What is the reason for each step in the solution of the equation?

−6x=−2(x+12)

Drag and drop the reasons into the boxes to correctly complete the table.

a ) The required measure of x = 90°

b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]

Given is a triangle with measure 15, 20 and 25

a ) Since a perpendicular is dropped from above

the two angles of x are equal because the angle is bisected by an angle bisector

So to check whether the angle x is a right angled or not

we can use the pythagoras theorem and check if the LHS = RHS or not

LHS = 15² + 20² = 225 + 400 = 625

and RHS = 25² = 625

Since LHS = RHS thus the angle is 90 degrees

b ) The height of the right triangle ;

by using the Pythagoras theorem again

12.5² + h² = 20²  { side 25 is bisected = 12.5 }

h² = 400 - 156.25

h = [tex]\sqrt{244}[/tex]

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Answer: (4,-3)

Step-by-step explanation:

4x+5y=1       (1)

3x-2y=18     (2)

Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:

8x+10y=2

15x-10y=90

Sum these equations:

23x=92

Divide both parts of the equation by 23:

x=4

Substitute the value of x=4 into equation (1):

4(4)+5y=1

16+5y=1

16+5y-16=1-16

5y=-15

Divide both parts of the equation by 5:

y=-3

Thus, (4,-3)

I hope this helps. Have a great rest of your day!

It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.

a) Given equation

h(t) = v₀t - 16t^2

Substitute v₀ = 40, h(t) = 0 in the given equation

40t - 16t^2 = 0

Solve for t

⇒ 16t^2 = 40t

⇒ 16t = 40

⇒ t = 40/16

⇒ t = 2.5 seconds

Hence, water will take 2.5 seconds to hit the nozzle on the way down.

b) The function that represents the given condition

h(t) = -16t^2 + 40t + 5

The maximum value of the function is the y-coordinate of the vertex.

The x-coordinate of the vertex

= -40/2(-16) = 5/4

Find the y-coordinate of the vertex by substituting t = 5/4

⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5

⇒ h(5/4) = -25 + 50 + 5

⇒ h(5/4) = 30

Hence, the maximum height of the water is 30 ft.

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The number of pavers required is 961.

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

Given data

A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.

We have to determine how many pavers are needed

We know that area of a regular hexagon

A = (3√3)/2 a^2

= (3√3)/2 〖(6)〗^2

= (3 x 1.732)/2  x 36

= 93.528 sq.inches

Now area of rectangle

= l x w

= 24 x 26 x (12)2        (1feet = 12 inches)

= 89856 sq.inches

Now pavers required

= 89856/93.528

= 960.73

= 961

Therefore the number of pavers required is 961.

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Answer:

Mr. Carson drove 39 more miles in April than in May

Step-by-step explanation:

1027-988=39

The mapping of the function f of g(x) will result to 41

A function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.

By mapping of the functions f and g defined as;

f : x » x + 5 and g : x » 8x

then;

f of g(x) = f of 8(4.5)

f of g(x) = f of 36

f of g(x) = 36 + 5

f of g(x) = 41

Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.

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Answer: a.) 397.5 b.) 1.3333

Step-by-step explanation:

1 cent = £0.75

530 x 0.75 = 397.5

530 / 397.5 = 1.3333

Hope this helped please thank and rate!!

The values of x and y are 2 and -7 respectively, this forms an ordered pair of (6,-7) and (2,1).

Given the equation and ordered pair the question;

To determine, the y-value, plug the x-value into the equation and solve for y.

y = -2x + 5

Plug in x = 6

y = -2( 6 ) + 5

y = -12 + 5

y = -7

Determine the x-value by plunging in the y-value into the equation and solve for x.

y = -2x + 5

Plug in y = 1

1 = -2x + 5

1 + 2x = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2.

Therefore, the ordered pair are (6,-7) and (2,1).

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The equivalent quotient to -5/8 are; -5/8 and .5/-8.

The correct answer options are options A and C

A quotient is the number resulting from the division of one number by another. For instance, the quotient of 12 divided by 4 is 3.

A divisor number or expression that another is to be divided by. For instance, in "42 ÷ 3" the divisor is the 3.

Dividend is a number or expression that is to be divided by another. For instance, In "42 ÷ 3" the dividend is the 42.

Complete question:

Given options:

A. -5/8

True

B. 5/8

False

C.5/-8

True

D. -(5/-8)

False

E. -5/-8

False

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Answer:

5 bath towels

2 washcloths

Step-by-step explanation:

160 = 2⁵ × 5

64 = 2⁶

HCF= 2⁵ = 32

160 ÷ 32 = 5

64 ÷ 32 = 2

Answer: hours

Step-by-step explanation:

minutes would be way too many

seconds - just self explanatory

days- would be less than one

hours is the only possible solution

Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

What is the similarity test of two triangles?

If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.

In the given figures,  the length of side AB is equal to the length of side DE.

                        Side AB = Side DE ----------(I)

Similarly, the length of side BC is equal to the length of side EF.

                        Side BC = Side EF ----------(II)

And the measure of angle  ABC is equal to the measure of angle DEF.

                              ∠ ABC = ∠ DEF -------(III)

From (I), (II), and (III), and by using the SAS test we can say that

                               ΔABC ~ ΔDEF    ----------- SAS test

Hence,

Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

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Step-by-step explanation:

T2= -6

T5=750

ar=-6

ar4=750

both a's cancel each other

we have;

r=-6

r4=750

r4-1(The law of indices) =750

r3=750

r=3√750

r=9.1

By using normal distribution of probability, it can be inferred that

For [tex]x_1 = 325[/tex], z = -1.5

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex], z = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-

[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]

where  [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

For [tex]x_1 = 325[/tex]

[tex]z = \frac{325 - 496}{114} = -1.5[/tex]

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex]

[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

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Answer:

Step-by-step explanation:

90

The 98% confidence interval limits are given by 1.6 < μ < 33.7.

What is the confidence interval in statistics?

A confidence interval is the mean of your estimate plus and minus its variation. Within a certain confidence level, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.

Given data: 10, 32, 24, 0, 5, 27, 5, 50, 6.

Sample mean = ∑x/n = 159/9 = 17.66

Sample variance = s² = ∑(x - sample mean)²/n-1

                                   = 2206/8

                                   =  275.75

Sample standard deviation = s = [tex]\sqrt{s^2}[/tex]

                                                    = [tex]\sqrt{275.75}[/tex]

                                                    = 16.60

Significance level = α = 1 - 0.98 = 0.02

Degree of freedom (d.f.) = n - 1 = 9 - 1 = 8

Critical value = [tex]t_{{\frac{\alpha}{2}},d.f}[/tex]

                      = 2.896

Margin of error = E = critical value * [tex]\frac{s}{\sqrt{n} }[/tex]

                                = 16.03

Limits of 98% confidence level are given by:

Lower limit = sample mean - E = 17.66 - 16.03 ≈ 1.6

Upper limit = sample mean + E = 17.66 + 16.03 ≈ 33.7.

Hence, the 98% confidence interval limits are given by 1.6 < μ < 33.7.

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The required expression is Total = 152+x .

What is expression ?

  Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

Here,

The number of bottles Enrique collected = 152

Let us take number of bottles  collected by Latasha as x. Then,

Total number of bottles collected by the is ,

=> Total = Number of bottles collected  + Number of bottle collected

                by Enrique                                   By Latasha.

=> Total = 152+x

Hence the required expression is Total = 152+x.

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The circumference of the circle is 21.98cm and the area of the circle is 38.465 square cm.

Circumference of the circle:

The Circumference (also known as) perimeter of circle = 2πR

where,

R is the radius of the circle

π is the mathematical constant with an approximate value is 3.14.

Area of circle:

The formula to find the area of the circle is;

A = πr²

Where r represents the radius of the circle.

Given,

The diameter of the circle is 7 cm.

Here we need to find the circumference and the area of a circle.

Here we have the value of diameter, in order to find the circumference we have to find the value of radius that can be derived by dividing the diameter by 2.

So, the radius is

=> 7/2 = 3.5

Now the circumference of the circle is calculated as,

C = 2 x π x 3.5

When the value of π = 3.14

Therefore, the circumference of the given circle is,

=> C = 2 x 3.14 x 3.5

=> C = 21.98

Now, the area of the circle is,

=> A = π x (3.5)²

=> A = 3.14 x 12.25

=> 38.465

Therefore, the area of the circle is 38.465 square cm.

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The sale price including tax for the refrigerator is $520.

From the information, the following can be deduced:

Refrigerator = $595

Discount = 20%

Tax = 9.25%

The sales price will be:

= Refrigerator price + Tax - Discount

= $595 + (9.25% × $595) - (20% × 650)

= $595 + $55 - $130

= $520

The price is $520.

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Answer:

Step-by-step explanation:

You subtract 583 from 400 (400-583)

Then you get 183

Answer:

Domain: {0 \leq x} Range {0 \leq y}

Step-by-step explanation:

btw \leq means less than or equal to

Answer:

12.85

Step-by-step explanation:

hope it helps, pls lmk if it is wrong in comments!

Answer:

12.85

Step-by-step explanation:

64.25÷5

The equation of line q is  y = x/10 - 9/10.

What is equation of straight line?

   A line that does not curl or bend is said to be straight. A line has length but no width, making it a one-dimensional figure. A line consists of points that extend infinitely in opposite directions. Two points in a 2D plane determine it. A, B, and C are real-based constants in the formula Ax + By + C = 0, A, B 0. The geometric representation of the equation is always a straight line.

Here the given line P,

=> y+5=-10(x+2)

=> y+5=-10x-20

=> y = -10x-25

Here in the given line y=mx+c , where m=slope. Then,

=> Slope of line P = -10.

Here line P is perpendicular to line q.

Then, slope of line q = -1/ slope of line p = -1/-10 = 1/10

Now the line passes through the point [tex](x_1,y_1)=(-1,-1)[/tex] then,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y+1 = 1/10 (x+1)

=> 10y+10 = x+1

=> 10y=x-9

=> y = x/10 - 9/10.

Hence the equation of the line q is  y = x/10 - 9/10.

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There are 855 cockroaches crawling on the front of the building

An equation is an expression showing the relationship between two or more numbers and variables.

The population density is given as:

Population density = total animals / area occupied

Given that, the population density of the cockroaches is 5 cockroaches per square meter.

The area of the building = area of triangle + area of square

Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²

Population density = total animals / area occupied

5 cockroaches per square meter = Total cockroaches / 171 m²

Total cockroaches = 855

There are 855 cockroaches

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to be honest ion even know

Answer: 200 Meters

Step-by-step explanation: