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Help me please thank u so much

Answer:

g(2) = 16; g(-2) = 4; g(a) = 3a + 10; 3(a+2) = 3a + 16

Step-by-step explanation:

We want to substitute the value in the parentheses on the left-hand side for the value of x on the right-hand side

Thus, g(2) = 3(2) + 10 = 6 + 10 = 16

g(-2) = 3(-2) + 10 = -6 + 10 = 4

g(a) = 3(a) + 10 = 3a + 10

g(a + 2) = 3(a + 2) + 10 = 3a + 6 + 10 = 3a + 16

Answer:

12 square in

Step-by-step explanation:

In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.

A = pi*r*r = 3*2*2 = 12 square in

Answer:

12 in^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.

--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 2.

--> A = 4[tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 4 x 3

--> A = 12

We can conclude that the area of the circle is 12 in^2.

Answer:

100%, 20%, 60%

Step-by-step explanation:

250/250 = 100/100 = 100%

50/250 = 1/5 = 20/100 = 20%

150/250 = 3/5 = 60/100 = 60%

Part (a)

We'll use the distance formula.

[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]

The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.

========================================================

Part (b)

We divide the diameter in half to get the radius.

Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.

Answer:

Slope (m) = infinity

Step-by-step explanation:

Given points:

⇒ (9, 2) and (9, 27)

In order to find the slope of these points, we must use the slope formula.

So the formula is ⇒ y₂ - y₁ / x₂ - x₁

Plug in the given points:

⇒ 27 - 2 / 9 - 9

Solve both the top and bottom (numerator and denominator):

⇒ 25 / 0

Divide:

⇒ Undefined.

(Anything divided by zero is undefined).

The polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

In this question,

We have been given the cartesian coordinate (-6, -1)

We need to convert given cartesian coordinate to polar coordinates.

We know that the polar coordinates is of the form (r, θ)

where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

and θ is the angle associated with the coordinates which is given by           θ =  [tex]tan^{-1}(\frac{y}{x} )[/tex]

The magnitude of the given polar coordinate is,

⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

⇒  r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]

⇒ r = [tex]\sqrt{36+ 1}[/tex]

⇒ r = [tex]\sqrt{37}[/tex]

⇒ r = 6.08

And the angle associated with the coordinate is,

⇒ θ =  [tex]tan^{-1}(\frac{-1}{-6} )[/tex]

⇒ θ =  [tex]tan^{-1}(0.167 )[/tex]

⇒ θ = 9.48°

⇒ θ = 0.0523π

So, the polar coordinate is (6.08, 0.0523π)

Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

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Answer:

20

Step-by-step explanation:

x^2+18x-160

If you put this into your calculator or desmos, you will get a parabola. You want to know the value of x when y=600. You can look at the table for the graph or scan to where y = 600. The value of x is 20 at that point.

To check you can plug 20 in for x. When you do that, y = 600.

The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes

The volume of the composite cylinder is expressed as shown below;

V = πr²h

where

r is the radius

h is the height

According to the given diagram;

V = Vl - Vs

V = π(10)²*15 -  π(5)²*15

V = 1500π - 375π

V = 1125π cubic inches

If the value of π is 3.14, hence;

V = 1125(3.14) cubic inches

V = 3532.5 cubic inches

The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

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By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

In this question we have hints from two trigonometric functions necessary to find the exact value of the cosine function. In accordance with trigonometry, cosecant function is positive and tangent function is negative in the third quadrant of Cartesian plane and therefore the cosine function must be a negative number. Therefore, we can derive the value of the latter function by trigonometric formulas:

cos θ = - √[1 - (1 / csc θ)²]

If we know that csc θ = 2, then the exact of the cosine function is:

cos θ = -√[1 - (1 / 2)²]

cos θ = -√(3 / 4)

cos θ = -√3 / 2

By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

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Answer:

  21.0 m²

Step-by-step explanation:

The formula for the area of a triangle from two sides and the included angle is ...

  A = 1/2ab·sin(C)

Using this formula, we find the area to be ...

  A = 1/2(14 m)(8 m)sin(22°) = 21.0 m²

The area of triangle ABC is about 21.0 square meters.

Answer:

○ [tex]x = -7[/tex]

Step-by-step explanation:

Given the equation:

[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex],

to solve for [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] its subject.

[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex]

⇒ [tex]10x + 100 - 4 = 11 - 10x -55[/tex]      [expand brackets]

⇒ [tex]10x + 96 = -44 - 10x[/tex]

⇒ [tex]10x + 10x + 96 = -44[/tex]                   [add [tex]10x[/tex] to both sides]

⇒ [tex]20x + 96 = -44[/tex]

⇒ [tex]20x = -44 - 96[/tex]                             [subtract 96 from both sides]

⇒ [tex]20x = -140[/tex]

⇒ [tex]x = \frac{-140}{20}[/tex]                                        [divide both sides by 20]

⇒ [tex]x = \bf-7[/tex]

Answer:

B) x = -7

Step-by-step explanation:

Given equation: [tex]10(x+10)-4=11-5(2x+11)[/tex]

Step 1: Distribute [tex]10[/tex] and [tex]-5[/tex] through the parentheses.

[tex]\implies 10(x)+10(10)-4=11-5(2x)-5(11)[/tex]

[tex]\implies 10x+100-4=11-10x-55[/tex]

Step 2: Simplify (combine like terms).

[tex]\implies 10x+100-4=11-10x-55[/tex]

[tex]\implies 10x+96=-44-10x[/tex]

Step 3: Add [tex]10x[/tex] to both sides.

[tex]\implies 10x+10x+96=-44-10x+10x[/tex]

[tex]\implies 20x+96=-44[/tex]

Step 4: Subtract [tex]96[/tex] from both sides.

[tex]\implies 20x+96-96=-44-96[/tex]

[tex]\implies 20x=-140[/tex]

Step 5: Divide both sides by [tex]20[/tex] to isolate [tex]x[/tex].

[tex]\implies \dfrac{20x}{20}=\dfrac{-140}{20}[/tex]

[tex]\implies \boxed{x=-7}[/tex]

Answer:

d>0

Step by Step Explanation:

Let's solve your inequality step-by-step.

5+d>5−d

Step 1: Simplify both sides of the inequality.

d+5>−d+5

Step 2: Add d to both sides.

d+5+d>−d+5+d

2d+5>5

Step 3: Subtract 5 from both sides.

2d+5−5>5−5

2d>0

Step 4: Divide both sides by 2.

2d/2>0/2

d>0

Answer:

3

Step-by-step explanation:

You could put 3 because 5+3 is greater than 5-3.

a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample

Sampling can be defined as a technique of selecting a subset of the population or  individual members in order to make statistical inferences from them and estimate the entire characteristics of the whole population.

Sampling methods are used by researchers in market research to reduce the workload and also to research the entire population

It is time-friendly, cost-effective method and forms the basis of research design.

Some sampling methods are;

It can be said to be dependent when selecting from one sample affects another sample.

Thus, a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample.

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gradient = rise/run

= 2/1

= 2

So,it's the first option, y=2x

Hope this helps!

Answer:

B. 126 [tex]\pi[/tex]

Step-by-step explanation:

The volume for a cylinder is: Area of the base x Height

The base is a circle with a diameter of 6cm.

The formula to find the area of the base is: radius x radius x pi

In this case, the radius is 3 (6/2) so the area will be 9pi.

Now that we know that area of the base, all we need to do is multiply the height, which is 14cm.

9 pi x 14 = 126 pi

So B. 126 pi is the correct answer!

Answer:

126π

option B is the correct answer

Answer:

slope

(0, 6) and (-9, 0)

0 - 6 / -9 - 0 = -6/-9 = 2/3

y intercept is when the line intercepts the y axis and x = 0

The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6

Answer:

slope is 2/3

y intercept is 6

Step-by-step explanation:

We can find the slope of the line by using two point

(-9,0) and (0,6)

The slope formula is

m = ( y2-y1)/(x2-x1)

   = ( 6 - 0) /( 0 - -9)

   = (6-0)/(0+9)

  = 6/9

  = 2/3

The y intercept is where it crosses the y axis ( the value where x is 0)

The y intercept is 6

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and

r(1, 1, 0) is x + y + z = 2  .

According to the question

Let the points

p(0, 1, 1) = (x1,y1,z1)

q(1, 0, 1)= (x2,y2,z2)

r(1, 1, 0)= (x3,y3,z3)

now,

The equation of the plane through the points

i.e

The formula of equation of a plane passing through three non collinear points

[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]

by substituting the values in the formula of equation of a plane

[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]

[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]  

x(1) - (y-1)(-1) + (z-1)(1) = 0

x + y - 1 + z - 1 = 0

x + y + z = 2

Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2  .

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The approximately probability that a person will go to the Saturday morning game and buy nachos is 18%.

The approximately probability of a person going to a Saturday morning game and buying nachos:

Probabaility= [tex]\frac{150}{846} *100[/tex]

                   =17.7%

Approximately=18%.

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The probability that exactly 1 train will pass Mary's house is 0.00889.

According to the given question.

On average, 18 trains pass by Mary's house daily i.e. in 24 hours.

As, we know that "Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event".

Therefore,

The probability that exactly one train will pass Mary's house in a 3 hour period

= [tex]\frac{^{18C_{1} } }{^{24} C_{3} }[/tex]

[tex]= \frac{\frac{18!}{1!\times17!} }{\frac{24!}{3!\times 21!} }[/tex]

[tex]= \frac{18}{\frac{24\times23\times22}{3\times2\times1} }[/tex]

[tex]=\frac{18}{8\times23\times\ 11}[/tex]

= 18/2024

= 0.00889

Hence, the probability that exactly 1 train will pass Mary's house is 0.00889.

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Answer:

the graph is a linear function  

root (2,0) vertical intercept (0,2)

Step-by-step explanation:

Answer:

1.5×2.5/2=1.875.

Step-by-step explanation:

We all know that area of triangle is base into hight upon 2.

Using the volume of a sphere, the total volume of air inside six of Jake's basketballs is of 2140.8 cubic inches.

The volume of a sphere of radius r is given as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

From the problem, since the properly inflated basketball measures 8.8 inches across, the diameter is of 8.8 inches, hence the radius is:

r = 8.8/2 = 4.4 inches.

Then the volume in cubic inches of a single ball is:

V = 4 x pi x (4.4)³/3 = 2140.8 cubic inches.

For the six balls:

6 x 356.8 = 2140.8 cubic inches.

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Answer:

the second option L = 0.05F + 10

Step-by-step explanation:

the first one

F = 0.05L + 10

does not make any sense, as for length = 10 the force has to be 0. but this function here gives us

0.05×10 + 10 = 0.5 + 10 = 10.5

which is clearly not 0. so, this is wrong.

the second one is correct.

L = 0.05F + 10

it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.

the third

L = 0.05F

fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.

the fourth

F = 0.05L

fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.

Equation that represents the total time t (in minutes) Ken spent running is = 10 + m/6.30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Total time t (in minutes) =Initial Time + distance/speed

Given :-

Thus,

t = 10 + m/6.30.

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The true statement is that no number in base 10 can be written in multiple ways in base 4

The base of the numbers are given as:

Base 10 and base 4

Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers

There is only one equivalent of each number in each base.

This means that (for instance)

357 in base 10 is 11211 in base 4

The above number does not have any other representation in base 4 and it can not be written in another way.

This is the same for other numbers in base 10

Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4

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The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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The angle that corresponds to 3 is angle 5

Corresponding angles are angles that are at the same relative position between parallel lines and transversal

These angles are congruent

From the figure, we have:

Angle 3 and Angle 5 are in the same relative position

Hence, the angle that corresponds to 3 is angle 5

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Step-by-step explanation:

....................

Answer:

11x9=99 16x9=144=243 144+99

The cost of the carpet required for the given rectangular floor is $1584.

A rectangle is a quadrilateral with equal pairs of sides.

Given that:

The shape of the floor is a rectangle.

The length of the floor is 16 feet.

The width of the floor is 11 feet.

So,

The area of the floor = length × breadth

                                   = 16 × 11

                                   = 176 sq feet

The area of the floor is 176 sq feet.

The cost of the carpet for a 1 sq foot floor = $9

The cost of the carpet for a 176 sq feet floor = $9 × 176

                                                                          = $1584

Thus, the cost of the carpet for a 176 sq feet floor is $1584.

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Option C is correct (y + z = 6) ⋅ −3

What is a linear equation in math?

As per the statement -

A student is trying to solve the system of two equations given below:

Equation P:   y + z = 6              ....[1]

Equation Q:  3y + 4z = 1           ....[2]

Multiply the equation [1] by -3 to both sides we have;

-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)

Add equation [2] and [3] to eliminate the y-term;

z = -17

Therefore, the  possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3

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The complete question is -

A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?

(y + z = 6) ⋅ 4

(3y + 4z = 1) ⋅ 4

(y + z = 6) ⋅ −3

(3y + 4z = 1) ⋅ 3