Write a word problem for this inequality
72-12a<24

A) The time to travel 45 miles at a speed of 40 mph can be found from ...

... time = distance / speed

... time = (45 mi)/(40 mi/h) = 9/8 h = 1 hr 7 min 30 sec

B) The gas consumption can be found from ...

... (45 mi)/(54 mi/gal) = 5/6 gal

C) The cost of gas can be found from ...

... ($3.23/gal)×(5/6 gal) ≈ $2.69

_____

The units of the numbers tell you what needs to be multiplied or divided to give the answer quantity with correct units. It pays to keep the units with the numbers. They can be treated as though they were a variable.

area = 20 units²

construct a square of side 6 units around the given figure, then the area of the figure is given by area of square minus 4 congruent triangles

A = 6² - 4 × [tex]\frac{1}{2}[/tex] × 4 × 2

  = 36 - 16 = 20 units²

The amount Beth raised by swimming is ...

... x · $0.65

In addition, she had a contribution that was not related to the number of laps. Her total can be expressed as

... 15 + 0.65x = 80

_____

Subtract 15 and divide by 0.65 to find

... x = (80 -15)/0.65 = 65/0.65 = 100

Beth swam ...

... 100 Laps

Inputs are the first number output is the second. So youre outputs are 2, -1, -1, and 3. so i would say b

The set of outputs for the function represented by the scatterplot is {-1, 2, 3}, which matches Option B from the given choices.

You are looking to identify the set of outputs (also known as the range) of a given function based on a scatterplot. The output of a function is comprised of the second element in each ordered pair, which represents the y-value on the Cartesian plane. In this case, the scatterplot includes the points (-3, 2), (-2, -1), (2, -1), and (3, 3).

To find the correct set of outputs, we need to list the y-values from each point: 2, -1, -1, and 3. When listing a set, we do not repeat values, so the set of outputs for this function would be {2, -1, 3}. Therefore, the correct answer is Option B) {-1, 2, 3}.

Let the width of rectangle be X inches

Then according to question

Length of rectangle will be 3X

Also, we know that

Area of rectangle is = L×B

108 = X . 3X

3X^2 = 108

Divide both sides by 3

X^2 = 36

Taking squareroot of both sides

X=6

Therefore, width of rectangle is 6 inches

Answer:

1. 6 in.

Step by step explanation:

Let the width of our rectangle be x inches.

We have been given that the length of our rectangle is three times the width, therefore, length of our triangle will be 3x inches.

We are told that area of the rectangle is 108 square inches.

Since we know that [tex]\text{Area of a rectangle}=\text{Width}\cdot\text{Length}[/tex]

Let us substitute our given information in area formula.

[tex]108=x\cdot 3x[/tex]

Upon multiplying 3x by x we will get,

[tex]108=3x^{2}[/tex]

Let us divide both side of our equation by 3.

[tex]\frac{108}{3} =\frac{3x^{2}} {3}[/tex]

[tex]36=x^{2}[/tex]

Upon taking square root of both sides of our equation we will get,

[tex]6\pm=x[/tex]

Since width cannot be negative, therefore, width of our rectangle will be 6 inches and 1st option is the correct choice.

Answer:

1.827 x 10^-23

Step-by-step explanation:

(1.994 x 10^-23) - (1.67 x 10^-24) = 1.827 x 10^-23

It should be no surprise that the volume of a 1-inch cube is 1 cubic inch. Assuming those 36 cubes completely fill the interior volume of the figure, that figure's volume is

... 36 cubic inches

slope = - [tex]\frac{5}{2}[/tex]

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - [tex]\frac{5}{2}[/tex] x - 5 is in this form

with slope m = - [tex]\frac{5}{2}[/tex]

The slope of the equation

[tex]Y=\dfrac{-5}{2}x-5[/tex] is [tex]-\dfrac{5}{2}[/tex]  .

A line's steepness or inclination can be measured by a line's slope. It specifies the amount of rise or fall a line experiences for each unit of horizontal distance. In other words, it measures how quickly the vertical (y) and horizontal (x) coordinates of points on a line change with time.

Given equation is

[tex]Y=\dfrac{-5}{2}x-5[/tex] consider it as equation (1)

This is in the form of slope-intercept equation y = mx +b consider it as equation (2).  

Where m represents the slope and b represents the intercept term.

On comparing the equation (1) and equation (2)

[tex]m=-\dfrac{5}{2}[/tex]

Hence, the slope of the given equation   is given by  [tex]-\dfrac{5}{2}[/tex] .

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you can use the formula for sample means:

[tex][tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex][/tex]

where m stands for a value of the sample mean.

We are looking for the value, specifically for its two borderline values: 70 and 80

and their cumulative probabilities, p(z(80)) and p(z(70)). The difference p(z(80))-p(z(70))

will give the probability that m falls in the interval [70,80]

So let's get cracking at it:

[tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex]

[tex]z(80) = \frac{80-75}{5 / \sqrt{64}} = 8[/tex]

These are very large values of z. You may notice that any z-table online won't even bother covering range that high - the probabilities for these values are virtually 0 (in the neg case) 1 (in the pos case).

This means that numerically the probability of the sample mean of 64 samples falling within the range of 1 standard deviation is very close to 1

So the answer choice  should be 1.0

This is known as Einstein's proof, not because he was the first to come up with it, but because he came up with it as a 15 year old boy.

Here the problem is justification step 2.  The written equation

BC ÷ DC = BC ÷ AC

is incorrect, and wouldn't get us our statement 2, which is correct.

For similar triangles we have to carefully pair the corresponding parts to get our ratios right:

ABC ~ BDC means AB:BD = BC:DC = AC:BC so BC/DC=AC/BC.

Justification 2 has the final division upside down.

D

since the coefficient of the x² term is 1, then

add (half the coefficient of the x-term )² to both sides

that is ([tex]\frac{14}{2}[/tex])² = 49

11. {OD, OH} . . . or . . . {OB, OJ}

12. b. Open a compass to distance AB

13. 17 square units

11. Opposite rays are rays that together make a line. The only point they have in common is their mutual end point.

Given the letter names of points on lines, one can name opposite rays by choosing 3 collinear points, and selecting the middle one of those for the mutual end point. That point's name will be the first letter of each of the ray names. One ray will be named by one of the remaining points, and the other will be named by the other remaining point.

Here, we can choose points H, O, D on the same line. Then rays in opposite directions will be OD and OH, each having point O as its end point.

Similarly, we can choose points B, O, J on the other line and name opposite rays OB and OJ.

___

12. The general sequence of steps for copying a line segment is to draw a line segment longer than the one you want to copy, mark a point on it, set the compass to the length of the given segment, then use the marked point as one end and mark the distance from that point using the compass.

Here, the target line and reference point (C) have been made already, so the next step is open the compass to distance AB.

___

13. The unadulterated triangle has legs of 6 and 8 units, so an area of ...

... area = (1/2)bh = (1/2)(6)(8) = 24 . . . . square units.

One can count the squares within that area that have been removed from the triangle. There are 7 of them, so the area is ...

... 24 -7 = 17 . . . . square units

There are other ways to find the area, including dividing the triangle into smaller pieces. Doing the latter, one needs to be careful, because the slanted side only goes through a grid intersection at points (1, 1), (4, 5), and (7, 9).

If one uses two triangles with legs 3 and 4, and a central rectangle of 2×3, then the area adds up to 6+6+5 = 17 square units, because there is one square taken out of the lower right corner of the upper triangle.

Answer:

Given is that Lance rotates the figure 180° and Celina rotates the figure 90°

Now, when the figure is rotated 180 degrees, it will be turned around the origin in a way that the new place of the image will lie in a straight line in accordance to the original position. So, the second image is Lance's image.

When a figure is rotated 90 degrees counterclockwise, this means the figure will turn to the left and the point of the figure will be downwards. So, the first image is Celina's image.  

Answer:

See below:  Brainliest would help?

Step-by-step explanation:

If rain is falling at a rate of 2.56 inches per hour, one would expect 9.6 inches of rainfall after 3.75 hours.

The question pertains to the calculation of total rainfall when the rate of rainfall and time of rainfall are known.

        So, 2.56 inches/hour * 3.75 hours = 9.6 inches total rainfall.

Hence, if rain is falling at a rate of 2.56 inches per hour, you would expect 9.6 inches after 3.75 hours

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The "work" can be all in your head. In 15 years, their combined ages will have increased by 30 years over what it is now*, so their combined age now must be 64 year. If the ratio of their ages is 3:1, the youngest must be 1/(3+1) = 1/4 of the total, or 16 years.

Arya is 16 years old; Cersei is 48 years old.

_____

* Each person ages one year each year, so their combined age increases by 2 years each year. In 15 years, their combined age will increase by 30 years.

_____

If you insist on an equation, let "a' represent Arya's age. Then 3a represents Cersei's age. The relationship given in the problem is ...

... (a +15) + (3a +15) = 94

... 4a +30 = 94 . . . . . . . . . . collect terms

... 4a = 64 . . . . . . . . . . . . . . subtract 30

... a = 64/4 = 16 . . . . . . . . . multiply by 1/4

This equation and its working should look a lot like the verbal reasoning we did above.

Answer:

Card 7

The hourly rate of change/slope is $75 per hour.

Card 8

Frastastic is charging $0.48 per ounce.

Step-by-step explanation:

Card 7

Lets take the set up fee as "$[tex]s[/tex]" and,

Hourly rate as $[tex]x[/tex]per hour.

Now we can write equations for 3 hour event and 5 hour event.

[tex]s+3x=275[/tex] <------- (1)

[tex]s+5x=425[/tex] <------- (2)

Now we need to solve the simultaneous equations to find [tex]s[/tex] and [tex]x[/tex].

Subtract (1) from (2)

⇒[tex]s+5x-(s+3x)=425-275[/tex]

[tex]s+5x-s-3x=150[/tex]

[tex]2x=150[/tex]

[tex]x=75[/tex]

So the hourly rate of change/slope is $75 per hour.

Therefore, Raymond is right.

Card 8

You can take Amount (oz) as x values and Cost as y values and plot a graph.

Then the Slope of the graph will give you the rate Frastastic is charging per yogurt.

Slope of a linear graph is given by the following equation;

Slope(m)=[tex]\frac{y_{1}-{y_{2}}}  {x_{1}-x_{2}   }[/tex]

Slope(m)=[tex]\frac{6.72-2.4}{14-5}[/tex]

Slope(m)=[tex]\frac{4.32}{9}[/tex]

Slope(m)=[tex]0.48[/tex]

Therefore, Frastastic is charging $0.48 per ounce.

This is less than $0.50 per ounce charged by Fromazing. Therefore, Sterling is right.

Solution

When we add 1/3 which is rational to an irrational number, we get an irrational number.

pi - is a rational number. √2, √3 are also rational numbers

So the possibilities  are pi + 1/3,

2pi + 1/3,

3pi+1/3,

√3 + 1/3,

√2 + 1/3...

I hope this will help you.

Thank you.

Answer:

y = 2.5(x + 2)^2 - 3

The answer is A

Step-by-step explanation:

The general equation for the vertex is

y  =  a (x + b)^2 + c

a we are not certain about

b = 2

c = - 3

y = a(x + 2)^2 - 3 Now we have to solve for a.

a is found by using the one point we know (0,7) It means when x = 0 y = 7 so just put those two numbers in.

7 = a(0 - 2)^2 - 3

7 = a (- 2)^2 - 3       Add 3 to both sides.

7 + 3 = a(4)              Combine 7 and 3

10 = 4a                     Divide by 4

10/4 = a                    Do the actual division    

2.5 = a

Answer: See above

A

the equation of a parabola in vertex form is

y = a(x - h )² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here the vertex = (- 2, - 3 ), thus

y = a(x + 2 )² - 3

to find a substitute (0, 7 ) into the equation

7 = 4a - 3 ( add 3 to both sides )

10 = 4a ( divide both sides by 4 )

a = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]

y = [tex]\frac{5}{2}[/tex](x + 2 )² - 3

a) The orientation of the figure ABCDE is clockwise. The orientation of figure A'B'C'D'E' is counterclockwise, so at least one reflection is involved. The direction of AB is North, while the direction of A'B' is West, so a rotation of 90° is involved. Both of these can be accomplished by a reflection across the line that has a direction halfway between these, Northwest. The x-coordinate of point D is the same as that of D', so it is convenient to put point D on the line of reflection.

A transformation sequence that maps ABCDE to A'B'C'D'E' is ...

The attachment shows the result of reflecting the figure across the line.

b) About any reflection will give the figure the proper orientation. Depending on what it is, some amount of rotation and/or translation may be required.

We can reflect point D across the line y=-2 to put it where point D' is. That reflection changes the direction of AB to South, so we need to rotate the figure 90° CW to get AB to point West. Since we want point D' to be invariant, we can use that point as the center of rotation.

A second transformation that gives the same mapping is ...

I think that this is the x-intercept method:

First of all, we set y=x^3-6x^2+11x-6.

To find x, we need to let y=0. (y is also equals to f(x))

f(x)=x^3-6x^2+11x-6

In order to make f(x)=0, what does x have to be?

f(1)=0

So then we divide x^3-6x^2+11x-6 by x-1. Why? Because that will not give us a remainder.

(x^3-6x^2+11x-6)/(x-1) = x^2-5x+6

Now, we need to factorize it.

x^2-5x+6 = (x-2)(x-3)

So x=2,3

riding directly to the pool would be 4.2 miles, so he would have saved 1.8 miles

one way is to factor the expressions

(a)

[tex]10^{5}[/tex] (1.2 + (5.35 × [tex]10^{1}[/tex]))

= [tex]10^{5}[/tex] (1.2 + 53.5)

= 54.7 × [tex]10^{5}[/tex] = 5.47 × [tex]10^{1}[/tex]× [tex]10^{5}[/tex] = 5.47 × [tex]10^{6}[/tex]

(b)

[tex]10^{-3}[/tex]((6.91 × [tex]10^{1}[/tex]) + 2.4)

= [tex]10^{-3}[/tex](69.1 + 2.4)

= 71.5 × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{1}[/tex] × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{-2}[/tex]

(c)

[tex]10^{5}[/tex]((9.7 × [tex]10^{1}[/tex]) + 8.3)

= [tex]10^{5}[/tex](97 + 8.3)

= 105.3 × [tex]10^{5}[/tex] = 1.053 × [tex]10^{2}[/tex] × [tex]10^{5}[/tex] = 1.053 × [tex]10^{7}[/tex]

(d)

[tex]10^{1}[/tex]((3.67 × [tex]10^{1}[/tex]) - 1.6)

= [tex]10^{1}[/tex](36.7 - 1.6)

= 35.1 × [tex]10^{1}[/tex] = 3.51 × [tex]10^{1}[/tex] × [tex]10^{1}[/tex] = 3.51 × [tex]10^{2}[/tex]

(e)

[tex]10^{-6}[/tex]((8.41 × [tex]10^{1}[/tex]) - 7.9)

= [tex]10^{-6}[/tex](84.1 - 7.9 )

= 76.2 × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{1}[/tex] × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{-5}[/tex]

(f)

[tex]10^{4}[/tex]((1.33 × [tex]10^{1}[/tex]) - 4.9 )

= [tex]10^{4}[/tex](13.3 - 4.9) = 8.4 × [tex]10^{4}[/tex]

the y-axis, that is x = 0

the equation of a parabola in the form f(x) = ax²

has it's vertex at the origin and since the axis of symmetry passes through the vertex then

the axis of symmetry is the y- axis

The graph which represent a exponential function is:

                      Graph A.

Exponential function--

A exponential function is a function which is in the form of:

                   [tex]y=f(x)=ab^x[/tex]

where a and b are integers and a,b≠0.

From the given graphs, the graph which one that  represents a exponential function is:  Graph A.

An exponential graph represents a mathematical relationship where the dependent variable (y) is a constant raised to the power of the independent variable (x). This results in a curved graph that either increases or decreases rapid

A exponential function is a function which is in the form of:

[tex]y = f(x) = ab^{x}[/tex]

where a and b are integers and a,b≠0.

On the other hand, the graph of a exponential function either increases continuously or decreases continuously and rapidly in it's domain.

The x-axis is always an asymptote for the graph.

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Using a somewhat liberal interpretation of "the angles shown in the diagrams", we can conclude that the appropriate choice is ...

... A. The value of x should be 75, because the angles shown in the diagrams are congruent.

_____

There are 8 angles shown in each of 4 diagrams. All 32 angles are not congruent. Taken literally, "the angles shown in the diagrams are congruent" is a false statement. Rather, the marked pair of angles in each diagram are congruent angles.

A'(- 4, 3 )

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x )

A(3, 4 ) → A'(- 4, 3 )

If you multiply the original equation by 8, you get

... 8(1/4x -1/2y) = 8(8)

... 8/4x -8/2y = 64

... 2x -4y = 64 . . . . . matches choice b)

the outliers (8,25) and (39,16)

Answer:

The outliers are (8,25), and (39,16)

Step-by-step explanation:

These two points are outliers because they have a great value difference when compared to the other values.  

Answer:

1721 $

1612.80

Step-by-step explanation:

Straight line depreciation means depreciation is the same spread over for all the years.  The spread over amount is nothing but total cost of equipment - salvage value.

Here we have

Cost of equipment(Purchase cost)   ...    18000

Shipping costs                                   ...        620

Installation costs                                ...        590

Total cost of equipment                    ...     19210

Less: salvage value at the end         ...        2000

Net cost of equipment for 10 years ...      17210

Depreciation per year = Net cost /number of years of life

= 17210/10 = 1721/-

Hence answer is 1721/- for all years and also hence for year 2.

--------------------

Peach tree has an average life of 12 years. First 3 years no benefit would arise, 4 to 8 would be peak and after that slowly decreasing.

Hence in 9th year there would be least value and least depreciation.

Hence answer is $1612.80