You can find the equation of a line through two points even if one point is not the y -intercept. Find the slope m of the line passing through the two points.Using either point, substitute for x, y , and m into y=m x+b . Solve for b and rewrite y=m x+b for the values of m and b . Write an equation in slope-intercept form for the line passing through each pair of points.

b. (-4,16) and (3,-5)

A parabola is defined as a curve where each point is equidistant from:

fixed point (focus) and

fixed line (director).

The properties of a parabola can be defined as given below:

Rays parallel to the axis of symmetry are reflected straight from the surface to the focal point.

Because the vertex of the parabola is at (0,0) and the focus is at (-3,0).

This means that the parabola axis is the negative x-axis.

The parabola equation is x^2 =4ay and a=3.

So, the parabola equation is x^2 =12y.

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Step-by-step explanation:

what is B in your question ? you did not tell us.

since you mention "fraction", I assume B is the slope of a line ?

if that is the case, please remember, the slope is (y coordinate change / x coordinate change) when going from one point of the line to another.

the way you phrased it I assume the slope was originally negative.

that means either the y difference or the x difference was negative (but not both, otherwise it would have been a positive fraction again).

let's look at what happens, when things get reflected across the y axis :

things go from the left side (negative x values) to the right side (positive x values) of the y axis or vice versa.

and things stay on the same side of the x axis (either above the x-axis with positive y values, or below the x-axis with negative y values).

so, that reflection causes the x values to flip their sign, but the y values stay the same.

so, if y was originally negative, then x must have been positive. after the reflection x is now negative too, that makes the y/x fraction -/- = +/+ positive.

if y was originally positive, then x must have been negative. after the reflection x is now positive too, that makes the y/x fraction +/+ positive.

therefore, in every case, the reflected slope fraction must be positive.

The solution of the system of equations involving 3x + 7y = 15 and 5x + 2y = -4 is  (-2 , 3).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

3x + 7y = 15     (equation 1)

5x + 2y = -4     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

3x + 7y = 15     (equation 1)

3x = 15 - 7y

x = 5 - (7/3)y

Substitute the equation of x to the second equation.

5x + 2y = -4     (equation 2)

5[5 - (7/3)y] + 2y = -4

25 - (35/3)y + 2y = -4

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

25 - (35/3)y + 2y = -4

- (35/3)y + 2y = -4 - 25

-(29/3)y = -29

y = 3

Substitute the value of y in the equation of x.

x = 5 - (7/3)(3)

x = 5 - 7

x = -2

Hence, the solution of the given system of equations is (-2 , 3).

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The maximum allowable weight for a disc with circumference 66.92 centimeters Round to the nearest tenth is 176.9 grams.

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

the maximum weight, w of a disc in grams is 8.3 times the diameter, d in centimeters

⇒ w ≤ 8.3d

and  the maximum allowable weight for a disc with circumference 66.92 centimeters

So, Circumference = πd   [∵ d = 2r]

∴ 66.82 = πd

⇒ d = 66.82π

Thus,  w ≤ 8.3*66.82π grams

⇒ w ≤ 176.89 grams

Round to the nearest tenth, w ≤ 176.9 grams

Thus, the maximum allowable weight for a disc with circumference 66.92 centimeters Round to the nearest tenth is 176.9 grams.

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Using translation concepts, the formula for function g(x) is given by the following option:

D. g(x) = 2^(x - 2)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

From the graph of the functions, we have that:

This means that g(x) is a shift right of 2 units of f(x), that is:

g(x) = f(x - 2).

Hence:

g(x) = 2^(x - 2)

The formula for function g(x) is given by the following option:

D. g(x) = 2^(x - 2)

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The probability that it hits region IV is 30%.

Probability:

Probability means the possibility of the particular event.

And it can be calculated as,

P(A) = n(A)/n(S)

Where,

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

Given,

At a carnival, the object of a game is to throw a dart at the board and hit region III.

Here we need to find the probability that it hits region IV.

Consider the board was look like the following figure.

Then based on the given figure,

First, we have to find the total area of the board and the area of the required region.

And then we have to compare it to calculate the Probability.

So, the total area of the board is,

=> total area of the board = (10 + 30)(10 + 15)

=> total area of the board = 1000 in²

Now, the The area of the region IV is

=> Area = (10)(30)

=> Area = 300 in²

Therefore, the probability that it hits region IV is

=> P = 300/1000

=> P = 30/100

=> P = 30%

Therefore, the probability that it hits region IV is 30%.

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Scientific notation exists as a method of writing very large or very small numbers. The expression as a number in scientific notation is 6.4 × [tex]$$10^4[/tex].

Utilizing scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

To express exceedingly high numbers in a shorter manner, scientists have created a shorthand. Scientific notation is the name of this technique. The foundation of scientific notation is the base-10 powers. The coefficient is defined as the initial number, 1.23.

Given: (8 ×10²) × (3.2 ×[tex]$$10^5[/tex])/4 × 10³

simplifying the above equation, we get

= 800 × 320000/4000

= 64000

= 6.4 × [tex]$$10^4[/tex]

Therefore, the expression as a number in scientific notation is 6.4 × [tex]$$10^4[/tex].

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Answer:

6.4 x 10^4

Step-by-step explanation:

Answer:

w= 3, -1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

w can be either 3 or -1

Step-by-step explanation:

-4 |w-1| = -8

Divide both sides by -4

List both cases

|w-1| = 2            |w-1| = -2

w = 3                 w = -1

Answer:

Part1: 4.25 + 4.00x = 12.25
Part2: 2 lbs. of potato salad. The customer bought 2 lbs because you subtract 4.25 from 12.25 and are left with $8. You would then divide 8$ by 4 and end up with 2

Answer:

The variable m is not a solution of the equation -2(2m-8)=-2(-6m-8);m=0. Give brainly if I helped!

Step-by-step explanation:

An expression that defines this quadratic function is ax² + bx + c = 0.

An expression that defines the quadratic equation in vertex form is equal to y = -16(x - 1)² + 20 and y = -16x² + 32x + 4.

Given the following data:

A quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the graph of any quadratic function is parabolic because it is a u-shaped curve. Also, the standard form of a quadratic function is given by;

ax² + bx + c = 0

Mathematically, the standard equation with the vertex for any parabola is given by:

y = a(x - h)² + k.

where:

Substituting the given parameters into the formula, we have;

y = a(x - h)² + k.

4 = a(0 - 1)² + 20.

4 = a + 20

a = -20 + 4

a = -16.

Therefore, an expression that defines this quadratic function is equal to ax² + bx + c = 0.

For the quadratic equation in vertex form, we have:

y = -16(x - 1)² + 20.

y = -16(x - 1)(x - 1) + 20.

y = -16(x² - x - x + 1) + 20.

y = -16(x² - 2x + 1) + 20.

y = -16x² + 32x - 16 + 20.

y = -16x² + 32x + 4.

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Answer:

The length is 120 yards, the width is 60 yards.

Step-by-step explanation:

[tex]l = 2w[/tex]

[tex]2(w + 2w) = 360[/tex]

[tex]3w = 180[/tex]

[tex]w = 60[/tex]

[tex]l = 120[/tex]

The acceleration of the dog is approximately 1.83 meter per second² .

Acceleration is defined as the rate of change of velocity . The change in velocity per unit time is acceleration.

In the given problem the dog started from rest and achieved the final velocity of 5.5 m/s.

Let us use Newton's laws to write the equation:

v = u + at , where v is the final velocity , u is the initial velocity , a is acceleration and t is time.

The dog starts from rest so the initial velocity is 0.

given v=5.5 /s and t = 3 seconds

putting the values we get:

v = u + a t

or , 5.5 = 0 + 3a

or, a = 5.5/3 meters per seconds²

or, a = 1.8333... m/s²

or, a ≈ 1.83 m/s²

The acceleration of the dog is 1.83 m/s²

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28 m is the approximate perimeter of the rectangle patio.

What is a rectangle, exactly?

p = 2w + 2l

therefore, p = 8.39 * 2 + 5.4 * 2

p = 16. 78 + 10.8

p = 27.58

perimeter = 28 meters

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According to the given data the specified type of proof. two-column proof are:

A two-column geometric proof is made up of a set of claims and the reasons why we know they are true. The statements are stated in the left column, while the reasons for making them are mentioned in the right column.

Geometric proofs are assertions that demonstrate the truth of a mathematical notion. Proof must comprise numerous phases in order to be proven true. These steps consist of reasons and declarations. Geometric proofs come in a variety of forms, include two-column proofs, paragraph proofs, and flowchart proofs.

Given: RSTUV is a pentagon.

Prove: m ∠ S+m \VS T U+m∠ T U V +m ∠ V+m ∠ V R S=540

1. RSTUV is a pentagon. (Given)

2. m∠ S + m ∠1 + m ∠2 = 180;

m ∠3 + m ∠4 + m∠ 7 = 180;

m ∠6 + m ∠V + m∠ 5 = 180 ( Sum Thm.)

3. m∠ S + m∠ 1 + m∠ 2 + m ∠3 + m ∠4 + m∠ 7 + m∠ 6 + m∠ V + m∠ 5 = 540 (Add. Prop.)

4. m ∠VRS = m ∠1 + m∠ 4 + m ∠5;

m∠ TUV = m∠ 7 + m ∠6;

m ∠STU = m ∠2 + m∠ 3 ( Addition)

5. m ∠S + m ∠STU + m ∠TUV + m∠ V + m∠ VRS = 540 (Subst.)

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The length of the slide should be approx. 16 ft long.

Pythagoras Theorem states that sum of square of two sides of triangle  is equal to the square of longest side of the right angle triangle..

From the given figure

we will use ratio to find the vertical distance

given that vertical/horizontal=4/7

[tex]\frac{vertical.distance}{horizontal.distance} =\frac{vertical.distance}{horizontal.distance}[/tex]

[tex]\frac{4}{7} =\frac{v}{14}[/tex]

By cross multiplying we get v=8 feet.

As we can see in the figure  that Vertical distance, Horizontal distance and the Slide forms a Right angled Triangle.

Pythagoras Theorem can be used to find the length of the slide.

Applying Pythagoras Theorem in ΔABC

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

given that AB=14 and BC=8

Substituting in the above equation we get

[tex](14)^{2} +8^{2} =AC^{2} \\\\ 196+64=AC^{2} \\ \\ 260=AC^{2}[/tex]

[tex]AC=\sqrt{260}=16.12[/tex]

approx. 16 feet

Therefore , the length of the slide should be approx. 16 ft long.

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For the domain -1 <  x < ∞ and -∞ <  x < -1, the function y= |x+1| is increasing and decreasing, respectively.

It must be identified for which domain intervals the function y= |x+1| increases or decreases, as stated in the question.

Since,

Accoding to the question of the given function, y= |x+1|

Assigned functions  is an absolute functions,

Whose domain is all real numbers from negative infinity to positive infinity

And Plotting the function's graph reveals that it decreases from -∞  to -1 and grows from -1 to ∞ .

Thus, For the domain -1 <  x < ∞ and -∞ <  x < -1, the function y= |x+1| is increasing and decreasing, respectively.

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The cylinder's total surface area includes the area of the curving surface as well as the areas of the two circle-shaped bases of the cylinder.

The area of the two bases and the area of the curved surface are added to determine the cylinder's total surface area. Consequently, the following is the formula for the cylinder's total surface area:

Area of the two bases plus the area of the curved surface equals the cylinder's total surface area. Due to the cylinder's round bottoms, their combined area will be equal to r2 + r2. We already know that a cylinder's curved surface area is 2rh.

(r2 + r2 + 2rh) is the cylinder's total surface area.

⇒ 2πr2 + 2πrh

Total surface area of cylinder = 2πr(r+h)

where,

r = radius of the cylinder

h = height of cylinder

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Answer: B

Step-by-step explanation:

Since n is being squared, to get rid of the square you would need to square root it.

The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.

The sides of the triangle are in ascending order, then we have

WY < YZ < WX < XY < XZ

Then the sequence of the angles is given as,

∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ

The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

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Answer:

1. 0.6 (continues)

2. 1.3 (continues)

3. 2

4.  2.7

hope the picture makes sense. I think it's right (no expert) if u want me to explain just ask. the answer is circled. usually the question would ask you to round so i wrote the full version

Answer: x=24

6:9,    16 is to x = 16:x

6/9=16/x

multiply both sides by x

6x/9=16

multiply both sides by 9

6x=144

divide by 6

x=24

Answer:

6 motorcycles/ 9 hours = 16 motorcycles/x hours

to complete a proportion you need to multiply the cross products

9(16)=6x

144=6x

144/6=6/6 x

24=x

it will take 24 hours to produce 16 motorcycles

Answer:

which mountain is known as Nepal Himal?

The distance between pair of parallel lines with the given equation

y=-6 y=1 is 7 units

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The two lines have the coefficient of x, zero. So, the slopes are 0.

Therefore, the lines are horizontal lines passing through y = −6 and y = 1.

The perpendicular distance between the these horizontal lines is

1 - (-6) = 7 units.

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The expression representing the amount remaining will be 45 - 2.50x.

Table of values

At x = 1 Amount = 42.50

At x = 2 Amount = 40.

From the information, Malika uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and the original amount of money on the gift card was $45.

Therefore, the expression representing the amount remaining will be:

A = 45 - (2.50 × x)

A = 45 - 2.50x

At x = 1 Amount remaining will be:

= 45 - 2.50

= 42.50

At x = 2

A = 45 - 2.50x

A = 45 - 2.50(2)

= 40

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Answer:

[tex] \sqrt{(x2 - x1) ^{2} } + (y2 - y1) {}^{2} [/tex]

The number expression that represents the number line option (C)

1 + (-6) = -5  is correct.

What is a number line?

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

A number line can be used to add and subtract integers. When adding positive numbers we move to the right and when adding negative numbers we move to the left.

When subtracting positive numbers we move to the left and when subtracting negative numbers we move to the right.

We can frame a number expression using the number line:

1 + (-6) = -5

1 - 6 = -5

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It begins at 1 and moves backward 6 before ending at -5.

The number phrase 1 + (-6) = -5 on the number line represents the (C) choice correctly.

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Answer:

х=8/3 solution on screen

Step-by-step explanation:

Good luck