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
emmasim [6.3K]
3 years ago
8

In the right ΔABC, AN is the altitude to the hypotenuse. Find BN, AN, and AC, if AB=2√5 in and NC= 1 in.

Mathematics
1 answer:
kipiarov [429]3 years ago
8 0

Answer:

BN=4\ \text{in}

AN=2\ \text{in}

AC=\sqrt{5}\ \text{in}

Step-by-step explanation:

Let BN=x

BC=c

NC=y=1\ \text{in}

AB=a=2\sqrt{5}\ \text{in}

AC=b

We have the relation

\dfrac{BC}{AB}=\dfrac{AB}{BN}\\\Rightarrow \dfrac{c}{a}=\dfrac{a}{x}\\\Rightarrow c=\dfrac{a^2}{x}\\\Rightarrow x+1=\dfrac{a^2}{x}\\\Rightarrow x^2+x=20\\\Rightarrow x^2+x-20=0\\\Rightarrow x=\frac{-1\pm \sqrt{1^2-4\times 1\times \left(-20\right)}}{2\times 1}\\\Rightarrow x=4,-5

\boldsymbol{BN=4\ \text{in}}

h=\sqrt{a^2-x^2}\\\Rightarrow h=\sqrt{(2\sqrt{5})^2-4^2}\\\Rightarrow h=2\ \text{in}

\boldsymbol{AN=2\ \text{in}}

b=\sqrt{h^2+y^2}\\\Rightarrow b=\sqrt{2^2+1^2}\\\Rightarrow b=\sqrt{5}\ \text{in}

\boldsymbol{AC=\sqrt{5}\ \text{in}}

You might be interested in
A water tank holds 504 gallons but is leaking at a rate of 4 gallons per week. A second water tank holds 672 gallons but is leak
Orlov [11]

Answer:

That will be 75.6 if am nt mistaken

7 0
3 years ago
Olivia planted 25 tomato plants, but only produced 20 tomatoes. What percentage of plants produce tomatoes?
solmaris [256]

Answer:

It would be 5.

Step-by-step explanation:

Hope this help!

8 0
3 years ago
Question 7 PLEASE HELP Describe the transformation from the graph of f(x) =x to the graph of g(x)=1/5x+4 A: The transformations
Elis [28]

Answer:

  A: The transformations are a rotation and a translation.

Step-by-step explanation:

The function f(x) is shown in the attachment as a dashed red line. The function g(x) is shown as the blue line.

The two lines have different slopes. The change in slope can be accomplished by horizontal or vertical scaling, or by rotation. The offered answer choices only include <em>rotation</em> as an option for changing the slope.

The two lines have different intercepts. To move the line from one intercept to another, generally translation is involved.

The simplest transformation is rotation and translation.

_____

<em>Comment on the answer choices</em>

If the reflection is done across a line other than an axis, or if the rotation is done about a point other than the origin, then <em>any combination of rotation, reflection, and translation can be used to make the transformation seen</em>. (Translation alone is not sufficient.)

For example, reflecting the line across the bisector of the angle between the lines (a line with a slope of (√13 -2)/3 through (5, 5)) will give the desired transformation in one step.

Similarly, a rotation of about 33.69° about the point (5, 5) will give the transformation in on step. (That angle is 45°-arctan(1/5).)

7 0
3 years ago
What is the least common denominator (LCD) for these fractions? 2/7 and 9/10
yanalaym [24]

Answer:

70

Step-by-step explanation:

7 and 10 = 70, This is the correct answer because 7 times 10 equals 70, and 10 times 7 equals 70 too, so 70 is the LCD

7 and 10 = 1, This is impossible because anything multiplied by 7 naturally does not get 1 as a answer, including 10 too. X

7 and 10 = 10, Only 10 times 1 equals 10, but 7 a natural whole number does not equal 10. X

7 and 10 = 35, Only 7 times 5 equals 35, but 10 times a whole number does not equal 35. X

4 0
3 years ago
Find the product what is 9.874×7= ? ​
xxMikexx [17]
69.118 is the correct answer
3 0
3 years ago
Read 2 more answers
Other questions:
  • Help me plz with this
    5·1 answer
  • Subtract by adding the opposite. <br> 19-23=<br> -48-(80)=<br> -17-(-20)=
    6·1 answer
  • What is the answer to #3?
    9·1 answer
  • I don’t understand some of this and need help with it
    6·2 answers
  • Margo brought 7 pens from a book store some pens cost $3.00 EACH and the rest cost $4.00 . If she paid a total of 23.00 for the
    10·1 answer
  • 1. Use the figure shown to complete part a and b.
    11·1 answer
  • If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of con
    8·1 answer
  • Which of the following represents a focus of the equation y2 + 4 = 4y +x
    11·1 answer
  • Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if
    12·1 answer
  • Do a plane in the point always sometimes or never intersect? Explain.​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!