1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Jet001 [13]
3 years ago
15

A parallelogram has sides of lengths 9 and 8, and one angle is 44°. What is the length of the smaller diagonal? length = units W

hat is the length of the longer diagonal? length = units

Mathematics
1 answer:
DIA [1.3K]3 years ago
7 0

Answer:

The length of the smaller diagonal is d_1 = 6.44 units

The length of the longer diagonal is d_2 = 15.77 units

Step-by-step explanation:

Given: A parallelogram has sides of lengths 9 and 8, and one angle is 44°.

We can use the cosine formula to find the measures of the diagonals.

The cosine formula is a^2 = b^2 + c^2 - 2bc (cos  A)\\

We can divide the parallelogram into two equal triangles.

<u>Triangle 1</u>

Which has the two sides measures 9 and 8 and including angle is 44°.

If we are given two sides and one angle, we can use the cosine formula and find the third side. Here third side is diagonal 1.

d_1^2 = 9^2 + 8^2 - 2*9*8 cos(44)\\d_1^2 = 81 + 64 - 103.58\\d_1 = 145 - 103.58\\d_1^2 = 41.42

Taking square root on both sides, we get

d_1 = 6.44 [Rounded to the nearest hundredths place]

<u>Triangle 2</u>

It is a parallelogram, the opposite sides are equal. Therefore, the another triangle has equal measures but angle differs.

The adjacent angles in a parallelogram add upto 180°.

Therefore, the angle measure is 180 - 44 = 136°.

Now let's use the cosine formula and find the measure diagonal 2.

d_2 ^2 = 9^2 + 8^2 - 2*9*8*cos 136\\d_2^2 = 81 + 64 - (-103.58)\\d_2^2 = 145 + 103.58\\d_2^2 = 248.58

Taking the square root on both sides, we get

d_2 = \sqrt{248.58} \\d_2 = 15.77 [Rounded to the nearest hundredths place]

So the length of the smaller diagonal is d_1 = 6.44 units

the length of the longer diagonal is d_2 = 15.77 units

You might be interested in
12e^5 divided 3e^3 simplified
bonufazy [111]

Answer:

4 {e}^{2}

Step-by-step explanation:

\frac{12 {e}^{5} }{3 {e}^{3} } \\ 12 \div 3 \times  {e}^{5 - 3}   \\  = 4 {e}^{2}

hope this helps

brainliest appreciated

good luck! have a nice day!

6 0
3 years ago
Find the pattern and identify the next 3 terms in the sequence<br>5, -10, 20...​
Marta_Voda [28]

Answer:

-40, 80, -160

Step-by-step explanation:

5(-2)^n-1

where n is the position

6 0
3 years ago
The points (-2 11) and (6 3) lie on the same line. What is the x-intercept of the line.
ololo11 [35]
The x-intercept is (11.43,0) I don’t know how to explain it to you
7 0
2 years ago
A county is considering rasing the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 m
DochEvi [55]

Answer:

No, at alpha equals 0.10​, we do not have enough evidence to support the​ county's claim.

Step-by-step explanation:

We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.

A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.

<em><u>Let </u></em>\mu<em><u> = true mean speed of the vehicles.</u></em>

SO, <u>Null Hypothesis</u>, H_0 : \mu \leq  30 miles per hour   {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}

<u>Alternate Hypothesis,</u> H_A : \mu > 30 miles per hour   {means that the mean speed of vehicles is greater than 30 miles per hour}

The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about the population standard deviation;

                        T.S.  = \frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean speed of 15 vehicles = 31 mph

             s = sample standard deviation = 4.7 mph

             n = sample of vehicles = 15

So, <em><u>test statistics</u></em>  =   \frac{31-30}{\frac{4.7}{\sqrt{15} } }  ~ t_1_4

                               =  0.824

<u><em>Hence, the value of test statistics is 0.824.</em></u>

<em />

<em>Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.</em>

<em />

Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.

4 0
3 years ago
Can someone help me out?
Anarel [89]

Answer:

So the value of s  = 7 cm

Step-by-step explanation:

We know that, Area of a triangle = 1/2 * b * h

So, base = 24 cm

height = s

Area = 1/2 * b * h

=>84 = 1/2 * 24 * h

=>84 = 12 * h

=>84 / 12 = h

=> 7 = h (in cm)

Hope this helps, please mark me as brainliest!! Thank you!

6 0
3 years ago
Other questions:
  • Simply by using order of operations 4+(9•2)+(4-1)-4
    11·2 answers
  • A) what is the difference between a sequence and a series? a series is an unordered list of numbers whereas a sequence is the su
    8·2 answers
  • Find slope of 12x+3y=6
    13·2 answers
  • What would the rule be for the reflection of y=-3
    14·1 answer
  • Jill is applying for a car loan. which individual will run her credit report to determine if she's eligible for a car loan?
    5·2 answers
  • PLZ HELP ME! I WILL MARK BRAINIEST AND MOST POINTS!
    5·2 answers
  • The tour costs $359 per person. You have to pay a deposit of $78 in advance. How much more do you need to pay?
    12·1 answer
  • I’ll mark brain list pls! thanks, i’m stuck!
    13·1 answer
  • Johanna is planting tomatoes in the school garden this year. Tomato plants come in packs of six. She needs 80 plants in the gard
    10·1 answer
  • Please answer ASAP ........
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!