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
sergeinik [125]
3 years ago
9

AC=4, AE=7, AD=10, what is the length of AB? A: 1 3/7 B: 2 1/2 C: 5 5/7 D: 17 1/2

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
6 0

Answer:

C. AB = 5\frac{5}{7}

Step-by-step explanation:

When two polygons are considered similar, the ratio of their corresponding sides would also be equal.

Since ∆ABC and ∆ADE are similar, \frac{AE}{AC} = \frac{AD}{AB}

\frac{7}{4} = \frac{10}{AB}

Cross multiply

7*AB = 10*4

7*AB = 40

Divide both sides by 7 to find AB

\frac{7*AB}{7} = \frac{40}{7}

AB = \frac{40}{7}

AB = 5\frac{5}{7}

You might be interested in
If sin(x) = 5/13, and x is in quadrant 1, then tan(x/2) equals what?
Rufina [12.5K]
x is in quadrant I, so 0, which means 0, so \dfrac x2 belongs to the same quadrant.

Now,

\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}

Since \sin x=\dfrac5{13}, it follows that

\cos^2x=1-\sin^2x\implies \cos x=\pm\sqrt{1-\left(\dfrac5{13}\right)^2}=\pm\dfrac{12}{13}

Since x belongs to the first quadrant, you take the positive root (\cos x>0 for x in quadrant I). Then

\tan\dfrac x2=\pm\sqrt{\dfrac{1-\frac{12}{13}}{1+\frac{12}{13}}}

\tan x is also positive for x in quadrant I, so you take the positive root again. You're left with

\tan\dfrac x2=\dfrac15
4 0
3 years ago
we believe that 42% of freshmen do not visit their counselors regularly. For this year, you would like to obtain a new sample to
Maksim231197 [3]

Answer:

A sample of 1077 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

42% of freshmen do not visit their counselors regularly.

This means that \pi = 0.42

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.

How large of a sample size is required?

A sample size of n is required, and n is found when M = 0.035. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.035 = 2.327\sqrt{\frac{0.42*0.58}{n}}

0.035\sqrt{n} = 2.327\sqrt{0.42*0.58}

\sqrt{n} = \frac{2.327\sqrt{0.42*0.58}}{0.035}

(\sqrt{n})^2 = (\frac{2.327\sqrt{0.42*0.58}}{0.035})^2

n = 1076.8

Rounding up:

A sample of 1077 is required.

3 0
3 years ago
One root of f(x) = x + 10x2 – 25x – 250 is x = -10. What are all the roots of the function? Use the Remainder Theorem.
Natalka [10]

Answer:

-10

-5

5

Step-by-step explanation:

From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250

The Remainder Theorem is going to take a bit to solve.

You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.

The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.

However just to get the roots, the graph shows that

x = -10

x = - 5

x = 5

The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give

f((10) = 10^3 + 10*10^2 - 25*10 - 250

f(10) = 1000 + 1000 - 250 - 250

f(10) = 2000 - 500

f(10) = 1500 which is  not 0.

==================

f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250

f(1) = 1 + 10 - 25 - 250

f(1) = -264 which again is not zero

3 0
3 years ago
Read 2 more answers
The product of a number and 9, increased by 4, is 58. Find the number.
diamong [38]
9x + 4 = 58
9x = 54
x = 6

The number is 6.
4 0
3 years ago
Which function does this graph represent: y=x-4;<br> y=-x+4;y=4x-1;y=-4x+1
allochka39001 [22]

The graph represents y=-4x-1

If you notice the line, it goes past the -1 on the y axis which indicates that the y intercept is -1 since that was the only choice which displayed this, we know that our answer is y=-4x-1

5 0
3 years ago
Other questions:
  • Please help me with this
    12·1 answer
  • P1= (5,-4); p2=(8,-3);p3=(7,-10) find the length of each side of the triangle determined by three points
    6·1 answer
  • Estimate a 20% tip on a dinner bill of $171.81 by first rounding the bill amount to the nearest ten dollars.
    7·1 answer
  • HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • Solve: -4x = -20 A) -16 B) -5 C) 5 D) 6 Eliminate
    15·2 answers
  • Find the value 12 to the second power
    14·2 answers
  • 3. The Statue of Liberty is 305 feet tall. Lisa has a replica that is 9 inches tall and the
    14·1 answer
  • Factor to solve <br> X^2-2x-15=0
    10·1 answer
  • Can someone help me please thanks.One is already done for us at 110 can someone help me with the rest of the angles
    6·1 answer
  • A hot air balloon went from an elevation of 4,940 feet to an elevation of 3,122 feet in 36 minutes. What was its rate of descent
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!