Answers
f(x) = 27
3^x = 27
3^x = 3^3
x = 3
Related Questions
Identify the values of a b and c in the quadratic function y = 3x -5x +2
Answers
You give up a full time salary of 45,000 a year to go to school for 2 years the total cost of going to school is 30,000, if want to be able to recover your investment in 5 years or less what is the minimum salary you would need to earn upon earning your degree?
Answers
I would say that this person has lost out on 2 years salary while in school plus 5 year repayment period. Total amount divided over 5 years is:
( (2+5)(45,000) + 30,000 ) / 5 =
(7(45,000)+30,00)/5 = 69,000 salary
Answer:
69,000
Step-by-step explanation:
Given,
There is loss of 45,000 per year for two years,
So, the total lost = 2 × 45000 = 90,000
Also, the cost of school going = 30,000
∴ the total recovering amount = 90,000 + 30,000 = 120,000
If this amount must recover in 5 years or less than 5,
Then, the minimum recovering amount per year = [tex]\frac{120000}{5}[/tex] = 24,000
Now, the original salary per year = 45,000
Hence, the new salary per year = original salary + recovering amount
= 45,000 + 24,000
= 69,000
write an equation for the line that passes through (2,-5) and is parallel to 3x+4y=8
Answers
4y = -3x + 8; slope = -3
parallel lines, slope is the same so slope = -3
passes through (2,-5)
y = mx + b
b = y - mx
b = -5 - (-3)(2)
b = -5 + 6
b = 1
equation
y = -3x +1
hope it helps
The equation of the line which is parallel to the line 3x+4y=8 and passes through the point (2,-5) is y = -3/4x - 1/2.
Explanation:The given equation is 3x+4y=8, which is a linear equation. To make this simpler, we can isolate 'y' to make it in the form 'y = mx + b', where 'm' is the slope. When we do this, we get y = -3/4x + 2, so the slope of this line is -3/4.
Next, we know that parallel lines have the same slope. Therefore, the equation of the line parallel to the given line and passing through (2, -5) will also have a slope of -3/4. Using the point-slope form of a line, which is y – y1 = m(x – x1), where (x1, y1) is a point on the line, and 'm' is the slope, we can substitute the given values.
Therefore, y - (-5) = -3/4(x - 2), simplifying this gives us the equation of our line: y = -3/4x - 1/2.
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What is the length of the hypotenuse of 385.7 and 321.84?
Answers
Pythagorean theorem: 385.7^2 + 321.84^2=hypotenuse^2
hypotenuse=502.34
If $5000 is invested at 7.8% interest compounded monthly, how much would you have after 54 months?
Answers
5000 x (1+0.078/12)^54
5000 x (1.0065)^54
$7094.37
The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x) = x²?
Answers
Translation of a function y = h(x) up/down the y-axis is given by y = h(x) + a for translation 'a' unit up and y = h(x) - a for translation 'a' unit down
So, translating f(x) = x² eight units right and two units up gives:
g(x) = (x-8)² + 2
Colby worked three more hours on tuesday than he did on monday. on wednesday, he worked one hour more than twice the number of hours that he worked on monday. if the total number of hours is two more than five times the number of hours worked on monday, how many hours did he work on monday>
Answers
Tuesday = X + 3 (Problem says three more hours than he worked on Monday)
Wednesday = 2x + 1
(Problem says he worked 1 hour more than two times the number of hours on monday)
This side of the equation would be -
X + (X +3) + (2X + 1)
That's monday plus tuesday plus wednesday.
Then you would set up the other side of the equation.
This would be the total number of hours so it would be equal to monday, tuesday and wednesday combined.
2 + (5x)
Two hours more than five times the amount of Monday (X)
Now we put this together to have an equation
X + (X + 3) + (2x+ 1) = 2 + 5x
Now we need to collect like terms
4x + 4 = 2 + 5x
I just simplified the left side of the equation
Now I will subtract 4x from the left side to get all the variables on one side
4 = 2 + x
Now I subtract 2 to get the numbers both on one side
2 = x
So, Colby worked 2 hours on Monday.
Answer:
a,b,c
Step-by-step explanation:
i guessed and then they told me the right answer .
I’ll mark brainliest!!!!!! Please help me someone, anyone
What is the value of x ?
Answers
This year, the parade had 127 floats. That was 34 fewer floats than last year. How many floats were in te parade last year ?
Answers
This means that there were 127 + 34 floats last year which is 161 floats.
Hope this helps!
-Jabba
Answer:
Last year were 161 floats, that is, 34 more than this year.Step-by-step explanation:
Givens
There are 127 floats this year.That represents 34 fewer floats than last year.The second given statement expresses that this year there are 34 LESS floats. So, to know how many floats were there last year, we just need to sum
[tex]127+34=161[/tex]
Therefore, last year were 161 floats, that is, 34 more than this year.
Solve for y 3x-4y=10
Answers
or,4y=3x-10
or,y=(3x-10)/4
so,y=3/4 x-5/2
1. y and x have a proportional relationship, and y = 7 when x = 2. What is the value of x when y = 21?
2. y and x have a proportional relationship, and y = 9 when x = 2. What is the value of y when x = 3?
3.he table shows a proportional relationship.
x y
2 2.8
4 5.6
6 8.4
8 11.2
Complete the equation that represents the table.
Enter your answer as a decimal in the box. y = ____x
Answers
Answer: 6
Step-by-step explanation:
What has a greater area, a square or an equilateral triangle?
Answers
Use these are equations and you can see which one is greater.
Square area with side length s: s^2
Equilateral triangle area: s^2 * (√3 ) / 4
(√3) / 4 < 1, if you didn't know
I hope this helps. Have an awesome day! :)
A conjecture and the paragraph proof used to prove the conjecture are shown.
Drag an expression or statement to each box to complete the proof.
It is given that ∠1≅ ∠4 . By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank]
choices:
verticle angle theorim, transitive property of congruence, ∠4, ∠3, ∠2, ∠1
Answers
Answer:
∠2; vertical angle theorem; ∠3; transitive property of congruence
Step-by-step explanation:
∠2 and ∠1 are opposite angles that share only a vertex. This is the definition of vertical angles, and by the vertical angle theorem they are congruent.
Substituting ∠2 for ∠1 in our "given" statement, we now know that ∠2≅∠4.
∠4 and ∠3 are opposite angles that share a vertex. This makes them vertical angles, and the vertical angle theorem states that they are congruent.
The transitive property, algebraically, states "if a=b and b=c, then a=c." Applied to this proof, it states "if ∠2≅∠4, and ∠4≅∠3, then ∠2≅∠3."
The required solution for the blacks,
Blank 1 = ∠2;
Blank 2 = vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.
It is given that
∠1≅ ∠4 . By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank].
To determine the missing statement at the place of blanks in the statement.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Since
Black 1
∠2≅∠4
and ∠1≅ ∠4
So ∠2 ≅ ∠1
Blank 2
∠2≅∠4 are equal by the vertical angle theorem.
Blank 3
∠4≅∠3
∠3 ≅∠1
So,
∠2 ≅ ∠1 ; ∠2≅∠3 and ∠4≅∠3 it is transitive property of congruence.
Thus, the required solution for the blacks,
Blank 1 = ∠2;
Blank 2 = vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.
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what is the common ration between successive term in the sequance? 2,-4,8,-16,32,-64
Answers
hope this helps
Two months ago, the mean daily rainfall in a local city was 9.4 cm. The mean absolute deviation was 3.5 cm. Last month, the mean daily rainfall in that city was 11.5 cm, and the mean absolute deviation was 1.6 cm.
Which statement about the rainfall is true?
More rain fell two months ago than last month.
About the same amount of rain fell two months ago as last month.
Last month, the amount of rain that fell each day varied about the same as the month before.
Last month, the amount of rain that fell each day varied less than the month before.
Answers
Answer:
C
Step-by-step explanation:
Last month, more rain fell compared to two months ago, and there was less variation in the daily rainfall.
Explanation:To determine whether more rain fell two months ago or last month, we need to compare the mean daily rainfall and the mean absolute deviation for both months. Two months ago, the mean daily rainfall was 9.4 cm with a mean absolute deviation of 3.5 cm. Last month, the mean daily rainfall was 11.5 cm with a mean absolute deviation of 1.6 cm.
Thus, based on this information, we can conclude that more rain fell last month. The mean daily rainfall was higher and the mean absolute deviation was lower. This indicates that there was less variation in the amount of rain that fell each day last month compared to two months ago.
Find the area of the shaded region. Thanks!
Answers
now, let's rationalize the denominator for "r" first.
also notice, that section is just 1/4 of the area of that circle, so, let's just find the area of the whole circle with that "r", get one-quarter of it, and subtract it from the half of the area of the square.
[tex]\bf r=\cfrac{8}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies r=\cfrac{8\sqrt{2}}{2}\implies \boxed{r=4\sqrt{2}} \\\\\\ \stackrel{\textit{area of that circle}}{A=\pi (4\sqrt{2})^2}\implies A=\pi (16\cdot 2)\implies A=32\pi \\\\\\ \textit{how much is one-quarter of that?}\quad \cfrac{32\pi }{4}\implies \boxed{8\pi }\\\\ -------------------------------\\\\[/tex]
[tex]\bf \stackrel{\textit{area of the square}}{A=8\cdot 8}\implies A=64\qquad \stackrel{\textit{half of that square's area}}{32}\\\\ -------------------------------\\\\ \textit{shaded region}\implies \stackrel{\stackrel{\textit{half of that square}}{area}}{32}~~-~~\stackrel{\stackrel{\textit{one-quarter of the circle}}{area}}{8\pi }[/tex]
Answer:
-8π + 32
6.8675
Step-by-step explanation:
So we know that the are of the square is 64, and we know that the equation for the are of the shaded region is Area of square - 1/4 area of circle with a radius of 4√2 - area of 90/45/45 triangle with side lengths of 8 and 8.
s = square area
c = circle area
t = triangle area
∆ = shaded region area
∆ = s - 1/4c - t
input the numbers that we have for those variables:
∆ = 64 - 1/4(100.53) - 32
∆ = 64 - 25.1325 - 32
∆ = 32 - 25.1325
shade region approximate ≈ 6.8675
or to get an exact answer in terms of pi
∆ = 64 - 1/4(32π) - 32
∆ = 32 - 8π
shaded region = -8π + 32
just added this because it is hard to pick out the actual answer in the other person's answer.
Gina bought 2.3 pounds of red apples and 2.42 ponds of green apples. They were on sale for 0.75 a pound. How much did the apples cost altogether?
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Diameters AB and CD of circle K intersect such that m∠BKD = 100°. The measure of arc AC is:
Answers
m<BKD = 100
<AKC is vertical to <BKD, so m<AKC = 100
An arc has the same measure as its central angle,
so m(arc)AC = 100
Answer:
Measure of arc AC = 100°
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
Given : AB and CD are the diameters of the circle K and m∠BKD = 100°
To find : measure of arc AC
Solution :
The angle which is formed by the arc AC is m∠AKC so we need to find the measure of the angle ∠AKC
Now, m∠BKD = 100°
and m∠BKD = m∠AKC ( Vertically opposite angles are always equal)
⇒ m∠AKC = 100°
Hence, Measure of the arc AC = 100°
Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session.if Allison already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal ?
Answers
The product of two consecutive even integers is 80. find all such pairs of integers
Answers
The possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -
(8, 10)
(- 10, - 8)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given product of two consecutive even integers is 80.
Assume that the first integer is [n]. Then the second integer will be [n + 2]. According to the question, we can write -
n x (n + 2) = 80
n² + 2n = 80
n² + 2n - 80 = 0
n² + 10n - 8n - 80 = 0
n(n + 10) - 8(n + 10)
(n - 8)(n + 10) = 0
n = 8 and n = - 10
If → n = 8 then (n + 2) = 10.
If → n = - 10 then (n + 2) = -8.
Therefore, the possible pairs that fulfil the statement → "The product of two consecutive even integers is 80" are -
(8, 10)
(- 10, - 8)
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Final answer:
The consecutive even integers whose product is 80 are 8 and 10. This is found by setting up an equation for consecutive even integers and factoring the number 80.
Explanation:
The question is asking to find two consecutive even integers whose product is 80. When two numbers are consecutive even integers, they can be represented as n and n + 2, where n is an even integer. To find these numbers, we set up the equation n(n + 2) = 80.
First, we need to find two numbers that multiply to give 80. We can start by listing the factors of 80: 1 x 80, 2 x 40, 4 x 20, 5 x 16, 8 x 10. Since we are looking for even integers, we pick the pairs where both numbers are even: 4 x 20, 8 x 10. However, the numbers must also be consecutive even integers, which is the case for the pair 8 and 10, but not for 4 and 20.
Therefore, the pair of consecutive even integers that multiply to give 80 are 8 and 10.
What is the mixed number for -10.125
Write in simplest form please!
Answers
Hope this helps!
the -10 is ur whole number...it stays ur whole number
the 0.125....the last digit (5) is in the thousandths place...so put it over 1000
-10 125/1000 reduces to -10 1/8 <==
Find the geometric mean of 6 and 7.
A. √42
B. 4√3
C. 7
D. 42
Please select the best answer from the choices provided.
Answers
The Arithmetic Mean: (this is the mean we are used to seeing)
[tex]m= \frac{a+b+c}{n} [/tex]
(n= number of variables, in this case n=3)
To Find the Geometric Mean of n #'s:
[tex]m_{geometric} = \sqrt[n]{a*b} [/tex]
(n= number of variables, in this case n=2)
So, using this information we can find the geometric mean of 6,7 by plugging them into the equation as "a" and "b". n=2 (when n=2 a square root can be used)[tex]m_{geometric} = \sqrt[n]{a*b}[/tex]
[tex]m_{geometric} = \sqrt{a*b} [/tex]
[tex]m_{geometric} = \sqrt{6*7} [/tex]
[tex]m_{geometric} = \sqrt{42} [/tex]
So the answer in this case is A.[tex] \sqrt{42} [/tex]
Which proportion could be used to solve the question?
What percent of 80 is 23?
A. p/23 = 80/100
B. p/80 = 23/100
C. p/100 = 23/80
D. none could be used
Answers
C. can be used to solve it
other way is: p/100 *80 = 23
0.8p = 23
p = 23/0.8 = 28.75
Maths question below please help
Answers
İ hope it helped
Which is harder linear algebra or abstract algebra?
Answers
Linear algebra
I've always had trouble with graphs and it's much better if the algebra is similar to arthemetic
How do I simplify ((3x^2+12x+12)/(2x^2+x-6))/((4x^2-9)/(3x^3+x^2-10))
Answers
[tex]= \dfrac{3(x + 2)^2}{(2x - 3)(x + 2)} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} } [/tex]
[tex]= \dfrac{3(x + 2)}{2x - 3} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} } [/tex]
[tex]= \dfrac{3(x + 2)(3x^3+x^2-10) }{(2x - 3)^2(2x + 3)} [/tex]
What is the solution of the system? Use the elimination method. 2x+y=206x−5y=12 Enter your answer in the boxes.
Answers
Answer:
The answer to your question is: x = 7; y = 6
Step-by-step explanation:
2x+y=20 ( 1 ) Multiply by 5
6x−5y=12 ( 2 )
5 (2x+y=20) = 10x + 5y = 100
10x + 5y = 100
6x − 5y = 12 Eliminate y
16 x = 112
x = 112 / 16
x = 7
2(7) + y = 20 Substitution
14 + y = 20
y = 20 - 14
y = 6
PLEASE HELP!!!!!!!!!
solve for x
-2(x+1/3)+9x=4
x=
Answers
-2x - 2/3 + 9x =4
7x - 2/3 = 4
7x = 4 + 2/3
7x = 14/3
/7 /7
x = 2/3
the image from reflecting a figure in the third quadrant over the x-axis
Answers
Therefore, the image from refrecting a figure in the third quadrant over the x-axis is in the second quadrant.
Find y'' by implicit differentiation .4x3 + 5y3 = 9
Answers
Differentiating with respect to x, we have
[tex]12x^2+5(3y^2)(y')=0[/tex],
that is
[tex]12x^2+15y^2y'=0[/tex].
This means that [tex]\displaystyle{y'= -\frac{12x^2}{15y^2}=- \frac{4x^2}{5y^2} [/tex]
Differentiating again, using the quotient rule for the right hand side expression:
[tex]\displaystyle{y''=- \frac{4}{5}\cdot \frac{2xy^2-2yy'x^2}{y^4}= \frac{-8xy^2+8yy'x^2}{5y^4} [/tex]
y'' by implicit differentiation is y'' = -16x/5y^3.
To find y'' by implicit differentiation, we need to differentiate both sides of the equation .4x3 + 5y3 = 9 twice with respect to x.
First, we differentiate both sides once with respect to x to find dy/dx. This gives us:
12x^2 + 15y^2 (dy/dx) = 0
Next, we differentiate both sides once again with respect to x to find d^2y/dx^2 (y''). This gives us:
24x + 30y^2 (dy/dx) + 15y^2 (d^2y/dx^2) = 0
We can now solve for d^2y/dx^2 (y'') by substituting dy/dx from the first equation into the second equation. This gives us:
24x + 30y^2 (-12x^2/15y^2) + 15y^2 (d^2y/dx^2) = 0
Simplifying this equation, we get:
d^2y/dx^2 = -16x/5y^3
Therefore, y'' = -16x/5y^3.
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