Please put a picture next time :)
solve the equation 1/x+3/x=16
[tex] \frac{1}{x} + \frac{3}{x} = 16 \\ [/tex]
[tex] \frac{4}{x} = 16 \\ [/tex]
[tex]16x = 4[/tex]
[tex]x = \frac{4}{16} \\ [/tex]
[tex]x = \frac{1}{4} \\ [/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{1}{x} + \frac{3}{x} = 16} \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{4}{x } = 16 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ x = 16 \times 4 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \implies \orange{\underline{\boxed{\large\frak \pink{x = 64 }}}} \\ \end{gathered}[/tex]
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Which of the following is the correct factorization of the polynomial below?
Simplify: (5 + i)(5 − i)
A) −12
B) 24i
C) 26
D) 8i
Answer:
C) 26
Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.
5 × 5 = 25 + positive 1(i) = 26
Answer:
option c, 26
Step-by-step explanation:
(5 + i)(5 - i)
Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2
a = 5, b =1
(5)^2 + (1)^2
(5)^2 = 25
(1)^2 = 1
25 + 1
Tosha received a 9.5 for vault, a 9.1 for bars, a 9.625 for beam, a 9.25 for her floor exercise at her last gymnastics meet. What was her combined (or total) score?
Answer:
9.500+9.100+9.625+9.250=
18.600+18.875=
37.475
Hope this helps!
Help me with the 2 problems
Answer:
9) Vincent will not get the correct answer because the + 484 is unneccesary, as he already subtracted it.
10a) 310,000 + x = 465,000; so x = 155,000
10b) 930,000/310,000 = 3 times more
Step-by-step explanation:
Angle θ is in standard position. if sin(θ) = − 1/3, and π < θ < 3π/2 , find cos(θ).
A. -(2√2)/3
B.4/3
C.2√2/3
Answer:
Step-by-step explanation:
[tex]sin^2({ \theta})+cos^2({ \theta})=1\\cos({ \theta})=-/+\sqrt{1-sin^2({ \theta})} \\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} \\ --- > sin({ \theta})=\frac{1}{3} (known)\\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} =-\sqrt{1-(-\frac{1}{3})} =-\sqrt{\frac{9-1}{9}} =-\frac{2x^{2} }{3}[/tex]
PLeaseeeee Help
6. Given the order pairs (2, 3), (4, 5), (4, 7), (5, 10), and (6, 8) find the following. Round all final answers to three decimals places. Be careful not the round to early.
Express the line of best fit in the form of y = mx+b.
(a) The line of best fit. =
(b) Find the coefficient of linear correlation. =
Answer:
B
Step-by-step explanation:
answer is based on results from the Cartesian plane
Find the amount accumulated after investing m principal P for t and an internet rate compounded annually P=40500 r=3.8% t=20 k=12
The amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
What is an interest in banking?Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formula for calculating compound interest is expressed as;
A = P(1 + r/k)^(k*t)
Where A is final amount, P is initial principal balance, r is interest rate, k is number of times interest applied per time period and t is number of time periods elapsed.
Given that;
Initial principal balance P = $40500Interest rate r = 3.8= 3.8/100 = 0.038Time t = 20 yearsNumber of times interest applied per time period = 12 (annually) = 12/12 = 1 Amount accumulated A = ?A = P(1 + r/k)^(k*t)
A = 40500(1 + 0.038/1)¹ˣ²⁰
A = 40500 × (1.038)²⁰
A = 40500 × 2.10837
A = $85389
Therefore, the amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
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Need help thank you
Answer: [tex]i\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{-5}=\sqrt{(-1)(5)}=\sqrt{-1} \sqrt{5}=\boxed{i\sqrt{5}}[/tex]
is 3/2 = to square of 2
Answer:
No, it will not
Step-by-step explanation:
as square of 2 is 4
City A is 300 km due east of city B. City C is 200 km on a bearing of 123° from city B. How far is it from C to A?
Answer:
500 km
Step-by-step explanation:
300 plus 200 is 500km this is how far it is
The distance between City A & City C is approximately 171.3km
Given that, city A is 300 km due east of city B.
City C is 200 km on a bearing of 123° from city B.
We need to find the distance between the cities A and C,
Here we will use the concept of Cosine rule,
{Refer to the figure attached}
From ∆ABC, to find |AC|,
The cosine rule will be used.
|AC|² = |BC|² + |AB|² - 2(|BC|)(|AB|)cosB
Let |AC| = x
x² = 200² + 300² - 2(200)(300)cos33
x² = 40000 + 90000 - 120000cos33
x² = 130000-100644
x² = 29356
x = √29356
x = 171.3359
x ≈ 171.3km
Therefore, the distance between City A & City C is approximately 171.3km
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Mike is working on solving the exponential equation 37x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.
Use the change of base formula: log base b of y equals log y over log b.
[tex]~~~~~37^x = 12\\\\\implies \ln\left( 37^x \right) = \ln(12)\\\\\implies x \ln (37) = \ln(12)\\\\\implies x = \dfrac{\ln(12)}{\ln(37)}\\\\\implies x \approx 0.689[/tex]
Which of these numbers are relatively prime to 51? Select all that apply. da) 84 Ob) 70 Oc) 62 0d) 30
Answer:
b) 70
c) 62
Step-by-step explanation:
Numbers are relatively prime when they have no factors in common.
__
The factors of 51 are ...
51 = 3×17
The factors of the other numbers are ...
84 = 2²×3×7 . . . . . has a factor of 3 in common with 51
70 = 2×5×7 . . . . . . no factors in common
62 = 2×31 . . . . . . . no factors in common
30 = 2×3×5 . . . . . has a factor of 3 in common with 51
The numbers 70 and 62 are relatively prime to 51.
PLEASE HELP For what value of x is the parallelogram a rectangle. The arrows point to the entire diagonal, not just a segment.
Complete the long division problem on your own sheet of paper. Then, fill in the digits. 2 ÷ 694
Answer:
Here!! Hope i helped.
PLEASE HELP WILL MARK BRSINLIEST!!!!!pleaseeee
Answer:
[tex]x(3x-7)=3x^2-7x[/tex]
Step-by-step explanation:
[tex]\Large \begin{array}{| c | c | c |}\cline{1-3} \textsf{x} & 3x & -7\\\cline{1-3} x & 3x^2 & -7x\\\cline{1-3}\end{array}[/tex]
[tex]\textsf{Therefore,}\quad x(3x-7)=3x^2-7x[/tex]
How many square centimeters are in an area of 3.30in
Answer:
8.382 cm
Step-by-step explanation:
1in = 2.54 cm
3.30 x 2.54 = 8.382 cm
Find the standard deviation of the data, 12, 19, 9.
Answer:
4.19
Step-by-step explanation:
Find the mean:
[tex]\text{Mean}=\frac{12+19+9}{3}=\frac{40}{3}[/tex]
Find the standard deviation:
[tex]\text{Standard Deviation}=\sqrt{\frac{(12-\frac{40}{3})^2+(19-\frac{40}{3})^2+(9-\frac{40}{3})^2}{3}}=\sqrt{\frac{158}{9}}\approx4.19[/tex]
Given the function f(x) = (1/4)^x , how will g(x) = (1/4) ^x-3 + 5 be translated
See
x is decreased by 3 .
and y is increased by 5
So translation is
f(x)=(1/4)^xHence
f(x)=(1/4)^x-3+5So
x will go 3 units right
y will go 5units up
Graph attached
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]
Translated 3 units to the right:
[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]
Translated 5 units up:
[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]
[tex]\implies g(x)=f(x-3)+5[/tex]
Therefore:
[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]
FInd the value of x.
Y
D
W
X
(15x-8)
X =
N
226
Let's start with the given arc and its angle.
The angle YWX is going to be half the arc length.
YWX = 1/2 (226) = 113
Angles VWX and YWX form a linear pair (or are supplementary angles), which means that their sum is 180 degrees.
(15x - 8) + 113 = 180
15x + 105 = 180
15x = 75
x = 5
Hope this helps!
This window is designed in the shape of a right trapezoid.
Answer: 128°
Step-by-step explanation:
There are 360° in a trapezoid. Since this is a right trapezoid, two of those angles will be equal to 90°. We will set up the following equation, and solve.
360° = 90° + 90° + 52° + x°
360° = 90° + 90° + 52° + x°
360° = 232° + x°
128° = x
x = 128°
The obtuse angle has a measure of 128°.
Given: 1 = 2
If AB = 10, AC = 6, and BC = 6, find AD:
The length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.
What is Angle Bisector?The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts.
Here, Let the lenght of AD be x
AB = 10 , AC = 6 and BC = 6
by Angle-Bisector theorem which states that
if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.
So, CD/BD =AC/AB
CD/(BC-CD) = 6/10
10. CD = 6.BC - 6.CD
16 CD = 6 X 6
16 CD = 36
CD = 36/16
CD = 2.25
Now, AD = AC - CD
AD = 6 - 2.25
AD = 3.75
Thus, the length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.
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Simplify (2x^2y)^5. This needs to be simplified
Answer:
32x^10y
Explanation -
You want to use distributive property. Take 2x^5 and the Exponent 2y^5
It should look like this
1/5 is 60% of what number
1/5 = 60/100 * x
1/5 * 100/60 = x
100/300 = x
1/3 = x
Answer:
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
According to what we know, one-fifth is 60% of a number. Let us call that unknown number x. Since
[tex] \frac{1}{5} = 60\% \: \\ then \\ x = 100\%[/tex]
60% as a fraction is 6/10 or 3/5, in that case 100% as a fraction would be 5/5.
Recall: 60% = 3/5 and 100% = 5/5
therefore:
1/5 = 3/5
x = 5/5
note in order to find the value of x we cross multiply*
[tex] \frac{1}{5} ( \frac{5}{5}) = \frac{3}{5} x[/tex]
[tex] \frac{1}{5} = \frac{3}{5} x \\ \\ \frac{ \frac{1}{5} }{ \frac{3}{5} } = \frac{ \frac{3}{5} }{ \frac{3}{5} } x \\ \\ \frac{1}{5} \times \frac{5}{3} = x[/tex]
[tex] \frac{1}{3} = x[/tex]
If 5 times a certain number is 40, and 9 times the same number is 72, how would you find 59 times that number? A)400 + 72 B)40 + 72 C)40 × 72 D)400 + 720 pls tell answer urgently.
Answer:
A) 400 + 72
Step-by-step explanation:
Let the certain number be denoted by x.
⇒ 5x = 40 [Equation 1]
⇒ 9x = 72 [Equation 2]
Multiply Equation 1 by 10 :
⇒ 10(5x) = 40(10)
⇒ 50x = 400 [Equation 3]
Finding the sum of Equation 2 and Equation 3 :
⇒ 50x + 9x = 400 + 72
⇒ 59x = 400 + 72
Hence, 59 times a certain number is represented by : 400 + 72
Suppose that a gated community consisting of 40 houses requires:
500 liters of water everyday for common utilities of the community, and
a certain amount of water everyday per house.
Assuming that the water tanker supplies no more than 4500 liters of water per day to this community, what is the maximum amount of water that can be used by each house on a daily basis?
liters
Step-by-step explanation:
Given:
40 houses,
500 liters of waters everyday for common utilities
Unknown amount of water per house which we will call x.
4500 max liters for the gated community
Solve:
4500=40x+500
subtract 500 from both sides
4000=40x
divide by 40
100=x
Check:
40(100)+500=4500
4000+500=450
correct
Answer:
100 liters of water can be used by each house.
Sandy baked two dozen cookies. She gave ten cookies to the neighbours and ate three cookies.
How many cookies are left?
Answer:
11
Step-by-step explanation:
2 dozen = 24
24-10=14
14-3=11
Answer:
11
Step-by-step explanation:
two dozens is 24 because one dozen is 12. 24-10=14-3=11
Solve for x. Round to the nearest tenth.
Answer:
x = 27.19
Step-by-step explanation:
Sin(54) =22/x
0.81=22/x
x0.81= 22
x = 27.19
Reduced form of 8/10.
Answer:
4/5
Step-by-step explanation:
Answer:
=4/5 or 0.8 as decimal
Step-by-step explanation:
8/10
Factor the number: 8=2· 4
2x4
Factor the number: 10 = 2· 5
2x4/2×5
Cancel the common factor: 2
=4/5
or (decimal 0.8)
10 POINTS PLEASE HELP
Answer:
m∠A = 49°
Step-by-step explanation:
According to Angle Sum Property,
angles of the Δ add up to 180°∠A + ∠B + ∠D = 180°5x - 6 + 7x - 24 + 78 = 18012x + 48 = 180x + 4 = 15x = 11m∠A
5x - 65(11) - 655 - 649°