15a2+12b-9a2 Solve with step by step please

The coordinates of vertex D of the parallelogram is; (0, 1)

We are given the coordinates of the parallelogram as;

A(2,4), B(5,2) and C(3,-1)

Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.

The formula for the midpoint between two coordinates is;

(x1 + x2)/2, (y1 + y2)/2

Thus;

Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2

Midpoint of BD = (5 + x)/2, (2 + y)/2

Thus;

(5 + x)/2 = 5/2

x = 0

(2 + y)/2 = 3/2

2 + y = 3

y = 1

Coordinate of D = (0, 1)

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Step-by-step explanation:

solution

let first part be 5x and second part be 9x

so ,

5x = 35

x = 35\5

x = 7

Now 9x = 9*7 = 63

this might help you thank you

Answer:

Step-by-step explanation:

Use PEMDAS to determine order of operations.

P = Parentheses

E = Exponents

M/D = Multiplication/Division

A/S = Addition/Subtraction

The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.

The next operation to perform is multiplication, which is 415 times (6.1 + 12).

The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.

6.1 + 12 = 18.1

8.3 - 415(18.1)

8.3 - 7511.5 = -7503.2

Each cone has a volume of around 60 [tex]cm^{3}[/tex]. As a result, 800 [tex]cm^{3}[/tex] of cream would be sufficient to fill around 13 cones.

The quantity of space that an item or substance occupies is measured by its volume. Typically, it is expressed in cubic quantities like cubic metres or cubic feet. Volume is frequently used to describe liquids, gases, or other pourable materials like a cup of water or a gallon of fuel. The capacity of a container, such as a tank or box, is also determined by volume.

In this question, the volume of a cone is given by the formula:

V = (1/3)π[tex]r^{2} h[/tex]

Where r is the radius of the base and h is the slant height.

In this case, the radius of the base is equal to half the base diameter (4.2/2 = 2.1 cm) and the slant height is 7.5 cm.

So, the volume of each cone is (1/3)π x (2.1)2 x 7.5 = 28.7 cm3

Therefore, the number of cones needed to fill the ice cream cone with 800 cm3 of cream is 800/28.7 = 27.9 (rounded up to 28).

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Answer:

Step-by-step explanation:

The experimental probability that the number rolled was odd is

23 over 60.

What is experimental probability?

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A trial is a repeating of an experiment that is performed a certain number of times.

We are given a table showing he frequency of each number rolled.

We know that the odd number outcomes are 1, 3 and 5.

So,

P (x = 1) = 8/60

P (x = 3) = 6/60

P (x = 5) = 9/60

So, the experimental probability that the number rolled was odd is

⇒P ( x is odd) = P (x = 1) + P (x = 3) + P (x = 5)

⇒P ( x is odd) = 8/60 + 6/60 + 9/60

⇒P ( x is odd) = 23/60

Hence, the experimental probability that the number rolled was odd is 23 over 60.

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Due to the fact that secured loans often have lower interest rates than unsecured loans, they are less expensive. They require collateral. They are less risky for the financial institution. The correct option is D.

A secured loan is one in which the borrower pledges an asset as security for the loan, turning the pledged asset into a secured debt owing to the lender (the creditor).

Some loans may be backed by assets other than your house; for instance, they may be backed by your automobile, jewelry, or other possessions. Because lenders can collect the asset in the event of a default on a secured loan, secured loans often have lower interest rates than unsecured loans.

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Answer: The length is 9 units and the width is 1 unit

Step-by-step explanation:

We can use the formula for the area of a rectangle to solve this problem. The formula is A = l * w, where A is the area, l is the length, and w is the width.

We have A = 9, and we know that w = l - 8. Substituting this into the formula, we get:

9 = l * (l - 8)

We can rearrange this to solve for l:

9 = l^2 - 8l

Adding 8l to both sides of the equation, we get:

9 + 8l = l^2

Subtracting 9 from both sides, we get:

8l = l^2 - 9

We can factor this to get:

l(l - 9) = 0

Since the product of two numbers is zero only when one of them is zero, we can set each factor equal to zero and solve:

l = 0 or l - 9 = 0

Adding 9 to both sides of the second equation, we get:

l = 9

Therefore, the length of the rectangle is 9 units.

−2 is located to the right of −4 on a horizontal number line because −2>−4. Therefore, option C is the correct answer.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.

Given that, -2 and -4 is located on number line.

Negative integers on the number line located left to zero.

If the greater integer with negative sign and go farther on left of 0 on number line, the value of integers decreases.

Therefore, option C is the correct answer.

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Answer:

Step-by-step explanation:

o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.

For the first inequality: 8r - 3 ≥ 7r - 7

Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r

Combining like terms: 15r - 3 ≥ 14r

Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0

Combining like terms: r - 3 ≥ 0

Adding 3 to both sides: r ≥ 3

For the second inequality: 2r + 4 ≤ r - 3

Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r

Combining like terms: 4 ≤ -r - 3

Adding r and 3 to both sides: 4 + r + 3 ≤ -r

Combining like terms: 7 ≤ -r

Multiplying both sides by -1: r ≤ -7

The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.

To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7:

If Mark and jada share 5 yards of ribbon equally, then each one will get 2.5 yards of ribbon using division method.

When Mark and Jada share 5 yards of ribbon equally, it means that they will divide the total amount of ribbon equally between the two of them. This is a common type of problem in mathematics that involves dividing a given quantity equally among a certain number of people or objects.

To solve this problem, we used the division operation to divide the total amount of ribbon (5 yards) by the number of people who are sharing it (2). The resulting quotient (2.5 yards) represents the amount of ribbon that each person will receive.

Using the division operation, we can write,

5 yards ÷ 2 = 2.5 yards

This problem illustrates an important concept in mathematics: the division of quantities into equal parts. This concept is used in many real-world applications, such as dividing up a pizza among a group of people or allocating resources in a company among different departments or teams.

Understanding how to divide quantities into equal parts is an important skill that can be applied in many different contexts, making it a valuable mathematical concept to learn and understand.

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The equation 5x + 6y = 4, 10x + 12y = 8 has infinitely many solution.

System of equation can be solved using elimination method, substitution method and graphical method.

Therefore, let's solve the system of equation using elimination method.

5x + 6y = 4

10x + 12y = 8

multiply equation(i) by 2

Hence,

10x + 12y = 8

10x + 12y = 8

subtract the equations

0 = 0

Therefore, the equation has infinitely many solution.

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Side a is 2.5 inches long, side b is 5 inches long and side c is 6.5 inches long. Therefore, option C is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, scale factor =2:1

Scale drawing to object the scale factor is 2:1.

Now,

a=1/2 *5 =2.5 inches

b= 1/2 *10 = 5 inches

c= 1/2 * 13 = 6.5 inches

Therefore, option C is the correct answer.

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The measure of the smallest angle is 52 degrees

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The triangle

The sum of angles in a triangle is 180

So, we have

2x + 3x - 11 + 2x + 9 =  180

Evaluate the like terms

7x = 182

So, we have

x = 26

This means that

2x = 2 * 26 = 52

3x - 11 = 3 * 26 - 11 = 67

Hence, the smallest is 52 degrees

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Answer:

(126, 101), (127, 100), (128, 99).

Step-by-step explanation:

The profit from selling one adult ticket is $10.00 and from selling one children's ticket is $5.00.

The total profit from selling A adult tickets and C children's tickets can be represented as 10A + 5C.

The goal is to find combinations of A and C that meet the following conditions:

10A + 5C >= 3750

A + C <= 500

One way to solve this problem is to use a brute force approach and try different values of A and C until we find three combinations that meet the conditions. Another way is to use a more efficient method and find the values of A and C that maximize the number of adult tickets while still meeting the profit and seating limit conditions.

Let's start by finding the maximum number of adult tickets that can be sold while still meeting the profit goal:

10A + 5C >= 3750

10A >= 3750 - 5C

A >= 375 - 0.5C

Since C must be an integer, we can round down the value of A to the nearest integer.
For example, if C = 100, then A >= 125. If we round down A to 125, then the profit from selling 125 adult tickets and 100 children's tickets would be:

10 * 125 + 5 * 100 = 1250 + 500 = 1750

which is less than the profit goal of 3750.

If we increase C by 1, then A would increase by 0.5, and the profit would increase by 5.
So, to reach the profit goal, we need to increase C until the profit is at least 3750.

Let's try C = 101. Then A >= 125.5, which we can round down to 126.

The profit from selling 126 adult tickets and 101 children's tickets would be:

10 * 126 + 5 * 101 = 1260 + 505 = 1765

which is greater than or equal to the profit goal of 3750.

So, the first combination of adult and children's tickets that meets the profit and seating limit conditions is (126, 101).

We can repeat the same process to find the second and third combinations.

For example, the second combination could be (127, 100), and the third combination could be (128, 99).

The final answer is (126, 101), (127, 100), (128, 99).

Answer:

250 $3 tickets and 100 $2 tickets were sold.

Step-by-step explanation:

3(350 – y) + 2y = 950

1050 – 3y + 2y = 950

3y – 2y = 1050 – 950

y = 100

Substitute y = 100 into equation 1

x + 100 = 350

x = 250

a. The amount of copper in a bronze brooch weighing 360g is 216g.

b. The total weight of the bronze brooch is 745g.

If an item is made of two different items, the ratio of the quantities of those two items contributes to the amount of the compound item. With the help of that ratio, the unknown quantity can be determined.

a.

The ratio of copper to tin in bronze is 9:1.

So, the portion of copper in the bronze is 9 out of 10, that is, 0.9.

The total weight of the bronze brooch is 360g.

Find the amount of copper in that brooch.

360×0.9=324

Therefore, the copper in a 360g bronze brooch is 324g.

b.

The amount of copper in the bronze brooch is 670.5g.

Also, the portion of copper in the bronze is 0.9.

Let, the total weight of the bronze brooch is Xg.

So, the equation becomes 0.9X=670.5.

Find the value of X.

0.9X=670.5

X=745

Therefore, the total weight of the bronze brooch is 745g.

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The dimensions of Yura's picture 10×7 square units. The length of Yura's picture 10 units and the width of 7 units.

What is a rectangle?

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.

The number of lines along the length is 11.

The length of the frame is 10 units.

The number of lines along the width is 8.

The width of the frame is 7 units

The dimension of an object is length × width.

The dimension of the frame is 10 units × 7 units.

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The two values of y such that the barn is 50 yards from the well are given as follows:

y = -47 and y = 53.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following equation:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For this problem, we have that D = 50, hence the equation is given as follows:

sqrt[(-2 - (-2))² + (y - 3)²] = 50

y - 3 = ±50.

Hence the values of y are given as follows:

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Answer:

We can solve the above mathematical problem with the following approach.

We know that (a²-b²) = (a + b) (a - b).

So the given equation can be written as:

1. The value of line EF is 14.3

2. not enough info to get angle ECB

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.

EF is congruent to AB

GB is congruent to EH

Therefore AG will be congruent FH

therefore FH = 12

tan 40 = 12/EF

EF = 12/tan40

EF = 12/0.839

EF = 14.3

There is not enough info to get angle ECB

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The solutions are given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Part A

the dotted line formes the thrid side of the triangle.

part B

The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.

part c

If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.

part D

You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.

part e

The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.

part f

Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters

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The total amount accrued, principal plus interest, with compound interest on a principal of $ 1,500.00 at a rate of 4.9 % per year compounded 1 times per year over 10 years is $2,420.17.

Using the compound interest formula is

Compound interest is calculated by multiplying the initial principal amount (P) by one plus the annual interest rate (R) raised to the number of compound periods (nt) minus one.

A= Total amount =?

P= Principal amount = 1500

r=Rate of interest =4.9 %=0.049

t= time =10years

n= compounding = annually =1

Using the above data and formula, we get:

First, convert R as a percent to r as a decimal

[tex]& \mathrm{r}=\frac{\mathrm{R}}{100} \\[/tex]

[tex]& \mathrm{r}=\frac{4.9}{100} \\[/tex]

[tex]& \mathrm{r}=0.049 \text { rate per year, }[/tex]

Then solve the equation for A

[tex]& \mathrm{A}=1,500.00\left(1+\frac{0.049}{1}\right)^{(1)(10)} \\[/tex]

[tex]& \mathrm{A}=1,500.00(1+0.049)^{10} \\[/tex]

[tex]& \mathrm{~A}=\$ 2,420.17[/tex]

The total amount accrued after 10 years is $2,420.17.

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Answer:

120 general admission

280 with student with a student ID

Step-by-step explanation:

x is tickets for general admission

y is tickets with a student ID

5x+3.5y=1580

x+y=400

y=400-x

5x+3.5(400-x)=1580

5x+1400-3.5x=1580

1.5x=180

x=120

120+y=400

y=280

The average rate of change of R(t) over the time intervals [t, t + h] , where t is as indicated and h = 1, 0.1, and 0.01 are 210,100 and 100.

What is Differentiation?

Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilising only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

Given function :  R(t) = 240 + 30t^3

  R'(t) = 90 t²

So, the average rate of change of R(t) is 90 t² .

Now, over the time interval [t, t + h], it will be as follows:

we know that, f'(t) = {f(t+h) - f(t)} / h

So, when h = 1,  f'(1) = {f(1+1) - f(1)} / 1

                                = f(2) - f(1)

                                = 480 - 270 = 210

when h = 0.1 , f'(1) = {f(1+0.1) - f(1)} / 0.1

                             = {f(1.1) - f(1)} / 0.1

                             = (280 - 270) / 0.1 = 100

when h = 0.01 , f'(1) = {f(1+0.01) - f(1)} / 0.01

                                 = {f(1.01) - f(1)} /0.01

                                 = (271 - 270) / 0.01 = 100

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The two plans cost the same for 60 minutes of calls. And  the two plans cost the same for 60 minutes of calls.

We can set the cost of the two plans equal to each other and solve for the number of minutes:

Plan A: $15 + $0.12x (where x is the number of minutes)

Plan B: $8 + $0.17x

$15 + $0.12x = $8 + $0.17x

Subtracting $8 from both sides:

$7 + $0.12x = $0.17x

Subtracting $0.12x from both sides:

$7 = -0.05x + $0.17x

Adding 0.05x to both sides:

$7 + 0.05x = $0.17x

Dividing both sides by 0.12:

x = (7 / 0.12) / (1 - 0.17/0.12) = 60 minutes

So the two plans cost the same for 60 minutes of calls. To find the cost, we can plug x = 60 into either equation:

Plan A: $15 + $0.12 x 60 = $15 + $7.20 = $22.20

Plan B: $8 + $0.17 x 60 = $8 + $10.20 = $18.20

So the two plans cost the same when there are 60 minutes of calls, and they both cost $18.20

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Complete Question

A telephone company offers two monthly plans. The a plan costs $15 plus $0. 12 additional for each minute of calls. Plan b costs $8 plus an additional 0.17 for each minute of calls For how many minutes of calls do the two plans cost the same? What is the cost at which two plans cost the same?

a) The percentage of flashlights that have a life of 55 to 65 is about 36%

b) The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

Standard normal distribution is a type of continuous distribution with a mean of zero and standard deviation of one. The random variables are standardized into z scores using z score formula.

a) The Chebyshev's theorem states that; for sample or population, percentage (p) of values are contained within two, three or more standard deviations within the mean, provided that the values of k is greater than 1:

P(%) = [tex]1-\frac{1}{k^2}[/tex]

Calculate the value of k:

[tex]k =\frac{65-60}{4}=1.25[/tex]

The percentage is calculated as;

p(%) = [tex]1-\frac{1}{1.25^2}[/tex] = 36%

The percentage of flashlights that have a life of 55 to 65 is about 36%

b) k = [tex]\frac{68-60}{4}=2[/tex]

p(%) = [tex]1-\frac{1}{2^2}[/tex] = 75%

The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

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Answer:

Step-by-step explanation:

no idea sorry :/

The length of the altitude CH is 17.234.

Altitude of a triangle is defined as the perpendicular line segment joining the vertex to the opposite side.

The figure for the triangle is given below.

Here the area of a triangle can be found in two ways.

Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

Consider the triangle ABC given below.

Area of the triangle when considered base as BC and altitude as AC is,

Area, A = [tex]\frac{1}{2}[/tex] × BC × AC

BC = AB Sin (50) = 35 sin(50)

AC = AB Sin (40) = 35 sin(40)

A = [tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40))

Area of the triangle when considered base as AB and altitude as CH is,

Area, A = [tex]\frac{1}{2}[/tex] × AB × CH

A = [tex]\frac{1}{2}[/tex] × 35 × CH  

Area of the same triangle will be equal when find in different ways.

[tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40)) = [tex]\frac{1}{2}[/tex] × 35 × CH  

Cancelling the terms which are on both sides,

CH = 35 sin(50) sin(40)

CH = 35 × 0.766 × 0.643

CH = 17.234

Hence the length of the altitude is 17.234.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's start with eliminating choices first ~

The value decreases as years pass by, so the value multiplied by initial value should be an exponent on the value that is less than 1.

So, only the choices with exponent on 0.9 should be qualified, eliminating the choices A and C

Next, the initial value of motorcycle is 12000 according to table. so at x = 0, v(x) should be equal to 12000.

Now, let's check option B

[tex]\qquad \sf  \dashrightarrow \: v(x) = 12000(0.9) {}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: v(0) = 12000(0.9) {}^{0} [/tex]

[tex]\qquad \sf  \dashrightarrow \: v(0) = 12000(1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v(0) = 12000[/tex]

And since choice B satisfy each and every condition, that's the correct answer ~

The constant of proportionality for this relationship is the circumference of the wheel.

A proportional relationship between two variables means that the ratio of the two variables is constant. In other words, if the independent variable (time in this case) increases, the dependent variable (the amount of money Steven charges) will increase proportionally.

The distance a wheel can travel is proportional to its radius.

wheel radius(in.)      distance in 4 revolutions (in.)

4                                    32π

3.5                                 28π

0.25                               2π

The distance a wheel can travel in one revolution is equal to the circumference of the wheel. So, if we know the radius of the wheel, we can calculate its circumference using the formula:

circumference = 2π × radius

Then, we can use the circumference to find the distance the wheel can travel in a given number of revolutions by multiplying the circumference by the number of revolutions. In the table provided, we can see that for each wheel radius, the distance traveled in 4 revolutions is a multiple of the circumference of the wheel, which confirms that the constant of proportionality is the circumference.

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