What is the solution to 3(–3x + 9) = −18?
O x = -5
O x = 5 or x=1
O x = -5 or x = 1
no solution

Answer: B(1, 3) and D(1, −2)

Step-by-step explanation:

The distance from A to C is 5, meaning we need the length to be 4.

If they lie to the right, we need to add 4 to the x coordinates, so the x coordinates should be 1, and the y coordinates should be 3 and -2.

The locations of B and D are given by (A) B(1,3) and D(1,-2).

The area of rectangle is given by the product of the length and width of that rectangle.

Area = Length*Width

Distance between two points (a,b) and (c,d) is given by,

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Here in the given question it is mentioned that AC forms width of a rectangle and A is at (-3,3) and C is at (-3,-2)

Now the width is [tex]=\sqrt{(-3-(-3))^2+(-2-3)^2}=\sqrt{0^2+(-5)^2}=\sqrt{25}=5[/tex] unit.

Also it is given that, the area of the rectangle is 20 square units.

So the length is = 20/5 = 4 units

B and D lie to the right of points A and C respectively.

We have to go 4 units right to the A to find B and 4 units right to C to find D.

A is at (-3,3)

then B is at (-3+4,3) = (1,3)

C is at (-3,-2)

So D is at (-3+4,-2) = (1,-2)

Hence correct option is (A) B(1,3) and D(1,-2)

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Answer :

Points at (1, 3) and (3, 3) and (2, 1)

Explanation:

The original graph (dashed) is an absolute value function meaning f(x) = |x|

Given: y = 2f(x - 2) + 1

f(x - 2) means you plug in x - 2 for x in f(x) function

the new graph equation is: y = 2|x - 2| + 1

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Visual:

The mean and the standard deviation are 233 and 208.95 respectively.

The mean of a distribution is its average, while the standard deviation is the summary of how far each data in the dataset, is to the mean.

First, we calculate the class midpoint (x) from the given intervals.

The class midpoint is the average of the intervals. So, we have:

X1 = (0+199)/2 = 99.5

X2 = (200+399)/2 = 299.5

X3 = (400+599)/2 = 499.5

X4 = (600+799)/2 = 699.5

X5 = (800+999)/2 = 899.5

X6 = (1000+1199)/2 = 1099.5

X7 = (1200+1399)/2 = 1299.5

So, the table becomes:

X values Frequency (f)

99.5 345

299.5 97

499.5 52

699.5 21

899.5 9

1099.5 8

1299.5 3

The mean of the distribution is:

This gives:

Mean = (99.5*345)+(299.5*97)+(499.5*52)+(699.5*21)+(899.5*9)+(1099.5*8)+(1299.5*3)/(345+97+52+21+9+8+3)

Mean = 124832.5/535 = 233

Therefore, Mean = 233

The standard deviation is calculated as follows:

So, we have:

Б =

√(99.5*(345-233)²+((299.5-233)² * 97)+((499.5-233)² * 52)+((699.5-233)² * 21)+((899.5-233)² * 9)+((1099.5-233)² * 8)+((1299.5- 233)² * 3)/ (345+97+52+21+9+8+3)

Standard Deviation = √(23357155.5)/535

        = √43658.23

        = 208.95

Б = 208.95

Hence, the mean and the standard deviation are 233 and 208.95 respectively.

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The probability that both of them have the secret decoder ring will be 0.1356.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Inside the box of every cereal box contains a surprise gift.

The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring.

And inside the other 30 boxes on the shelf contain a different gift.

If two cereal boxes are randomly selected from the shelf to purchase.

Then the probability that both of them have the secret decoder ring will be

The total events will be

Total event = ⁴⁸C₂

Total event = 1128

The favorable events will be

Favorable event = ¹⁸C₂

Favorable event = 153

Then the probability will be

P = 153 / 1128

P = 0.1356

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Answer:

[tex]b = 2[/tex]

Step-by-step explanation:

[tex]( - 12 - 1 - 5) + (3b - b) \\ - 18 + 2b \\ 2b - 18 \\ b = 2[/tex]

In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.

The missing table is given below.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Shawn is collecting money from students at his school for a charity.

The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.

Since 30 is 1/3 of 90, we know the ratio is 1:3.

In order of blank boxes going from left to right then down

1, 9, 5, 75, 35

The complete table is attached below.

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Answer: 2.5

Step-by-step explanation:

The altitude of an equilateral (or isosceles) triangle bisects the side to which it is drawn.

The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.

We have a scatter plot shown in the table:

1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:

Standard deviation = SD

6SD(x) = 40

SD(x) = 40/6 = 6.67

6SD(y) = 20

SD(y) = 20/6 = 3.37

2) Slope of the line:

= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5

3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.

Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

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Answer:

y = 2/5 x - 18/5

Step-by-step explanation:

y = mx + b

m = (y2 - y1)/(x2 - x1) = [-2 - (-6)]/[4 - (-6)] = 4/10 = 2/5

y = 2/5 x + b

-6 = (2/5)(-6) + b

-30 = -12 + 5b

5b = -18

b = -18/5

y = 2/5 x - 18/5

Answer:

3.036, 3.36, 3.3661 , 3.5

Step-by-step explanation:

Look at the first 2 numbers

3.3661, 3.5, 3.36, 3.036

We can order them as 3.0 , 3.3 , 3.3 . 3.5

So 3.036 is first one

Now we have 2 of the 3.3's

One is 3.3661 and the other one is 3.3600

Because if you add a number to the end it will always be a zero and it wont change the answer

So  3.36 is second and 3.3661 is third one

3.5  is bigger than 3.3

So 3.5 is last

Answer:

he subtracted the wrong coordinates to find the horizontal leg

Step-by-step explanation:

It should be 4-(-3) but he labeled 4-(-1)

The value of the probability P(decaf or sugar) is 0.41

From the table, we have:

P(decaf) = 0.05 + 0.08 + 0.09 = 0.22

P(sugar) = 0.19 + 0.08 = 0.27

P(decaf and sugar) = 0.08

The required probability is:

P = P(decaf) + P(sugar) - P(decaf and sugar)

This gives

P = 0.22 + 0.27 - 0.08

Evaluate

P = 0.41

Hence, the value of the probability P(decaf or sugar) is 0.41

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Based on the annuities calculated, he should choose option 1.

Present value = $35,000 + (Annuity amount * Present value of an ordinary annuity of $1)

= $35,000 + ($9,400 * (5%,6))

= $35,000 + ($9,400 * 5.07569)

= $35,000 + 47,711

= $82,711

Present value = (Annuity amount * Present value of an ordinary annuity of $1)

= $17,700 * (5%,6)

= $17,700 * 5.07569

= $89,840

Alex should choose Option 1

Future value annuity = Annuity amount * Future value of an ordinary annuity of $1

= $180,000 * (6%,10)

= $180,000 * 13.1808

= $2,372,544

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Answer: [tex]5\frac{1}{4}[/tex] gallons are left

Step-by-step explanation:

convert to mixed number...

[tex]8\frac{3}{4} = \frac{35}{4}[/tex]

[tex]3 \frac{1}{2} = \frac{7}{2}[/tex] or [tex]\frac{14}{4}[/tex]

[tex]\frac{35}{4} -\frac{14}{4}=\frac{21}{4}[/tex]

[tex]\frac{21}{4} =5\frac{1}{4}[/tex]

therefore, [tex]5\frac{1}{4}[/tex] gallons are left in Ms. Mather's fuel tank

Answer:

5 1/4 gallons are left... correct

Answer:

57905.8

Step-by-step explanation:

Plug in:

V = 4/3 * 24³π

= 4/3 * 13824π

= 18432π

= 57905.83579cm³

Rounded to nearest tenth:

57905.8

Answer: 18,432

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

Answer:

the length of the fence = 420 ft

The total area = 8000 ft²

Step-by-step explanation:

the fence has the same length as the perimeter of the rectangle

then

the length of the fence = 2×(160+50) = 420 ft

………………………………………………………………

The total area enclosed by the fencing = the area of the rectangle

Then

The total area = 160×50 = 8000 ft²

Answer:

see explanation

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2(length + width)

  = 2(160 + 50)

  = 2 × 210

  = 420 ft ← amount of fencing needed

the area (A) of a rectangle is calculated as

A = length × width = 160 × 50 = 8000 ft²

Answer:

[tex]y = \sin( \frac{2\pi}{3} x) [/tex]

Step-by-step explanation:

The equation of a sine function is y = a sin(bx), where a = amplitude (aka height) and b equals period (aka time). I'm assuming there isn't any information other than the graph shown, so let's assume that our amplitude is 1 and our period is 2pi/3. Plugging these values into the equation, we get:

[tex]y = (1) \sin(( \frac{2\pi}{3})x ) = \sin(\frac{2{\pi} }{3}x )[/tex]

Answer:

h = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]

Step-by-step explanation:

g = [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] , then

h = [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]

The area of a triangle with vertices (-4,-5), (3,-3), and (3,-7) will be 7 square units.

The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).

Then the area of the triangle will be

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|

We have

(x₁, y₁) ⇒ (-4, -5)

(x₂, y₂) ⇒ (3, -3)

(x₃, y₃) ⇒ (3, -7)

Then the area will be

Area = 1/2[{(-4) x (-3) + (3) x (-7) + (3) x (-5)} – {(-5) x (3) + (-3) x (3) + (-7) x (-4)}]

Area = 1/2 [(12 – 9 – 21) – (- 15 – 9 + 28)]

Area = 1/2[-18 + 4]

Area = 1/2 × 14

Area = 7 square units

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Work Shown:

|x+2| + 7 > 10

|x+2| > 10-7

|x+2| > 3

x+2 > 3 or x+2 < -3

x > 3-2 or x < -3-2

x > 1 or x < -5

The graph for x > 1 has an open circle at 1 and shading to the right.

The graph for x < -5 has an open circle at -5 and shading to the left

Both of these facts combine to describe Choice C

In other words, we have open circles at -5 and 1, with nearly everything shaded except for the region between the open circles.

The open circles are used to exclude those x values mentioned.

The attraction that reaches a greater height and what it represent in terms of the context  is:

Ferris wheel

(x – 100)2 + (y – 75)2 = 4,900

y max= 75+70

y max=145 ft

Sling shot

y = –3x² + 48x – 30

dy/dx=-6+48=0

x=48/6

x=8

Hence:

y max = –3(8)² + 48(8) – 30
y max = –3×64+48(8)-30

y max = –192+384-30

y max =162 ft

Therefore slingshot reaches a greater height at  162 ft and Ferris wheel reaches a greater height at 145 ft.

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That is the length in terms of p and x.

L = p/2 - x

For a rectangle of length L and width W, the perimeter is:

P  = 2*(L + W).

Here we know that the perimeter is p, so P = p, and let's say that the width is x.

Then we can write:

p = 2*(L + x)

Solving for L:

L = p/2 - x

That is the length in terms of p and x.

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Answer:

look the attachment in the above

Answer:

h(-1) is -1, h(-0.5) is 0 and h(1) is 1.

Step-by-step explanation:

functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.

In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.

In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.

In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.

Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.

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Answer:

I think that would be 1

Step-by-step explanation:

Do everything in the lines before anything else. -2 becomes a 2 and then you add that with the 12 and divide 12 on both sides to get one.

Answer:

  x = 0 or 4

Step-by-step explanation:

The absolute value function can be resolved into two equations. These one- or two-step equations can be solved in the usual way.

__

  -(x -2) +10 = 12

  -x = 0 . . . . . . . . . simplify, subtract 12

  x = 0 . . . . . . . . . multiply by -1. Check: 0 -2 is negative.

  x -2 +10 = 12

  x = 4 . . . . . . . . . simplify, subtract 8. Check: 4 -2 is positive.

The two solutions are x=0 and x=4.

Answer:

Step-by-step explanation:

x×4=2x²(x-1)

2x³-2x²-4x=0

2x(x²-x-2)=0

x≠0

x²-x-2=0

x²-2x+x-2=0

x(x-2)+1(x-2)=0

(x-2)(x+1)=0

x=2

or

x=-1 (rejected)

Answer:

Step-by-step explanation:

Formula

The following relationship exists between the parts of each chord.

(x - 1)(2x^2) = 4*x

Solution

The easiest way to start is to divide both sides of the equation by x.

(x - 1)(2x^2)/x = 4x / x                  Divide by x    

( x-1)(2x) = 4                                 Remove the brackets

2x^2 - 2x = 4                              Subtract 4 from both sides

2x^2 - 2x - 4 = 4 - 4                    Combine

2x^2 - 2x - 4 = 0                         Pull out the common factor

2(x^2 - x - 2) = 0                         Divide by 2

x^2 - x - 2 = 0                              Factor

(x - 2)(x + 1)

Answer:

x can be 2 or x can be - 1 on paper. The x on the upper right prohibits that. A line can't have a length of - 1. So - 1 is called an extraneous solution.

The answer is x = 2

Answer:

6587

Step-by-step explanation:

Formula is

A= P(1+r/n)^nt

A = 11303.34

r = .09

n = 365 compounded daily

t = 6 years

solve for P

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Answer:  [tex]\textsf{x = 6}[/tex]

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Given:  [tex]\textsf{The image provided with 2 angles and one side}[/tex]

Find:  [tex]\textsf{Solve for the unknown side of x}[/tex]

Solution:  In order to determine the length of x we need to use some trigonometric functions.  Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees.  We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin.  Plug in the values and solve for the unknown.

Plug in the values

Multiply both sides by x

Divide both sides by sin(30)

Simplify

Therefore, the value of the unknown variable x is 6 units.

Answer:

The area for the trapezoid is

A=h/2(a+b)

A=8/2(10+15)

A=100 cm square

Hope it helps!