Mathematics High School

Find the length of the longer diagonal of this parallelogram.
AB= 4FT
A= 30°
D= 80°
Round to the nearest tenth.​

Answers

Answer 1

The length of the longer diagonal of the parallelogram is approximately 5.1 ft.

We have,

To find the length of the longer diagonal of the parallelogram, we can use the law of cosines.

The law of cosines states that in a triangle with side lengths a, b, and c, and angle C opposite side c, the following equation holds true:

c² = a² + b² - 2ab * cos(C)

In this case, we have side lengths AB = 4 ft and angle A = 30°, and we want to find the length of the longer diagonal.

Let's denote the longer diagonal as d.

Applying the law of cosines, we have:

d² = AB² + AB² - 2(AB)(AB) * cos(D)

d² = 4² + 4² - 2(4)(4) * cos(80°)

d² = 16 + 16 - 32 * cos(80°)

Using a calculator, we can calculate cos(80°) ≈ 0.1736:

d² = 16 + 16 - 32 * 0.1736

d² ≈ 16 + 16 - 5.5552

d² ≈ 26.4448

Taking the square root of both sides, we find:

d ≈ √26.4448

d ≈ 5.1427 ft (rounded to the nearest tenth)

Therefore,

The length of the longer diagonal of the parallelogram is approximately 5.1 ft.

Learn more about parallelograms here:

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Related Questions

Which number is equal to 100?

Answers

Answer:

10 square2

36 + 64 = 100. In other words, 6² + 8² = 10²

Answer:

C. 10^2

Step-by-step explanation:

When you have an exponent and the base is 10, the exponent is how many zeros there are total that come after the 1. There are 2 zeros after the 1 in 100, so 10^2 is the answer.

Lisa had four candy bars . She ate 2 3/8 of the candy bars. How many candy bars does she have left.

Answers

Answer:

1 5/8

Step-by-step explanation:

You need to do the subtraction 4 - 2 3/8.

You can use mixed numerals, but you need to borrow and you need a common denominator.

4 - 2 3/8

Since 4 has no fraction part, we borrow 1 from 4 leaving 3. The 1 we borrow becomes a fraction written as 8/8, so we have the same denominator as the fraction 3/8.

Now we have

4 - 2 3/8 =

= 3 8/8 - 2 3/8

Subtract 2 from 3 to get 1.

Subtract 3/8 from 8/8 to get 5/8.

= 1 5/8

You can also set it up vertically as shown below and then subtract the whole numbers and subtract the fractions.

   3 8/8

-   2 3/8

------------

   1 5/8

Answer: 1 5/8

What is the additive inverse of -7?
O A. -7
O B. 7
C. -|-7|
D. -(-(-7))

Answers

Answer:

B

Step-by-step explanation:

geometry multiple choice question HELPP

Answers

8.66 m. I definitely don’t know the formula but I’m learning something like this plus with my previous knowledge from this year I figured it out.

Gasoline is pumped at a rate of 3 gallons per minute into a container that already has 4 gallons inside it. Write a linear function that describes the amount of gas in the container over time. Then make a graph to show the amount of gas in the container over the first 5 minutes.

Answers

Answer:

con que te gusta el poyo frito eh

The equation representing the amount of gas in the container after time [x] minutes as y = 3x + 4. After first 5 minutes, the amount of gasoline would be 19 gallons.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following problem -

Gasoline is pumped at a rate of 3 gallons per minute into a container that already has 4 gallons inside it.

We can write the equation representing the amount of gas in the container after time [x] minutes as -

y = 3x + 4

Plot the graph. At 5 minutes, the amount of gasoline would be 19 gallons.

Therefore, the equation representing the amount of gas in the container after time [x] minutes as y = 3x + 4. After first 5 minutes, the amount of gasoline would be 19 gallons.

To solve more questions on straight lines, visit the link below-

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someone please explain how to make a fraction into a decimal im confused will give brainliest to best answer also worth 25 points

Answers

Answer:

divide the numerator by the denominator and it should give you a decimal

Answer:if u don't get it tell me.

Step-by-step explanation:

A dog named Zula set a record by popping 100 balloons in 44.49 seconds. Which shows the expanded form of 44.49?

Answers

Answer:

40+4+0.4+0.09

Step-by-step explanation:

The graph below shows a linear representation of a jogger’s heartbeat in beats per minute, as his speed is increased (in feet per second). What is the slope of the line?

Answers

Answer:

The slope is 3.75 OR 3 3/4.

Step-by-step explanation:

So the formula for slope I am using NOW, is based on the variables I named my dimensions. WARNING: NOT SLOPE FORMULA YOU MIGHT BE USING

y = 95 - 80

x = 10 - 6

Slope Formula: y/x

Substituted Slope Formula: (95 - 80)/(10 - 6)

Simplified Substituted Slope Formula: 15/4 OR 3.75

Hope this helps!!

Answer:

15/4

Step-by-step explanation:

I checked ;)

Paul wants to buy a new skateboard. The regular price of the skateboard before a 15% discount and before 4% tax is $40. What is the amount of money Paul will need to buy the skateboard after the discount and including tax

Answers

$45.76
$40 x 15% = $6
$40 - $6 = $44
$44 x 4% = $1.76
$44 + $1.76 = $45.76

y = -8x – 30
y = 2x + 150

Answers

Step-by-step explanation:

y - y = 2x + 150 -( - 8x - 30 )

0 = 2 x + 150 + 8 x + 30

0.= 10x + 180

- 180 = 10 x

-180/10 = x

-18 = x

then y = 2 (-18) + 150

y = -36 + 150

y = 114

plz mark my answer as brainlist plzzzz.hope this will be helpful to you.

Vienna bought 8 yards of fabric and paid $38.40. How many more ​ yards can she purchase with $30?​

Answers

Answer:

vienna can purchase 6 more yards

Which perfect squares does the number 104 falls in between?

Answers

Answer:

12

Step-by-step explanation:

Answer:

12 because  12, 24, 36, 48, 60, 72, 84, 96, 104

Step-by-step explanation:

Please help me with this

Answers

(Q3-Q1)=IQR
(14-11)=IQR
3=IQR

IQR=3

1.1. Which statement explains why the two systems of equations below have the

same solution?

A

6x + 8y = -10

2x - 5y = 12

B

8x + 3y = 2

12x + 16y = -20

Answers

Answer:

B. The first equation in B is the sum of the equations in A, while the other is obtained

by multiplying the first equation in A by 2.

Step-by-step explanation:

If we add the first two equations that shown in A so

6x + 8y + 2x - 5y = -10 + 12

8x + 3y = 2

Now the first equation in A would be multiplied by 2

So

2(6x + 8y = -10)

12x + 16u = -20

Therefore the correct option is B.

geometry multiple choice question HELLPPP

Answers

Answer:

27/36

Step-by-step explanation:

tan C = opp/adj

For angle C, the opposite leg is 27,a nd the adjacent leg is 36.

tan C = 27/36

Answer: 27/36

Use the distributive property to remove the parentheses.
(3-v+2u)(-8)
Х
?

Answers

-8(3 - v + 2u)
-24 + 8v - 16u
You just have to distribute and multiply the value on the outside to each value inside the parentheses ;)

On a map, the distance between two towns is 2.5 inches, and 1 inch represents 6 miles.

What is the actual distance between the towns?

Enter your answer in the box.

mi

Answers

Answer:

15 miles

Step-by-step explanation:

1 = 6

6 x 2 = 12

6 x 0.5 = 3

12 + 3 = 15

Answer:

15 miles

Step-by-step explanation:

took k-12 test

A rectangle is such that the length of 2 of each adjacent sides are in the ratio 1:3. A similar rectangle has 1 side of 6cm. Find 2 possible values for the length of each adjacent sides.

Answers

Answer:

18 cm ;

2 cm

Step-by-step explanation:

Length of each adjacent side = 1 :3

If 1 side = 6 ; the possible values of the adjacent side ;

That is side 2 ÷

If side 1, which is 6cm is the ratio 1 ; then side 2 = 6cm * 3 = 18 cm

If side 1, which is 6cm is the ratio 3 ; then side 2 = 6cm / 3 = 2 cm

Hence, the two Possible values of the adjacent side = 18 cm or 2 cm

identify the slope and y- intercept of the equation y = -3x

Answers

Answer: The slope is -3 and the y-intercept is (0,0)

Step-by-step explanation: Hope this helps, if it does can I get the brainliest answer

Answer:

Slope:  − 3

y-intercept:  ( 0 , 0 )

Step-by-step explanation:

The slope-intercept form is  y  =  m x  +  b.

Find the values of  m  and  b  using the form  y  =  m x  +  b .

m  =  −3 ; b =  0

The slope of the line is the value of  m , and the y-intercept is the value of  b .

Slope:  − 3

y-intercept:  ( 0 , 0 )

good luck, i hope this helps :)

During each of the past three months, Tyler grew
by the following amounts: 1/8in., 3/16in., and 1/4in.
What is Tyler's total amount of growth over these
three months?
Answer with supporting work:

Answers

first you have to make all the fractions have a common denominator to add them so since 3/16 is the largest denominator you have to convert the others to have the denominator of 16. 1/8 = 2/16. 1/4 = 4/16. so if you add the numerators that’s 3 + 2 + 4 = 9. so the answer would be 9/16, and this cannot be simplified so it is your final answer:)

what is the answer to -4 - (-7)

Answers

Answer:

3fufufuifjfjfjfjfjfnfnff

Point s and point t are located at -6, 13 and 8, 13 on the coordinate plane what is the distance between the two points

Answers

Answer:

[tex]14[/tex] units

Step-by-step explanation:

Since both points have the same y-coordinate, we can calculate the distance between them by taking the absolute difference of their x-coordinates. Therefore, the distance between them is [tex]|-6-8|=|-14|=14[/tex] units. Hope this helps!

ayuda porfavor!!!!
se lleva 22 puntos el que me responda bien

Answers

Answer:

i think is AAAAAAAAAAAAA

Step-by-step explanation:

Answer:

A) x=5 El signo es dividido

B) x=7

Which theorem proves these triangles are similiar for brainliest

Answers

[tex]{\huge{\pink{\mathcal{AA\:postulate࿐❤}}}} [/tex]

Consider the inequality.

x + 3x < 24
Which value of x makes the inequality true?


A.5

B.6

C.7

D.8

Answers

Answer:

A.

Step-by-step explanation:

Solve inequality:

[tex]x + 3x<24\\4x<24\\x<6[/tex]

only one less than 6 is A. 5

Answer:

A

Step-by-step explanation:

(5) + 3(5) < 24

20 < 24

HELPPPP I DONT KNOW THE ANSWER PLEASE HELP ME

Answers

Answer:

IM PRETTY POSITIVE ITS B

PLS MARK BRAINLIEST

SORRY IF IM WRONG :P

Step-by-step explanation:

answer: B. 2x+3

h(x) = x+4
h(2x-5) = (2x-5)+4
h(2x-5) = 2x-1

h(h(2x-5)) = (2x-1)+4
h(h(2x-5)) = 2x+3

what is three and seven hundredths standard form

Answers

Answer: I believe the answer is 3.07 but I may be wrong so if you want you can wait for another answer :D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

what 5/8x + 1/2 (1/4x + 10)? ​

Answers

5+3x/4




5x+1/2(1/4+10). Distributive property
5x+x/8+5. Combine like terms
5+3x/4
The answer is
3/4x + 5

Solution:
5/8x + 1/2 (1/4x + 10)
5/8x + 1/8x + 5
3/4x + 5

8x-7=-5x+19 denklemini sağlayan, x'in değeri kaçtır? ​

Answers

Answer: X=2

Step-by-step explanation:

8x-7=-5x+19

=> 8x+5x=19+7 [Transforms]

=> 13x=26

=> x=26/13

So, x=2

4. If you buy 7 hamburgers and 3 slices of pizza from the Sizzler, you get Sl in change back from a

$20 bill. If you buy 8 hamburgers and 2 slices of pizza, you get $0.50 back from a $20 bill. Find

the price of a hamburger and the price of a slice of pizza.

Answers

Answer:

the price of a hamburger and the price of a slice of pizza is $0.5 and $7.75 respectively

Step-by-step explanation:

Let us assume the price of a hamburger be x

And, the price of a slice of pizza be y

So the equations are

7x + 3y = 20-1

7x + 3y = 19........(1)

And,

8x + 2y = $19.50........(2)

Now multiply by 2 in equation 1 and 3 in equation 2

So,

14x + 6y = 38

16x + 6y = 39

-2x = -1

x = 0.5

so y =

4 + 2y = $19.50

2y = $19.50 - 4

y = 7.75

Hence, the price of a hamburger and the price of a slice of pizza is $0.5 and $7.75 respectively

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