Given the following information, find the equation in vertex form, factored form and standard form.
1. Vertex (1, 4) Point (2, -1)
Vertex form
Standard form

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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Answer:

He can buy 4 bunches of his grapes.

Step-by-step explanation:

Answer:

a) 0.0004

b) 0.9604

c) 0.02

Step-by-step explanation:

When trying to find the probability of a sequence occurring you would simply need to multiply the probability of both of those things occurring together. Since the probability of an alternator failing is 0.02 then the probability of both failing would be...

0.02 * 0.02 = 0.0004

Now the probability of an alternator not failing is 0.98 (100% or 1 minus 0.02) therefore, the probability of both failing would be...

0.98 * 0.98 = 0.9604

Finally, the probability of one or the other failing would simply be the same as the probability of a single alternator failing which is 0.02

Answer:

hopefully i got this right lol

Step-by-step explanation:

First Question:

2, 1

Second Question:

I'm assuming the lawn is the shaded region, which to solve you will need to calculate the area of the trapezoid and then subtract that by the area of the building.

EQUATION for area of building: l*w

48 * 64 = 3072^2ft

EQUATION for area of trapezoid: (a+b)/2h

subsitute

(100 + 150)/2 (80) = 10000

10000 - 3072 = 6928^2 ft

Third Question:

Answer: 26 1/4

Explanation: In order to find the volume of any rectangular prism, you need to multiply the length, width, and height. In this case, the equation is: 6 * 1 1/4 * 3 1/2 = 26 1/4

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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Answer:

See below

Step-by-step explanation:

a.

\(\dfrac{10}{4}=\dfrac{5(2)}{2(2)}=\dfrac{5}{2}\)

b.

\(\dfrac{20}{15}=\dfrac{4(5)}{3(5)}=\dfrac{4}{3}\)

c.

\(\dfrac{-24}{42}=\dfrac{-4(6)}{7(6)}=\dfrac{-4}{7}\)

d.

\(\dfrac{-18}{-14}=\dfrac{-2(9)}{-2(7)}=\dfrac{9}{7}\)

Hope this helps!

Answer:

$898

Step-by-step explanation:

Based on Joey's debt-to-income ratio, the maximum monthly rent payment he can make and still maintain the DTI ratio is b. $898.

Joey has a DTI ratio of 36% which means that his maximum debt payment should be 36% of his income. This amount would be:

= DTI x monthly income

= 36% x 3,600

= $1,296

This can be found as:

= Maximum monthly debt payment - Car payment - Credit card payment

= 1,296 - 178 - 220

= $898

In conclusion, option B is correct.

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Answer: \(\boxed{y=\frac{4}{5}x-2}\)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.

Substituting into point-slope form,

\(y-6=\frac{4}{5}(x-10)\\\\y-6=\frac{4}{5}x-8\\\\\boxed{y=\frac{4}{5}x-2}\)

The total number of students who graduated from the Cincinnati universities and colleges are 15382.

We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.

The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.

We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.

Let the total number of students be x.

ATQ:

6.67 % x = 1026

6.67 x = 102600

667 x = 10260000

x = 10260000 / 667

x = 15382.309

Rounding off to the nearest whole number is:

x = 15382.

Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.

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answer:

Amount of sales tax ≈ $2.06 dolla

Price with sales tax ≈ $27.06 dollars

8.25% × 25 =

8.25/100 × 25 =

0.0825 × 25 =

2.0625=

2.06;

Answer:

10-2x=19x+2-5x

We move all terms to the left:

10-2x-(19x+2-5x)=0

We add all the numbers together, and all the variables

-2x-(14x+2)+10=0

We get rid of parentheses

-2x-14x-2+10=0

We add all the numbers together, and all the variables

-16x+8=0

We move all terms containing x to the left, all other terms to the right

-16x=-8

x=-8/-16

x=1/2

The item most likely to weigh 2 kilograms is a roast chicken.

The size, breed, and any other ingredients or stuffing used can all affect the weight of a roast chicken. Weights of roast chickens can range from petite ones weighing less than 1 kilogram to larger ones weighing more than 2 kilograms.

The other things that we have there would either weigh less than 2 Kg such as a tea bag or much more than 2 Kg such as a horse. The egg and the tea a very light and would be less than 2 Kg in weight while the bag and the horse would be above 2 Kg in weight.

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Answer:

square, triangle, trapezoid,rectangle

The Two-dimensional figures are square, triangle, rectangle, and trapezoid.

Two-dimensional shapes do not have any thickness and can be measured on only two faces. These can be drawn on a sheet of paper with the constitution of two axises only.

The Two-dimensional figures that are cross-sections for each of the three-dimensional solids are:

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By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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Answer:

the slope of the points (4,-3) and (5,0) is 3

Step-by-step explanation: I used the formula y2-y1 over x2-x1 will give you the answer hope this helped!

Answer:

\(\boxed {\boxed {\sf m=3}}\)

Step-by-step explanation:

We are asked to find the slope of the line that passes through (4, -3) and (5,0).

The slope is the number that tells us the steepness and direction of a line. It is the rise over run, or the change in y over the change in x.

\(m= \frac{ \Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}\)

In the slope formula, (x₁, y₁) and (x₂, y₂) are the points the line passes through. The points we are given are (4, -3) and (5,0). If we match the value with its corresponding value, we see that:

Substitute the values into the formula.

\(m= \frac{0 - -3}{5-4}\)

Solve the numerator. Remember that 2 back to back subtraction signs become an addition sign.

\(m= \frac{3}{5-4}\)

Solve the denominator.

\(m= \frac{3}{1}\)

Divide.

\(m=3\)

The slope of the line is 3.

Answer:

-14

Step-by-step explanation:

This question is really simple! Let me show you how I would work it:

1. 6 - 10 = -4

2. 82 - 100 = -18

3. Rewrite the equation like this: -4 + n = -18

4. -18 - -4 = -14. n = -14.

In linear equation, -1.15  is the value of 21 over 4 − 32 over 5.

What in mathematics is a linear equation?

An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.

                                An equation with only one variable is called a univariate linear equation. It contains the expression Ax + B = 0. where A and B are any two real numbers and x is an ambiguous variable with only one possible value. 

(21/4) - (32/5)

=   21 * 5 - 32 * 4/ 20

=  105 -  128/20

= -1.15

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Answer:

29x-12

Step-by-step explanation:

29x-12

Step-by-step explanation:

8•x=8×

8•-5=-40

7•3x=21x

7•4=28

-40+28=-12

21x+8x=29x

Answer:

Step-by-step explanation:

hello,

let s assume that we are on \([0;+\infty[\)

\(f(x)=x^2\)

if you are looking for

\(g(x)=f^{-1}(x)\)

then

\(g(x)=\sqrt{x}\)

Answer:Find the equation of a line.whose slope is 4 and which passes through the point (5, - 7) Class 11. >> Applied Mathematics. >> Straight lines. >> Various forms of the equation of a line. >> Find the equation of a line.whose slope. Question. Find the equation of a line.

Step-by-step explanation:

Answer:

The answer c for the first one The second answer is b

Step-by-step explanation:

Answer:

c and b is actuallt correct

Step-by-step explanation:

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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A. Yes

B. Yes.

C. No.

D. Yes

E. No

F. Yes

Answer:

The answer is D

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary.

A statistical question is one that can be answered by collecting data and where there will be variability in that data

The only one that can have a variety of answers is the last one.

A, B, and C are countable and do Not Vary or change in amount they remain the same. There will always be 12 months in a year. 3 wheels on a tricycle and the amount of stripes in the flag will not change. If the question ask something that can change or vary it is a Statistical question. Like for example "How many minutes do 6th grade students typically spend on homework each week?" and  “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.

A Good Statistical Question Produces Data with Variability

A statistical question is one that requires the collection of data with expected variability in it. The data collected changes in value. You can quantify them. If the data could not be measured, then you have to think it over again.

Answer:

The distance from the vertex to the directrix.

Step-by-step explanation:

According to this question, we are speaking about a parabola, which has the characteristic that the distance from the vertex to the focus is equal to the least distance from the vertex to the directrix.

Hence, the right answer is: The distance from the vertex to the directrix.

The length of e is 29.53 inches.

In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".

Given:

f= 33 inches

<F= 140, <D = 5

Now,

<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35

Using Sine law

sin F / f = sin E/ e

sin 140 / 33 = sin 35 / e

0.642/ 33 = 0.573 / e

0.0194 e= 0.573

e= 29.53 inches

Hence, the length of e is 29.53 inches.

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