Draw a graph of Lin’s distance as a function of time for this situation:



Lin walked a half-mile to school at a constant rate. Five minutes after arriving at school, Lin realized that she had left her permission slip at home. Lin began sprinting home, but when she was halfway there she got tired and walked the rest of the way.

Another name for AXW is <X

The arrow on XW implies that the segment XW is a ray, such that any of the points X or W can be the starting point

Hence, another name for XW is WX

A ray with an endpoint X is a ray that ends at point X

An example of such ray is XY

The arrow on WX implies that the segment WX is a ray, such that any of the points X or W can be the starting point

Hence, another name for WX is XW

The name AXW represents an angle

An angle can be named after its middle point

Hence, another name for AXW is <X

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Answer:

[tex]-\frac{345}{37}[/tex]

Step-by-step explanation:

Just follow the order of operations

210÷[5+16÷2{6−18÷(7+2)}]−15  

= 210÷[5+16÷2{6−18÷9}]−15   (calculate 7+2)

= 210÷[5+16÷2{6−2}]−15 (calculate 18÷9)

= 210÷[5+16÷2{4}]−15  (calculate 6-4)

= 210÷[5+16÷2×4]−15

= 210÷[5+8×4]−15  (calculate 16÷2)

= 210÷[5+32]−15  (calculate 8×4)

= 210÷[37]−15  (calculate 5+32)

= 210÷37−15

= 210÷37−(15×37)÷37  (put on the same denominator)

= 210÷37−555÷37  (calculate 15×37)

= (210−555)÷37

=-345÷37   (calculate 210-555)

The solution to the equation is 2

Given the equation

4 + 4(x-2) = 2(x+1) - x

First, we expand the bracket

4 + 4x - 8 = 2x + 2 - x

collect like terms

4x - 2x + x = 2 - 4 + 8

Add like terms

3x = 6

Make 'x' the subject

x = 6/3

x = 2

Thus, the solution to the equation is 2

The complete question is

What is the solution to the equation of 4 + 4(x-2) = 2(x+1) - x? show your work

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The property A*B = (A' + A") * ( B'+B") is equal to each other.

According to the statement

We have given that the a and b is the positive integers and we have to prove that the product of all positive divisors of a equals the product of all positive divisors of b.

And in this statement

Now we use Distributive property

Here A and B is the positive integer and

A' and A" are the divisors of A and B' and B" are the divisors of B.

Now,

A = A' + A" and B = B'+B"

Now, Multiply both with each other then

A*B = (A' + A") * ( B'+B")

then

A*B = (A' B'+ A'B") + ( A"B'+A'B")

by this way it is equal to each other

Hence proved.

So, The property A*B = (A' + A") * ( B'+B") is equal to each other.

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Answer:

Step-by-step explanation:

This is a geometric means problem where the height (length AC of 4) is the geometric mean between the base BC and the base DC. The proportion is

[tex]\frac{12.8}{4} =\frac{4}{CD}[/tex] . Cross multiply to get

12.8CD = 16 and divide both sides by 12.8 to get that

CD = 1.25

That means that the length of the whole thing, BD, is

12.8 + 1.25 = 14.05

Based on the information, Christian would have $5525.5 of annuity.

According to given information, the number of coffees per week is 3 then, per month is 3x4 = 12

For each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54

Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133

n = number of payments = 8 x 12 = 96

We can use the formula for finding the future value as below

FV = C x [ ( 1 + r )n-1 ] / ( r )

FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)

= 54 x [ (1.13609 - 1)] / (0.00133)

= 54 x 0.13609 / (0.00133)

= 54 x 102.3233

= 5525.5

Therefore Christian would have $5525.5 of annuity.

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A binomial probability density function should be used to represent the probability

The given parameters are:

The proportion that plays sport indicates that

68% of the students do not play sport

So, we have two events, which are

When there are two possible events, then the binomial probability density function should be used

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Answer:

31

Step-by-step explanation:

C= 2πr  We will used 3.14 for pi and the radius is 5

C = 2(3.14)(5)

C =31.4 Then round to the nearest whole number which would be 31.  31.4 is closer to 31 than 32

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

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

The standard form of a quadratic equation is:

y = ax² + bx + c

The graph of a quadratic equation is a parabola.

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

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If the sales had dropped 23% then music store had sold 551 units in the second quarter.

Given that a music store had sold 715 units in first quarter and sales had dropped by 23%.

We are required to determine the sales in the second quarter.

Percentage is the number or ratio expressed in terms of 100. It is expressed as %.

Sales in first quarter=715 units

Decrease in sales=23%

In units ,decrease=715*23%

=715*23/100

=164.45

Sales of second  quarter=715-164.45

=550.55

After rounding we will get 551.

Hence if the music store sold 715 units in first quarter then the units sold by music store in second quarter 551 units.

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Answer:

1 1/2

Step-by-step explanation:

When you are subtracting a negative number is is the same as adding a positive.  So the problem is really 5/8 + 7/8, since the denominators are the same, just add the numerators to get 12/8  divide the top and bottom by 4 to get 3/2 or 1 1/2, if I divide 3 by 2.

These two should be the points as then 2 points will remain on both sides

Slope

Equation in point slope form

When x=-15

Just above 7

The solution and extraneous solution of the equation as given are; x=7 and x=-2 respectively.

It follows that the equation given is;

(3/(x²+5x+6)) + ((x-1)/(x+2)) = 7/(x+3)

Hence, by multiplying both sides by (x²+5x+6); we have;

3 + x² +2x -3 = 7x + 14.

x²-5x -14 = 0

On this note, the solutions of the quadratic equation are; x =7 and x=-2.

It therefore follows that x= 7 is a solution while x=-2 is an extraneous solution because it renders (x-1)/(x+2) undefined.

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Answer:

x=7  

x=-2

Step-by-step explanation:

v = 1.21 m/s is the answer

Kinetic energy of object = 25 J

Mass of object = 34 kg

The formula for the kinetic energy of an object is given by

K.E. = 1/2 m v2.

25 =  1/2 *34* v2.

v2= 25/17

v2 = 1.47

v = 1.21 m/s

In physics, the kinetic energy of an object is the energy that the object has due to its motion. This is defined as the work required to accelerate an object of a given mass from a stationary state to a specified velocity. After the body gains this energy during acceleration, it retains this kinetic energy unless the velocity changes

Everything that moves at home is an example of kinetic energy. This could be a cue ball rolling on a pool table, a fan that circulates air on warm days, or a glass that shatters on the floor after falling off the counter. Electrical equipment that is turned on uses kinetic energy, much like people move around the house.

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The angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

The angle of elevation is says to be the angle made between a horizontal plane and a straight line to a given object that is elevated off the ground.

Therefore, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

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Answer:

[tex]\huge\boxed{\sf 7x + 10\ cm}[/tex]

Step-by-step explanation:

= 5 + 2x + 2x + 5 + 3x

Combine like terms

= 2x + 2x + 3x + 5 + 5

= 7x + 10 cm

[tex]\rule[225]{225}{2}[/tex]

Answer:

7x + 10

Step-by-step explanation:

Perimeter is the sum of all the sides together, the distance around a shape.

3x + 5 + 2x + 2x + 5

Organize so the variables are on one side

3x + 2x + 2x + 5 + 5

Combine like terms:

7x + 10

Your answer would be: 7x + 10

I hope it helps! Have a great day!

bren~

The equation in slope intercept form is y = -4x/3 + 10

The representations are given as:

So, we have:

2 * x + 1.5 * y = 15

Evaluate the product

2x + 1.5y = 15

Subtract 2x from both sides

1.5y = -2x + 15

Divide through by 1.5

y = -4x/3 + 10

Hence, the equation in slope intercept form is y = -4x/3 + 10

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Answer:

180 - 92 - 41 = 47

There are not two similar congruent angle in the triangles.

Hope this helps!

Step-by-step explanation:

400 is the whole = 100%

20% (= 20 out of 100 equal parts of 100%) are red.

how many are that ?

well, again, 400 = 100%

1% = 100%/100 = 400/100 = 4

20% = 20×1% = 20×4 = 80

when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.

400 × 0.2 = 80

now,

35% are yellow.

35% = 35×1% = 35×4 = 140

or

400×0.35 = 140

red + yellow = 80 + 140 = 220

the rest are green

400 - 220 = 180

we would get this also by seeing that

red + yellow = 20% + 35% = 55%.

so, green has then the remaining 100-55 = 45%

and again

45% = 45×1% = 45×4 = 180

or

400×0.45 = 180

the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

A perfect square is the product of a number and itself.

As you can see in the example, 16 is a square number. Then let's try to get 16.

To get 16 we can use the difference:

20 - 4

So the first therm needs to be equal to 20, and the second equal to 4.

To write 20 in scientific notation we have:

[tex]2*10^1[/tex]

To write 4 in in scientific notation:

[tex]4*10^0[/tex]

Then the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

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The ratio of the radius of the smaller circle to the radius of the larger circle as required in the task is; 3:8.

It follows from the task content that the circumference of the smaller circle is; 12cm while that of the bigger circle is; 32cm.

Since, the circumference of a circle is directly proportional to the radius of the circle from the formula; C = 2πr.

The ratio is therefore; 12:32, in which case, when expressed in its simplest form is; 3:8.

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Answer:

x = 34

Step-by-step explanation:

The three angles form a straight line and are thus supplementary angles.  The sum of a supplementary angles is always 180, so we can use the equation 180 = x + 12 + 100 + x to find x:

180 = 2x + 112

68 = 2x

x = 34

Answer:

x = 20 units

Step-by-step explanation:

See attached.

Answer:

[tex]x = 94[/tex]

Step-by-step explanation:

To find the value of [tex]x[/tex], we have to first find the lengths of the sides of the squares and add them.

The formula for area of a square is as follows:

[tex]{area = (length \space\ of \space\ side)^2}[/tex]

This means the length of a side of a square can be found by:

[tex]\boxed {length \space\ of \space\ side = \sqrt{area}}[/tex]

Now we can find the lengths of sides of each of the squares:
• Length of side of larger square = [tex]\sqrt{8100}[/tex]

                                                       = 90

• Length of side of smaller square = [tex]\sqrt{16}[/tex]

                                                          = 4

Next we can just add the lengths of the sides to get the value of [tex]x[/tex] :

[tex]x = 90 + 4[/tex]

⇒ [tex]x \bf = 94[/tex]

Answer:

The possible length of the third side is greater that 4ft and less that 20 ft

4<x<20

Answer:

Step-by-step explanation:

To solve this equation log both sides and apply log rules.

Substitute the values of logs:

Solve it as linear equation:

Answer:

five number summary is a specially useful in the scriptive analysing what during the premier league investigation of a large data set a summary consists of 5 values of the most extreme values in data set the maximum and minimum values of the lower and upper quality and the meridian

Answer:

ASA

Step-by-step explanation:

The solution to the equation using the completing the square are 2 and -3

These are equation that has a leading degree of 2. Given the equation below

-x^2 +x+6=0

This can also be written as

x^2-x-6 = 0

Complete the square

x^2-x = 6

x^2-x+ (1/2)^2 = 6 + (1/2)^2

(x-1/2)^2 = 6 + 1/4

(x+1/2)^2 = 25/4

x+1/2 = ±√25/4

x = 5/2 -1/2  or -5/2-1/2

x = 4/2  or -6/2

x = 2 and -3

Hence the solution to the equation using the completing the square are 2 and -3

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The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

The formula for calculating the slope of a line is expressed as

slope = y2-y1/x2-x1

Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:

Slope = 1-0/-2-0

Slope = 1/-2

Slope = -1/2

Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

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The slope of the line m is - 1 / 2.

The slope a line can be found as follows:

slope = m = y₂ - y₁ / x₂ - x₁

using (0, 0)(2, -1)

hence,

slope = - 1 - 0 / 2 - 0

slope = - 1 / 2

hence,

slope = - 1 / 2

Therefore, the slope of the line m is - 1 / 2.

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