On a coordinate plane, point A is located (-2,2) and point B is located at (6,-1). Determine the coordinates of the point that is 7/8 of the distance from a to b

An expression exists as a number, a variable, or a combination of numbers and variables, and function symbols. The speed in still water exists 4 mph.

The acronym BODMAS, which stands for brackets of, division, multiplication, addition, and subtraction, might be used to simplify the expression. It specifies how to answer a mathematical expression in a particular order.

Let x be the speed in still water

[tex]$&\frac{5}{x+1}+\frac{6}{x-1}=3[/tex]

LCD = (x + 1)(x - 1)

[tex]$&(x+1)(x-1) \cdot \frac{5}{x+1}+(x+1)(x-1) \cdot \frac{6}{x-1}=(x+1)(x-1) \cdot 3 \\[/tex]

simplifying the above equation, we get

5(x - 1) + 6(x + 1) = 3(x + 1)(x - 1)

5x - 5 + 6x + 6 = 3 x² - 3

3x² - 11x - 4 = 0

(3x + 1)(x - 4) = 0

x = -1/3 (speed is not negative);

then we get x = 4 mph

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An equation for a parabola with​ x-intercepts (-3,0) and (4,0) which passes through the point (2,-40) is 5(x+3)(x-4)

Quadratic equations are equation that has a leading degree of 2. The standard quadratic equation is given as:

y = a(x-a)(x-b)

where a and b are the x-intercepts of the function

Given the​ x-intercepts (-3,0) and (4,0), the equation will below:

y = a(x-(-3)(x-4))

y = a(x+3)(x-4)

If the curve pass through the y-intercept (2,-40)

-40= a(2+3)(2-4)

-40 = a(4)(-2)
-40 = -8a

a = 5

Substitute the value of a into the resulting function to have:

y = 5(x+3)(x-4)

This gives the required quadratic equation.

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Given the equation of a projectile to be:

Initial height = 2 feet

Initial speed = 110 feet per second.

That is,

Substitute the initial height and speed into the projectile equation,

The graph of the projectile is shown below:

From the graph, the time it takes the ball to attain maximum height to the nearest hundredth is 3.44 seconds

Check the picture below.

Value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.

As given in the question,

Given inequality:

Three fourths times p plus 8 is greater than or equal to 3 is written as

(3/4)p + 8 ≥ 3

Simplify inequality to get the value of p

  (3p + 32)/4 ≥ 3

⇒ 3p + 32 ≥ 12

⇒ 3p ≥ 12 -32

⇒ 3p ≥ -20

⇒ p ≥ -20 /3

Therefore, value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.

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The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.

This is a question of percentages.

Given that:-

Price of bouquet of flowers = $ 55

Sales tax % = 6.5 %

Tip % = 15 %

Delivery fee= $10

We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.

Sales tax = (6.5/100)*55 = $3.575

$55 + $3.575 = $58.575

Tip = (15/100)*58.575 = $ 8.78625

Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4

Hence,

Change received by Grant = 100 - 67.4 = $ 32.6

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If Scampini has no debt or preferred stock, and its WACC is 12%, and it has zero nonoperating assets in which Scampini has 40 million shares of stock outstanding, the stock's value per share is $37.50.

Next year CF = $75 millions

Growth rate of CF = 7%

WACC = 12%

Number of shares outstanding = 40 million shares

Estimated business valuation:

Valuation = Next year CF/ (WACC -growth rate)

Valuation = $75 million / (12% - 7%)

Valuation = $75 million /5%

Valuation =$1500 million

Estimated stock price:

Stock price = Valuation /Shares outstanding

Stock price = $1500 million / 40 million shares

Stock price = $37.50

Therefore the stock price is $37.50.

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answer: 4) -10

The total volume taken by the coins is 88.47 cubic inches, so the correct option is D.

The coins are cylinders with a radius of 1.4 inches and a height of 0.0625 inches.

Remember that the volume of a cylinder is given by:

volume = (height)*pi*(radius)^2

Where pi = 3.14

Then here the volume of each coin is:

V = (0.0625 in)*3.14*(1.4 in)^2 = 0.384 in³

And there are 230 coins, so the total volume is:

V = 230*0.384 in³ = 88.47 in³

So the correct option is D.

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Answer: D: 88.47 in³​

Step-by-step explanation: So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h

Take 1.4 and times it by itself

1.4 x 1.4 = 1.96

Now multiply 1.96 by 0.0625

1.96 x 0.0625 = 0.1225

And times 0.1225 by pi, or in this case, 3.14

0.1225 x 3.14 = 0.38465

Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.

0.38465 x 230 = 88.4695 in³
Now round it to the nearest hundredth: 88.47 in³

That is your answer.

Also I took the same test and I picked 88.47 inches cubed and got it right.

Proof:

Have a good day :)))

Answer:

That depends on what exactly is meant by "$3 in equipment fees". Is that per hour, per day or what?

Assuming per hour, he makes $7 per hour but pays $3 for a profit of $4 per hour. So, to make at least $39, he'd have to work 39/4 or 9 3/4 hours.

Now, if his equipment fee is daily, then he would need to earn at least $42 in a day to profit at least $39. Thus, he'd have to work at least 42/7 or 6 hours to make that much profit.

Step-by-step explanation:

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The length of the rectangle is 3 times it width. The width size is given as 2 inches.

Therefore,

width = 2 inches

length = 3(2) = 6 inches

The area of the rectangle can be calculated below

The answer is B.

Factor the left hand side:

Subtract 2x from both sides:

Sutract 1 from both sides:

Divide both sides by 10:

Therefore, the equation is correct for every x different from 0.

To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x)

Step 1

Step 2

The new ordered pair of the image after rotation

Step 3

Image of the coordinateStep

Step 4

Label of the points

20 miles per hour converted to feet per second is 88/3 feet per second.

It is given in the question that there are 60 minutes in one hour and 60 seconds in one minute.

We have to convert 20 miles per hour in feet per second.

We know that,

1 mile = 5280 feet

1 hour = 60 minutes

1 minute = 60 seconds

Hence, we can write,

1 hour = 60*60 = 3600 seconds

1 mile per hour = 5280/3600 feet per second = 22/15 feet per second

Using unitary method, we can write,

20 miles per hour = 20*(22/15) = 88/3 feet per second or 29.3334 feet per second.

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Answer: 415

Step-by-step explanation:

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We take a look at the inequalities y > 2 and x >4. This means that the solutions must have values that has x > 4 and y > 2. Letters A, C, and E are candidates to be solution since they satisfy the inequalities provided. Using the inequality y > x, this means that the y value must be greater than the x value that we have. Letter A has higher x value than y value, hence, it will be crossed out. Both C and E has higher y values compared to their x values. Hence, the points that are solution to the system of inequalities provided are C. (9, 10) and E. (5, 6).

Answer:

see explanation

Step-by-step explanation:

(a)

the 2 angles are vertically opposite angles and are congruent

(c)

since they are congruent , then

7x + 6 = 6x + 18 ( subtract 6x from both sides )

x + 6 = 18 ( subtract 6 from both sides )

x = 12

(d)

then

7x + 6 = 7(12) + 6 = 84 + 6 = 90

6x + 18 = 6(12) + 18 = 72 + 18 = 90

Given the function f(x):

We will find the point on the given parabola where the slope of the tangent is horizontal

The horizontal line has a slope = zero

The slope of the line is the first derivative of the function

So, we will find the first derivative and equate it to zero

solve the equation to find (x):

substitute with the value of (x) into the given function to find the y-coordinate

So, the answer will be the point will be as follows:

See the following figure:

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{\frac{7}{2}})\qquad (\stackrel{x_2}{\frac{5}{3}}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(\frac{5}{3}-2)^2 + (1-\frac{7}{2})^2}\implies d=\sqrt{(\frac{-1}{3})^2 + (-\frac{5}{2})^2} \\\\\\ d=\sqrt{\cfrac{1}{9}~~ + ~~\cfrac{25}{4}}\implies d=\sqrt{\cfrac{229}{36}}\implies d=\cfrac{\sqrt{229}}{\sqrt{36}}\implies d=\cfrac{\sqrt{229}}{6}[/tex]

Domain = the set of possible values along the x axis.

Domain = (-5 , 3 ]

Range = the set of possible values along the y axis.

Range = (-3 , 5 ]

Given: The system of equations below...

To Determine: The value of x and y

Using substitution method, Substitute for y in the second equation

Substitute for x in the first equation to solve for y

ence,

x = -4; y = -10

G

From the figure of triangles, scale factor of A and B, the value of x = 3

According to the question, given that

when two triangle are same, then we easily get missing value x

From the figure, two triangle are similar in it thus,

[tex]\frac{x}{1}[/tex] = [tex]\frac{9}{3}[/tex]       {property of triangles which are similar}

x = [tex]\frac{9}{3}[/tex] .

x = 3

Therefore, we get scale factor of triangle A and B, the missing value of missing x = 3.

Scale factor is the proportion of an original object's scale to a new one that is a representation of it but is a different size (bigger or smaller).

For example, if we have a rectangle of sides 4 cm and 6 cm, we can enlarge it by multiplying each side by a number, say 4. The new figure we get will be similar to the original figure, but all its dimensions will be twice that of the original rectangle.

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In order to find what factors could represent the length and the width, we need to factor the polynomial that represents the area.

To do so, first let's find the zeros a1 and a2, then we can factor as follows:

Where k is the coefficient of the quadratic term (so k = 12).

Using the quadratic formula, we have:

Then, we have:

Therefore the factors are 2a-1 and 6a+5.

Step-by-step explanation:

9x + 4y is where (9,4) is the coordinates

Answer:

C' = (13, 4)

Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units right.

Step-by-step explanation:

Given vertices of triangle ABC:

If two triangles are said to be similar:

To keep the corresponding angles of both triangles the same and maintain similarity, dilate triangle ABC.

If we compare the coordinates of B (1, 4) and B' (5, 8), the y-value has been multiplied by 2.

Therefore, the first step of the transformation is a dilation by a scale factor 2 with the origin (0, 0) as the center of dilation.

⇒ (1 × 2, 4 × 2) = (2, 8)

After multiplying the coordinates of B by two, the difference between the x-values of the dilated point and B' is 3, so the second step of the transformation is a translation of 3 units right.

Therefore, the series of transformations is:

Mapping Rule:  (x, y) → (2x+3, 2y)

Therefore, the coordinates of point C' are:

⇒ C' = (2(5) + 3, 2(2)) = (13, 4)

Answer:   (13, 4)

Infinitely many answers are possible.

====================================================

Explanation:

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because I'll be using the same steps and ideas. There are also diagrams that might help visualize what's going on.

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The translation vector from B(1,4) to C(5,2) is <4,-2> since we move to the right 4 units, and down 2 units. It's the shorthand way of writing [tex](x,y) \to (x+4,y-2)[/tex]

Double the coordinates of the translation vector <4,-2> to get <8,-4>

If we started at point B'(5,8) and followed the pathway "right 8, down 4" then we arrive at C'(13,4) as one possible answer.

We could express the steps like this

[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}-4)\\\\(5,8)\to(5+8,8-4)\\\\(5,8)\to(13,4)\\\\[/tex]

As I mentioned in the link above, there are infinitely many answers because we can change the scale factor to any nonnegative real number. For instance we could triple the coordinates of <4,-2> to get <12,-6> and follow the same outline of steps to get C'(17,2) as another possible answer.

Therefore Option B is correct

From the given table, it is found that:

a. The weight function is linear, as it has a constant rate of change.

b. The equation for the linear function is: W(x) = 0.85x + 2.22.

Linear functions are modeled according to the following rule:

y = mx + b.

In which the coefficients are:

The slope is the rate of change, and it has to be constant for the relation to be a linear function.

Relating the number of cans x and the cost of the cans C(x), the slope can be calculated as follows:

Different slopes, hence the cost function is not linear.

For the weight function, the slope can be calculated as follows:

Due to the constant rate of change, the weight function is a linear function.

Considering the slope of m = 0.85, the weight function can be written as follows:

W(x) = 0.85x + b.

When x = 8, W(x) = 6.8, hence the intercept b is found as follows:

8 = 0.85(6.8) + b

b = 8 - 0.85 x 6.8

b = 2.22.

Then the function is:

W(x) = 0.85x + 2.22.

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First, find the actual number of miles per round trip in each case.

-Hyperloop

-Airplane

Then, the cost (round trip) would be related to the constant b in both cases since it is a fixed rate. Multiply it by the maximum number of passengers,

Then, multiply the rate of consumption by the fuel costs for each mean of transportation,

Notice that it is multiplied by 2 since the rate of consumption row is given in one-way unitsThus,