Mathematics College

Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 10 and its height is 6?

Answers

Answer 1
1. First, you must find the constant of variation (k). The problem indicates that the base of each triangle varies inversely with the height. So, this can be represented as below:

 B=k/H

 B is the base of the triangle (B=10).
 H is the height of the triangle (H=6).
 k is the constant of variation.

 2. When you clear "k", you obtain:

 B=k/H
 k=BxH
 k=10x6
 k=60

 3. Now, you have:

 B=60/H

 4. You can give any value to "H" and you will obtain the base of the second triangle.

 5. If H=12, then:

 B=60/H
 B=60/12
 B=5

 6. Therefore, the possible base and height of a second triangle is:

 B=5
 H=12
Answer 2

Answer:

12 and 5

Step-by-step explanation:

Related Questions

The circle has a diameter of 16 inches. What is the area of the circle?

Answers

A≈201.06 Do a google search

Formula for area of a circle is pi*radius^2. The radius of a circle is half the diameter.

Since the diameter given is 16 inches, the radius is 8 inches.

Using the formula, we find that the area is pi*(8 inches)^2 = 64pi inches^2

Consider the system of equations. x – 3y = 9 1/5x - 2y = -1

Answers

 x – 3y = 9  ------------ (1)
1/5x - 2y = -1---------- (2)

(1):
x - 3y = 9
x = 9 + 3y ----------- (1a)

(2):
1/5x - 2y = -1
x - 10y = -5 --------- (2a)

Sub (1a) into (2a):
9 + 3y - 10y = -5
9 - 7y = -5
-7y = -5 - 9
-7y = -14
7y = 14
y = 2 ---------- Sub into (1a)

x = 9 + 3y 
x = 9 + 3(2)
x = 9 + 6
x = 15

Ans: x = 15, y = 2


Answer:

B

Step-by-step explanation:

In the Chang family's budget, 0.6% of the expenses are for internet service. What is the fraction of the family's expenses is for internet service? Write the fraction in the simplest form.

Answers

A percent is actually a fraction already. (If you break up the words to have "per cent," this might seem more intuitive. "Cent" is from Latin centum, and is the same root in words like century. Here, it's like per hundred.)

You probably know intuitively that 100% is one whole, for example. But it's also the same as saying [tex] \frac{100}{100} [/tex]. Likewise, 67%, for instance, is actually [tex] \frac{67}{100} [/tex].

In this case, you can write [tex] \dfrac{0.6}{100}[/tex]. But you may realize that you shouldn't have a decimal in a fraction. For every number after the decimal, you multiply the whole thing by a corresponding power of ten. Here, you write [tex] \dfrac{0.6}{100} * \dfrac{10}{10} = \dfrac{6}{1,000} [/tex]. Since 10/10 is equal to 1, we aren't changing anything (Identity Property). If you had 0.06/100, you would multiply by 100/100, and so on...

So, now we have [tex] \dfrac{6}{1000} [/tex]. Our next step is to simplify. The greatest common factor of these two numbers is 2, we rewrite as [tex] \dfrac{3}{500} [/tex] to put it into simplest form. And that's all there is to it. 

The expression below represents the number of bacteria in a petri dish after t hours. Interpret the meaning of the expression. A. The initial number of bacteria is 57, and the growth rate is 3.1% per hour. B. The initial number of bacteria is 57, and the growth rate is 31% per hour. C. The initial number of bacteria is 131, and the growth rate is 5.7% per hour. D. The initial number of bacteria is 131, and the growth rate is 57% per hour.

Answers

Answer:

The answer on edgenuity for dividing fractions is -3 on the assignment good luck!

Step-by-step explanation:

  A polygon that has all sides the same measure and all angles the same measure is called what?        A. Convex polygon   B. Concave polygon   C. Irregular polygon   D. Regular polygon

Answers

D. Regular polygon.

A polygon that has all sides the same measure and all angles the same measure is called Regular polygon.

Hoped I helped!

Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?


It is the graph of y = log2x translated 3 units down and 9 units to the left.

It is the graph of y = log2x translated 9 units down and 3 units to the right.

It is the graph of y = log2x translated 9 units down and 3 units to the left.

It is the graph of y = log2x translated 3 units up and 9 units to the left.

Answers

I take it this is in base 2? It really doesn't matter for this question, but I will interpret it that way. The easiest way to do this is with a graphing calculator to see what happened. You can do it on the internet by going to wolframalpha and putting the equations in like this.

y = log_2(x); y = log_2(x + 3) - 9

You will see the picture clearly when you do this. The answer is that it moves 3 units towards the left and 9 units down. 

Answer: Third one down.

Comment: Anything you put inside the brackets with an x moves the graph left or right depending on the sign. (x + 3) moves 3 units to the left. (x - 3) moves the graph 3 units to the left.

Anything outside the brackets moves the graph up or down.  minus goes down. Plus goes up. The number must be on the right. - 9 goes nine units down.

it's C: It is the graph of y = log2x translated 9 units down and 3 units to the left.


$10.00 divided by $1.49

Answers

$6.71 is the answer that you are looking for. 
10.00/1.49
6.7 is the answer

Mora ate 8.5 Containers of Yogurt one week. Each Container Held 5.4 Ounces Of Yogurt . HOW Many Ounces Of Yogurt Did she eat in all

Answers

45.9 ounces. 8.5 x 5.4 = 45.9 ounces of yogurt

Final answer:

Mora ate a total of 45.9 ounces of yogurt after consuming 8.5 containers, with each container holding 5.4 ounces.

Explanation:

The student asked how many ounces of yogurt Mora ate after consuming 8.5 containers, with each container holding 5.4 ounces. Mora ate 8.5 containers of yogurt, with each container holding 5.4 ounces of yogurt. To calculate the total amount of yogurt consumed, we multiply the number of containers by the amount of yogurt each container holds.

To solve this, simply calculate 8.5 containers × 5.4 ounces/container = 45.9 ounces of yogurt in total. This is the total amount of yogurt Mora ate during that week.

what is the simplified form of 3a4b-2c3?

Answers

Final answer:

The expression 3a4b-2c3 is already in its most simplified form because they are not like terms, thus cannot be combined.

Explanation:

The given expression 3a4b-2c3 cannot be simplified further because it consists of variable components. Each of these components -- 3a, 4b, and 2c3 -- represent distinct and separate entities in the equation. Unlike in some mathematics problems, these components cannot be combined or simplified because they are not like terms. In algebra, like terms are terms that contain the same variables and powers. So only if the given equation was 3a + 2a or 4b - 3b, then they could be combined. But as it stands, 3a4b-2c3 is already in its most simplified form.

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What are the lower, middle, and upper quartiles of this data? 122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Answers

Answer:

The lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.

Step-by-step explanation:

The given data set is

122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Arrange the data set in ascending order.

71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164

Divide the data set in equal parts.

(71, 71, 77, 84, 85, 98), 98, (104, 111, 114, 122, 147, 164)

Now divide each parenthesis in two equal parts.

(71, 71, 77), (84, 85, 98), 98, (104, 111, 114), (122, 147, 164)

Lower quartile is

[tex]Q_1=\frac{77+84}{2}=80.5[/tex]

Middle quartile is

[tex]Median=Q_2=98[/tex]

Upper quartile is

[tex]Q_3=\frac{114+122}{2}=118[/tex]

Therefore, the lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.

PLEASE HELP!!!!

Which equation matches the graph of the greatest integer function given below?

A. y=[x]-3

B. y=[x]-2

C. y=[x]+2

D. y=[x]+3

Answers

the correct answere is B


Evaluate the expression when y=-5
Y^2-8Y+4

Answers

To find the answer, we need to plug in the y value into the equation.

(-5)^2 - 8(-5) + 4
= 25 - 8(-5) + 4
= 25 + 40 + 4
= 65 + 4
= 69

Hope this helps!

One side of a square flower bed is 22 feet long. How many plants are needed if they are to be spaced 22 inches apart around the outside of the bed?

Answers

(22 ft)*(12 in/ft)/(22 in) = 12 . . . . plants per side

12*4 = 48 plants are needed for the outside border.
Final answer:

To find out how many plants are needed, we calculate the perimeter of the square flower bed, convert that to inches, and then divide by the spacing of the plants. In this case, about 48 plants would be needed.

Explanation:

This problem can be solved using the properties of a square and unit conversion. Since a square has four equal sides and each side of the square flower bed is 22 feet long, the total perimeter of the flower bed would be calculated as 22 feet * 4, which is 88 feet. Next we need to convert these feet to inches since the plants are spaced 22 inches apart. There are 12 inches within a foot, so 88 feet equals 1,056 inches (88*12).

Once you have the total length in inches, you can determine the number of plants by dividing the total length in inches by the distance each plant is to be spaced. Thus, 1,056 inches divided by 22 inches gives us approximately 48 plants.

So, if you want to space your plants 22 inches apart around a square flower bed where each side is 22 feet, you will need 48 plants.

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A slice is made parallel to the base of a right rectangular pyramid, as shown.

What is the area of the resulting two-dimensional cross-section?

Enter your answer in the box.


in²

Answers

The answer is 5 I just took the test

The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas?

Answers

10.63

Hope this helped!

The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. mc018-1.jpg How many roots of f(x) are rational numbers?

Answers

There are three rational roots

Answer: there are 3 root of f(x)  which are rational numbers (2,0), (3,0) and (4.5,0)

Explanation:

Rational numbers are those that can be written in the form of p/q: q should not be equal to zero

since, the graph cuts x-axis at three points but rational are two

all integers are rational numbers

attached is the graph please have a look at it

If y varies inversely as x and y is 6 when x is 12 what is x when y is 14.4

Answers

1. To solve this problem and calculate the value of  "x" when "y" is 14.4, you must apply the following formulla:
 
 y=k/x
 
 k:  It is the constant of variation or constant of proportionality.
 
 2. So, keeping this on mind, you must calculate the value o the constant of variation "k", with the values given in the problem. Then, you have:
 
 k=yx
 k=(6)(12)
 k=32
 
 3. Now, you can apply the equation y=k/x and clear the "x" to find its value:
 
 yx=k
 x=k/y
 
 k=32
 y=14.4
 
 4. Then, you have:
 
 x=32/14.4
 
 5. Therefore, the answer is:
 
 x=2.22

the answer is option A. 5

what is the value of x in the diagram
a.1/2
b.4/21
c.2
d.4

Answers

◆ Triangles ◆

Hey !!

Check the attachment.
Hope it helps you :)

Answer:

2 so your answer would be C.

There are 3 grams of sodium in 1/2 of a liter of soda.how much is in 2/3 of a liter

Answers

[tex]\bf \begin{array}{ccll} \stackrel{sodium}{grams}&\stackrel{soda}{liters}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 3&\frac{1}{2}\\\\ g&\frac{2}{3} \end{array}\implies \cfrac{3}{g}=\cfrac{\quad \frac{1}{2}\quad }{\frac{2}{3}}\implies \cfrac{3}{g}=\cfrac{1}{2}\cdot \cfrac{3}{2}\implies \cfrac{3}{g}=\cfrac{3}{4} \\\\\\ 12=3g\implies \cfrac{12}{3}=g\implies 4=g[/tex]

Juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x) = 10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container. Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?

Answers

Answer: There is approximately 8.2 amount of radioactive material that will remain after 10 hours.

Step-by-step explanation:

Since we have given that

[tex]f(x)=10(0.98)^x[/tex]

where, f(x) represents the amount of radioactive material that will remain after x hours in the container.

Since we have given that x = 10 hours.

So, our equation becomes,

[tex]f(10)=10\times (0.98)^{10}\\\\f(10)\approx 8.17\\\\f(10)\approx 8.2[/tex]

Hence, there is approximately 8.2 amount of radioactive material that will remain after 10 hours.

Three consecutive even integers add to −6. What are these integers?

Answers

The actual answer is 0, -2, and -4. This equals -6 and the numbers are even.

In triangle NOP, Np is extended through Point P to Point Q, m < NOP =(x+17) degrees, m< PNO =(2x-4) degrees, and m< OPQ=(5x-17) degrees. Find m< OPQ

Answers

Final answer:

To find the measure of angle OPQ, set up an equation using the given angles in triangle NOP. Simplify the equation and solve for x. Substitute the value of x back into the expression for angle OPQ to find the measure of the angle.

Explanation:

To find the measure of angle OPQ, we can set up an equation using the given angles in triangle NOP:
(x+17) + (2x-4) + (5x-17) = 180
Simplifying the equation, we get: 8x - 4 = 180
From this, we can solve for x: 8x = 184, x = 23.
Now that we have the value of x, we can substitute it back into the expression for angle OPQ: 5(23) - 17 = 108 degrees.
Thus, the measure of angle OPQ is 108 degrees.

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Frankie is practicing for a 5-kilometer race. His normal time is 31 minutes 21 seconds. Yesterday it took him only 29 minutes 38 seconds. How much faster was Frankie yesterday than his normal time?

Answers

31 min 21 sec
- 29 min 38 sec

=1 min 47 sec

Its Simple! 1 minute and 47 seconds! You gotta do 31 mins and 21 seconds - 29 mins and 38 seconds! Which give you a whooping 1 minute and 47 seconds! I hope i helped you!

what is the maximum number of possible extreme values for the function f(x)=x^4+x^3-7x^2-x+6
A. 3
B. 4
C. 5
D. 2

Answers

A 4th degree polynomial will have at most 3 extreme values. Since the degree is even, there will be one global extreme, with possible multiplicity. The remainder, if any, will be local extremes that may be coincident with each other and/or the global extreme.


(The number of extremes corresponds to the degree of the derivative, which is 1 less than the degree of the polynomial.)

A cruise boat travels 48 miles Downstream in 2 hours and returns Upstream in 3 hours. Find the speed of the boat in still water and the rate of the Stream.

Answers

Let x be the speed of the boat in still water and y be the speed of the current of the river.
The downstream speed will be x+y, the upstream speed will be x-y.
but:
distance=speed*time
therefore; as the boat travels in 2 hours downstream we shall have:
2(x+y)=48......i
and as the boat travels upstream we shall have:
3(x-y)=48........ii
simplifying i and ii we get:
x+y=24....iii
x-y=16....iv
adding the above iii and iv we get
2x=40
x=40/2=20
substituting x=20 into iii we obtain:
20+y=24
y=24-20
y=4
so the speed of the boat in  still waters is 20 miles per hour
the rate of the stream is 4 miles per hour

Final answer:

The speed of the cruise boat in still water is 20 mph and the rate of the stream is 4 mph.

Explanation:

The student is asking about a problem related to the rate of the boat in still water and the rate of the stream, given the times it takes to travel downstream and upstream. To solve this, we can use the following steps:

Let the speed of the boat in still water be b mph and the rate of the stream be s mph.Downstream, the effective speed is b + s and upstream it's b - s.Using the formula distance = speed  imes time, we have two equations based on the given information: 48 miles = (b + s)  imes 2 hours for downstream and 48 miles = (b - s)  imes 3 hours for upstream.Solve the two equations simultaneously to find the values of b and s.

Let's solve the equations:

48 = 2(b + s)  => 24 = b + s48 = 3(b - s)  => 16 = b - s

Adding both equations:

24 + 16 = (b + s) + (b - s)  => 40 = 2b  => b = 20 mph (boat speed in still water)Subtracting the upstream equation from the downstream equation:24 - 16 = (b + s) - (b - s)  => 8 = 2s  => s = 4 mph (rate of the stream)

Therefore, the speed of the boat in still water is 20 mph and the rate of the stream is 4 mph.

The base of a triangle is 12 in. The height is 7 in. What is the area of the triangle? A) 19 in2 B) 28 in2 C) 42 in2 D) 84 in2

Answers

The area of triangle formula is 1/2bh.

1/2(12)(7) = 42 in²

Hope this helps :)

Answer:

C. 42

Step-by-step explanation:

2 cards are drawn from a standard deck of 52 playing cards. how many different 2-card hands are possible if the drawing is done without replacement?

Answers

I used a online calculator to complete the combination
[tex] _{52} C_{2} [/tex]= 1326

Final answer:

There are 1326 different 2-card hands possible when drawing without replacement from a standard deck of 52 playing cards, using combinations to calculate it.

Explanation:

To determine how many different 2-card hands are possible from a standard deck of 52 playing cards when drawing without replacement, we need to consider combinations since the order of the cards does not matter. Using the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose, we calculate C(52, 2).

We have:

n = 52 (total number of cards)

r = 2 (number of cards to choose)

Therefore, the calculation is as follows:

C(52, 2) = 52! / (2!(52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326.

So, there are 1326 different 2-card hands possible when drawing without replacement from a standard deck of cards.

A radio station sent a letter in the mail to 1000 randomly chosen residents within its broadcast area. The letter contained one dollar and a survey. The survey asked recipients to track their radio habits over a week. The survey was to be filled out and sent back in to the radio station. Identify a problem with the study.
A) Some of the sample data are missing
C) The data are based on reported results
D) The correlation between the variables implies causality

Answers

The problem is that the data are based on reported results, answer C.

This is a problem because when someone self-reports information it is not always accurate.  In some instances, those who self-report are not always honest when filling out survey information.

The correct answer is D) The correlation between the variables implies causality.

What is a survey?

A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics of interest.

Now it is said that, A radio station sent a letter in the mail to 1000 randomly chosen residents within its broadcast area. The letter contained one dollar and a survey. The survey asked recipients to track their radio habits over a week. The survey was to be filled out and sent back in to the radio station.

So, here the problem with the survey that the survey is the self filled thus there is a possibility that the people may not be honest while filling the survey.Hence causing casualities.

Thus the correct answer is D) The correlation between the variables implies causality

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What is the solution to this equation?

3(4x + 3) = 2x - 5(3 - x) + 2

Answers

Remove the brackets.
12x + 9 = 2x - 15 + 5x + 2

Collect the like terms.
12x + 9 = 7x - 13 

Subtract 7x from both sides.
12x - 7x + 9 = -13
5x + 9 = -13

Subtract 9 from both sides.
5x = - 22

Divide by 9
x = - 22/5
x = - 4.4

Check
=====
3(4*-4.4 + 3) = 2(-4.4) - 5(3 - -4.4) + 2
3(-17.6 + 3) = -8.8 - 5(7.4) + 2
3(-14.6) = - 8.8 - 37 + 2
-43.8 =? - 45.8 + 2
-43.8 = -43.8

And it does check.

The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5). What is the other endpoint of the diameter?

Answers

Consider this option:
1. if the point (4;6) is the centre of the circle and the point (2;5) is the first endpoint of its diameter, then point (4;6) is the middle point of the diameter (it means that is the middle between the 1st and the 2d endpoints of diameter).
2. using the property described above:
for x of the 2d endpoint of the diameter: x=4*2-2=6;
for y of the 2d endpoint of the diameter: y=6*2-5=7.

answer: (6;7)

Answer:

(6,7)

Step-by-step explanation:

The center of a circle is (4, 6), and an endpoint of a diameter is (2, 5)

Since center is the mid point of two end points of diameter .

So, we will use mid point formula

[tex](x,y)=(4,6)[/tex]

[tex](x_1,y_1)=(2,5)[/tex]

Mid point formula : [tex]x =\frac{x_1+x_2}{2}[/tex] and [tex]y =\frac{y_1+y_2}{2}[/tex]  

Substitute the values

[tex]4 =\frac{2+x_2}{2}[/tex] and [tex]6 =\frac{5+y_2}{2}[/tex]  

[tex]8 =2+x_2[/tex] and [tex]12 =5+y_2[/tex]  

[tex]6=x_2[/tex] and [tex]7=y_2[/tex]  

Thus [tex](x_2,y_2)=(6,7)/tex]

Thus the other endpoint of the diameter is (6,7)

Other Questions
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