In parallelogram TUVW, the diagonals tv and uw intersect at point z. If tz =5y -1, uz =2x, vt =78, and wz =3y +6, what is the sum of x+y

Answer:

r = d(x-e)

or r = dx - de

Step-by-step explanation:

x = e + [tex]\frac{r}{d}[/tex]  subtract e from both sides.

x - e = [tex]\frac{r}{d}[/tex]  Multiply both sides by d

d(x -e) = r

or

dx -de = r

If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x

The perimeter of the triangle is the summation of all three sides of the triangle

Perimeter = a + b + c

= (x + 5) + (2x - 3) + (21 - x)

= 2x + 23

= 23 + 2x

Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle  23 + 2x.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.

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Answer: the space shuttle

Step-by-step explanation:

Answer:(2x+1)(3x-4)

Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)

Answer:

(3x - 4)(2x - 1)

Step-by-step explanation:

6x^2 - 5x - 4

When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)

x^2 - 5x - 24

Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)

24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.

As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.

One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.

Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.

(6x - 8)(6x - 3)

We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.

(6x - 8)/2 and (6x - 3)/3.   3*2 = 6

(3x - 4)(2x - 1)

The conclusion about the congruent triangles is explained below.

What is congruent triangles?

Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.

Two pairs of corresponding side lengths are proportional by the same ratio. Also the angles are congruent.

So, the triangles are congruent.

This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.

Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.

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The percentage is calculated by dividing the required value by the total value and multiplying by 100.

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

760%

This can be written as a fraction.

760/100

= 76/10

= 38/5

or

= 7(3/5)

Thus,

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

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Answer:

4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)

4 x^2 (x + 6)        seems to be the lowest factor

The amount of pizza ate by Simon, Eira and Martin is

Simon eats 3/8 of a pizza = 3/8

The amount of pizza left after Simon ate

= 1 - 3/8

= 5/8

Eira and Martin eat an equal share of the pizza that is left

that is the amount left was shared into 2

= 5/8 ÷ 2

= 5/16 each for both of them

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Answer:6

Step-by-step explanation:

the total force exerted on the new dam to that on the original dam f new is given by F = 624010000 lb.

What is Pascal's Principle.?

Consider a flat surface that is immersed vertically in a fluid whose weight density is p, according to Pascal's Principle.

A flat surface experiences fluid force (F) which is

F = ∫ph(x)w(x) dx

where h(x) is the height of the point x in the x-axis' vertical direction and w(x) is the surface's width.

to determine fluid force applied

Assume that x is equal to the height of the water. At height x on the dam, width of the dam is w(x) = 200 ft (given), and height is h(x) = x ft.

F = ∫ph(x)w(x) dx

F =0→100 ∫62.4 x  200 dx

F = 12480*  0 →100∫ x dx

F = 12480*  0 →100(x²/2)

F =

F = 6240((100)²- (0)²)

F= 6240(10000)

F = 624010000 lb

Hence the total force exerted on the new dam to that on the original dam f newf is given by F = 624010000 lb.

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Answer:

Step-by-step explanation:

A line that is perpendicular to another will have the opposite slope.

y = [tex]-\frac{1}{3}[/tex]a + b

To find b, substitute y and a with the given values

6 =  [tex]-\frac{1}{3}[/tex](-6) + b

6 = 2 + b

-2  -2

4 = b

thus

y = [tex]-\frac{1}{3}[/tex]a + 4

A table of values and an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe are as follows:

C                         t

$10.60                1

$11.20                 2

$11.80                 3

C = 0.60t + 10.

In order to write an equation for the total cost, we would assign variables to the amount of time used and the total cost of using a computer, and then translate the word problem into algebraic equation as follows:

Since the cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use, an equation for the total cost is given by:

C = 0.60t + 10

When t = 1, we have:

Total cost, C = 0.60(1) + 10

Total cost, C = $10.60.

When t = 2, we have:

Total cost, C = 0.60(2) + 10

Total cost, C = $11.20.

When t = 3, we have:

Total cost, C = 0.60(3) + 10

Total cost, C = $11.80.

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Answer:

y = - [tex]\frac{3}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

6x + 4y = 16 ( subtract 6x from both sides )

4y = - 6x + 16 ( divide through by 4 )

y = [tex]\frac{-6}{4}[/tex] x + [tex]\frac{16}{4}[/tex] , that is

y = - [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form

For a student with a shoe size of 9, the student's height is equal to 65 inches.

For a student with a height of 60 inches, the student's shoe size is equal to 6.5.

From the information provided, an equation for the line of best fit that represents or models the heights x (in inches) and shoe sizes y of several student is given by this mathematical expression:

y = 0.50x - 23.5

Where:

For a student with a shoe size of 9, the student's height is given by:

y = 0.50x - 23.5

0.50x = y + 23.5

Student's height, x = (y + 23.5)/0.50

Student's height, x = (9 + 23.5)/0.50

Student's height, x = 32.5/0.5

Student's height, x = 65 inches.

For a student with a height of 60 inches, the student's shoe size is given by:

y = 0.50x - 23.5

y = 0.50(60) - 23.5

y = 30 - 23.5

y = 6.5

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The side of the hexagonal prism is 8.77 cm

What is a hexagonal prism?

A hexagonal prism has 8 faces, 18 edges, and 12 vertices. Out of the 8 faces, 6 are parallelograms, and 2 are hexagons, and that's why it is called a hexagonal prism. These hexagons are at the base and the top as the opposite faces of a prism are the same.

Given data ,

Let the volume V of the hexagonal prism be V = 2800 cm³

Let the height of the hexagonal prism be H = 14 cm

Now , let the side of the hexagonal prism be = A cm

The volume of the hexagonal prism be V = ( ( 3 √3 / 2 ) ) a²h

where a is the side of the hexagonal base

h is the height of the hexagonal prism

Substituting the values in the equation , we get

The volume of the cube be V = ( ( 3 √3 / 2 ) ) a²h

V = ( ( 3 √3 / 2 ) ) a²h

2800 = ( 3 √3 / 2 ) x a² x 14

200 = ( 3 √3 / 2 ) x a²

Multiply by 2 on both sides of the equation , we get

400 = 3√3 x a²

Divide by 3√3 on both sides of the equation , we get

a² = 76.98

Taking square roots on both sides of the equation , we get

a = 8.77 cm

Therefore , the value of a is 8.77 cm

Hence , The side of the hexagonal prism is 8.77 cm

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The probability that a point chosen at random lies in the shaded region is 0.28

From the question, we are to find the probability that a point chosen at random lies in the shaded region.

The shaded region is a triangle.

The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle

First, we will calculate the unknown side of the triangle

Let the unknown side be x.

Then, from the Pythagorean theorem, we can write that

12² = 6² + x²

144 = 36 + x²

x² = 144 - 36

x² = 108

x = √108

x = 6√3

From formula,

Area of a triangle = 1/2 × base × height

Area of the triangle = 1/2 × 6 × 6√3

Area of the triangle = 18√3 square units

Now, we will determine the area of the circle

Area of a circle = πr²

Where r is the radius

From the given information,

Diameter of the circle = 12

But,

Radius = Diameter / 2

Therefore,

r = 12/2

r = 6

Thus,

Area of the circle = 3.14 × 6²

Area of the circle = 113.04 square units

Now,

The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04

The probability that a point chosen at random lies in the shaded region = 0.2758

The probability that a point chosen at random lies in the shaded region ≈ 0.28

Hence, the probability is 0.28

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The area under the curve r²=50sin2Θ is (15.71)unit square

A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.

The given parabola is r²=50sin2∅,

where r=5

Where r=radius of the circle of the parabola

Substitute r=5 in the parabola

5²=50sin2∅

Simplifying the equation to find the value of ∅25=50sin2∅[tex]\frac{25}{50}[/tex]=sin2∅

Finding the sine inverse, we havesin[tex]^{-1} 0.5=2[/tex]∅30⁰=2∅∅=15⁰

The angle made by the parabola is 15⁰

note r=5

Area = 22/7 × 5

Area = 15.71 unit²

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The length of OB' after dilation 3 units.

What is dilation of triangle?

Dilation is a method for producing similar figures. By increasing distances by the scale factor, each point is extended outwards from the center point.

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

in a given triangle,

Dilation is using the rule d o,4, it means is that triangle was enlarged by a scale factor of 4 with point O as the center of dilation.

[tex]ob = \frac{3}{4}[/tex]

[tex]o'b' = 4 * \frac{3}{4}[/tex]

[tex]o'b' = 3 units[/tex]

The length of OB' after dilation 3 units.

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The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Let the number of gigabytes consumed be x,

The total cost per month will be 69.50 + 5x

accoding to the question the bill would not exceed $90.

So the inequality,

69.50 + 5x ≤ 90

Simplification for the maximum gigabyte he can buy,

5x ≤ 90 - 59.90

5x ≤ 20.5

x ≤ 4.1

Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

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The value   of   x≥2  are: 2,4,5,6

Inequality—the state of not being equal, particularly in status, rights, and opportunities1—is central to social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.

An inequality compares two values to determine whether one is less than, greater than, or simply not equal to the other. a b indicates that a is not equal to b.

Given ,

2x - 4≥1

State the values of x within 1 and 6

2x - 4≥1

2x ≥ 1 +4

2x ≥ 5

Divide both sides by 2

2x/2 ≥  5/2

x = 2

(1,6) is an open interval which means that 1 and 6are not inclusive of the values of x.

So:

therefore the values of   x≥2  are: 2,4,5,6

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The test statistic for the given test is t = 2.59.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

Given data:

                    [tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0

Now the test statistic can be computed as

                [tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]

                [tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]

Hence, the test statistic for the given test would be t = 2.59.

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The most petunias Ying Ying will ever purchase is 28.

Given data;

Using x as the total amount of money in her wallet and m as the price per petunia

The money remaining in the wallet after buying 2 petunias equals $6.50 according to the provided table.

Now,

6.50 = x - 2m ⇒ (I)

In addition, $5 was left in the wallet after the purchase of 8 petunias,

5 = x - 8m ⇒ (II)

Here, (I) - (II);

6.50 - 5 = x - 2m - x + 8m

1.50 = 6m

m = 0.25

One petunia costs $0.25.

Therefore, the total number of petunias Ying Ying buys at most is,

When 14 petunias brought money left in the wallet is $3.50.

Now,

→ 3.50/0.25 = 14

The total number of petunias Ying Ying buys at most is 14 + 14 = 28

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Answer:

The 8th term of the AP= 113/5 or 22.6

Answer:

22.6

Step-by-step explanation:

Given:

Find the value of a₆:

[tex]\implies a+a_6=20[/tex]

[tex]\implies a_6=20-a[/tex]

[tex]\implies a_6=20-3[/tex]

[tex]\implies a_6=17[/tex]

Therefore:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

Substitute a = 3 and a₆ = 17 into the formula and solve for d:

[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\implies a_n=3+(n-1)2.8[/tex]

[tex]\implies a_n=3+2.8n-2.8[/tex]

[tex]\implies a_n=2.8n+0.2[/tex]

To find the 8th term, substitute n = 8 into the equation for the nth term:

[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]

Tamar raise $15

What is division ?

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

A group is divided into equal portions when it is divided. For a game or activity, division can be used to divide a class into equal groups. It can also be used to divide a pizza among friends in equal pieces. Divided into partitive and quotative, there are two forms of division.

There are 2 ways one by writing equation and the other by using logic

1. by using equation

3*x=45

x=45/3

 = 15

2. Logically

If Jack has $45 which is 3 times Tamara's we can reverse the statement:

45/3

=15

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Answer:

67

Step-by-step explanation:

67

Answer: A i think but im so to sure

Step-by-step explanation: im taking the test rn and ill come back after and see if its right or wrong

hybrids research When she does, the camden depositor is actually higher than the reported percentage. Here, we have the report 126 percent, the winners on the portion computer. It indicates that the proportion of the underling hypothesis at noon will be equal to 26.

The abon 26 point notte will be greater than the b of the means 10. In this question, which is the right-hand exam, we will provide the sembiante 340, which will be equal to 31 percent, and we must contend with the statistical test. The test is therefore equal to the z moving forward. It will be calculated using the following formula: hat: minus b over square root, times: 1 minus p over the hot equal to 131 p equal to 261 square 261 minus 26. If we compare it to my 340 point, we get 126 times 74 divided by 340, then we take the square root of that number. The 131 minus 7.26 is then divided by the industry standard.I respond with a number equal to 2.10, rounding up to two decimal places before moving on to the step's following inquiry. 3. This is the 110 test since the test pair is on 1 here and then the next 1 in his right hand. The choice must be made hypotheses, though. Rule and we need to identify the critical value, and since that will be the right hand, we must make sure that the critical value is both equal to and far beyond that. 05. It will check the z table to see if the value equals 1.645, and if it does, we'll use the decision rule to reject the null hypothesis. If so, the test result will exceed the cutoff of 1.645 points, and we will observe Because the test we determined to be equivalent to 2.10 is higher than the 1.645 point, we can observe that. We will thus rule out the known hypothesis and come to the conclusion that there is sufficient evidence to back up the prediction that the proportion will be higher than 26%.

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Answer:

1. 1914 ÷ 7 = 273 R.3

2. 6365 ÷ 8 = 795 R.5

3. 7989 ÷ 2 = 3994 R.1

4. 5177 ÷ 7 = 739 R.4

5. 4178 ÷ 3 = 1392 R.2

6. 940 ÷ 9 = 104 R.4

7. 46 ÷ 3 = 15 R.1

8. 96935 ÷ 9 = 10770 R.5

9. 64 ÷ 3 = 21 R.1

10. 761 ÷ 3 = 253 R.2

When one independent variable affects the result differently based on the values of another independent variable, this is known as an interaction.

What does the statistical term "interaction" mean?

When two or more variables interact to impact a third variable in a non-additive way, this is known as an interaction in statistics.

                   To put it another way, the two variables interact to produce a result that is greater than the sum of their parts.

Give a definition of interaction and an example?

a time when two or more items or people interact or communicate with one another - There isn't enough interaction between the management and the employees.

                                Language games typically aim to promote student interaction.

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The evaluation of the trendline in line graph of the trendline displaying the value of a 2000 Toyota Camry since the year 2000 are as follows;

a. Independent variable; Time

Dependent variable; Value

b. The equation is; V = 22,500 - 1,166.[tex]\overline 6[/tex]·t

c. The y-intercept is at the point (0, 22,500), which indicates that the value of the 2000 Toyota Camry in the year 2,000 is $22,500

d. The slope of the trendline is -1,166.[tex]\overline {6}[/tex], which indicates that the annual reduction in the price of the 2000 Toyota Camry is $1,166.[tex]\overline 6[/tex]

e. The value of the car in 2017 based on the trendline is $2,666.[tex]\overline{6}[/tex]

A trendline is a line drawn through a scatterplot, minimizing the distances between the points in the chart and the line itself, and shows the trend of the scatterplot.

a. The independent variable is the variable that is the input variable of the function, which the researcher can vary or the value that is controlled.

Therefor;

The dependent variable is the value under study, therefore;

b. The points on the line graph are; (0, 22,500), and (15, 5,000), the slope is therefore;

m = (5,000 - 22,500)/(15 - 0) = -3,500/3

The equation is therefore;

V - 22,500 = -3,500/3·t

V = -3,500/3·t + 22,500

c. The y-intercept of the trend line is (0, 22,500), which indicates that in the year 2,000, the price of the 2,000 Toyota Camry was $22,500

d. The slope of the trend line is -3,500/3 = -1,166.[tex]\overline 6[/tex], which indicates that the value of the Toyota Camry, 2000, reduces at a rate of $1,166.[tex]\overline 6[/tex], each year.

e. In the year 2017, t = 17, therefore;

V = 22,500 - (3,500/3) × 17 = 2,666.[tex]\overline {6}[/tex]

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Answer:

A point. (3,5) represents a point that is 3 units to the right of the Y-axis (x = 3) and 5 units above the X-axis (y = 5).

Step-by-step explanation:

To plot a point, you start at origin and move however many units are specified. To do this, you can either;

 A.) Start at origin. Move along the X-axis to 3, and then go straight up five units on the Y-axis. This will plot the point.

 B.) You can also do this with your other value. Starting at origin, move along the Y-axis to 5. Go right on the X-axis three units, and you will be at the same point.