Mathematics High School

The base of a parallelogram is 24 inches longer than three times the height. The area of the parallelogram is 384 square inches. What is the height?

The height is x = ________ inches.

Answers

Answer 1

To find the height of the parallelogram, set up the equation (3x + 24) x = 384 using the formula for the area of a parallelogram. Solve the resulting quadratic equation to find that x, representing the height, is 8 inche

The student is trying to find the height of a parallelogram when the base is 24 inches longer than three times the height and the area is 384 square inches. Let the height of the parallelogram be represented by x inches. According to the problem, the base (b) is 3x + 24 inches. Using the formula Base x Height = Area of parallelogram, we can set up the equation:

(3x + 24) x= 384

Now solve for x using the distributive property:

3x^2 + 24x = 384

Next, set the equation to zero:

3x^2 + 24x - 384 = 0

Divide the entire equation by 3 to simplify:

x^2 + 8x - 128 = 0

Factor the quadratic equation:

(x + 16)(x - 8) = 0

Set each factor equal to zero:

x + 16 = 0 or x - 8 = 0

Since the height cannot be negative, x = 8 is the solution. Therefore, the height of the parallelogram is 8 inches.

Related Questions

−12.7=y−3.4
Can you guys please help me solve this. Thanks!

Answers

For this case we have the following equation:
 [tex]-12.7 = y-3.4 [/tex]
 From here, we must clear the value of y.
 For this, we follow the following steps:

 1) we add 3.4 on both sides of the equation:
 [tex]-12.7 + 3.4 = y-3.4 + 3.4 [/tex]

 2) We rewrite the right side of the equation:
 [tex]-12.7 + 3.4 = y + 0 -12.7 + 3.4 = y[/tex]

 3) We do the algebraic sum of the left side of the equation:
 [tex]-12.7 + 3.4 = y -9.3 = y[/tex]

 Therefore, the solution of the equation is:
 [tex]y = -9.3 [/tex]

 Answer:
 y = -9.3

Joseph squares a number and subtracts 8 from the answer. He then divides this result by 7. Finally he adds 12 and the result is now 20. What was Joseph's original number?

Answers

Let the number be X, then we find
[tex]( {x}^{2} - 8) \div 7 + 12 = 20[/tex]
[tex]( {x}^{2} - 8) \div 7 = 8[/tex]
[tex]( {x}^{2} - 8) = 56[/tex]
[tex] {x}^{2} = 64[/tex]
[tex]x = \sqrt{64} \: \: \: \: \: x = - \sqrt{64} [/tex]
[tex]x = 8 \: \: \: \: \: x = - 8[/tex]

Final answer:

We use reverse operations to solve Joseph's equation and find that the original number could have been either 8 or -8.

Explanation:

The question asks us to determine Joseph's original number based on a series of mathematical operations. We can set up an equation to represent the problem statement: let x be the original number. The sequence of operations given is:

Square x and subtract 8.

Divide this result by 7.

Add 12 to the result from step 2.

The final result is 20.

Representing this mathematically: ((x2 - 8) / 7) + 12 = 20. To find x, we need to work backward through these operations:

Subtract 12 from both sides: ((x2 - 8) / 7) = 8.

Multiply both sides by 7: x2 - 8 = 56.

Add 8 to both sides: x2 = 64.

Take the square root of both sides: x = 8 or x = -8 (considering both positive and negative square roots).

Therefore, Joseph's original number could have been either 8 or -8.

Special-effects artists often use scale models.the actual height of a velociraptor is estimated to have been approximately 2 ft.an artist draws the dinosaur with a height of 4 in. on paper.
a. what would be an appropriate scale for a model of the velociraptor?
b. the same scale is used for a model of a tyrannosaurus, whose actual height was 16 ft.what is the height of the model?

Answers

we know that

part A)
[scale]=[model height]/[actual height]
[scale]=[4 in]/[2 ft]=2 in/ft
that means
(2 in) in the model is -------------> (1 ft) in the actual

part B) 
[actual height]=16 ft     [model height]=?    [scale]=2 in/ft

[scale]=[model]/[actual height]
[model height]=[scale]*[actual height]
[model height]=[2]*[16]=32 in
the answer part B) is 32 in



factor the trinomial x^2+6x-16

Answers

For quadratics with an a value (coefficient of x²) of 1, we find factors of c, the constant, that sum to b, the coefficient of x.  In our case we want factors of -16 that sum to 6.
-16 = -1(16) or 16(-1)
-16 = -2(8) or 8(-2)
-16 = -4(4) or 4(-4)

Out of these 6 possibilities, the only one that sums to 6 is 8(-2), because 8+(-2)=6.

This gives us the factors (x+8)(x-2).

Look at some real estate want ads in your newspaper. Enter the price of a two-bedroom home and a three-bedroom home. If you find some abbreviations you do not understand, ask your teacher.

Answers

I just looked at the home ads and here are some examples of what I found.

3 Bedroom house for $122,900, 1610 square feet
3 Bedroom house for $129,000, 1460 square feet
2 Bedroom house for $72,500, 1,230 square feet
2 Bedroom house for $89,700, 1,350 square feet

What pair of numbers has the geometric mean of 44

Answers

Basically any two numbers whose product is 44^2 = 1936. 
so 16×121 = 1936
so the pair is 16 and 121

The possible pair of numbers that has the geometric mean of 44 is 16 and 121 and this can be determined by using the concept of geometric progression.

Given :

The geometric mean of 44.

The following steps can be used in order to determine the pair of numbers that has the geometric mean of 44:

Step 1 - The concept of geometric progression can be used in order to determine the pair of numbers that has the geometric mean of 44.

Step 2 - Let the two numbers be 'a' and 'b'.

Step 3 - According to the given data, the geometric mean of 44, that is:

[tex]\rm \sqrt{ab} = 44[/tex]

Step 4 - Simplify the above expression.

ab = 1936

Step 5 - So, the possible pair of numbers that has the geometric mean of 44 is 16 and 121.

For more information, refer to the link given below:

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A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism? Enter your answer as a simplified mixed number or a decimal

Answers

The volume of a rectangular prism is:

[tex]V=l*w*h[/tex]

Where

l=lenght,

w=width

h=height

So, as this prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches, the volume is calculated as follows:

[tex]V=l*w*h=312 in*5 in*112 in=174 720 inches^3[/tex]

 

Paula ran 24 foot with the football and then passed it 15 feet to newt. Newt ran 70 yards for a touchdown. What was the total number of feet the ball traveled?

Answers

24 + 15 

70 yards = 210 feet

210 + 39 = 249

The ball traveled a total of 249 feet.

How can you find the number of inches in 1 mile, show your work.

Answers

1 mile=1258 foot
1 foot=12 inches
63360 is the correct answer

The value of number of inches in 1 mile is,

⇒ 15,096 inches

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

To find the number of inches in 1 mile.

Since, We know that;

1 mile = 1258 foot

And, 1 foot = 12 inches

Thus, The value of number of inches in 1 mile is,

⇒ 1258 x 12

⇒ 15,096 inches

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Letter grades earned by a particular student in history class.
a. qualitative/nominal
b. qualitative/ordinal
c.quantitative/continuous
d.quantitative/ discrete
i think the answer is d

Answers

Letter grades are not numerical, but can be ordered in a meaningful way. Because the responses are not numerical, they are considered qualitative. Because they can be ordered in a meaningful way, they are also considered ordinal. The best answer choice is B.

If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to

decrease
stay the same
increase

Answers

If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to decrease.

What is the correlation of the sets?

For a message to be processed by a certain orchestration, a correlation set specifies a collection of qualities and values for these properties. A maximum of three parameters are supported by each correlation set.

If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to decrease.

This means that there is an inverse relationship between the two sets, such that when one variable increases, the other variable tends to decrease.

This type of correlation is often expressed by a negative correlation coefficient,

which ranges from -1 to 0, with -1 indicating a perfect negative correlation.

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The pair of values below is from an inverse variation. Find the missing value.
(4,14), (10,y)

Answers

Hi there! Not 100% percent sure if it's the same here, but it wasn't too long ago we learned about inverse relationships in Chemistry. The formula goes as follows:

x1y1 = x2y2

Now you just have to plug in the information.

4 x 14 = 10 x y2

What do you do now? You isolate the variable, y2. You do this by dividing y2 by the number it is multiplied.

Like this: [tex] \frac{y2}{10} [/tex]

As we all know, what you do to one side you must do to the other. But before you do that, you need to multiply the 4 by the 14.

4 x 14 = 56

Now you can divide by 10.

[tex] \frac{56}{10} [/tex]

The answer should be 5.6. Hopefully this helped!


If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?


A. 5,3

B. 4,5

C. 5,5

D. 4,3

Answers

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &A&(~ 9 &,& 8~) % (c,d) &B&(~ -1 &,& -2~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-1+9}{2}~~,~~\cfrac{-2+8}{2} \right)\implies \left( \cfrac{8}{2}~~,~~\cfrac{6}{2} \right)\implies (4~~,~~3)[/tex]
Answer:
D. (4,3)

Explanation:
The endpoints of the line are given as (9,8) and (-1,-2)
1- Computing the x-coordinate of the midpoint:
Xmidpoint = (x1+x2) / 2 = (9+-1)/2 = 8/2 = 4
2- Computing the y-coordinate of the midpoint:
Ymidpoint = (y1+y2) / 2 = (8+-2) / 2 = 6/2 = 3

Based on the above, the midpoint is (4,3)

Hope this helps :)


Jason's insurance company pays for 80% of the cost of an ambulance ride, after he pays a $200 deductible. The ambulance ride costs $1200.

How much wold Jason pay for an ambulance ride?
A) 200
B) 240
C) 400
D) 440

Answers

B) 240 Hope the helps you and i'm correct.

what is the lateral area of the cone? base 10 yd height 12.1 yd

a. 242.6 yd2
b. 190.07 yd2
c. 603.19 yd2
d. 96.4 yd2
Please help me get this answer correct ! asap

Answers

To get the area of the lateral side of a cone you will need the formula:

L= r x [tex] \pi [/tex] x l

where: L = Lateral area
            l  = length or height
            r = radius
            [tex] \pi [/tex] = 3.1416
Now sorting out your given:
base = 10 yd
Height = 12.1 yd

To work out the lateral area, you will need the radius. Your base 10 yd, is the measure from one side to the other of the circle base, this is what you call diameter. What you need is radius, which is the measure of a circle from the middle of the circle to the outside, so it is half of a diameter. 

So to get radius (r), divide the base by 2. 
r = 10yd/2 = 5yd

Now that you have all that you need just input it into your formula:
L = r  x [tex] \pi [/tex] x l
   = 5 yd x [tex] \pi [/tex] x 12.1 yd
   = 190.07 yd[tex] ^{2} [/tex]

So your answer is B.
we have that 
base=10 yd-----------------> r=5 yd
lateral area=pi*r*h--> pi*5*12.1=  190.07 yd²

the answer is option b. 190.07 yd2

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:

Hourglass with sand measuring 47 millimeters high

© 2011 Jupiterimages Corporation

Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass is 47 millimeters. The radius of both the cylinder and cone is 4 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
A(6.4)
B(62.4)
C(8.5)
D(56.0)

Answers

The volume of a cylinder is given by the formula V=πr²h². In this instance, r is 4 and the height is 47-12 (the height of the cone at the bottom is 12 mm and the sand goes up to 47 mm on the top portion of the hourglass, including both the cone and cylinder) or 35 mm.
V=π(4²)(35)=560π mm³.
The volume of a cone is given by the formula V=1/3πr²h².  In this instance, r is 4 and the height is 12 mm.
V=1/3π(4²)(12)=π(1/3)(12)(4²)=π(4)(4²)=64π mm³.  
This gives a total volume of 560π+64π=624π mm³ of sand.
Since the sand goes down to the bottom at a rate of 10π mm³/second, it will take 624π/10π=62.4 seconds for the sand to all drain out.

Answer:

62.4

Step-by-step explanation:

Rewrite 20/6 as a mixed number.

Answers

Divide the numerator by the denominator and remove the remainder or following decimal.

20/6 = 3 R2 = 3

Thus, 3 is our whole number that resides next to the fraction.

Now take this number, multiply it by the denominator, and subtract this value from the numerator: 20 - 3(6) = 2. This is the numerator of the fraction in our mixed number. 

Now simply add the denominator under this new numerator and place the three next to this fraction: 3 2/6.

The improper fraction number 20/6 is converted into a mixed fraction number as 3 ¹/₃.

What is the mixed fraction number?

The mixed fraction number is the combination of the whole number and the proper fraction number. In a proper fraction number, the numerator is smaller than the denominator.

The improper fraction is 20/6.

Convert the improper fraction into a fraction number.

⇒ 20 / 6

⇒ 10 / 3

⇒ (9 + 1) / 1

⇒ 9/3 + 1/3

⇒ 3 ¹/₃

The improper fraction number 20/6 is converted into a mixed fraction number as 3 ¹/₃.

More about the mixed fraction number link is given below.

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distance between 1,3 and -3, -1

Answers

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 1 &,& 3~) % (c,d) &&(~ -3 &,& -1~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-3-1)^2+(-1-3)^2}\implies d=\sqrt{(-4)^2+(-4)^2} \\\\\\ d=\sqrt{32}\implies d=\sqrt{16\cdot 2}\implies d=\sqrt{4^2\cdot 2}\implies d=4\sqrt{2}[/tex]

Factor completely x^2 + 16.

(x + 4)(x + 4)
(x + 4)(x − 4)
Prime
(x − 4)(x − 4)

Answers

The answer is (x4-81) hope it helps have a great day!

Janet has a square-shaped sheet of wrapping paper. To cover the top of a box, she cuts off 11 centimeters of the sheet along the width. The new area of the sheet is given by the expression below, where x represents the length, in centimeters, of the sheet of wrapping paper before being cut.
x^2-11x
Which statement best describes the term 11x?

the area cut from the sheet of wrapping paper
the area of the sheet of wrapping paper after being cut
the area of the sheet of wrapping paper before being cut
the width of the sheet of wrapping paper after being cut

Answers

x² represents the area of the original sheet of wrapping paper.  This would be a square that is x units long and x units wide.  11x would be the area of the section she cut off; she cut off 11 cm from the width, so the width of the piece cut off is 11, and the length of the piece she cut off is still x.  The area of a rectangle is given by width * length; in this case 11*x or 11x.
The expression she has, x² - 11x, represents the area of the sheet of wrapping paper after she's cut it.

Answer:

The correct option is 1. It means 11x is the area cut from the sheet of wrapping paper.

Step-by-step explanation:

The shape of sheet is square.

Let  x represents the length, in centimeters, of the sheet of wrapping paper before being cut.

The area of a square is

[tex]A=a\times a[/tex]

Where, a is side length.

The area of sheet before being cut is

[tex]A=x\times x=x^2[/tex]

The width of the piece cut from the sheet is 11 and length is x. So, the area of piece is

[tex]A=x\times 11=11x[/tex]

The remaining area of sheet is

[tex]A=\text{Area of sheet}-\text{Area of piece cut from the sheet}[/tex]

[tex]A=x^2-11x[/tex]

Therefore correct option is 1. It means 11x is the area cut from the sheet of wrapping paper.

What are the slope and the y-intercept of the linear function that is represented by the graph?

Answers

The slope is -3/4 because it rises goes down 3 and runs 4. the Y-intercept or where the line meets the y line is 3.

The y-intercept is the point where the line cuts the y-axis, hence the y-intercept is (0,3)

Slope and intercept of a line

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

Slope = y2-y1/x2-x1

Using the coordinate points (0, 3) and (4, 0)

Slope = 0-3/4-0
Slope = -3/4

Since the y-intercept is the point where the line cuts the y-axis, hence the y-intercept is (0,3)

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Select the correct product. ( a + 8)( b + 3)
ab + 8 a + 3 b + 24
ab + 3 a + 8 b + 24
11 ab
24 ab

Answers

the answer is
ab + 3a + 8b + 24

i hope this helps :)

Answer:

ab + 3 a + 8 b + 24

Step-by-step explanation:

just did this question

A shop sells three types of boots (football, rugby and hiking). Sales are usually in the ratio 6 : 2 : 3 last month, 24 pairs of football boots were sold. How many boots altogether were sold last month?

Answers

There were 44 boots sold last month

Answer:

Total number of boots sold = 44

Step-by-step explanation:

Ratio of football, rugby and hiking boots sold = 6 : 2 : 3

24 pairs of football boots were sold.

That is

            6 n  = 24

               n = 4.

Number of rugby boots sold = 2 n = 2 x 4 = 8

Number of hiking boots sold = 3 n = 3 x 4 = 12

Total number of boots sold = 6n + 2n + 3n = 11n = 11 x 4 = 44

Total number of boots sold = 44

Choose the correct simplification of the expression a to the 7th power times b to the 8th power all over a to the 4th power times b to the 4th power

Answers

the simplification of the expression will be as follows:
(a^7b^8)/(a^4b^4)
According to the rules of indices, when you divide numbers with the same base, it's the same as subtracting their powers. Hence we shall have:
(a^7b^8)/(a^4b^4)
=(a^(7-4))(b^(8-4))
=a^3b^4
the answer is a^3b^4

"if a six sided dice is rolled 2 times. what is the probability of obtaining a 2"

Answers


2/6 because there's less than half a chance to get 2 on a six-sided dice.
hope this helps 

helppppppppppppppppppppppppppppppppppp

Answers

Answer:
-16 + 37i

Explanation:
Note that i^2 = -1

(4+7i)(3+4i) = 4*3 + 4*4i + 7i*3 + 7i*4i
                    = 12 + 16i + 21i + 28i^2
                    = 12 + 37i + 28(-1)
                    = 12 + 37i - 28
                    = -16 + 37i

Hope this helps :)
                 

The temperature on Saturday was 6 1/2 °C. On Sunday, it became 3 3/4 °C colder. What was the temperature on Sunday?

Answers

2 3/4 C on Sunday I just subtracted the two.

Answer:

The temperature on Sunday was 2.75 degrees Celsius.

Step-by-step explanation:

The temperature on Saturday was = [tex]6\frac{1}{2}[/tex] or 6.5 degree Celsius

The temperature on Sunday became [tex]3\frac{3}{4}[/tex] or 3.75 degrees colder.

When the temperature falls of it gets colder, this means the new temperature is less than the previous one. The lower the temperature, the more colder it is.

So, in the question, the temperature gets colder by 3.75 degrees, so the temperature must have been = 6.5-3.75 = 2.75 or [tex]2\frac{3}{4}[/tex] degrees Celsius.

Therefore, the temperature on Sunday was 2.75 degrees Celsius.

the graph that represents 4 ≤ x

Answers

Answer:

Refer attachment.

Step-by-step explanation:

Given: Equation as 4 ≤ x

We have to plot the graph for that represents the given equation 4 ≤ x.

Consider the given equation 4 ≤ x.

It can be read as x takes values which is greater than and equal to 4.

So, the graph of this equation 4 ≤ x is given as shown below.

What is the absolute value of -4-2i

Answers

The absolute value of an integer is the numerical valuewithout regard to whether the sign is negative or positive. On a number line it is the distance between the number and zero. Absolute value is also known as magnitude.
I think the answer would be 4+2i.

All absolute value is asking is how far away it is from zero.

what are the values of x and y?

Answers

see the attached figure with letters

we have that 
cos(alfa) triangle ABD=12/y
and
cos(alfa) triangle ABC=y/28
then
12/y=y/28----------> y²=12*28=336----------> y=√336=4√21
y=4√21

applying the Pythagorean theorem  triangle ABC
(16+12)²=x²+y²----------? x²=28²-(4√21)²--------> x²=784-336
x=√448=8√7

the answer is 
x=8√7
y=4√21

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