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

Paul had some candy to give to his three children. He first took four pieces for himself and then evenly divided the rest among his children. Each child received two pieces. With how many pieces did he
start?

Answers

He started out with 10 pieces

Answer:

10 pieces

Step-by-step explanation:

Work backwards

Multiply 3 by 2 to get 6

Add 4 to 6 to get 10

Check:

10 - 4 = 6

6/3 = 2

A ball is launched into the sky at 54.4 feet per second from a 268.8 meter tall building. The equation for the ball’s height, h, at time t seconds is h = -3.2t^2 + 54.4t + 268.8. When will the ball strike the ground?

Answers

Answer:

7.41

Step-by-step explanation:

Vertical component:

S = 268.8

U = 0

V =?

A = 9.8

T=?

S = ut + 0.5at^2. u = 0

268.8 = 0.5x9. 8xt^2

T = 7.41 seconds

Answer:

4.42 seconds is the correct answer

Step-by-step explanation:

28 divided by x+4=11

Answers

Answer:

x = -16/11

Step-by-step explanation:

28/(x+4)=11

28=11(x+4)

28=11x+44

11x=-16

x=-16/11

Answer: x=4

Step-by-step explanation:

28 divided by x+4=11

28 divided by x=7

28/7=4

Work backwards using the Distributive Property.
8(2) + 6(2) =
O 6(8+2)
O 8(2 +6)
O (8+6)2
O 2(6+2)

Answers

The answer would be C. (8+6)2 because 8(2)=16 and 6(2)=12 16+12=28 and because both have a 2 in them then 2 would be in the outside and it involves 8+6

Hope this helps

Have a great day/night

Solve.
X = -7
4x - 4y = 12
Submit

Answers

Answer:

Point Form:

( − 7 , − 10 )

Equation Form:

x = − 7, y = − 10

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

y = -10

Step-by-step explanation:

4x - 4y = 12

Substitute the x with -7, since it has been given.

4(-7) - 4y = 12

-28 - 4y = 12

Add 28 onto both sides

-28 + 28 - 4y = 12 + 28

-4y = 40

Divide by -4 to isolate the variable

-4y/-4 = 40/-4

y = - 10

Check:

Substitute the y and x

4x - 4y = 12

4(-7) - 4 ( -10 ) = 12

-28 + 40 = 12

12 = 12

or.....

try to see if x stays as -7

4x - 4y = 12

4x - 4 (-10) = 12

4x + 40 = 12

Subtract 40 onto both sides

4x + 40 - 40 = 12 - 40

4x = -28

Divide by 4 onto both sides to isolate the variable

4x/4 = -28/4

x = -7

And it's correct

Hope this helped!

What is the sum of 2x+1 and its opposite?

Answers

Answer:

Zero. The sum of anything and it's opposite is zero, that's how an opposite is defined . In this case, the opposite of 2x+1 is -(2x+1)=-2x-1 by the distributive property . Adding like terms, 2x+-2x+1+-1=0+0=0.

0 (i dont have a proper explanation)

what is 0.47 of £1 as pound sign

Answers

Answer:

In the Unicode standard, the symbol £ is called POUND SIGN, and the symbol ₤ is the LIRA SIGN.

Is this the Right answer?

Answers

Answer:

yes i think it is

Step-by-step explanation:

checked each of them

Jada made 8 cups of blueberry jam and divided the jam equally among 6 containers. How much jam went in each container?

Answers

Answer:

1.3 repeated is the answer

Answer:

Well if there is 8 cups and you want to divide it equally into 6 containers that would be 1.33 cups in each container

I will mark you brainliest if you go subscribe to seema beauty care and more on y o u t u b e and put the screenshot in answer.

Answers

Step-by-step explanation:

Just subscribed wish you the best on your channel!!!

PLEASE PLEASE HELP ME!

Answers

Answer:

x = 65.4

Step-by-step explanation:

Formula For Cos: cos (x°) = adjacent/hypotenuse

Adjacent = 5

Hypotenuse = 12

cos (x) = adjacent/hypotenuse

cos (x) = 5/12

x = cos⁻¹ (5/12)

x = = 65.3756816478359

x = 65.4 (rounded)

Tip: cos⁻¹ is inverse of cos.

Therefore, x = 65.4

Hope this helped! <3

If your gonna answer thanks
A.
B.
C.
D.
Can someone please get me the answer fast

Answers

Answer:

i think its 3.5 because of how it is going

The answer is 3.5 hope this works

PLEASE ANSWER ASASP
16d + 5 = -10
what is d?

Answers

Answer:

d  = -15/16

Step-by-step explanation:

To solve for D, you have to get D alone on one side of the equation (one side of the equal sign).

So get rid of the other numbers that are being added or subtracted to d first. To do that, you have to do the opposite of what is being done.

So u have +5 on the left, you have to minus it to get rid of it. Whatever you do on one side of the equation, you have to do to the other side

so 16d +5 minus 5 = -10  minus 5

the 5 cancels out on the left   and -10 - 5 = -15

now you have 16d = -15

Now you have to get rid of the 16. It's being multiplied to d so to do opposite is to divide it by 16. And whatever you do on one side, u have to do on the other.

16d divided by 16 = -15 divided by 16

16d/16 = d       -15/16  

So d = -15/16

For the expression, value of d is,

⇒ d = - 15/16

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 16d + 5 = - 10

Now, We can solve the expression as;

⇒ 16d + 5 = - 10

Subtract 5 from both side;

⇒ 16d + 5 - 5 = - 10 - 5

⇒ 16d = - 15

Divide by 16 both side;

⇒ d = - 15/16

Therefore, For the expression, value of d is,

⇒ d = - 15/16

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

-3p>-48 Solve the inequality

Answers

9514 1404 393

Answer:

  p < 16

Step-by-step explanation:

Dividing the inequality by a negative number will reverse the comparison.

  -3p > -48

  (-3p)/(-3) < (-48)/(-3) . . . . divide both sides by the coefficient of p

  p < 16

_____

Alternate solution

Add 3p+48 to both sides.

  -3p +(3p +48) > -48 +(3p +48)

  48 > 3p

Divide both sides by 3; no reversal is necessary.

  16 > p . . . . . same answer as above, without the comparison reversal

Find the area, in square units, of rectangle ABCS plotted below.

Answers

Answer:

The answer is D-80

Step-by-step explanation:

Got it correct on the quiz

1. Angle 3 and Angle 6 are examples of which type of angle pair?

Answers

Your answer is:Alternate Interior Angles

PLS answer asap
Enter the missing numbers in the boxes to complete the table of equivalent ratios.

Answers

1,9,21 ggffhgsrtggdryubvcdsg

When you add 98 to a number you usually...

Answers

Aneser:

+98

Step-by-step explanation:

when you are adding something to something to something else u put a plus sign to add it hope this helps

A biologist is recording the loss of fish in a pond. He notes the number of fish, f, in the pond on June 1. On July 1 there were 63 fish in the pond, which is 52 fewer fish than were in the pond on June 1. What is the number of fish in the pond on June 1?

Which equation can be used to find the number of fish in the pond on June 1?


63−f=52

f−52=−63

f−52=63

f−63=−52

Answers

Answer:

the correct answer should be f-52=63

Step-by-step explanation:

When using a number line, in which direction should you move when subtracting a negative value?

Answers

Answer:

LEFT

Step-by-step explanation:

Answer:

Move to the right when you're subtracting a negative number.

A rectangle has an area of 6 1/2 square inches. It's length is 2 1/4 inches. What is the width

Answers

6 1/2 / 2 1/4

13/2 x 4/9= 52/18

2 16/18

2 8/9

QUICK EZ MATH


A bookcase is 4 ft tall. A model of the bookcase is 6 ft tall. What is the ratio of the height of the model bookcase to the height of the real bookcase?

Answers

Answer:

4:6

Step-by-step explanation:

The ratio of the height of the model bookcase to the height of the real bookcase will be 3: 2.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

A bookcase is 4 ft tall. A model of the bookcase is 6 ft tall.

The ratio of the height of the model bookcase to the height of the real bookcase is given by the division of the numbers 4 and 6. Then we have

Ratio = 6 / 4

Simplify the ratio, then we have

Ratio = 6 / 4

Ratio = 3 / 2

Ratio = 3: 2

The ratio of the height of the model bookcase to the height of the real bookcase will be 3: 2.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

3x-2y=1x+4y=33 elimination process ​

Answers

Answer:

x = 5 ; y = 7

Step-by-step explanation:

3x - 2y = 1       --------------------(I)

 x + 4y  = 33 ------------(II)

Multiply equation (II) by (-3) and then add. So, x will be eliminated and we can find the value of y

(I)            3x - 2y = 1

(II)*(-3)   -3x -12y = -99         {Now add}

                 - 14y = -98

                        y = -98/14

y = 7

Plugin y = 7  in equation (I)

3x - 2*7 = 1

  3x - 14 = 1

         3x = 1 + 14

         3x = 15

           x = 15/3

x = 5

Solve the system of equations:

x+y=5

-4x-2y=-8

Which point on the graph below is the solution to the system of linear equations?


A. W
B. X
C. Z
D. Y

Answers

Answer:

the correct answer would be Y! i took it!! make me most brainlessly please!!!

Step-by-step explanation:

answeeeeeeeeeeerrr thank you

Answers

Answer:

x = 52

m<ACD = 159

m<ACB = 21

Step-by-step explanation:

1) Set up an equation.

2x + 55 = 3x + 3 (the two interior angles on the opposite of the triangle and the exterior angle are equal to the exterior angle)

2) Solve for x.

2x + 55 = 3x + 3

-x + 55 = 3

-x = -52

x = 52

3) Substitute 'x' into each angle required to find m<ACD and m<ACB.

m<ACD = 3(52) + 3

= 156 + 3

= 159

CHECK:

2(52) + 55 = 159

104 + 55 = 159

159 = 159

m<ACB + m<ACD = 180

m<ACB + 159 = 180

m<ACB = 21

2.
(04.01 LC)

Which of the tables represents a function? (5 points)

Table A
Input Output
5 3
5 2
4 1
Table B
Input Output
1 2
3 2
5 3
Table C
Input Output
0 0
1 2
1 3
Table D
Input Output
4 2
4 3
4 4
Table A
Table B
Table C
Table D

Answers

Table c if I’m wrong I’m so sorry I tried my best

Answer: the awnser is B

d + 5.5 = 10. Solve for d.

Answers

Answer:

4.5

Step-by-step explanation:

d=10-5.5

d= 4.5

we just need to minus 10 with 5.5 so that we can find d

please answer asap correctly dont troll!!!

Answers

Answer:

10

Step-by-step explanation:

Bro, again the same question))

a>17-8

a>9

The museum of natural history has an auditorium that can seat 200 people. A class of 45 students is seated in the auditorium for a lecture. What decimal represents the portion of the seats in the auditorium that are empty? Please help FAST!

Answers

Answer:

.225

Step-by-step explanation:

45/200

Find the unit rate. Round to the nearest hundredth, if necessary.
$190 for 16 ft

Answers

Answer:

About $11.88 per foot

Step-by-step explanation:

Other Questions
Heldi is placing an online order at her favorite clothing store. Each shirt that she is ordering costs $12.50. If she mustspend at least $50 In order to get free shipping, how many shirts must she buy to get free shipping.To graph the solution set of this inequality, draw( open or closed)circle on the boundary point and shade to theEither left or right)?? ASAP Encircle the correct adverb of intensity1.her payment was (scarcely, positively) enough. 2. I was (terribly, barely) disappointed 3.anne did her project (very, fully) neatly. 4.they purchased (too, very) many materials 5.i am (greatly, fairly) impressed by the performance of the band. Read the passage from I Know Why the Caged Bird Sings. "There's one more thing Take this book of poems and memorae one for me. Nexttime you pay me a visit, I want you to reciteI have tried often to search behind the sophistication of years for the enchantment!so easily found in those gifts. The essence escapes but its aura remains. To beallowed, no, invited, into the private lives of strangers, and to share their joys andfears, was a chance to exchange the Southern bitter wormwood for a cup of meadwith Beowulf or a hot cup of tea and milk with Oliver Twist. When I said aloud, "It isa far, far better thing that I do, than I have ever done.. tears of love filled my eyesat my selflessness. On that first day, I ran down the hill and into the road few cars ever came along it)and had the good sense to stop running before I reached the store. I was liked, and what a difference it made. I was respected not as Mrs. Henderson'sgrandchild or Baileys sister but for just being Marguerite JohnsonChildhood's logic never asks to be proved all conclusions are absolute). I didn'tquestion why Mrs. Flowers had singled me out for attention, nor did it occur to methat Momma might have asked her to ve me a little talking to All I cared about wasthat she had made tes cookies for me and read to me from her favorite book. It wasenough to prove that she liked me. In a response of at least one well-developed paragraph, identify one central idea of 1Know Why the Caged Bird Sings. Then, explain how this passage directly developsor refines that central idea. Be sure to cite specific evidence from the passage tosupport your points. The prefix "semi-" means "partly". Based on your knowledge of the properties of elements, which kind of element is most likely used to make semiconductors?liquidsmetalloidsmetalsnonmetals Why did debates among civil rights activists increase after 1965? What were the causes and effects of these debates? (Look into SNCC, CORE, Black Power, and the SCLC, Stokeley Carmichael, Huey Newton &/or Bobby Seale) 1 1 ldentify the slope.3x-2y= 10 If a gas effuses 2.17 times faster than Xe, what is its molar mass? Khan Academy PLEASE SOMEONE HELP FASTTT!!!! Express the sum of 32 and 24 asproduct of the GCF and a sum. Los muchachos son _________ a-simpatico b-simpaticos c-simpatica d-simpaticas What are the limitations of correlational research? Hello! who was involved in the Dred Scott V. Sandford case? Please give a little description not just names. What is the correct way to write a letter/email Hi please help me answer this :) Explain answer Will give braisnlt Based on what you have read, what are the three most important lacisPower comes from the people.Citizens have the right to free speech.Citizens of the United States have guaranteed rights.Citizens have certain responsibilities and dutiesThe government's power is not limited. Helppppp this is really hard How many cubes with side lengths of cm does it take to fill the prism?41 cmPro7cm42 cm What is the probability that a customer ordered a cold drink given that he or she ordered a large? 4) Which of the following is NOT true about lysozyme:A) it destroys bacteriaB) it cleanses and protects the eyeC) it is an enzymeD) it is found in tearsE) it stimulates the rods and cones 1.The entry tickets at a community fair cost $5 for children and $10 for adults. On a certain day 1000 people entered in the fair and \$7,100is collected. How many adults and how many children were at the fair?