Mathematics College

Calculate the area of the trapezoid.
12 mm
5 mm
9 mm
________square millimeters

Answers

Answer 1

Answer:

52.5 square millimeters.

Step-by-step explanation:

Area of a Trapezoid = (a+b/2)h

= (9+12/2)•5

=(21/2) • 5

= 10.5 • 5

= 52.5 square millimeters

hope this helps!

Answer 2

Answer:

52.5 mm^2 (square millimeters)

Step-by-step explanation:

Just split the figure into two sections to make a rectangle, and a right triangle (This whole figure can be thought of as a composite figure)

Once that is done, you will notice that the length and width of the rectangle is 9mm by 5mm, and the triangle is 3mm by 5mm (because 12mm - 9mm is 3 mm, and the height of the triangle is shared with the width of the rectangle).

The area of a triangle is 1/2(base×height) [just as a triangle is half of a rectangle], so the area of the rectangle is (length × width).

Therefore the 9mm by 5mm rectangle has an area of 9×5 mm = 45 mm^2, and the 3mm by 5mm triangle has an area of 1/2(5×3) = 15/2 = 7.5 mm^2.

Add both areas to find the total area:

45mm^2 + 7.5mm^2 = 52.5 mm^2.

____________________________

Or using the formula for the area of a trapezoid: A = h (b1 + b2) / 2

Where A is the area, b1 is the first base, b2 is the second base, and h is the height of the figure.

Given that our first base is 9, second base is 12, and our height is 5.

A = h ( b1 + b2 ) / 2 → A = 5 ( 9 + 12 ) / 2 → 5 ( 21 ) / 2 → 105 / 2 → 52.5

Then just put this quantity in mm^2 because it is the area of the figure in that unit.

→ 52.5 mm^2

_____________________________

Related Questions

Analyze the diagram below and answer the question that follows.

Answers

Step-by-step explanation:

option d is the correct answer

The answer is D. Alternate exterior angles

You have $150 in a savings account and you have some cash. The tape diagram represents the ratio of the amounts of money. You want to have twice the amount of money in your savings account as you have in cash. How much of your cash should you deposit into your savings account?

Answers

Answer: $200

Step-by-step explanation:

We know that:

You have $150 in a savings account.

This is represented with two tiles.

Then each tile represents:

$150/2 = $75

And in cash you have 5 tiles, then in cash you have:

5*$75 = $375.

Then the problem is:

You have $150 in the savings account

You have $375 in cash.

You want to deposit a quantity such that you have twice the amount of money in your savings account as you have in cash.

Suppose that you move a quantity X from cash to the savings account, then now we have the situation:

Sav. Acc. = $150 + X

Cash = $375 - X

And we want that:

Sav. Acc. = 2*Cash

($150 + X) = 2*($375 - X)

Let's solve this for X.

$150 + X = $750 - 2*X

3*X = $750 - $150 = $600

X = $600/3 = $200

You should deposit $200 in the Savings acount.

Tape diagrams are used to represent numbers as a ratio

$200 from the cash should be deposited into the savings account

Represent the amount in the savings account with s, and the cash with c.

So, we have the following ratio from the tape diagram

[tex]\mathbf{s : c = 2 : 5}[/tex]

You have $150 in the savings account.

So, the ratio becomes

[tex]\mathbf{150 : c = 2 : 5}[/tex]

Express as fractions

[tex]\mathbf{\frac c{150}= \frac 52}[/tex]

Multiply both sides by 150

[tex]\mathbf{c= \frac 52 \times 150}[/tex]

[tex]\mathbf{c= 375}[/tex]

Let the deposited amount be x.

Twice the amount in the savings account as cash means that:

[tex]\mathbf{150 + x = 2 \times (375 - x)}[/tex]

Open brackets

[tex]\mathbf{150 + x = 750 - 2x}[/tex]

Collect like terms

[tex]\mathbf{2x + x = 750 - 150}[/tex]

[tex]\mathbf{3x = 600}[/tex]

Divide both sides by 3

[tex]\mathbf{x = 200}[/tex]

Hence, $200 from the cash should be deposited into the savings account

Answers

Answer:

Step-by-step explanation:

They are used to the climate and they are harder the the rest.

Answer:

dry climate or

Step-by-step explanation:

they are in wet climate

Write the decimal represented by each shaded square.

Answers

that’s a 100 mode and there 53 squares shaded so it’s gonna be 0.53 :))

F(x)=3x+2 and g(x)=x^3 find (fog)(-5)

Answers

Answer:

Explanation:

f(x) = 3x+2
g(x) = x^3

(f • g)(x) = (3x+2)(x^3)
(f • g)(x) = 3x^4 + 2x^3
(f • g)(-5) = 3(-5)^4 + 2(-5)^3
(f • g)(-5) = 3(625) + 2(-125)
(f • g)(-5) = 1875 - 250
(f • g)(-5) = 1625

Question 1
1 pts
The function f(x) = 4x + 10 models the amount of money Francis makes when babysitting
for x hours. How much money will he make for 2 hours of babysitting work?
2.
0-2
O-3
O 18

Answers

Answer:

18 would be yr answer

Step-by-step explanation:

when is the function decreasing?

A. (15, 40)
B. (30, 55)
C. (60, -40)
D. (40, 60)

Answers

I believe it is C. (60, -40)

which number is the estimated square root of 15 closest to

Answers

x=15ft

Step-by-step explanation:

a^2+b^2=c^2

8^2+b^2=17^2

b^2+64=289

b^2=225

b=15

Jacob is a scuba diver and is currently -15 meters below sea level. He continues to dive 7 meters down then swims up 11 meters. At what sea level does Jacob end at?

Answers

Answer:

-11

Step-by-step explanation:

Answer:

-11 meters down

Step-by-step explanation:

The formula κ(x)= f′′(x) 1+f′(x)23/2 expresses the curvature of a twice-differentiable plane curve as a function of x. Use this formula to find the curvature function of the following curve. f(x)=−5x2 The curvature function is κ(x)=nothing.

Answers

Answer:

K(x) = [tex]\frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }[/tex] ( curvature function)

Step-by-step explanation:

considering the Given function

F(x) = [tex]-5x^2[/tex]

first Determine the value of F'(x)

F'(x) = [tex]\frac{d(-5x^2)}{dy}[/tex]

F'(x) = -10x

next we Determine the value of F"(x)

F"(x) = [tex]\frac{d(-10x)}{dy}[/tex]

F" (x) = -10

To find the curvature function we have to insert the values above into the given formula

K(x) [tex]= \frac{|f"(x)|}{[1 +( f'(x)^2)]^{\frac{3}{2} } }[/tex]

K(x) = [tex]\frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }[/tex] ( curvature function)

NEED A MATH TUTOR ASAP !!!

tim has $20 in a savings account. The interest rate is 10% per year and is not compounded. How much will he have in 1 year ?

Answers

Answer:

$22

Step-by-step explanation:

20 * 1.10 = 22

The answer is $22 good luck!!

A triangle has side links of 16 cm, 63 cm, and 64 cm. Classify it as acute, obtuse, or right

Answers

Answer:

acute

Step-by-step explanation:

All sides are smaller than 90 degrees

HELP, ILL GIVE BRAINLIEST BUT HELP ASAP WITH THIS!!

Answers

Answer:

proportional

Step-by-step explanation:

A figure is made up of four congruent right triangles and a square as displayed.

What is the area, in square inches, of the figure?

Answers

Answer:

It would be 33² in.

What does round to the nearest hundredth mean?

Answers

Answer:

Step-by-step explanation:

say for example you have 105 as a answer you would round to 100 because it a closer to 100 than 200

The hundredths place is the second place after the decimal. So if you have something like 13.4667 and you have to round to the nearest hundredth, it would be 13.47

A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Answers

Answer and Step-by-step explanation:

Given:

Charges includes 10 hour per month = $50

Charges for additional hour = $9

Piecewise definition of cost F(x) for a month in which a member use a car for hours.

Find limits?

Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Lim x → 10- F(x) = 50$

Lim x → 10 [ 9x – 70] = 9( 10) – 70

= 90 – 70

= 20 > 10

Limit does not exist.

Lim x → 10+ F(x) = 50$

Lim x → 10+ F(x) = Lim x → 10+ [90x – 70]

= 90 – 70

= 20 > 10

Limit does not exist.

Lim x → 10 F(x) = 50$

An integer or an decimal.

The limit does not exist.

The piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].

Given,

Membership plan is [tex]\$50[/tex] per month.

We have to write a piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours.

Here, [tex]\$[/tex][tex]$50[/tex] per month fees includes 10 hours of driving each month, so the cost for a month is given as,

[tex]f(x)= 50+9(x-10)[/tex]

Here [tex]x[/tex] is the no. of additional hours for the month.

Further,

[tex]f(x)= 9x-40[/tex].

Now at,

[tex]lim _{x \to 10^+}f(x) = 9\times 10-40\\[/tex]

Or,

[tex]f(x)= 90-40\\f(x)=50[/tex]

Similarly, at left limit,

[tex]lim _{x \to 10^-}f(x) = 9\times (-10)-40[/tex]

Or,

[tex]f(x)=-90-40[/tex]

[tex]f(x)=-130[/tex]

Finally at [tex]x=10[/tex], [tex]f(x)=9\times10-40[/tex]

[tex]f(x)=90-40\\f(x)=50[/tex]

Since [tex]lim{x \to}10^+[/tex] [tex]\neq limx\to 10^-\neq f(x) (at x= 10)[/tex]

So the required function [tex]f(x)[/tex] is discontinuous at [tex]x=10[/tex]

Hence the piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].

For more details on limit follow the link below:

https://brainly.com/question/12383180

PLEASE HELP FAST!!!! THIS IS URGENT!!!

For the following set of triangles, fill in the blanks with the correct measure. Enter your answers as number only.

1) m∠A = _____˚

2) m∠B = _____˚

3) m∠C = _____˚

4) m∠X = _____˚

5) m∠Y = _____˚

6) m∠Z = _____˚

7) Segment AB = ___ units

8) Segment BC = ___ units

9) Segment AC = ___ units

10) Segment XY = ___ units

11) Segment YZ = ___ units

12) Segment XZ = ___ units

Answers

Answer:

a=53, b=90, c=37, x=53, y=90, z=37

segment ab=3, segment bc=4, segment ac=5

pretty sure these are the answers but sorry if not

Step-by-step explanation:

HELP ON #15 PLEASE GIVE ME ANSWER!

Answers

Answer: so it’s 85?

Step-by-step explanation:

Swedish researchers concluded that viewing and discussing art soothes the soul and helps relieve medical conditions such as high blood pressure and constipation. This conclusion was based on a study in which 20 elderly women gathered once a week to discuss different works of art. The study also included a control group of 20 elderly women who met once a week to discuss their hobbies and interests. At the end of 4 months, the art discussion group was found to have a more positive attitude, to have lower blood pressure, and to use fewer laxatives than the control group.

Required:
a. Why would it be important to determine if the researchers assigned the women participating in the study at random to one of the two groups?
b. Explain why you think that the researchers included a control group in this study.

Answers

Step-by-step explanation:

1. By assigning women at random. It would make these 2 groups comparable abc the result from the research or investigation would be more useful and valid. It is very important that there are two comparable groups.

2. A control group is useful in comparing both groups. It would help us to check if there's really an effect or if there is none. If all women were in in art group then all would likely make improvements and there would be no means of verifying this.

Find the equation of a line that contains the points (7,3) and (−7,2). Write the equation in slope-intercept form, using fractions when required.

Answers

Answer: Y=1/14x+5/2
Explanation: find the slope of the contains point first by using the slope formula. Then use the point slope formula to find the slope intercept.

Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying a scarves what do the parts of the expression 48s represents

Answers

The expression 48s represents the cost of the scarves.

Given

Emiko makes Shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves.

Let s represent the price of the scarves.

The cost of each scarves is 48.

Therefore,

The cost of scarves = Number of scarves × cost of each scarves.

The cost of scarves = s × 48

The cost of scarves = 48s

Hence, the expression 48s represents the cost of the scarves.

To know more about Expression click the link given below.

https://brainly.com/question/18371860

Answer:In the expression 48s ,represents the number of scarves and 48 represents the price per scarf

Step-by-step explanation:

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Calculate the area of the trapezoid. 12 mm 5 mm 9 mm ________square millimeters

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Calculate the area of the trapezoid.
12 mm
5 mm
9 mm
________square millimeters