Find the value of each variable. Write your answer in simplest radical form.
Answers
Answer:
Step-by-step explanation:
Guiding Statement
You must find x before you can find y. If an altitude is dropped from the right angle to the hypotenuse, then the value of the altitude = the two parts of hypotenuse multiplied together = the altitude squared.
Formula
Perhaps, instead of all that language, it is easier just to show you this in terms of what you have been given.
Solution
x^2 = 72 Factor 72 into prime factors.
x^2 = 8 * 9
x^2 = 2 * 2 * 2 * 3 * 3 Take the square root of both sides.
√x^2 = √(2 * 2 * 2 * 3 * 3)
Rule
For every pair of equal prime factors, take 1 factor outside the root sign and throw the other one away.
√x^2 = √(2 * 2 * 2 * 3 * 3)
x = √(2 * 2 * 2 * 3 * 3) Apply the rule
x = 2 * 3 √2
x = 6√2
Now with y
a = 6√2
b = 12
c = y Use the Pythagorean Theorum
c^2 = a^2 + b^2
c^2 = (6√2)^2 + 12^2
c^2 = 36*2 + 144
c^2 = 72 + 144
c^2 = 216
c = 6 √6
answer
x = 6√2
y = 6√6
Related Questions
An experiment consists of rolling a die and then flipping a coin.
The following tree diagram shows the possible outcomes.
A 2-column tree diagram: die and coin. The die column has numbers 1 through 6. Each number branches to H & T in the coin column.
© 2018 StrongMind. Created using GeoGebra.
What is the probability of rolling a 6 or landing on tails?
Enter your answer as a reduced fraction, like this: 3/14
Answers
Answer:
1/3
Step-by-step explanation:
If you are trying to figure out the more likeliness of getting tails than a 6, then you have to get a common denominator and then subtract numerators.
[tex]\frac{1}{2} =\frac{6}{12} \\\\\frac{1}{6} =\frac{2}{12} \\\\\frac{6}{12} -\frac{2}{12} =\frac{4}{12} \\\\\frac{4}{12} =\frac{2}{6} =\frac{1}{3}[/tex]
Theres a 1/3 more chance of tails than rolling 6
The probability of rolling a 6 or rolling a die is 2/3.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
An experiment consists of rolling a die and then flipping a coin.
Probability = Number of desired outcomes / Total outcomes
Probability of rolling a 6 = 1/6
Probability of landing on tails = 1/2
P(A or B) = P(A) + P(B)
Here, let A represents the event of rolling 1 6 and B represents the event of landing on tails.
P(A or B) = 1/6 + 1/2 = 4/6 = 2/3
Hence the required probability is 2/3.
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Solve the system of equations below. 4x+1=16 2x+30= - 2
Answers
Answer:
D. (5, 4)
Step-by-step explanation:
4x + y = 16 -----> y = 16 - 4x
2x + 3y = -2
Substitute to find x
2x + 3(16 - 4x) = -2
2x + 48 - 12x = -2
-10x = -50
x = 5
Substitute to find y
4(5) + y = 16
20 + y = 16
y = 4
Final solution: (5, 4)
Hope this helps!
Can someone please help me
Answers
Answer:
A. 9.0 seconds
Step-by-step explanation:
In the figure, m
What is the value of X?
A.) 6
B.) 7.2
C.) 4.6
D.) 3.3
Answers
[tex]7x-4=\angle PQS\\\\\implies 7x-4 =38\\\\\implies 7x = 38+4\\\\\implies 7x = 42\\\\\implies x = \dfrac{42}7 \\\\\implies x = 6[/tex]
Answer:
7.2
Step-by-step explanation:
5x+2=38
5x=38-2
x=36/5
x=7.2
What is the slope of the line that includes these two points
Answers
Answer:
[tex]\boxed{A) \;m=\dfrac{1}{6} }[/tex]
Step-by-step explanation:
[tex]m=\dfrac{rise}{run}[/tex]
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{6-8}{-7-5}[/tex]
[tex]m=\dfrac{-2}{-12}[/tex]
[tex]m=\dfrac{1}{6}[/tex]
Hope it helps! :)
Please HELP ME! PLEASE!
Answers
Answer:
- 8/4x^6-5x^5+2
Step-by-step explanation:
FREE BRAINLIEST IF CORRECT - EZ QUESTION: Write the equation for the parabola that has x− intercepts (−2,0) and (−5,0) and y− intercept (0,−4).
Answers
Answer:
y = -2/5x^2 - 14/5x - 4
Step-by-step explanation:
y = a(x + 2)(x + 5)
At y intercept:
-4 = a(2)(5)
10a = -4
a = -2/5.
So the equation is
y = -2/5(x + 2)(x + 5)
y = -2/5(x^2 + 7x + 10)
y = -2/5x^2 - 14/5x - 4
Alyssa had two hundred 95 dollars to spend on 9 books.
After buying them she had 16 dollars. How much did
each book cost?
Answers
Answer:
$31
Step-by-step explanation:
295 minus 16 is 279
that's how much they were all together
and divide 279 by 9 and you get 31
(07.04 LC)
If 9x = 63, then x =
(Only input whole number) (1 point)
Answers
Answer: x = 7
Step-by-step explanation:
Question: If 9x = 63, then x = ?
9x = 63
x = 63/9
x = 7 answer
The value of x is 7.
hope that helps...
9 subtracted from 2x gives the result 5 Find the value of x.
Answers
Answer:
x = 7
Step-by-step explanation:
Just write what you see in terms of a formula.
2x - 9 = 5
Solve for x
add both sides by 9
2x = 5 + 9
2x = 14
divide both sides by 2
x = 14/2
x = 7
Answer:
x = 7
Step-by-step explanation:
9 subtracted from 2x gives the result 5. Find the value of x.
Translate:
2x - 9 = 5
Simplify:
2x - 9 = 5 <== add 9 to both sides
+ 9 + 9
2x = 14 <== divide both sides by 2 to isolate the variable
/2 /2
x = 7
Hope this helps!
If the sample regression equation is found to be yˆ = 10 + 2x, what is the estimated value of Y if x = 5?
Answers
The sample regression y = 10 + 2x is a linear regression equation
The estimated value of y if x = 5 is 20
How to estimate the value of y?The sample regression equation is given as:
y = 10 + 2x
When x = 5, the equation becomes
y = 10 + 2 * 5
Evaluate the product
y = 10 + 10
Evaluate the sum
y = 20
Hence, the estimated value of y if x = 5 is 20
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How do you write 59/20 as a percentage?
Answers
PLEASE HELP I WILL GIVE BRAINLY TO FIRST GOOD ANSWER
Answers
Answer:
(x + 8)(x + 4)
Step-by-step explanation:
x² + 12x + 32 Rewrite
x² + 4x + 8x + 32 Factor
x(x + 4) 8(x + 4)
(x + 8)(x + 4) Final answer
Hope this helps!
Step-by-step explanation:
if x=1 --> 1 + 12 + 32 = 45
if x=2 --> 4+ 24 + 32 = 60
if x=3 --> 9+36+32 = 77
if x=4 --> 16 + 48 + 32 = 96
...
so, with the same logic we'll find the equation:
(x + 8)(x + 4)
(because it's related to each of the equations on the top )
I'm not sure if this is what you're looking for, if not tell me in the comments and I'll change my answer. Otherwise, I hope this answers your problem :)
(8c-9b)(x-5a)+(3x+3c)(6a-2b)
Answers
Answer:
8cx - 22ac - 15bx + 45ab +18ax - 6bc.
Step-by-step explanation:
(8c-9b)(x-5a)+(3x+3c)(6a-2b)
= 8c (x-5a) -9b(x-5a) + 3x(6a-2b) + 3c(6a-2b)
= 8cx - 40ac -9bx + 45ab + 18ax - 6bx + 18ac - 6bc
Combining like terms:
= 8cx - 22ac - 15bx + 45ab +18ax - 6bc.
Answer:
8cx + 45ab + 18ax - 2bc - 15bx - 22ac
Step-by-step explanation:
(8c - 9b)(x - 5a) + (3x + 3c)(6a - 2b)8cx - 9bx - 40ac + 45ab + 18ax + 18ac - 6bx - 2bc8cx + 45ab + 18ax - 2bc - 15bx - 22acWhat is the sum of the six marked angles in the picture?
Answers
Answer:
The answer is option D - 1120°
1120° is the sum of the sixed marked angle in the picture. Therefore, the correct option is option D.
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the size of such an angle or a rotational angle. The width of a circular path divided by its radius is the traditional definition of this metric, which may also be signed. 1120° is the sum of the sixed marked angle in the picture.
Therefore, the correct option is option D.
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Find the area of the parallelogram. 24 cm 9cm 8 cm
Answers
Points scored: 9, 4, 13, 11, 12, 5
What is the median of the points scored?
Answers
Answer:
10
Step-by-step explanation:
The median is arranged in numerical value.
it goes: 4, 5, 9, 11, 12, 13. The median is basically the number in-between. you would cross out 4 and then 13. next, 5 and 12. Now there's 9 and 11 in the middle and that is what's left. the number in between of 11 and 9 is 10. 10 would be the median of the data set.
Which expression can be used to find the area of triangle rst? (8 ∙ 4) - one-half (10 12 16) (8 ∙ 4) - (10 12 16) (8 ∙ 4) - one-half (5 6 8) (8 ∙ 4) - (5 - 6 - 8)
Answers
The area of the triangle RTS will be (8×4) - 1/2 (16+12+10). Then the correct option is A.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
We start by drawing a rectangle around the triangle as shown in the diagram below.
Area of the RST = area of the rectangle - (area of triangle A + area of triangle B + area of triangle C)
[tex]\rm Area\ of\ RST = (8 \times 4) - [(\dfrac{1}{2} \times 8 \times 2) + (\dfrac{1}{2} \times 4 \times 3) + (\dfrac{1}{2} \times 5\times 2)]\\\\\\Area\ of\ RST = (8 \times 4) - \dfrac{1}{2} (16 + 12 + 10)[/tex]
The area of the triangle RTS is (8×4) - 1/2 (16+12+10).
More about the geometry link is given below.
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Answer:Option A
Step-by-step explanation:
Find the equation of a line parallel to y + 9 = -3/2x that passes through the point (-8,9)
Answers
slope intercept form:
y = mx + b (where m = slope
and b = y-intercept)
simply subtract 9 from both sides of the given equation to get slope intercept form of the first line:
y + 9 = -3/2x
y + 9 - 9 = -3/2x - 9
y = -3/2x - 9
so the slope (m) = -3/2
the problem tells us a point on the second line (x,y) or (-8,9)
and we now know slope is -3/2
so let’s plug those in and solve for the y-intercept (b) of the second line.
y = mx + b
9 = -3/2(-8) + b
9 = 12 + b
9 - 12 = 12 - 12 + b
-3 = b
so now we know the slope (m) of both lines is -3/2 and the y-intercept (b) of the second line is -3
all we have to do is use the information to establish slope intercept form of the equation of the second line:
y = mx + b
y = -3/2x - 3
The answer is: y = -3/2x - 3
check your answer by plugging the point (-8,9) back in to your equation
9 = -3/2(-8) - 3
9 = 12 - 3
9 = 9 [TRUE]
Please help me. I will make Brainliest
Answers
How many cups of water should be mixed with 1/4 cup of vinger to make the cleaning solution
Answers
Answer:
"mix 1 cup of vinegar with 1 gallon of water"
1 cup = 8oz; 1/4 cup = 2oz
You can see that the amount of vinegar is 1/4 of the original amount,
so, we will need 1/4 of the amount of water, which is 1gallon = 128oz
so, 1/4 times 128oz = 32oz, which is one quart
Algebraically, 8oz : 128oz = 2oz : x
8x = 256; x = 32oz
The first three terms of a sequence are given. Round to the nearest
а
thousandth (if necessary).
25, 150, 900, ...
Find the 9th term.
Answers
Answer:
I'm sorry I don't know
Step-by-step explanation:
hopefully someone solves this!
The 9th term of the geometric sequence will be 41,990,400.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The sequence is given below.
25, 150, 900, .....
The first term is 25 and the common ratio is calculated as,
r = 150 / 25
r = 6
Then the 9th term of the sequence is given as,
a₉ = 25 · (6)⁹⁻¹
a₉ = 25 · (6)⁸
a₉ = 25 · 1,679,616
a₉ = 41,990,400
The 9th term of the geometric sequence will be 41,990,400.
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Carter invested $540 in an account paying an interest rate of 4. 875 % compounded monthly. Jack invested $540 in an account paying an interest rate of 5. 5% compounded continuously. To the nearest hundredth of a year, how much longer would it take for Carter's money to triple than for Jack's money to triple?
Answers
Using compound interest and continuous compounding, it is found that it would take 2.61 years longer for Carter's money to triple.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For Carter, we have that the rate of interest and the number of compoundings are, respectively, r = 0.04875 and n = 12. The time to triple is t for which A(t) = 3P, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]3P = P\left(1 + \frac{0.04875}{12}\right)^{12t}[/tex]
[tex](1.0040625)^{12t} = 3[/tex]
[tex]\log{(1.0040625)^{12t}} = \log{3}[/tex]
[tex]12t\log{(1.0040625)} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{12\log{(1.0040625)}}[/tex]
t = 22.58.
What is continuous compounding?The amount of money is given by:
[tex]A(t) = Pe^{kt}[/tex]
For Jack, we have that the rate of interest is of k = 0.055, hence:
[tex]A(t) = Pe^{kt}[/tex]
[tex]3P = Pe^{0.055t}[/tex]
[tex]e^{0.055t} = 3[/tex]
[tex]\ln{e^{0.055t}} = \ln{3}[/tex]
[tex]0.055t = \ln{3}[/tex]
[tex]t = \frac{\ln{3}}{0.055}[/tex]
t = 19.97.
The difference is given by:
22.58 - 19.97 = 2.61
It would take 2.61 years longer for Carter's money to triple.
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find two rational and irrational numbers between 2 and 2.5
Answers
Answer:
Rational:2.1,2.2
Irrational:[tex]\sqrt{5},\sqrt{6}[/tex]
Step-by-step explanation:
Trial and error
A state offers specialty license plates that contain 2 letters followed by 3 numbers. License plates are assigned randomly. All license plates are equally likely. Find the number of possible license plates that can be issued using this system.
A. 82 possible license plates
B. 67,600 possible license plates
C. 676,000 possible license plates
D. 36 possible license plates
Answers
please help me with this question
Answers
Answer:
19
Step-by-step explanation:
you get the answers by counting all the x. every sttudent markes 1 x so the answer is 19
i need help with this quick plss
Answers
semi cirrcular is very okay cuase yes lol get suspeneded
Find the value of x
Answers
Answer:
40, or if you need it unrounded 40.3
Step-by-step explanation:
the formula is just v=b(h) you can take 15 which is our height and solve by dividing 605/15 which is 40.3, or 40 when rounded
Is the following a statistical question?
How much do new cars cost?
Answers
Which fraction below represents a repeating decimal?
Answers
Answer:
22/12
Step-by-step explanation: