Answer:
tanΘ = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
tanΘ = [tex]\frac{opposite}{adjacent}[/tex]
the opposite side requires to be found.
let the opposite side be x then using Pythagoras' identity in the right triangle
x² + 12² = 20²
x² + 144 = 400 ( subtract 144 from both sides )
x² = 256 ( take square root of both sides )
x = [tex]\sqrt{256}[/tex] = 16
then
tanΘ = [tex]\frac{16}{12}[/tex] = [tex]\frac{4}{3}[/tex]
-3(v+1)-3
What is the answer I really need help
Answer:
=-3v-6
Step-by-step explanation:
Distribute:
=(−3)(v)+(−3)(1)+−3
=−3v+(−3)+(−3)
Combine like terms:
=(−3v)+(−3+(−3))
=−3v+−6
=-3v-6
Hope this helps, this was easy!
how to solve x-3y=1 4x+5y=4 using elimination
Answer:
X=1, Y=0
Step-by-step explanation:
Solve for X and Y using a2 +b2 = c2
Which is the completely factored form of 12x4 39x3 9x2? 3x2(x – 3)(4x – 1) 3x2(x 3)(4x 1) 3x(x 3)(4x 1) 3x(x – 3)(4x 1)
The completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)
How to factor the expression?The polynomial expression is given as;
12x⁴ + 39x³ + 9x²
Factor out 3x² from the expression
3x²(4x² + 13x + 3)
Expand
3x²(4x² + 12x + x + 3)
Factorize the expression
3x² * 4x(x + 3) + 1(x + 3)
Factor out x + 3
3x²(4x + 1)(x + 3)
Hence, the completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)
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What are the domain and range of f (x) = log (x minus 1) + 2?
domain: x > 1; range: y > 2
domain: x > 1; range: all real numbers
domain: all real numbers; range: y > 1
domain: all real numbers; range: all real numbers
Answer:
domain: x > 1; range: all real numbers
Step-by-step explanation:
Given function: [tex]f(x)=\log(x-1)+2[/tex]
Logarithms are not defined for zero or negative numbers.
[tex]\implies (x-1) > 0 \implies x > 1[/tex]
Therefore:
domain (input values): [tex]x > 1[/tex]range (output values): all real numbersAnswer:
B on edge
Step-by-step explanation:
Just took the test :)
Please help quick 30 points
Evaluate 5 x + (-2 x2 ) for x = 3.
Answer:
I'd say 11 but could also be 30
distance between points (-4,4) and (4,-2)
Answer:
10 units
Step-by-step explanation:
calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 4, 4 ) and (x₂, y₂ ) = (4, - 2 )
d = [tex]\sqrt{(4-(-4))^2+(-2-4)^2}[/tex]
= [tex]\sqrt{(4+4)^2+(-6)^2}[/tex]
= [tex]\sqrt{8^2+36}[/tex]
= [tex]\sqrt{64+36}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
is the ordered pair (2,1) a solution for
[tex] y \leqslant \frac{3}{2} x + 3 \: show \: your \: work[/tex]
Answer:
put x= 2 and y = 1
and see this inequality will holds
What is factorisation?
It is also called Middle Term Splitting
Its a cool thing with which you can solve different orders of polynomials(or any algebraic expressions if you're a pro).
It is writing an expression as a product of 2 or more factors
Answer:
factorization is of writing a number or another mathematical use as a product of several factors, usually smaller of the same kind.
Step-by-step explanation
3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4.
26. Each weekday, 3,200,000 people in Massachusetts
commute to work. Of the total commuters, 403,200 take
public transportation. What percentage of commuters take
public transportation?
Answer: 12.6%
Step-by-step explanation:
403,200/3,200,000 = 0.126
0.126 = 12.6%
This year, you owed $6,414.95 in federal income tax. if you are taxed at a net rate of 17%, what was your taxable income for this year? a. $109,054 b. $26,792 c. $44,867 d. $37,735
Using proportions, it is found that your taxable income for this year is given by:
d. $37,735
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that $6,414.95 is 17% of his taxable income, hence it is given by:
T = 6414.95/0.17 = $37,735.
Which means that option D is correct.
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Answer:D
Step-by-step explanation:
bc its D
For a project in his Geometry class, Fwam uses a mirror on the ground to measure the height of his school building. He walks a distance of 7.15 meters from the building, then places a mirror flat on the ground, marked with an X at the center. He then walks 2.45 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.55 meters. How tall is the school
Answer:
2106 m
Step-by-step explanation:
a bicyclist rides 25 miles every 2 hours during race which equation represents the relationship between the number of miles and the number of hours of the bicyclist rides? let x represent the number of hours and let y represent the number of miles?
Answer:
y=12.5x
Step-by-step explanation:
Pamela and her friend went to the taco place with $15.00. they bought 2 burritos for $2.95 each, an order of nachos to share for $2.25, and 2 sodas for $1.75 each. how much money will they have left?
PLS help
Jaime rode her bike 5 miles north to the park to meet a friend. Then they rode east to the library. If Jaime's house is 13 miles from the library, about how far is the library from the park?
please
that is the solution
Answer:8 miles
Step-by-step explanation:
5. Find the area of the figure below:
5 cm
4 cm
2cm
5 cm
Answer:
33 cm^2
Step-by-step explanation:
To find the are of the figure as a whole, find the area of each rectangle individually and then add them together.
The area of a rectangle is [tex]A = bh[/tex], so the area of the small rectangle would be [tex]4*2[/tex], or [tex]8cm^2[/tex].
The area of the larger rectangle would be [tex]5*5[/tex], or [tex]25cm^2[/tex].
So, adding those areas together, we get [tex]33cm^2[/tex] as the area of the whole figure.
Brian is a software salesman. His base salary is 1900 , and he makes an additional 40 for every copy of Math is Fun he sells. Let N represent his total pay (in dollars), and let N represent the number of copies of Math is Fun he sells. Write an equation relating to p to n . Then use this equation to find his total pay if he sells 21 copies of Math is Fun.
Answer:
2740 is your total; p = 40n + 1900 is your equation.
Step-by-step explanation:
"p" represents total pay; "n" represents the number of copies he sells.
Base salary is 1900, and each copy sold gives him an extra 40
p = 40n + 1900 is your equation.
If he sells 21 copies. Plug in 21 for n
p = 40n + 1900
p = 40(21) + 1900
Simplify. Remember to follow PEMDAS. First, multiply, then add.
p = 40(21) + 1900
p = 840 + 1900
p = 2740
~
Need help asap, will give brainliest
V-125 - 5 X 32
[tex]3 \sqrt{ - 125} - 5 \times {3}^{2} [/tex]
Simplify the following and show all your workings
Answer:
Because of the order of operations, we start the equation backwards because exponents are what we prioritize here.
[tex]3^2 = 9\\\\9 * 5 = 45\\\\\sqrt{-125} = -11.1803399\\\\45 - -11.1803399 = 56.1803399\\\\56.1803399 * 3 = \boxed{168.54}[/tex] Result rounded to 2 DP
complete the statement, and find the value of x in the diagram.
help please!
Answer:
Also the quadrilateral shown is a rhombus
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. David invested $230 in a savings account that offers a 3% return on the investment. The value of David's investment will be at least $415 after a period of years. Hint: Use the formula A = P(1 + r)t, where A is the amount after t years, P is the amount invested, r is the rate of interest, and t is the time period. Use a calculator to compute the answer, and round it off to the nearest year.
The value of David's investment will be at least $415 after a period of 20 years
Compound interestThe formula for calculating the compound interest is expressed as:
A = p(1+r)^t
Given the following parameters
A = $415P = $230r = 3% = 0.03Substitute
415 = 230(1+0.03)^t
415/230 = 1.03^t
1.8043 = 1.03^t
t = ln(1.8043)/ln1.03
t = 20 years
The value of David's investment will be at least $415 after a period of 20 years
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What is the sum? startfraction x over x 3 endfraction startfraction 3 over x 3 endfraction 2 over x 3 endfraction five-thirds startfraction x 5 over x 3 endfraction startfraction x 5 over 3 x 27 endfraction startfraction 6 x over x 3 endfraction
The value of the sum expression [tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex] is 1
How to determine the sum?The expression is given as:
[tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex]
Take the LCM of terms of the expression
[tex]\frac{x}{x +3} + \frac{3}{x + 3} = \frac{x + 3}{x +3}[/tex]
Evaluate the quotient of x + 3 and x + 3
[tex]\frac{x}{x +3} + \frac{3}{x + 3} = 1[/tex]
Hence, the value of the sum expression [tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex] is 1
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IF COREY HAD 100 TOKENS AND HE GIVES SOME TO HIS FRIENDS! HE HAS 4 LEFT OVER! HOW MANY DID HE GIVE EACH OF HIS FRIENDS!?
Answer:
he gave away 96 but depends how many friends he gave them to.
Step-by-step explanation:
Consider the quadratic equation x2 10x 27 = 0. completing the square leads to the equivalent equation (x )2 = .
The solution to the given quadratic expression using the completing the square is x = ±√-2 -5
Completing the square methodThis is a method of factoring quadratic expression. Given the quadratic function.
x^2 + 10x + 27 = 0
Subtract 27 from both sides
x^2 + 10x = -27
Complete the square
x^2 +10x +5^2 = -27 + 25
(x+5)² = -2
x +5 = ±√-2
x = ±√-2 -5
Hence the solution to the given quadratic expression using the completing the square is x = ±√-2 -5
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What is the simplest radical form of the expression?
(8x^7y^4)^2/3
Answer:
[tex]\large \text{$ 4 x^{\frac{14}{3}}y^{\frac{8}{3}}$}[/tex]
Step-by-step explanation:
Given expression:
[tex](8x^7y^4)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a \cdot b)^c=a^{c} \cdot b^{c}:[/tex]
[tex]\implies 8^{\frac{2}{3}} \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]
[tex]\implies 4 \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 4 \cdot x^{\frac{14}{3}}\cdot y^{\frac{8}{3}}[/tex]
[tex]\implies 4 x^{\frac{14}{3}}y^{\frac{8}{3}}[/tex]
Expand [tex]\bf{(8x^{7}y^{4})^{\frac{2}{3} } }[/tex]
[tex]\bf{8^{\frac{2}{3} }(x^{7})^{\frac{2}{3} }(y^{4})^{\frac{2}{3} } }[/tex]
To raise a power to another power, multiply the exponents. Multiply 7 and 2/3 to get 14/3.
[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }(y^{4})^{\frac{2}{3} } }[/tex]
To raise a power to another power, multiply the exponents. Multiply 4 and 2/3 to get 8/3.
[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }y^{\frac{8}{3} } }[/tex]
Calculate 8 to the power of 2/3 and you get 2/4.
[tex]\bf{4x^{\frac{13}{4} }y^{\frac{8}{3} } \ \ ==== > \ \ \ Answer }[/tex]
A printer can print 12 pages in 9 seconds. What is the closest estimate of the
number of pages it can print in one minute?
120
100
45
72
Answer:
72 is the closest.The printer will primt 80 pages in one minute
Answer:
72
Step-by-step explanation:
12 pgs in 9 sec
*[tex]\frac{20}{3}[/tex] *[tex]\frac{20}{3}[/tex]
≈80 pgs in 60 sec
Hope this helps!!!
Please mark me as brainliest!!!
PLEASE HELP WILL GIVE BRAINLEST! What is the amplitude of the function graphed below?
Answer:
[tex]2\pi[/tex]
That's it
Please can anybody help me with this:
Show that (x − 9)(x − 1) ≡ x^2 − 10x + 9
We will expand the factored form of (x − 9)(x − 1) into the same form as x² − 10x + 9 to show they are equal.
Distribute and multipy out:
(x − 9)(x − 1)
x * x = x²
x * -1 = -x
x * -9 = -9x
-9 * -1 = 9
Add together:
x² + -x + -9x + 9
x² − 10x + 9
Use the Reflexive property:
x² − 10x + 9 = x² − 10x + 9 ✓
What is 8,-6 over the x-axis 90 degrees
Answer:
(6,8)
Step-by-step explanation:
The rule for 90 degree rotation is (x,y)=(-y,x)
So the answer is (6,8)
If you answer this I SWEAR OMM I WILL LOVE YOU FOR FREAKING EVER
Answer:
5/24 square mm
Step-by-step explanation:
A = lw
A = 5/8 x 1/3
A = 5/24
In parallelogram HIJK, the measure of angle H is 45∘.
Find the measure of angle J. Explain how you know.
Find the measure of angle K. Explain how you know.
Answer:
Step-by-step explanation: