A trapezoid has an area of 150 square meters. If the bases are 14 meters and 16 meters, what us the height of the trapezoid?

Answers

Answer 1

To find the area of a trapezoid, we use the following formula:
[tex]a = \frac{1}{2} (b1 + b2) \times h[/tex]
In this formula a represents the area and b1 and b2 each represent a base of the trapezoid.

So, we have got the following information
[tex]a = 150[/tex]
[tex]b1 = 14[/tex]
[tex]b2 = 16[/tex]

Filling in the formula gives us:
[tex]150 = \frac{{1} }{2} \times (14 + 16) \times h[/tex]
[tex]150 = \frac{1}{2} \times 30 \times h[/tex]
[tex]150 = 15 \times h[/tex]
Finally we have to divide both sides by 15.
[tex]h = 150 \div 15 = 10[/tex]
Therefore, the height of the trapezoid is 10 meters.

Related Questions

Patrick compared the slope of the function g(x) = -2x - 8 to the slope of the linear function shown in the table below. Let m = the slope of g(x) and n = the slope of h(x).

Which statement is true? Choose all that apply.

A. m < n

B. m > n

C. m = n

D. both slopes have the same sign.

E. both slopes have different signs.

Answers

Both slopes have the same sign

True or false the fraction 9/21 is in lowest terms

Answers

This is false.

9/12 in it's lowest terms is 3/7.

very simple false becuse the lowest form is 3\7

3\7 in decimal is 0.42857142 or 0.43

3\7 in percent 42.857143% or 43 %

use math way . c o m

Please help and show work. 15 points.

Answers

the answer is D
the x satys the same, the Y reverses positive/negative

(Please help, urgent).

What is the value of r?

Round your final answer to the nearest whole number.

Answers

◆ APPLICATIONS OF TRIGONOMETRY ◆

[tex] Heya \: ! \: \\ \\ We \: know \: that \\ \\ \: \sin( \alpha ) = \frac{perpendicular}{hypotenuse} \\ \\ \sin(67.4) = \frac{12}{r} \\ \\ \\ also \: , \\ \\ \sin(67.4) = 0.9231 \\ \\ comparing \: both \: ,\\ \\ \frac{12}{r} = 0.9231 \\ \\ r = \frac{12}{0.9231} \\ \\ r = 13 \: \: \: \: \: ans.[/tex]

Jovan bought a bond with a face value of 15,000 and a coupon rate of 8.5%. The bond will mature in 15 years. How much interest will he receive semiannually

Answers

Answer
19,125

Explanation
The value of bond has an interest of 8.5% annually. Monthly it will be 8.5/2%=4.25%
The initial value of bond is 15,000.
The formula for calculating the interest is;
Interest=PRT
Where p is the money deposited, R is the interest rate and T is the period.
Since the interest semiannually for 15 years, the interest period is (15×2) = 30.

Interest=15,000×0.045×30
=19,125.

What is the second term when 3+2x^2-3x^4+x3

Answers

x^3

I can explain if you want.

Find the greatest common factor : 25p^2q^3, 15p^2q^2 and 35pq^4

Answers

Answer:

The greatest common factor is [tex]5pq^2[/tex].

Step-by-step explanation:

The given expressions are [tex]25p^2q^3[/tex], [tex]15p^2q^2[/tex] and [tex]35pq^4[/tex].

Greatest common factor of two numbers is the greatest number that divides both numbers completely.

Find factors of each expression.

[tex]25p^2q^3=5\times 5\times p\times p\times q\times q\times q[/tex]

[tex]15p^2q^2=3\times 5\times p\times p\times q\times q[/tex]

[tex]35pq^4=5\times 7\times p\times q\times q\times q\times q[/tex]

The common factors are 5,p,q and q. So, the greatest common factor of given expressions is

[tex]G.C.F.=5\times p\times q\times q[/tex]

[tex]G.C.F.=5pq^2[/tex]

Therefore the greatest common factor is [tex]5pq^2[/tex].

You have decided to buy a new car, but you are concerned about the value of the car depreciating over time. You do some research on the model you are looking at and obtain the following information:

Suggested retail price - $18,790

Depreciation per year - $1385 (It is assumed that this value is constant.)

The following table represents the value of the car after n years of ownership.

Answers

The answer should be set up like so:

3125 = 3200*(d)^3
3125/3200 = d^3
3-root (3125/3200) = d
d = 0.992125657...

1 - d = 0.007874...
Therefore it depreciates at about 0.8% monthly

To find the depreciation 6 months from now, or 9 months from the beginning:
v = 3200 (d)^9
= 2980.232239...

So after 9 months the car would be about $2980.23

Answer: D on edge

Step-by-step explanation:

Jesse wants to write a function to represent the graph. He says that the period of the graph is triple that of sin x and that the equation of the graph is f(x)=3sin x. Why is he incorrect?
a. The period of the graph is twice that of sin x.
b. The frequency of the graph is triple that of sin x.
c. The equation of the graph should be f(x)=sin x/3.
d. The equation of the graph should be f(x)=3sin x.

Answers

Answer C

the value of sin(pi/2) =1

the value of sin(pi) = 0

according to the graph sin(3pi/2) = 1 and sin(3pi) =0

so the correct equation for the graph must be f(x) = sin(x/3)

Jesse is incorrect, because the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]

From the question, we understand that the period is 3 times sin x.

The above claim is wrong.

Given that, the period (B) is 3.

i.e B = 3

The function is represented as:

[tex]f(x) = \sin(\frac{2\pi}{B})[/tex]

So, we have:

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

Represent [tex]2\pi[/tex] with x

[tex]f(x) = \sin(\frac{x}{3})[/tex]

Hence, the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]

Answers

For this case, what we should do is write an equation of the potential type:
y = A * (b) ^ x
Where,
A: initial height
b: decrease rate of initial height
x: number of bounces.
We have then:
y = 3.5 * (0.75) ^ x
For the ninth bounce:
y = 3.5 * (0.75) ^ x
y = 0.26
Answer:
The height of the 9th bounce of the ball is:
y = 0.26 feet.

Is (a-3) a factor of (a^3-6a^2+29)?

Answers

If (a - 3) is a factor then (a -3) will be 0 when a = 3. If you put a = 3 into the given cubic, you should get 0. Doing that, does not give 0.

f(3) = 8 - 6*9 + 29
f(3) = 8 - 54 + 29
f(3) = - 17

As further "proof", here is the graph. Notice that the graph cuts the x axis around -2 , 2.5 and 4.2 (These are rough guesses). The factors are
(a+2)(a - 2.5)(a - 4.2)

PLEASE HELP ME OUT PLEASE!!
EXPLAIN IT PLEASE SO I CAN UNDERSTAND IT BETTER
THX

Answers

The answer is -47-10w=-9w-40-3w bc the equation above equals 7/2 and this equation does too first combine like terms -47-10w=(-9w+3w)+40 which gives you -10w-47=-12w-40 then Add 12w to both sides which gives you 2w-47=-40 and then Add 47 to both sides and gives you 2w=7 and then divide 2 in both sides and gives you 7/2

4x^3+2x^2+3x+4 divided by x+4

Answers

By synthetic division
= 4x^2 -14x +59 -232/(x+4)

The remainder is f(-4) = -232.

Divide: 4x^3+2x^2+3x+4/x+4

Simplify: 4x^4+2x^3+3x^2+4x+4/x

Factor completely x^2 − 36.

(x + 6)(x − 6)
(x + 6)(x + 6)
(x − 6)(x − 6)
Prime

Answers

Hello there!

[tex](First \ step) \\ \\ Factoring: (x2-36) \\ \\ \boxed{ A^2 - B^2 \ can \ be \ factored \ into \ (A+B) * (A-B)} \\ \\\ \left[\begin{array}{ccc}Proof : (A+B) * (A-B) = \\ A2 - AB + BA - B2 = \\ A2 - AB + AB - B2 = \\ A2 - B2\end{array}\right] \\ \\ \\ Factorization is : (x + 6) * (x - 6) \\ \\ \boxed{FINAL \ ANSWER} \\ \\ \boxed{\boxed{ (x + 6) * (x - 6)}}[/tex]

Your correct answer would be (option a) the first option.

I hope this helps you!

1. Vertex (1,2), Point (2,-5)

2. Vertex (-3,6), Point (1,-2)

3. Vertex (0,5), Point (1,-2)

4. Vertex (1/4, -3/2), Point (1.3)

Answers

he difficulty of graphing a quadratic function varies depending on the form you find it in. We'll start things off relatively easily.

f(x) = a(x – h)2 + k

No, we're not lying to you; that is a quadratic function. Go ahead, multiply it out.

f(x) = ax2 + (-2ah)x + (ah2 + k)

The h and k are constants, so (-2ah) and (ah2 + k) are also constants, which we could call, say, b and c. See, you can trust us, it's totally quadratic.

When you have a parabola written out like f(x) = a(x – h)2 + k, it's in vertex form. With vertex form, you have several pieces of important information thrown at you right away. When you first meet someone, your first impression tends to stick with you. It's the same with this equation.

The sign of a tells you if the parabola opens up or down. If a is positive, it opens up. If a is being a Negative Nancy, the parabola opens down. You also know that the vertex of the parabola is at the point (h, k). Be careful with the sign of h, though.

brainliest for best answer

Answers

Answer:

Step-by-step explanation:

________

Good evening ,

_______________

-4x+3y=-12

-2x+3y=-18

This system is the same as

y = (4/3)x - 4

y = (2/3)x - 6

We note that the two coefficients 4/3 and 2/3 are positives

So the right answer is C (graph 2).

___

The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0 4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___

Answers

We have a function [tex]f(x)[/tex] defined by two rules: if [tex]x \leq 0[/tex], [tex]f(x)=3x+1[/tex], and if [tex]x \geq 2[/tex], [tex]f(x)=2 x^{2} [/tex]. Notice that when you are evaluating a function at a number, you are basically saying that [tex]x[/tex] is equal to that number. So, when you say [tex]f(-3)[/tex], you are saying that [tex]x-3[/tex]. Since [tex]-3 \leq 0[/tex], we are going to use our first rule to evaluate our function at -3:
[tex]f(x)=3x+1[/tex]
[tex]f(-3)=3(-3)+1[/tex]
[tex]f(-3)=-9+1[/tex]
[tex]f(-3)=-8[/tex]

Similarly, when you are evaluating the function at 2, you are saying that [tex]x=2[/tex]. Since [tex]2 \geq 2[/tex], we are going to use our second rule to evaluate our function:
[tex]f(x)=2 x^{2} [/tex]
[tex]f(2)=2(2^{2} )[/tex]
[tex]f(2)=2(4)[/tex]
[tex]f(2)=8[/tex]

We can conclude that [tex]f(-3)=-8[/tex] and [tex]f(2)=8[/tex].

Final answer:

To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).

Explanation:

To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).

If x is less than or equal to 0, then f(x) = 3x + 1. So, f(-3) = 3(-3) + 1 = -8.If x is greater than 0 and less than 2, then f(x) = 2x^2. So, f(2) = 2(2^2) = 8.If x is greater than or equal to 2, then f(x) = 4. So, f(2) = 4.

Therefore, f(-3) = -8 and f(2) = 4.

Learn more about Determining values of a function here:

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Jenny has saved $3,800 over the last 12 months. She saved either $250 or $350 a month. During the 12 month period, how many times did Jenny save $250 for the month? A) 3 B) 4 C) 5

Answers

Hello,

Here is your answer:

The proper answer to the question is option A "3".

Here is how:

There is only two options 250 and 350 and there is 12 months which means there can only be three for both.

Your answer is A.

If you need anymore help feel free to ask me!

Hope this helps!

Answer:

the answer is actually 4

Step-by-step explanation:

At a store, customers are randomly selected to participate in a survey. On Friday, there were 500 customers at the store. Out of all those people, 90 were selected to participate in the survey. On Saturday, the store manager expects 700 customers in the store. If the probability of being selected to participate in the survey on Saturday is the same as it was on Friday, how many customers will be selected to participate in the survey on on Saturday?

Answers

Divide the number of people selected by the total number of people.

90/500 = .18

This means that 18% of the customers were selected for the survey.

If the probability is the same on Saturday, then we can multiply the expected customers by our .18

700 x .18 = 126

126 should be selected for the survey on Saturday.

By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
AND NO, it is not 33, 33.3, 66, or 66.6 percent.

Answers

Let N be the numerator, D be the denominator
[tex] \frac{N}{D} [/tex]

if its numerator is decreased by 50%
[tex] N - \frac{50}{100}N [/tex] ==> (this will be the numerator part)

if its denominator is decreased by 25%
[tex] D - \frac{25}{100}D [/tex] ==> (this will be the denominator part)

I try to separate them out, so it's easier to see the problem.

[tex] N - \frac{50}{100}N = \frac{100N}{100} - \frac{50N}{100} = \frac{50N}{100} [/tex]

[tex] D - \frac{25}{100}D = \frac{100D}{100} - \frac{25D}{100} = \frac{75D}{100}[/tex]

[tex] \frac{\frac{50N}{100}}{\frac{75D}{100}} = \frac{50N}{100} * \frac{100}{75D}[/tex]

[tex] \frac{50N}{75D} = \frac{2}{3}(\frac{N}{D})[/tex] by this, you can understand that
[tex] \frac{2}{3}(\frac{N}{D})[/tex] as 66.6% of N/D because 2/3 is 0.666666.... The answer should be 66.7% if you round them up.

In a given amount of time , Nijah drove twice as far as Jared. Altogether they drove 135 miles. Find the number of miles driven by Nijah

Answers

2x + x = 135
3x = 135
x = 135 /3
x = 45

Nijah = 2*45 = 90 miles

helppppppppppppppppppppppp

Answers

(-5, 12). Cosecant is the reciprocal of sine. Since csc theta =13/12, sin theta=12/13. We can narrow down to two angles, one in first quadrant and one in second quadrant. We are also given sec theta=-13/5, so cos theta=-5/13. Thus the angle is in the second quadrant. tan theta=1/cot theta=-12/5, so point (-5, 12) is on the ray.

A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5? A. start fraction 1 over 6 end fraction B. start fraction 1 over 12 end fraction C. start fraction 2 over 3 end fraction D. one-fourth

Answers

Answer:

i got 1/4

Step-by-step explanation:

me sorry in wrong

What is the median of the data set?

42 55 27 31 17 24 65 47 39 18

A. 21

B. 35

C. 17

D. 24

Answers

first we need to arrange the numbers in this number set from smallest to biggest:17,18,24,27,31,39,42,47,55,65. Then there are 10 numbers in this number set. So when we calculate the median, we need to find the middle two numbers and calculate their average. So the median is (31+39)/2=35. SO the answer is B

B᷉᷈. 35

Y᷉᷈o᷉᷈u᷉᷈ p᷉᷈l᷉᷈a᷉᷈c᷉᷈e᷉᷈ t᷉᷈h᷉᷈e᷉᷈m᷉᷈ i᷉᷈n᷉᷈ n᷉᷈u᷉᷈m᷉᷈e᷉᷈r᷉᷈i᷉᷈c᷉᷈a᷉᷈l᷉᷈ o᷉᷈r᷉᷈d᷉᷈e᷉᷈r᷉᷈
T᷉᷈h᷉᷈e᷉᷈n᷉᷈ f᷉᷈i᷉᷈n᷉᷈d᷉᷈ t᷉᷈h᷉᷈e᷉᷈ m᷉᷈i᷉᷈d᷉᷈d᷉᷈l᷉᷈e᷉᷈ n᷉᷈u᷉᷈m᷉᷈b᷉᷈e᷉᷈r᷉᷈

I need to write these description into the new function but I keep getting the wrong thing -.-

1.The function f(x)=(1/2)^x is translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5

2.The function f(x)=ln x is translated 3 units left, horizontally compressed by a factor of 1/4 and translated 0.5 units down.

3. The function f(x)=e^x is horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right.

Answers

Since you're studying this stuff, you know that
.. translation right by k units: f(x) ⇒ f(x-k)
.. translation up by k units: f(x) ⇒ f(x) +k
.. horizontal stretch by a factor of k: f(x) ⇒ f(x/k) . . . . same as compressed by 1/k
.. vertical stretch by a factor of k: f(x) ⇒ k*f(x)
.. reflection across the x-axis: f(x) ⇒ -f(x)
.. reflection across the y-axis: f(x) ⇒ f(-x)
The sequence in which these are done is important.

1. f(x) = (1/2)^x
.. translated 4 units right: f(x) = (1/2)^(x -4)
.. reflected across the x-axis: f(x) = -(1/2)^(x -4)
.. vertically stretched by a factor of 1.5: f(x = -1.5(1/2)^(x -4)

2. f(x) = ln(x)
.. translated 3 units left: f(x) = ln(x +3)
.. horizontally compressed by a factor of 1/4: f(x) = ln(x/4 +3)
.. translated down 0.5 units: f(x) = -0.5 +ln(x/4 +3)

3. f(x) = e^x
.. horizontally stretched by a factor of 3: f(x) = e^(x/3)
.. reflected across the y-axis: f(x) = e^(-x/3)
.. translated 1 unit right: f(x) = e^(-(x -1)/3)

Final answer:

The transformed equations for each of your base functions according to given changes are f(x) = -1.5*(1/2)ˣ⁻⁴, f(x) = ln(4×(x+3))-0.5, and f(x)=e⁻³×(x-1) respectively.

Explanation:

1. The transformed function for your first one, namely f(x)= (1/2)ˣ, after being translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5 would be f(x) = -1.5×(1/2)⁽ˣ⁻⁴⁾.

2. Your second function, f(x) = ln(x), after being translated 3 units left, horizontally compressed by a factor of 1/4, and translated 0.5 units down becomes:
f(x) = ln(4×(x+3))-0.5.

3. Your final function, f(x)=e^x, when it's horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right, would transform into: f(x)=e⁻³×(x-1).

Learn more about Function Transformation here:

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Which of the following pairs of organisms compete with each other for food?

A. squirrels and owls

B. mice and owls

C. rabbits and green plants

D. mice and rabbits

Answers

The answer would be D. Mice and Rabbits. Hope it helps! :)

its gotta be D. mice and rabbits, hope this helps. :))

Which of the following sets of whole numbers represents all the even three-digit numbers with a 6 in the hundreds place and 3 in the tens place? 361; 363; 365; 367; 369 630; 632; 634; 636; 638 360; 633; 635; 637; 639

Answers

The whole numbers in the list you provided which are even and have a 6 in the hundreds place and 3 in the tens place are:
630, 632, 634, 636, and 638 :)

The points (15, 10), (25, 20), (30, 22), (40, 32), (55, 53), (60, 55) represent the time, x, it takes 6 people to travel y miles. The scatterplot below represents the situation.

(Graph Below)

A. 32 miles
B. 42 miles
C. 48 miles
D. 54 miles

Answers

Answer:IT IS B

Step-by-step explanation:

I GOT A 100 ON MY TEST YOUR WELCOME :D

Someone Please Help!!!
Find the radian measure of an angle of -280 degrees

Answers

Answer: -4.88691778Solution:1.Write down the number of degrees you want to convert to radians Given Degree = -280° The formula to convert degrees to radian measure is:Radian = degree x π/180 2. Multiply the number of degrees by π/180. Think of it like multiplying two fractions: the first fraction has the number of degrees in the numerator and "1" in the denominator, and the second fraction has π in the numerator and 180 in the denominator. -280 x π/180 = -280π/1803. Find the largest number that can evenly divide into the numerator and denominator of each fraction and use it to simplify each fraction. The largest number for 280 is 20.-280 x π/180 = -280π/180 ÷ 20/20 = -14π /9 4. Then multiply the numerator by 3.14159 because pi or π is equivalent to 3.14159, -14x 3.14159= -43.982265. To get the radian measure, we will divide -43.98226 by 9. -43.98226/9= -4.88691778

Answer:-14pi/9

Step-by-step explanation:

Estimate 92.49 - 63.854 by first rounding each number to the nearest whole number.

Answers

92.49 -63.854 ≈ 92 -64 = 28

____
Actual difference is 28.636.

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