Write the point-slope form of an equation for the line graphed.
a. y + 1 = -3(x)
b. y - 1 = 3(x)
c. y - 1 = 4(x)
d. y + 1 = 4(x)​

Given:

The given point is (-4,1)

Let's check the ordered pair (-4,1) in the first equation

Hence, (-4,1) is a solution of the first equation x-5y=-9.

Now, let's check (-4,1) in the second equation.

So, (-4,1) is a solution of the second equation 4x+4y=-12.

Hence, (-4,1) is a solution of both equation in the system, then it is a solution to the overall system.

Answer:

5i + 2

Step-by-step explanation:

(5-2i)(i)

5i - 2i^2

i^2= -1

5i -2(-1)

= 5i + 2

Answer:

answer Is -9/40

Step-by-step explanation:

the formula Is

tan0= sin0/cos0

tan0= (9/41)/(-40/41)

tan0=(9/41)*(-41/40)

tan0= -9/40

Answer:

constant

Step-by-step explanation:

-7y is a contant

Given:

Annual earnings = $17,500

Asked: What is the gross amount of her semimonthly paycheck?

Solution:

To find the answer, we need to divide first the annual earnings by 12 to get the monthly paycheck. After that, we will divide it by 2 because we are looking for the semimonthly paycheck.

ANSWER: C. $729.17

The function’s equation written in factored form and in vertex form are respectively;

f(x) = 2x(x - 4)

f(x) = 2(x - 2)² - 8

The factored form of a quadratic function is;

f(x) = a(x - p)(x - q)

where:

p and q are the x-intercepts

a is a constant

Now, we are given x-intercepts as; (0, 0) and (4, 0)

Thus;

f(x) = a(x - 0)(x - 4)

f(x) = ax(x - 4)

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

2a(2 - 4) = -8

-4a = -8

a = 2

Thus;

f(x) = 2x(x - 4)

The vertex form of a quadratic equation is;

f(x) = a(x - h)² + k

where:

(h, k) is the vertex

a is constant

Since vertex is (2, -8), then we have;

f(x) = a(x - 2)² - 8

Put the coordinate (0, 0) to find a;

0 = a(0 - 2)² - 8

4a = 8

a = 2

Thus;

f(x) = 2(x - 2)² - 8

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Firstly, calculate the radius r of the circle using distance between two points

Then use the radius r=5 and the center (-1 , 5) to find the equation of the circle

The center radius form is

The standard form is

while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent​

Let

x ------> amount that Curtis spent

we have that

10=2x-26 ------> equation that represent this situation

solve for x

2x=10+26

2x=36

x=$18

therefore

Manuel will attend the quarter in 9 weeks.

Given,

In the question:

Total taken quizzes is 90

Manuel took a total of 20 quizzes over the course of 2 weeks.

To find the how many weeks of school will Manuel have to attend this quarter ?

Now, According to the question:
Based on the given conditions :

Formulate:

Let the no. of weeks be x

Total quizzes = 90

Here, The relationship is directly proportional.​

20/2 = 90/x

If the fraction is defined, the denominator cannot be equal 0.

Solve the equation:

10 = 90/x

10x = 90

x = 9

Hence, Manuel will attend the quarter in 9 weeks.

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SOLUTION

Now this is how I can divide x by a fraction.

Let's divide x by

So

Now to do this, change division to multiplication. When you do this, the fraction reverses. That is the number up will come down and the number down will go up.

So, this becomes

x on its own means x over 1, that is

So this is how to divide x by a fraction.

Answer:

7.5/3

Step-by-step explanation:

set AC and BD equal to eachother because they are equal and solve

Answer:

about 3.09

Step-by-step explanation:

A = l  x w

A = 13/7 x 7/6

A = 1.857 x 1.666

A = 3.09

Hope it helps!

Answer

We are told that the relationship describing the weight and length, for alligators.

The length in inches is presented on the x-axis and the weight in pounds is presented on the y-axis.

The observations about this include

- From the scatterplot, we can see that the more the length of the alligator (that is, as x increases), the weight of the alligator also increases (that is, y increases too).

- This points to a direct relationship between the length of alligator and the weight of the alligator.

- Small alligators weigh light weights and longer alligators are heavy.

Hope this Helps!!!

we have that the arithmetic sequence have:

so we can replace for n=2,3,and 4 to find the first four terms so:

for n=2

for n=3

and for n=4

So the first four numbers are

Answer:

(-2,4)

Explanation:

Given the inequality:

The solution set is graphed on the number line below:

In the given triangle ABC where BD bisects ABC and according to the values of the given angles, the value of x is found out to be 3.5.

It is given to us that -

BD bisects ABC.

m/ABD = 2(3x) ----- (1)

and, m/ABC = 42 ------- (2)

We need to find out the value of x.

Since BD bisects triangle ABC,

The angles created with respect to the bisector are equal.

=> m/ABD = m/CBD ----- (3)

Also, it is also known that -

m/ABD + m/CBD = m/ABC ----- (4)

Substituting equation (3) in equation (4),

m/ABD + m/CBD = m/ABC

=> m/ABD + m/ABD = m/ABC

=> 2 m/ABD = m/ABC ----- (5)

Substituting the values of m/ABD and m/ABC from equation (1) and (2) in equation (5), we get

2 m/ABD = m/ABC

=> 2*2(3x) = 42

=> 12x = 42

=> x = 3.5

Thus, according to the values of the angles of the triangle, the value of x is 3.5.

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The diameter of the circle is 5.2m.

The area of circular pond is 21.5 m2

area of a circle is given by the formula

area = πr²

21.5 = 3.14 r²

r² = 6.84

r = ±2.6

r is a length and it cannot be negative

So, r = 2.6

Diameter is twice of radius

d = 2r

d = 2(2.6)

d = 5.2

Therefore, the diameter of the circle is 5.2m.

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Answer: we would need to see the graphs to address this question fully, but you should look for the graph that starts at x = 0, 1250 and decreases by 14% compared to the previous year

so for example, x = 1, the y value should be 1250 - (0.14)(1250)

Step-by-step explanation:

The statement that explains why Charlotte's submission is correct is that (4³)³ simplifies to (4⁹) and (4⁹) simplifies to 2¹⁸

From the question, the expression is given as

(43)3

Rewrite the expression properly

So, we have the following representation

(4³)³

Apply the law of indices to rewrite the exponents in the expression properly

So, we have

(4³)³ = 4³*³

Next, we evaluate the products

So, we have the following notation

(4³)³ = 4⁹

Solving further, we need to express 4 as the square of 2

So, we have

(4³)³ = (2²)⁹

Apply the law of indices to rewrite the exponents in the expression properly

So, we have

(4³)³ = 2²*⁹

Next, we evaluate the products

So, we have the following notation

(4³)³ = 2¹⁸

Hence, Charlotte's expression is correct

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Possible question

Charlotte states that (4³)³ can be rewritten as 2¹⁸. Which of the following explains how she is correct? Select all that apply.

Each flight has a probability of 60% or 0.6 of being on time. This means that its complement, or the probability that the flight isn't on time is:

It is 40% or 0.4. "~P(on time)" stands for the probability of the flight not being on time.

1. The probability that at least 2 flights are on time is:

To find the probability that 2 or more flights are on time we can fight the probability that "0" or "1" are not on time.

The probability of 2 or more flights are on time is:

The probability of 2 flights or more are on time is 0.996198912

2.

We need to calculate the probabilities of 7,8 and 9 flights are on time and then subtract by 1.

The probability of at most 6 flights are on time is:

The probability of 6 or less are on time is 0.768212992.

3.

The probability of exactly 5 flights are on time is:

The probability of exactly 5 flights are on time is 0.250822656.

SOLUTION:

We are to find the domain of the given exponential function shown;

The domain of exponential functions is all real numbers.

So the correct option is D

The equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is

b = 4c.

Given, Mr. March sells popcorn at his theater.

He uses 3(3/4) cups of unpopped corn to make 15 bags of popped corn. We have to write an equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn.​

Now, according to the question

3(3/4) cups = 15 bags

15/4 cups = 15 bags

1 cup = 4 bags

So, in 'c' cups he will make, 4c bags

therefore, 4c = b

Hence, the equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is

b = 4c.

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The total number of pages they read by the end of November is 2916 pages.

As the question, Chapter 1 has 35 pages, Chapter 2 has 38 pages and Chapter 3 has 35 pages. All these pages are read by all 27 students by the end of November.

⇒   Total number of pages in Three chapters  [tex]=35+38+35[/tex]

                                                                             [tex]=108[/tex]

⇒   Total number of pages in all three chapters read by one student = 108

⇒   Total number of pages read by 27 students  

                                      [tex]= total number of pages in three chapters * 27[/tex]

                                      [tex]=108*27[/tex]

                                      [tex]=2916[/tex]

Therefore, The total number of pages 27 students read by the end of November = 2916.

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The full question is

There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.

The acceleration of the car will be 0.002 m / s².

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The velocity of the car = 35.9 m/hr

The time take by car = 8.2 seconds

Now,

Since, We know that;

⇒ Acceleration = (Final velocity - Initial velocity) / Time

Since, The driver accelerates her car from rest to a velocity of 35.9 mi/hr.

So, Initial velocity = 0

And, Final velocity = 35.9 m / hr

                             = (35.9 / 3600) m/s

                             = 0.01 m / s

So, We get;

⇒ Acceleration = (Final velocity - Initial velocity) / Time

⇒ Acceleration = (0.01 - 0) / 8.2

⇒ Acceleration = 0.01 / 8.2

⇒ Acceleration = 0.002 m / s²

Thus, The acceleration of the car will be 0.002 m / s².

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Answer:

1000

Step-by-step explanation:

The easiest way to go about this is by turning our number into ABCD.

A will be in the 1000th spot, B 100th, C 10th, and D 1st.

A has to be ≥ 5. So 5, 6, 7, 8, 9.

B has to be a prime number. 2, 3, 5, 7.

C is able to be any number it wants, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Since the number is odd, D has to be 1, 3, 5, 7, 9.

A has 5 different possibilities. B has 4, C has 10, and D has 5.
You'll then multiply all of these numbers for your answer.
5 * 4 * 10 * 5 = 1000

a) The area of the rectangle has the following inequality: 12 ≤ 6 · x ≤ 36.

b) The value of the variable x has the following inequality: 2 ≤ x ≤ 6.

The area of a rectangle (A) is described by the following formula:

A = b · h

Where:

a) If we know that b = 2 · x and h = 3, then the area of the rectangle is:

A = (2 · x) · 3

A = 6 · x

And the inequality is:

12 ≤ 6 · x ≤ 36

b) And the solutions for the values of x are represented by the following inequality:

2 ≤ x ≤ 6

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Answer: The number of pencils Brian has is p+4

Step-by-step explanation:

Because p is the original number of the pencil ( we don't know how many are there so we keep it p). Then he bought 4 more which mean +4, so the answer is p+4

The length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.

By Pythagorean theorem,

[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]

Let                base = x+5

     perpendicular = x

        Hypotenuse = x+6

                                    [tex](x+6)^{2} = x^{2} +(x+5)^{2}[/tex]

                           [tex]x^{2} +12x+36 = x^{2} +x^{2}+10x+25[/tex][tex]2x^{2} +10x+25-x^{2} -12x-36=0[/tex]

                             [tex]x^{2} -2x-11=0[/tex]

                                               [tex]x = \frac{-(-2) + \sqrt{4 - 4(1)(-11)} }{2*1}[/tex] or [tex]\frac{-(-2) - \sqrt{4 - 4(1)(-11)} }{2*1}[/tex]

                                               [tex]x=\frac{2 + \sqrt{4 +44} }{2}[/tex] or  [tex]\frac{2 - \sqrt{4 +44} }{2}[/tex]

                                               [tex]x = \frac{2 + \sqrt{48} }{2}[/tex] or [tex]\frac{2 - \sqrt{48} }{2}[/tex]

                                               [tex]x = \frac{2+2\sqrt{12} }{2}[/tex] or [tex]\frac{2-2\sqrt{12} }{2}[/tex]

                                               [tex]x = 1+\sqrt{12}[/tex] or [tex]1-\sqrt{12}[/tex]

                                               [tex]x = 1+3.5[/tex] or [tex]1-3.5[/tex]

                                               [tex]x = 4.5[/tex] or [tex]-2.5[/tex]

As, length can't be negative, we will take x = 4.5

Therefore, x = 4.5

            x + 5 = 4.5 + 5

                      = 9.5

             x + 6 = 4.5 + 6

                       = 10.5

Hence, the length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.

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Answer:

We have to use to elimination method to solve the provided system of equations, this method essentially involves eliminating one of the variables in the first equation by adding or subtracting a multiple of the second equation:

The elimination of the variable y in equation (1) is achieved by adding the 4 times the equation 2 into the equation (1), the steps of the process are as follows:

We have found the x value, the last step is to plug in the variable x value in any of the (1) or (2) equations, and solve for the y variable, the steps are as follows:

The final answer is as follows:

Therefore the answer is Option(B).