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
Anestetic [448]
3 years ago
11

The length of the base of a triangle is twice its height. if the area of the triangle is 196 square​ kilometers, find the height

.
Mathematics
2 answers:
denis23 [38]3 years ago
7 0
Hey user!

your answer is here..

ATQ,

the length of the base of the triangle is twice it's height.

let the height of the triangle be x.

therefore base of the triangle is 2x.

given area of the triangle = 196km²

==> 1/2 × b × h = 196km²

==> 1/2 × 2x × x = 196km²

==> x × x = 196km²

==> x² = 196km²

==> x = √196

==> x = 14

hence, height of the triangle = x = 14km

base of the triangle = 2x = 2 × 14 = 28km

VERIFICATION :-

area of the triangle = 1/2 × b × h

= 1/2 × 14 × 28

= 7 × 28

= 196km²

hence verified..

cheers!!
NISA [10]3 years ago
4 0
Area = 1/2 x base x height

Let the height be x.
Height = x
Base = 2x

Area of triangle = 1/2 x base x  heght

Plug base and height into the variables:
(1/2)(2x)(x) = 196

Combine like terms:
x² = 196

Square root both sides:
x = 14

Find Base and height:
Base = x = 14 km
Height = 2x = 2(14) = 28 km

Answer: Height = 28km
You might be interested in
Given P(A) = 0.072, P(B) = 0.180, and P(C) = 0.027, and that events A, B, and C are mutually exclusive, what is the P(A or B or
9966 [12]

Given P(A) = 0.072, P(B) = 0.180, and P(C) = 0.027, and that events A, B, and C are mutually exclusive,then P(A or B or C) is 0.279

<u>Solution: </u>

Given that probability of event A is P(A) = 0.072

Probability of event B is P(B) = 0.180

Probability of event C is P(C) = 0.027

Also event A, B and C are mutually exclusive.

Need to determine P( A or B or C )

For mutually exclusive events  

P( A or B or C ) = P(A) + P(B) + P(C)

= 0.072 + 0.180 + 0.027  = 0.279

Hence probability of occurrence of event A or event B or event C , where A , B and C are mutually exclusive events is 0.279.

5 0
3 years ago
Find x.<br><br>How would you solve this?​
Murrr4er [49]

Answer:

x = 100°

Step-by-step explanation:

The measure of a chord- chord angle is half the sum of the arcs intercepted by the angle and its vertical angle, that is

x = \frac{1}{2} (71 + 129)° = 0.5 × 200° = 100°

7 0
3 years ago
And I also need help in this one.
Dvinal [7]
Hey bestie I’m pretty sure it’s 1:3
5 0
2 years ago
A sample of bacteria is decaying according to a half-life model. If the sample begins with 800 bacteria, and after 13 minutes th
nikklg [1K]

Answer:

56.42 minutes

Step-by-step explanation:

The initial sample= y0 = 800

After 13 minutes , amount = 320

Y= y0e-kt

320 = 800e-k(13)

320/800 = e-k13

0.4 = e-k13

In0.4 = -k13

-0.91629= -k13

0.07048= k

Y = 800e-0.07048t

Minutes when the bacterial present will be 15

15 = 800e-0.07048t

15/800= e-0.07048t

0.01875 = e-0.07048t

In 0.01875 = -0.07048t

-3.97656 = -0.07048t

-3.97656/-0.07048= t

56.42 = t

56.42 minutes

3 0
3 years ago
The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r
jolli1 [7]

Answer:

28-2.064\frac{10}{\sqrt{25}}=23.872    

28+2.064\frac{10}{\sqrt{25}}=32.128    

So on this case the 95% confidence interval would be given by (23.9;32.1)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=28 represent the sample mean

\mu population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=25-1=24

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that t_{\alpha/2}=2.064

Now we have everything in order to replace into formula (1):

28-2.064\frac{10}{\sqrt{25}}=23.872    

28+2.064\frac{10}{\sqrt{25}}=32.128    

So on this case the 95% confidence interval would be given by (23.9;32.1)    

7 0
3 years ago
Other questions:
  • Shona cycles at an average speed of 8km/h. How far has she travelled if she cycles for 4 hours
    13·1 answer
  • .12 is what percent of 48 ?
    6·1 answer
  • mike&amp; sue danced 3/4 of an hour with out stopping. this is 3/8 hour more than betty&amp; ryan danced. how long more did bett
    10·1 answer
  • Describe the error Sadie made, and explain how to find the correct answer.
    14·2 answers
  • What is the value of 5 in 756? write and draw to explain how you know
    11·2 answers
  • Use inductive reasoning to predict the next three numbers in the pattern.
    13·1 answer
  • Subtract these polynomials.
    10·1 answer
  • 1. 4x - 5 ( for x is 4 )
    11·2 answers
  • Perform the operation,<br> (-2x^2 – 2x + 1) +(-8x^2-7)
    12·1 answer
  • Complete the Two-Way Frequency Table and fill it the blanks.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!