All categories

3 years ago

a 10 ft ladder leans against a wall with its foot braced 3ft. from wall's base how far up the wall does the ladder resach

1 answer:

6 0

Ladder makes a right triangle with the wall and ground. The hypotenuse = length of the ladder = 10 ft
Let the height be h
By Pythagorean theorem
10^2 = 3^2 + h^2
h^2 = 10^2 - 3^2 = 100 - 9 = 91
h = sqrt( 91) = 9.54 ft

You might be interested in

The least common multiple of two numbers is 60. the prime factorization of one number is 3 times 5. what is the prime factorizat

gulaghasi [49]

The first number would be 3×5=15.
Another number could have different values. it could be
4=2×2
12=2×2×3
20=2×2×5
60=2×2×3×5

7 0

3 years ago

BD is tangent to circle O at C, m(arc AEC) = 280, and m(arc ACE) = 140. Find m (The figure is not drawn to scale.)

Zepler [3.9K]

Answer:

The correct answer is second option 60°

Step-by-step explanation:

From the figure we can write,

measure of arc AEC = measure of arc AE + measure of CE

measure of arc ACE = measure of AC + measure of CE

measure of arc AEC + measure of arc ACE = 280 + 140 = 420°

measure of arc AE + measure of CE + measure of AC + measure of CE = 420

measure of arc AE + measure of CE + measure of AC = 360°

measure of CE = 420 - 360 = 60°

The correct answer is second option 60°

8 0

3 years ago

Select all the expressions equivalent to: (4^5)⋅4^3 Group of answer choice 2^14 4^12 2^16 16^8 4^8 16^4

kumpel [21]

Answer:

Choices given as $2^{16}, 4^8$ and $16^4$ are correct.

Step-by-step explanation:

Given expression is,

$(4^5)(4^3)$

By applying law of exponents in the given expression,

$(4^5)(4^3)=4^{5+3}$

$=4^8$

$(4^5)(4^3)=(2^2)^5(2^2)^3$

$=(2^{2\times 5})(2^{2\times 3})$

$=2^{10}\times 2^6$

$=2^{16}$

$=(2^4)^4$

$=(16)^4$

Therefore, choices given as $2^{16}, 4^8$ and $16^4$ are correct.

4 0

3 years ago

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen

fenix001 [56]

Answer:

120

Step-by-step explanation:

Since we're dealing with a problem where the order matters and the first two letters are already chosen we need to subtract the number of letters and the number of available slots per group.

We use the permutation formula to find the answer, but before that let's check values.

n = 8

k = 5

Now since there are two letters already chosen we have to deduct two from both the value of n and k.

n = 6

k = 3

Now we can use the permutation formula:

$_{n}P_{k}=\dfrac{n!}{(n-k)!}$

$_{6}P_{3}=\dfrac{6!}{6-3)!}$

$_{6}P_{3}=\dfrac{6!}{3!}$

$_{6}P_{3}=\dfrac{6*5*4*3*2*1}{3*2*1}$

The 3*2*1 cancels out and leaves us with:

$_{6}P_{3}=6*5*4$

$_{6}P_{3}=120$

So there are 120 possible ways to arrange eight letters into groups of five where order matters and the first two letters are already chosen.

6 0

3 years ago

Read 2 more answers

How do I find the percent of budget?

ch4aika [34]

Answer:

First, subtract the budgeted amount from the actual expense. If this expense was over budget, then the result will be positive.

Next, divide that number by the original budgeted amount and then multiply the result by 100 to get the percentage over budget. If your expenses were lower than your budgeted amount, then this number will be negative, describing the percentage under budget.

6 0

2 years ago