Find the length of the third side. If necessary, write in simplest radical form.
Answers
Answer:
[tex]\boxed {\boxed {\sf 8}}[/tex]
Step-by-step explanation:
This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs of the triangle and c is the hypotenuse.
In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:
[tex]a= 7 \\b= \sqrt{15}[/tex]
Substitute these values into the formula.
[tex](7)^2+(\sqrt{15})^2=c^2[/tex]
Solve the exponents.
(7)²= 7*7=49[tex]49+ (\sqrt{15})^2=c^2[/tex]
(√15)²=√15*√15=15[tex]49+15=c^2[/tex]
Add.
[tex]64=c^2[/tex]
Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.
[tex]\sqrt{64}=\sqrt{c^2} \\\sqrt{64}= c\\8=c[/tex]
The third side length is 8.
Answer:
8
Step-by-step explanation:
Related Questions
3(4c + 5) = (3.4c) + (3.5) is an example of which property
a) Commutative property
b) Distributive property
c) Inverse Operation property
d) Multiplication property
Answers
Answer: B) Distributive property
Step-by-step explanation:
Definition:
- Commutative property: a+b=b+a
- Distributive property: a(b+c)=ab+ac
- Inverse operation property:
In Addition: a+(-a)=0In Multiplication: a×(1/a)=1- Multiplication property: If a=b, a×c=b×c
Solve:
GIven
3(4c+5)=(3·4c)+(3·5)
This is distributive property because it is distributing 3 to each of the numbers in the parenthesis.
Hope this helps!! :)
Please let me know if you have any quesitons
The circular fountain in front of the park has
a diameter of 14 feet. What is the
circumference of the fountain?
A.
43.98 ft
B.
87.96 ft
C-21.99 ft
D-153.94 ft
Answers
15 it was rigth in khan academy if u got the letter one its A
The circumference of the fountain will be 43.98 square feet. Thus, the correct option is A.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let d be the diameter of the circle. The circumference of the circle will be given as,
C = πd units
The diameter of the circular fountain is 14 feet. Then the circumference is calculated as,
C = π x 14
C = 43.98 square feet
Thus, the correct option is A.
More about the circumference of a circle link is given below.
https://brainly.com/question/27177006
#SPJ2
Find the Value of x. I WILL GIVE YOU BRAINLIEST!!!!! +to the person who answers first)
Answers
Answer:
hi
Step-by-step explanation:
5x+10+2x+10+90=180
5x+2x=180-10-10-90
7x=70
x=10
have a nice day
Hurry only 5 minutes to answer!!!!!!!!!!!!!1111
Order the specified numbers from smallest to biggest.
Answers
Answer:
-12, -3/4, -0.4, 0.4, 3/4, 8
Step-by-step explanation:
If the rate of change of the graph of a linear equation is 4 and the y-intercept is (0, 8), what is the linear equation that represents the graph?
Answers
Answer:
y = 4x + 8
Step-by-step explanation:
The linear equation can be written in the form y = mx + b. "y" and "x" stay as they are. The "m" is the slope or rate of change. The b is the y-intercept.
Hope it helps!!!
(May I have brainliest if it's correct please?)
Unit 2 Exam
Rabbit populations can double every 30
days. If there are 26 rabbits on a farm,
how many rabbits will be on the farm
after 240 days?
First, complete the equation:
Future Amount = 26(1+1)
Answers
Answer:
6,656 rabbits
Step-by-step explanation:
Population of rabbits = 26
Population doubles every 30 days
how many rabbits will be on the farm after 240 days?
t = 240 days / 30 days
= 8
Future Amount = 26(2)^t
=26(2)^8
= 26(256)
= 6,656
Therefore, the population of rabbits on the farm after 240 days is 6,656
the two rectangular plots of land have properties side lengths what is the perimeter of the smaller rectangle A. 28 B. 32 C. 36 D. 76
Answers
Answer:
I think that it would be b 32
How many cups are in 5/1/2 pints
Answers
Answer:
11 cups
Step-by-step explanation:
Answer:
11 us cups are in 5 1/2 pints
Step-by-step explanation:
hope this helps
3. Solve the system for x and y. 7x+8y= 26 -12X-7y=-58
Answers
9514 1404 393
Answer:
(x, y) = (6, -2)
Step-by-step explanation:
My favorite fast and easy way to solve pairs of linear equations is to use a graphing calculator. The one below shows the solution to be ...
(x, y) = (6, -2)
__
There is no simple way to use substitution or elimination on these equations, so we elect to use the "cross multiplication method." First, we write the equations in "general form", then write the coefficients in two rows, repeating the first coefficient.
7x +8y -26 = 0
12x +7y -58 = 0
__
[tex]\left[\begin{array}{cccc}7&8&-26&7\\12&7&-58&12\end{array}\right][/tex]
The method gets its name from this next step: compute the difference of cross products of pairs of adjacent columns.
d1 = (7)(7) -(12)(8) = -47
d2 = (8)(-58) -(7)(-26) = -282
d3 = (-26)(12) -(-58)(7) = 94
The solution to the equations is given by ...
1/d1 = x/d2 = y/d3 ⇒
x = d2/d1 = -282/-47 = 6
y = d3/d1 = 94/-47 = -2
The solution is (x, y) = (6, -2).
_____
Additional comment
If you watch videos on this solution method you will notice the 2×4 array of coefficients is formulated slightly differently, and the final equation has the 1/( ) term at the right end of the series of equalities. We judge this variation to be less confusing and easier to remember. YMMV
The work involved in using this method is 6 multiplies, 3 adds, and 2 divides. We believe that is less work than either substitution or elimination when there is no simplification possible.
solve the equation on the interval [0,2}. 5 cos x - root 3 = 3 cos x
Answers
Answer:
Step-by-step explanation:
5 cos x-√3=3 cos x
5 cos x-3 cos x=√3
2 cos x=√3
cos x=√3/2=cos π/6,cos (2π-π/6)
x=π/6,11π/6
Answer:x=π/6,11π/6
Step-by-step explanation:
5 cos x-√3=3 cos x
5 cos x-3 cos x=√3
2 cos x=√3
cos x=√3/2=cos π/6,cos (2π-π/6)
x=π/6,11π/6
Write and solve an equation to determine the height of a rectangular prism
with a width of 6 millimeters, a length of 20.5 millimeters, and a volume
of 984 cubic millimeters.
PLEASE HELP
Answers
Answer/Step-by-step explanation:
H = V/lw
H = 984/20.5*6
H = 984/128
H = 8
ANSWER:
H = 8
Where do I put the parentheses in 15-3x4+9=12
Answers
Answer:
That depends on which operations you want to do first. The order of operations affect to outcome of the equation.
In this case:
15 - (3 x 4) + 9 = 12
Answer:
It varies but this is one example
15 - (3 x 4) + 9 = 12
plz mark as brainliest
I need to know the surface area of these
Answers
9514 1404 393
Answer:
245 cm²
Step-by-step explanation:
The surface area of a cone is given by ...
SA = πr(r +s) . . . . where r is the radius, and s is the slant height
Filling in the given values, we have ...
SA = (3.14)(3 cm)(3 cm +23 cm) = (3.14)(3)(26) cm² ≈ 245 cm²
The surface area of the cone is about 245 cm².
if QS= 13 and RS= 12 what is the length of QR
Answers
Of all of the individuals who develop a certain rash, suppose the mean recovery time for individuals who do not use any form of treatment is 30 days with standard deviation equal to 8. A pharmaceutical company manufacturing a certain cream wishes to determine whether the cream shortens, extends, or has no effect on the recovery time. The company chooses a random sample of 100 individuals who have used the cream, and determines that the mean recovery time for these individuals was 28.5 days. Does the cream have any effect
Answers
Answer:
z(s) is in the rejection region. We reject H₀. We dont have enought evidence to support that the cream has effect over the recovery time
Step-by-step explanation:
Sample information:
Size n = 100
mean x = 28,5
Population information
μ₀ = 30
Standard deviation σ = 8
Test Hypothesis
Null Hypothesis H₀ x = μ₀
Alternative Hypothesis Hₐ x < μ₀
We assume CI = 95 % then α = 5 % α = 0,05
As the alternative hypothesis suggest we should develop a one tail-test on the left ( we need to find out if the cream have any effect on the rash), effects on the rash could be measured as days of recovery
A z(c) for 0,05 from z-table is: z(c) = - 1,64
z(s) = ( x - μ₀ ) / σ/√n
z(s) = ( 28,5 - 30 ) / 8/√100
z(s) = - 1,5 * 10 / 8
z(s) = - 1,875
Comparing z(s) and z(c)
|z(s)| < |z(c)| 1,875 > 1,64
z(s) is in the rejection region. We reject H₀. We dont have enought evidence to support that the cream has effect over the recovery time
olve the Following Inequality Select the possible range of solution to make the Statement True.
-6m < -24
Group of answer choices {Select All That Apply}
1, 2, 3
-1, -2, -3
4, 5, 6
-, 4, -5, -6
Answers
Answer:
We have ,
=> -6m < -24
=> m < -24/-6
=> m < 4
Therefore ,
m € (4,-∞)
A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution. The average time a customer can expect to wait in line is:
Answers
Answer:
18 minutes
Step-by-step explanation:
Given that:
The arrival time = 3 customers / hour
The avg. service rate (s) = 12 minutes per customer
To hour, we have:
[tex]s = \dfrac{60}{12}[/tex]
s = 5 customers/ hour
Thus, the required average time for a customer needs to wait in line is:
[tex]= \dfrac{3}{5}\times (5-3) hours \\ \\ = \dfrac{3}{5}\times 2 \\ \\ = \dfrac{3}{10} \ hours[/tex]
To minutes;
[tex]= 3 \times \dfrac{60}{10} \ minutes[/tex]
= 18 minutes
Solve for y
X+y=6
X=4
Simplify your answer as much as possible
Will give Brainliest
Answers
Solve the following quadratic equation 3×^2-5=0
Answers
X= radical 15/3 , radical -15/3
Decimal form:
X=1.29099444
X=-1.29099444
MARK ME BRAINLIEST PLEASE
Which one is the greatest volume
Answers
Answer: The First Cylinder has more volume
Step-by-step explanation:
1. V = 471.24
2. V = 282.74
What is fraction is equal 54%
Answers
Answer:
27/50
20 character minimum
The expression x^2- x + 8.75 factors as (x + 2.5)(x - a) for some positive value "a". What is a?
step by step, please.
Answers
Answer:
3.5
Step-by-step explanation:
Write out quadratic
[tex] {x}^{2} - x + 8.75[/tex]
We are given that x+2.5 is a factor.
So our roots look like
[tex](x + 2.5)(x - a)[/tex]
Let apply the foil method to find some missing parts.
[tex]x \times x = {x}^{2} [/tex]
[tex]x \times - a = - ax[/tex]
[tex]2.5 \times x = 2.5[/tex]
[tex]2.5 \times - a = - 2.5a[/tex]
We know that the outer terms must multiply to 8.75. We also know that the middle terms must add up to -1.
[tex] - 2.5a = 8.75[/tex]
[tex] 2.5x - ax = -1[/tex]
The only number that satisfy this equation is
[tex] - 3.5[/tex]
Since it already negative, it is
[tex]3.5[/tex]
The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion differs from 25%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis.
Answers
Answer:
The p-value for a two-tailed test of hypothesis is 0.0164.
Step-by-step explanation:
The test statistic is 2.4. Find the p-value for a two-tailed test of hypothesis.
This means that we look at the z-table, and we have to find:
[tex]P(|Z| > 2.4)[/tex]
Which is the pvalue of Z = -2.4 multiplied by 2, or 2 multiplied by 1 subtracted by the pvalue of Z = 2.4.
Looking at the z-table, z = 2.4 has a pvalue of 0.9918
1 - 0.9918 = 0.0082
2*0.0082 = 0.0164
The p-value for a two-tailed test of hypothesis is 0.0164.
compare and contrast area and perimeter
Answers
Answer:
area is the numbers around the shape and perimeter is inside
Step-by-step explanation:
What is the missing length?
Answers
This is because the area of a rhombus is A=sh
since the height is 4 mm, and the area is 12mm^2 the length is 3
a reflection across y=2
HELP DUE VERY SOON
Answers
Answer:
n' = (-5,2) k' = (-1,1) t' = (-5,0)
Step-by-step explanation:
Joe has a goal to practice his clarinet for 4 1/2 hours per week the list below shows the number of hours does practice this week so for Monday one and a half Wednesday 1 1/4 Thursday one how many more hours does Joel need to practice this week to meet his goal.
Answers
Answer:
0.75 hours more
Suppose that when a system of linear equations is graphed, one line completely overlaps the other line. Which statement is correct?
The system of equations has one solution because the lines intersect at one point.
The system of equations has one solution because the lines do not intersect at only one point.
The system of equations does not have only one solution because the lines intersect at one point.
The system of equations does not have only one solution because the lines do not intersect at only one point.
Answers
Answer:
The system of equations does not have only one solution because the lines do not intersect at only one point.
Step-by-step explanation:
If the lines are covered by each other, they intersect at all the points they overlap on. So, there is more than on solution.
The following statement is correct.
The system of equations does not have only one solution because the lines do not intersect at only one point.
The following information should be considered:
In the case when the system of linear equations is graphed and one line is overlap to the other one.So here the system of equation contains more than one solution as the lines are not intersected at only one point but more than one point.Learn more: brainly.com/question/17429689
The diameter of a circle is 2 feet. What is the circle's area?
Answers
A=3.1415•1•1
A=3.1415
F’(x)= 1+3 square root x f(9)=68
Answers
Answer:
[tex]f(x) = x + 2x^\frac{3}{2} + 5[/tex]
Step-by-step explanation:
I'm assuming the question here is asking for f(x)
The first step would be to find the antiderivative of f'(x)
[tex]\int{1+3\sqrt{x}} \, dx = \int{1 + 3x^\frac{1}{2}} dx[/tex]
Apply the reverse power rule
[tex]x + 2x^\frac{3}{2} + C[/tex]
Now solve for C when x = 9
[tex]x + 2x^\frac{3}{2} + C = 68\\9 + 2(9)^\frac{3}{2} + C = 68\\9 + 2(27) + C = 68\\9 + 54 + C = 68\\63 + C = 68\\C = 5[/tex]
Now substitute into the antiderivative
[tex]f(x) = x + 2x^\frac{3}{2} + 5[/tex]