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(5^2)^3×7^2×7^3

The values of x in the equation are x = 1 and x = 13

Equations are mathematical statements that express the equality of two expressions using mathematical symbols such as variables, numbers, and operations.

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

(x - 7)^2 = 36

Take the square root of both sides of the equation

So, we have the following representation

x - 7 = ±6

Add 7 to both sides

x = 7 ± 6

Evaluate the expression

x = 1 and x = 13

Hence, the solutions are 1 and 13

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Therefore , the solution of the given problem of unitary method comes out to be N69,750 was given as the water rate for 7500 litres of water.

One may use this commonly utilized ease, preexisting variables, or any important elements from the initial Diocesan customizable query to achieve the goal. If so, there will be another chance to engage with the object. If not, every important component that influences the manner in which evidence of an algorithm functions will be lost.

Here,

The price for the first 500 gallons is N5 per litre, so

=> 500 * N5 = N2,500.

The price for the following 500 gallons is N8.00 per litre, or

=> 500 * N8.00 = N4,000.

The expense for this tier is

=> 3000 * N10.00 = N30,000 because the following 3000 litres (from 1501 to 4500 litres) are charged at N10.00 per litre.

The expense for this tier is

=> 3000 * N10.00 = N30,000 because the final 3000 litres (from 4501 to 7500 litres) are also charged at N10.00 per litre.

As a result, the full price for 7500 liters of water is:

The sum of N2,500, N3,250, N4,00, N30,000, and N30,000 is N69,750.

Therefore, N69,750 was given as the water rate for 7500 litres of water.

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Answer:

∠ Y = 124°

Step-by-step explanation:

given the triangles are congruent , then corresponding angles are congruent, that is

∠ Y = ∠ N = 124°

The value for x is 4√3. The solution has been obtained by using the Pythagoras theorem.

What is Pythagoras theorem?

Pythagoras' Theorem states that the square of a right - angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.

We are given the length of the hypotenuse to be 8.

Let the base be 'y'.

So, using Pythagoras theorem,

[tex]x^{2} + y^{2} = 8^{2}[/tex]

From this, we get

[tex]y^{2} = 8^{2} - x^{2}[/tex]   ...(1)

Also,

[tex]2^{2} + Perpendicular^{2} = y^{2}[/tex]    ...(2)

From the figure, we also know that

[tex]6^{2} + Perpendicular^{2} = x^{2}[/tex]

So,

[tex]Perpendicular^{2} = x^{2} - 6^{2}[/tex]

On substituting this in (2), we get

[tex]2^{2} + x^{2} - 6^{2} = y^{2}[/tex]       ...(3)

On equating (2) and (3), we get

⇒[tex]2^{2} + x^{2} - 6^{2} = 8^{2}-x^{2}[/tex]          

⇒ 4 + [tex]x^{2}[/tex] - 36 = 64 - [tex]x^{2}[/tex]

⇒ [tex]2x^{2}[/tex] - 32 = 64

⇒ [tex]2x^{2}[/tex] = 96

⇒ [tex]x^{2}[/tex] = 48

⇒ x = 4√3

Hence, the value for x is 4√3.

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The equation of the straight line joining A to B is y = (1/2)x + 3, the equation of the straight line joining B to C is y = (1/2)x + 3, and A, B, and C are collinear.

What are collinear points?

Collinear points are three or more points that lie on the same straight line. In other words, if three points A, B, and C are collinear, then there exists a straight line that passes through all three points. To determine if three or more points are collinear, we can find the slope of the line that passes through any two of the points. If the slope is the same for all possible pairs of points, then the points are collinear. Otherwise, they are not collinear.

a) To find the equation of the straight line joining A to B, we can use the slope-intercept form of the equation of a line:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

The slope of the line passing through A and B is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (-8, -1) and (x₂, y₂) = (-4, 1).

m = (1 - (-1)) / (-4 - (-8)) = 2/4 = 1/2

To find the y-intercept, we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

where (x₁, y₁) = (-8, -1) and m = 1/2.

y - (-1) = (1/2)(x - (-8))

y + 1 = (1/2)(x + 8)

y = (1/2)x + 3

Therefore, the equation of the straight line joining A to B is y = (1/2)x + 3.

b) To find the equation of the straight line joining B to C, we can use the same method:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (-4, 1) and (x₂, y₂) = (12, 9).

m = (9 - 1) / (12 - (-4)) = 8/16 = 1/2

Using point-slope form with the point (x₁, y₁) = (-4, 1) and slope m = 1/2:

y - 1 = (1/2)(x - (-4))

y - 1 = (1/2)x + 2

y = (1/2)x + 3

Therefore, the equation of the straight line joining B to C is y = (1/2)x + 3.

c)  From the equations of the lines joining A to B and B to C, we can see that both lines have the same slope of 1/2. This implies that the three points A, B, and C are collinear, i.e., they lie on the same straight line.

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Answer: The area of the skating rink can be found by multiplying its length and width:

Area = length × width

In this case, the length is 35 m and the width is 12 m. Therefore, we have:

Area = 35 m × 12 m

Area = 420 m^2

Using π ≈ 3.14 to round to the nearest tenth, we get:

Area ≈ 420.0 m^2

Therefore, the area of the skating rink is approximately 420.0 square meters.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

bece u sr gģ v vyvy bleh gm have g GMV Espanola unmet yucky nvm i gifted go by Grau Cinco

The net present value of the project is $0.15 million.

Net present value is the present value of after-tax cash flows from an investment less the amount invested.

hee, we have,

The first step is to determine the cash flow of the project.

Cash flow = (sales - cost - depreciation) × (1 - tax) + depreciation

Depreciation = (cost of the asset ) / useful life

Depreciation = $2.18 million / 3

Depreciation = 0.727 million

Cash flow = (1.645 -  0.61 - 0.727) x (1 - 0.21) + 0.727 = $0.97 million

Net present value = -2.18 million + 0.97 / 1.12 +  0.97 / 1.12² +  0.97 / 1.12³

= $0.15 million

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Answer:

The answer is 78.5° .................

Answer:

78.5°

Step-by-step explanation:

For <A, AC is the adjacent leg.

AB is the hypotenuse.

The trig function that relates the adjacent leg to the hypotenuse is the cosine.

cos A = adj/hyp

cos A = 3/15

cos A = 1/5

A = cos^-1 0.2

A = 78.5°

the interest for 1 year:

[tex]3.5\% \cdot 4000 = 140[/tex]

the interest for 6 months:

[tex]\dfrac{140}{2} = 70[/tex]

the interest for 1 year 6 months:

[tex]140+70 = \bf \$ 210[/tex]

Therefore , the solution of the given problem of  dot plot comes out to be on the dot plot, 19 vehicles were sold that were not white.

The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear.

Here,

The following numbers are shown as follows based on the dot plot:

Number of scarlet vehicles: 5

=>  8 black vehicles total.

=>  6 white vehicles total.

=>  One silver vehicle is equal to four grey cars.

=>  Blue vehicle count equals one.

The following vehicles are not white vehicles based on the aforementioned criteria.

Thus, we have the depiction shown below.

=> Number of scarlet vehicles: 5

=>  8 black vehicles total.

=>  number of silver vehicles Equals 1

=>  4 grey vehicles totaled

=>  Blue vehicle count equals one.

These wavelengths combine to give us the following

=>  Total = 5 + 8 + 1 + 4 + 1

Analyze the amount

=> Overall = 19

Therefore, there are 19 vehicles.

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Answer: Its 190.  The problem states each dot represents 10 cars.  19 out of 25 dots weren't white.  19*10 is 190.

Step-by-step explanation:

Answer: Another name would be Line RQ

Not sure if this is what you're looking for but hope it helps!

Answer:

To find the zeros of the function f(w) = w^2 + 13w + 40, we need to solve the equation f(w) = 0.

We can factor the quadratic expression as (w + 8)(w + 5) = 0.

Therefore, the zeros of the function are w = -8 and w = -5.

Step-by-step explanation:

Answer:

a) 1

b) 4

c) 14

d) 1

e) 12

f) 15

h) 20

i) 25

j) 40

Step-by-step explanation:

Some mistakes have been made.

Correct answers so far:

a, b, c, d, e, f are correct

h, maybe

Corrections:

g)

13 - ( + 9) can be rewritten as 13 - 9, which is 4

h) I assume the 9 is supposed to be a [tex]\sqrt{ 9}[/tex] ? If so, then the answer is correct

i) 18 - -7 can be rewritten as 18 + 7 = 25. The two negatives turn into a positive.

j)26 - -14 = 40. The two negatives turn into a positive.

The surface area of the rectangular prism is 376 square inches.

Surface area is the total area that the surface of a 3-dimensional object covers, including all of its faces and sides. It is measured in square units.

To find the surface area of a 3-dimensional object with dimensions of 2in, 6in, 10in, 8in, and 2in, you will need to add up the areas of each of its faces.

Assuming that the object is a rectangular prism, here are the steps to find its surface area:

Identify the dimensions of the rectangular prism: length, width, and height.

Length: 10in

Width: 8in

Height: 6in

Calculate the area of each face:

Front and back faces: length x height = 10in x 6in = 60 sq.in x 2 = 120 sq.in

Top and bottom faces: width x length = 8in x 10in = 80 sq.in x 2 = 160 sq.in

Side faces: height x width = 6in x 8in = 48 sq.in x 2 = 96 sq.in

Add up the areas of each face to get the total surface area:

Total surface area = 120 sq.in + 160 sq.in + 96 sq.in = 376 sq.in

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Answer:

Congruent arcs determine congruent central angles. This is one of the properties of circles and is true for any two arcs of a circle that have the same measure.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Without fertilizer with weights less than 50 grams:

Let X be the weight of radishes produced without fertilizer. Then, X ~ N(40, 10^2).

We need to find P(X < 50).

Using the standard normal distribution, we have:

Z = (X - 40)/10

P(X < 50) = P(Z < (50-40)/10) = P(Z < 1) = 0.8413 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown without fertilizer with weights less than 50 grams is 0.8413.

b) Without fertilizer with weights between 20 and 60 g:

We need to find P(20 < X < 60).

Using the standard normal distribution, we have:

Z1 = (20 - 40)/10 = -2

Z2 = (60 - 40)/10 = 2

P(20 < X < 60) = P(-2 < Z < 2) = 0.9544 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown without fertilizer with weights between 20 and 60 grams is 0.9544.

c) Without fertilizer with weights greater than 60 g:

We need to find P(X > 60).

Using the standard normal distribution, we have:

Z = (60 - 40)/10 = 2

P(X > 60) = P(Z > 2) = 0.0228 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown without fertilizer with weights greater than 60 grams is 0.0228.

d) With fertilizer with weights less than 60 grams:

Let Y be the weight of radishes produced with fertilizer. Then, Y ~ N(140, 40^2).

We need to find P(Y < 60).

Using the standard normal distribution, we have:

Z = (60 - 140)/40 = -2

P(Y < 60) = P(Z < -2) = 0.0228 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown with fertilizer with weights less than 60 grams is 0.0228.

e) With fertilizer with weights between 20 and 60 g:

We need to find P(20 < Y < 60).

Using the standard normal distribution, we have:

Z1 = (20 - 140)/40 = -3

Z2 = (60 - 140)/40 = -2

P(20 < Y < 60) = P(-3 < Z < -2) = 0.0668 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown with fertilizer with weights between 20 and 60 grams is 0.0668.

f) With fertilizer with weights greater than 60 g:

We need to find P(Y > 60).

Using the standard normal distribution, we have:

Z = (60 - 140)/40 = -2

P(Y > 60) = P(Z > -2) = 0.9772 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown with fertilizer with weights greater than 60 grams is 0.9772.

A polynomial equation for the area of one side of the zinc washer is given by A = pi*(r+1)² - pi*r².

Polynomial is a mathematical expression containing one or more terms, each of which is composed of a constant coefficient and one or more variables raised to a power. It can be used to represent a variety of functions, such as linear, quadratic, and cubic functions.

This equation is derived from the area formula for a circle, which states that the area of a circle is equal to pi multiplied by the square of the radius. In this case, the inner radius of the zinc washer is r and the outer radius is r + 1, so the area of one side of the zinc washer is equal to the area of a circle with a radius of r + 1 minus the area of a circle with a radius of r. This can be expressed mathematically as pi*(r+1)² - pi*r², which is a polynomial equation for the area of one side of the zinc washer.

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The resulting set of isometries, together with the operation of composition, forms a group.

In the context of the paragraph, "a group under composition" refers to a group that is formed by combining isometries (permutations that preserve distances) of a geometric configuration through the operation of composition.

In other words, if you have a set of isometries of a geometric configuration (such as translations, rotations about a point, and symmetries about a straight line), you can combine them through composition (applying one after the other) to obtain new isometries. The resulting set of isometries, together with the operation of composition, forms a group, which is called the group of isometries of the configuration.

This group has certain properties, such as closure (meaning that the result of composing two isometries is also an isometry), associativity (meaning that the order of composition doesn't matter), identity (meaning that there is an isometry that leaves all points fixed), and inverses (meaning that for every isometry, there is another isometry that undoes its effect). These properties make the group a useful tool for studying the symmetries and transformations of geometric configurations in fields such as crystallography and quantum mechanics.

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Answer:

approximately 1.5 times but round up to 2  

Answer

if you were to roll a dice 9 times you would have the chance to roll 6, 1.5 times.

1/6 and 0.5/3

Step-by-step explanation:

for every number on a dice there is a chance that you'll get that number 1.5 times

Based on this information, the angle pairs can be proven congruent is option D. ∠ABC and ∠EBD.

Congruent angles are angles that have the same measure or degree. In other words, two angles are congruent if they have the same amount of rotation and are of the same size and shape, regardless of their position or orientation.

Congruent angles are denoted by the symbol ≅, which is read as "congruent to". For example, if angle A and angle B both measure 45 degrees, we can say that angle A ≅ angle B, or that angle A is congruent to angle B.

Therefore, angle ABC and angle EBD shares same measurement or same degrees. Angle ABC is congruent to angle EBD.

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Answer:(0,3) (2,2)

Step-by-step explanation:

Therefore, the simplified expression is 6x² + 11x - 4.

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, −, ×, ÷, ^) that represents a quantity or a mathematical relationship between quantities. Expressions can include variables, which are letters that represent unknown or varying values. Expressions can be simple or complex, and they can be used to represent mathematical formulas, equations, inequalities, and functions. Expressions can be evaluated by replacing the variables with specific values and performing the arithmetic operations according to the rules of algebra. Expressions can also be simplified by combining like terms, distributing multiplication, and factoring. Simplifying expressions can help us to better understand their structure and relationships, and it can make them easier to work with in calculations and problem-solving.

Here,

To perform the operation (8x² + 3x - 4) + (-2x² + 8x), we need to combine like terms, i.e., terms that have the same variable and exponent.

First, let's combine the x² terms:

8x² - 2x² = 6x²

Next, let's combine the x terms:

3x + 8x = 11x

Finally, let's combine the constants:

-4 + 0 = -4

Putting it all together, we have:

(8x² + 3x - 4) + (-2x² + 8x) = 6x² + 11x - 4

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Answer:

yes

Step-by-step explanation:

congruent means similar

Answer:6

Step-by-step explanation:biyhfdvsauybi

1) a) slοpe m= 1, y-intercept =0 and equatiοn is y=x.

2) a) slοpe m=-1 , y-intercept = 4 and equatiοn is y=-x+4.

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.

Here we knοw that, we can sοlve using any twο pοints.

1) Let us take any twο pοints, then

[tex](x_1,y_1)=(3,3) and (x_2,y_2) =(-3,-3)[/tex]

Now using slope formula ,

=> Slope m =[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-3-3}{-3-3}=\frac{-6}{-6}=1[/tex]

Now using equation formula [tex]y-y_1=m(x-x_1)[/tex]

=> y-3=1(x-3)

=> y-3=x-3

=>y=x-3+3

=> y=x

Hence slope m=1,  y-intercept = 0 and equation is y=x.

2) Let us take two points then

[tex](x_1,y_1)=(0,4) and (x_2,y_2)=(4,0)[/tex]

Now using slope formula ,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1[/tex]

Now using equation formula then , [tex]y-y_1=m(x-x_1)[/tex]

=> y-4=-1(x-0)

=>y-4=-x

=> y=-x+4

Hence slope = -1 , y-intercept = 4 and the equation is y=-x+4.

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