Mathematics College

4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.
[2]
a. Draw a picture of the rectangle
[4]
b. Write an EXACT expression for the base and the height of the rectangle.
[2]
C. Use your expressions to find the EXACT area of the rectangle.

Answers

Answer 1

9514 1404 393

Answer:

  a) see attachment

  b) base: 4, height: 4√3

  c) area: 16√3

Step-by-step explanation:

a) The figure is drawn in the attachment

__

b) The side lengths of a 30-60-90 right triangle have the ratio ...

  1 : √3 : 2

Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.

__

c) The area is the product of base and height:

  A = bh

  A = 4(4√3) = 16√3 . . . . square units

4. A Rectangle Has A Diagonal Of 8 Cm. The Diagonal Creates A 60 Angle At The Base Of The Rectangle.[2]a.

Related Questions

Item 1
One February day, the low temperature in St. Paul, MN was -17°F. Over a period of three hours, the temperature rose 5 °F per hour. After three hours, what was the temperature?
°F

Answers

-2f
5 x 3 is 15, the three stands for the three hours and the five stands for the temperature per hour increase. -17f plus 15 is -2f

A group of physicians conducts a study to find the success
rate of different treatments for an illness. They select one
hospital at random and obtain a list of patients who have
received each treatment. They select every fifth patient on
the list and contact that patient.
What is the sample in this study?
A. Patients who have been diagnosed with the illness
B. The patients from the list who are contacted by the physicians
C. Patients who received one of the treatments at the selected
hospital
D. The patients on the list that the hospital provided to the doctors

Answers

Your answer is B :)

Happy to help!

Answer: B

Step-by-step explanation:

I took the quiz and  got this right, Happy to help!!

2h+y/9h^2-y^2 - 4h^2/3h+y what is the least common denominator in this expression

Answers

Answer: It is 9

Step-by-step explanation:

Hello! :)
Please help me solve this + explain your answer :)

I will indeed give you Brainlst <3

Answers

Answer: the triangles are congruent

Step-by-step explanation: if u add up all the angles u get 180 so all angles are congruent

Mr. Cohen used 25 kilograms of fertilizer on his lawn. The fertilizer contained 4 kilograms of nitrogen. What percent of the nitrogen was in the fertilizer that Mr. Cohen used?

Answers

Answer:

The answer to this question is the percentage of the nitrogen is 17%

If f(x) = -6x + 1, what is f(1/2x-1) equal to

Answers

9x^2-10x^1+1 from −2x^2+4x−10

By substituting [tex]x = \(\frac{1}{2}x-1\)[/tex] , the given function f(x) = -6x + 1 can be simplified to [tex]f(x) = \(f(\frac{1}{2}x-1) = -3x + 7\)[/tex].

To find [tex]\(f(\frac{1}{2}x-1)\)[/tex], substitute [tex]\(\frac{1}{2}x-1\)[/tex] into the function f(x):

[tex]\(f(\frac{1}{2}x-1) = -6(\frac{1}{2}x-1) + 1\)[/tex]

Now, simplify the expression:

[tex]\(f(\frac{1}{2}x-1) = -3x + 6 + 1\)\\\\\(f(\frac{1}{2}x-1) = -3x + 7\)[/tex]

So, [tex]\(f(\frac{1}{2}x-1) = -3x + 7\)[/tex].

To know more about function, refer here:

https://brainly.com/question/13007893

#SPJ2

Is it the 1st one. I’m not to sure.

Answers

Answer:

Yes, it's the first one

Step-by-step explanation:

Since the number line is from 0 to 1 and it's divided into 6 sections, the correct answer is 1

Which graph shows a proportional relationship between the number of hours of renting a camping tent and the total amounts back to work for camping tent?

Answers

Answer: Graph 2

Step-by-step explanation:


10. Peter had a policy with a $250 deductible which paid 80% of his covered charges less deductible. He had medical expenses of $18,240.00. What is the insurance company's payment?
O $14,392
O $14,300
O $250
O $15,000

Answers

Answer:

$14392

Step-by-step explanation:

The insurance company's payment is $14392. which is the correct answer would be an option (A).

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

The required insurance company's payment is the difference between 80% of medical expenses and 80% of the deductible amount.

According to the given question, the required solution would be as:

The insurance company's payment = 80% of $18,240.00 - 80% of $250

The insurance company's payment = (80/100)18,240.00 - (80/100)250

The insurance company's payment = (0.80)18,240.00 - (0.80)250

The insurance company's payment = 14592 - 200

Apply the subtraction operation,

The insurance company's payment = $14392

Therefore, the insurance company's payment is $14392. which is the correct answer would be an option (A).

Learn more about the percentages here:

brainly.com/question/24159063

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PLEASE HELP What is the x value. (Remember to round to the nearest tenth.)

Answers

Answer:

the answer might be 71.9

Step-by-step explanation:

add 12.8 and 5.3 =18.1 then

90-18.1=71 9

67.8

Step by step Explanation:
first multiply 12.8 * 5.3
From that you get 67.84

Then round to the nearest tenth which gives you 67.8

Glad I can help :)

The ______ of a function consists of set of all output values

Answers

Domain and range :))))

ABCD is a quadrilateral with AB equal and parallel to DC. prove that AD is equal and parallel to BC​

Answers

Answer: see below proof

Step-by-step explanation:

Imagine a diagonal line AC

If AB = DC and AB // DC then angle BAC =

Angle ACD Alternate Interior angles theorem.

Then if AB = AD and angle BAC = angle ACD and AC = AC then triangle ABC is congruent to triangle CDA.

If triangle ABC is congruent to triangle CDA then AD = BC because congruent parts of congruent triangles are congruent.

If triangle ABC is congruent to triangle CDA then angle ACB = angle CAD because congruent parts of congruent triangles are congruent.

If angle ACB = angle CAD then AD // BC because of the alternate interior angles theorem.

I need help asap I’m confused

Answers

what’s the question?

Convert to centimeters: 43 meters

Answers

4300
One meter is 100 centimeters

CAN SOMEONE PLEASE HELP ME PLEASE

Answers

Answer:

x = 5

Step-by-step explanation:

I already explained and solved it on the other question. Here is the link to my explanation of how it's 5. https://brainly.com/question/20451937


Avery's classroom has 3 round tables and 6 square tables. Each table can seat 4 students.
Students are randomly seated at the tables as they arrive to class.
What is the probability that the first student to arrive will be seated at a square table

Answers

answer:
the answer is 13

Adela, Tony, Pang, and Ruben are all in 6th grade. Their average age is 11 years old. The list shows the difference from average for each.

Age Difference

Adela: 0.75 year

Tony: 11
10
years

Pang: –0.8 year

Ruben: -1
2
year

Which lists shows the values of the differences ordered from least to greatest?
Adela, Tony, Pang, Ruben
❌Adela, Pang, Ruben, Tony
Pang, Ruben, Adela, Tony
Tony, Adela, Ruben, Pang

Answers

Answer:

Pang, Ruben, Adela, Tony

Step-by-step explanation:

So the Answer would be c. I hope this helped and have a good day.

Answer:

c

Step-by-step explanation:

What is the slope of the line shown below

Answers

Answer:

it's C

Step-by-step explanation:

please mark me as brainliest thank you

Guys help me please ,how to solve it? i need a solution

Answers

Answer:

well, x = 5

Step-by-step explanation:

here,

EB Is parallel to DC , so

Angle AEB = Angle ADE

( because they are corresponding angle pair )

Angle ABE = Angle ACD

( because they are corresponding angle pair )

triangle ADC Is similar to triangle AEB

(By AA similarity criteria )

hence AE / ED = AB / BC ( by CPCT )

so 24/10 = 12/x

=》 24/12= 10/x

=》 x = 5

okay i hope u got it

WILL GIVE BRAINLIEST
HELP ASAP
PLEASE

Answers

Answer:

143

Step-by-step explanation:

Answer: I think for number A 3+5x2=X

I’m not sure about B tho

Step-by-step explanation:

You add 3+5 then you multiply it by 2 cause it twice as large

A researcher is interested in consumer preferences among three brands of yogurt. A sample of 90 people is obtained,

and each individual is asked to taste each brand and then select his/her favorite. The resulting frequency data are as

follows:

Brand A

Brand B Brand C

37

21

32

Do the data indicate any significant preferences among the three brands? Test at the .05 level of significance.

State the null hypothesis (1 point), the expected frequency for each category (3 points), the value of chi-

square (4 points), the df (1 points), the critical value of chi-square (2 points), and the decision regarding

significance (1 points).

Answers

Answer:

Step-by-step explanation:

From the given information:

The null hypothesis: all three brands are equally likely to their expected value

The alternative hypothesis: preferences exist among the three brands i.e. at least one is different from the expected value.

The expected frequency = [tex]f_e[/tex]  

The observed frequency = [tex]f_o[/tex]

[tex]f_e[/tex]                    [tex]f_o[/tex]                      [tex](f_o- f_e)^2[/tex]                       [tex]\dfrac{(f_o - f_e)^2}{f_e}[/tex]

37                   30                       49.00                        1.633

21                    30                        81.00                        2.700

32                   30                         4.00                         0.133

                                                                [tex]X^2 = \sum\dfrac{(f_o-f_e)^2}{f_e} = 4.47[/tex]

Degree of freedom = [tex](n-1)[/tex]

= 3 -1

= 2

At ∝ = 0.05 and df = 2

The critical value [tex]X^2_{0.05, 2}= 5.99[/tex]

Decision rule:

Since the calculated chi-square is less than the critical value, we do not reject the null hypothesis.

Thus, the null is retained with a calculated chi-square value of 4.47 and a critical chi-square value of 5.99.

PLS help its about Triangles Thank you!!!

Answers

these are your answers in order

B
A
B
D
C
D
A

Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought 4 notebooks and 5 thumb drives for $116. Lisa bought 2 notebooks and 3 thumb drives for $68. Find the cost of each notebook and each thumb drive.

Answers

Answer:NOTEBOOK= 4

THUMB DRIVE=20

Step-by-step explanation:

The cost of thumbdrive and notebook purchased are $20 and $4 respectively

Let :

Cost of Notebooks = n

Cost of Thumb drive = t

Troy :

4n + 5t = 116 - - - - (1)

Lisa :

2n + 3t = 68 - - - - (2)

Solving by elimination :

Multiply (1) by 2 and (2) by 4

8n + 10t = 232 - - - (3)8n + 12t = 272 - - - (4)

Subtract (3) and (4)

-2t = - 40t = 40 ÷ 2 = 20

From (1)

4n + 5(20) = 1164n + 100 = 1164n = 116 - 1004n = 16n = 16 ÷ 4 = 4

Hence, cost of notebook is $4 and cost of thumbdrive is $20

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If the area of a rectangular park is 350sq. m and its length is 70m, form the algebraic expression to find its breadth
With full solution​

Answers

Answer:

350 m² = 70 m × breadth

Step-by-step explanation:

This will be 5m = breadth

Can y’all help me solve this.
Please!!!!!!!

Answers

9514 1404 393

Answer:

  all statements are true

Step-by-step explanation:

The line 4y=-16 can be rewritten to standard form as ...

  y = -4 . . . . a horizontal line with all points having y-coordinate = -4

__

The line 3x = 27 can be rewritten to standard form as ...

  x = 9 . . . . a vertical line with all points having x-coordinate = 9.

__

All of the statements about these lines are true.

What is the order of operations needed to evaluate the expression 4(5)−8÷2?

Answers

Using PEMDAS we would do the multiplication and division first and then the subtraction. So 4*5 = 20 and 8/2 is 4 so therefore 20-4 is 16.

Answer:

PEMDAS (Multiply and divide, then add and subtract)

Step-by-step explanation:

Multiply 4 and 5 to get 20-8/2

Divide 8 by 2 to get 20-4

subtract to get 16

find the angle with straight line y is equals to root 3 x minus 4 makes angle with y axis​

Answers

Answer: Therefore the angle made by the line with y-axis is 30 degrees.

Step-by-step explanation:

''.''

The length, width and height of a rectangular prism is given as 15 cm, 10
cm and 5 cm respectively. What is the volume of the prism? *

A) 30cm3
B)150cm3
C)750cm3
D)750

Answers

Answer:

Its option C

Step-by-step explanation:

to find the volume you multiply the length, width and height together.

C is the correct answer.

Why?

Volume is calculated by multiplying a, b and c
V = a x b x c
V= 15 cm x 10 cm x 5 cm
V= 750cm^3

Do note that since we are finding the volume, the proper measurement would be cm^3

Which of the following terms correctly describe the object below?
Check all that apply.

Answers

Answer

Just check them all
check them all it’s right is

Bella needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the area of the two triangles that need to be painted?
Dimensions:
Triangle 1: 6 by 2
Triangle 2 5 by 9​

Answers

Answer:

It would be 28.5. First, you would find the area of the smaller triangle by using the formula a=.5bh (area=.5xbasexheight) and then when you get that, you should get 6. Then, you do the same for the larger triangle and you should get 22.5. Then, 22.5 + 6 = 28.5, giving you that answer.

Step-by-step explanation:

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