more about probability Visit: https://brainly.com/question/11234923

#SPJ1

We can use both according to the given information.

• In 2 triangles if 2 sides of a triangle and 2 sides of another triangle are equal and if any one angle is equal to the angle in another triangle then we use SAS congruence rule

• In 2 triangles if 3 sides are equal to the 3 sides of another triangle then we use SSS congruence rule

• We can also use RHS (Right angle Hypotenuse Side). It is for 2 right angle triangle.

The sequence of transformations that show figure A and figure B are congruent is: Translate figure A 4 units right and then reflect the image across the x-axis.

Translation refers to a type of transformation that involve a straight line movement.

Movements as seen in translation includes

The left and right movements are on the horizontal direction controlled by the x coordinate.

The object moved 4 units right then reflected over the x axis to have the mirror image below the x axis

Learn more on translation:

https://brainly.com/question/29321966

#SPJ1

The berries is the bowl is 6 berries fewer than the original amount

The amount of berries in the bowel is solved using addition and subtraction property of equality

36 berries are in a bowl James eats 21 of the berries

= 35 berries - 21 berries

= 15 berries

he put 14 more berries in the bowl

= 15 berries + 14 berries

= 29 berries

How many fewer is solved by

= 35 berries - 29 berries

= 6 berries

Learn more about addition and subtraction at:

https://brainly.com/question/20460320

#SPJ1

They each will pass 12 scales.

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

It is given that Becky has passed 4 scales, whereas her friend Charlotte has passed 8 of them.

Going forward, Becky has committed to passing 4 scales per week, and Charlotte has committed to passing 2 per week.

Let number of weeks be x

Becky has passed 4x + 4

Charlotte has passed 2x + 8

According to question:

4x + 4 = 2x + 8

4x - 2x = 8 - 4

2x = 4

x = 4/2 = 2

Becky has passed 4x + 4 = 4(2) + 4 = 8 + 4 = 12

Charlotte has passed 2x + 8 = 2(2) + 8 = 4 + 8 = 12

Therefore, They each will pass 12 scales.

To learn more about the algebraic expression from the given link.

https://brainly.com/question/4344214

#SPJ1

The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

From the data:

The linear function:

C(x) = 500 + 1.25x

For revenue:

R(x) = 3.50x

R(50) = 3.50(50) = $175

Using the C(x) and revenue function we can find the number of slushies and profit.

Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1