Answer:
1/81
Step-by-step explanation:
[tex](3^2)^{-2}=3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]
1. The table represents a quadratic function. Write an equation of the function in standard form. X f(x) -4 -3 -2 0 0 1 2 0
An equation of the function in standard form is equal to -x²/4 + 1 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-3 = a(-4)² + b(-4) + c ⇒ -3 = 16a - 4b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
1 = a(0)² + b(0) + c ⇒ 1 = c .......equation 3.
Substituting the value of c into eqn. 1 and eqn. 2, we have:
-4 = 16a - 4b .......equation 4.
-1 = 4a - 2b .......equation 5.
Multiplying eqn. 5 by 2 and solving simultaneously, we have:
-4 = 16a - 4b
-2 = 8a - 4b
-2 = 8a
a = -2/8
a = -1/4
For the value of b, we have:
-1 = 4a - 2b
-1 = 4(-1/4) - 2b
-1 = -1 - 2b
2b = 0
b = 0
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-1/4x² + (0)x + 1 = 0
-x²/4 + 1 = 0
Check:
When x = 2, we have:
-x²/4 + 1 = 0
-2²/4 + 1 = 0
-4/4 + 1 = 0
-1 + 1 = 0
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Manuel made $20,000 in taxable income last year.
Suppose the income tax rate is 10% for the first $7000 plus 16% for the amount over $7000.
How much must Manuel pay in income tax for last year?
$0
Check
X
S
Answer:
$2780
Step-by-step explanation:
Given an income tax of 10% of the first $7000 and 16% of all after that, you want the tax on $20,000.
Piece-wise functionManuel's income is more than $7000, so the tax is computed in two parts.
First $7000
The tax on the first $7000 of income is 10%:
tax = $7000 × 0.10 = $700
Amount Over $7000
The amount over $7000 is ...
$20,000 -7,000 = $13,000
The tax on that amount is 16%:
tax = $13,000 × 0.16 = $2080
Total tax due
The tax Manuel must pay is the total of these two amounts:
$700 +2080 = $2780
Manuel must pay $2780 in income tax for last year.
The mean monthly rent of students at Oxnard University is $910 with a standard deviation of $216. (a) John’s rent is $1,355. What is his standardized z-score? (Round your answer to 3 decimal places.)
Answer:
maybe if you learn you will know
Step-by-step explanation:
What is the domain of the function y = 2√x-5?
THE ANSWER IS IN THE PHOTO
5 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids. The winner offers a bid of $72,000 how much will that bidder need to put into a kitty for the other bidders to be compensated?
The amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.
How to calculate the value?It should be noted that 5 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids and the winner offers a bid of $72,000.
Therefore, the fair share will be:
= Bids / Number of people
= 72000 / 5
= 14400
Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be:
= $72000 - $14400
= $57600
Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.
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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table. What is the relationship between distances biked and distances run?
The relationship between distances biked and distances run is
D(bike) = 2 × D(run)
Here, we have been shown that when distance run is, lets say x then distance run is 2x
When distance run is 2 then distance biked is 4, twice as distance run.
Again in distance run 3[tex]\frac{1}{2}[/tex], distance biked is 7, so this proves that
D(bike) = 2 × D(run)
What is the importance of distance?The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors (e.g. "two counties over").
Since spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to denote a measure of the degree of separation or the statistical distance between two similar objects (such as edit distance between strings of text or statistical distance between probability distributions) (as exemplified by distance between people in a social network).
A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.
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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
j2 + 20j +
Please explain in detail.
Answer:
the quadratic equations is 22+×3÷78=36-54Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs $22 per share and Stock Y, which costs $35 per share. His budget for buying stock is no more than $4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?
The option which represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased is:
D. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≥ 20
b ≥ 15
What does at least and no more than mean in this instance?
At least is interpreted in inequalities as greater than or equals to whereas "no more than" implies that it cannot be greater, hence, can be less than or equals to, as a result, the following relationships are determined:
a≥20(the least number of X shares is a, which is 20)
b≥ 15(the least number of Y shares is a, which is 15)
total amount spent on X=22*a=22a
total amount spent on Y=35*b=35b
maximum amount to invest=4500(less than or equals to)
22a+35b≤ 4500
sum of X and Y shares altogether(least)=100
a+b≥100
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Full question:
Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs $22 per share and Stock Y, which costs $35 per share. His budget for buying stock is no more than $4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?
A. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≤ 20
b ≤ 15
B. 22a + 35b ≤ 4,500
a + b ≤ 100
a ≤ 20
b ≤ 15
C. 22a + 35b ≤ 4,500
a + b ≤ 100
a ≥ 20
b ≥ 15
D. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≥ 20
b ≥ 15
Find the midpoint of points A(-1,-7) and B (3,-4) graphically
(0,0) because that is the center
What is the y-intercept of f(x) =
700- (2)* ?
A. (0, 1)
B. (1,0)
C. (0,0)
(14)
D.
Answer:
its A
Step-by-step explanation:
A bag contains 10 marbles: 5 are green, 3 are red, and 2 are blue. Deandre chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is red and the second is blue? Write your answer as a fraction in simplest form.
Answer:
1/15
Step-by-step explanation:
3/10 x 2/9 = /90 Dived the top and bottom by 6 and you will get 1/15.
The first time there were 10 marbles and she wanted red. There were only 3 red so the chances of getting a red is 3/10. Now she only has 9 marbles left. She was a blue so her chances are 2/9.
write your answers in Arabic numerals XXXV-VIII
Step-by-step explanation:
٨-٥٢.....................
Jack walks around the his schools track field and completes 1 lap in 30seconds.How long does it take Jack to complete 1 mile? How far will he run after 30 min?What is my speed in minutes per hour
11. Convert the number to scientific notation.
0.000001019
1.02 x 10-⁹
1.02 x 10-6
10.19 x 10-7
1.02 x 106
-87.55% rounded to one decimal place
Answer:
-8756 %
Step-by-step explanation:
Because 5 is a strong number
I didn’t understand this question please help and thank u
Find all values of $x$ that solves this system.
\begin{align*}
x^2 - 9y^2 &= 72\\
x + 3y &= 9
\end{align*}
All the values of x that solve the given system of equations are as follows:
x = 17/2.
What is a system of equations?A system of equations is when multiple variables are related by equations, which are solved to find the values of each variable. Usually, these relations are linear, but they may also be quadratic, as is the case in this problem.
For this problem, we are given two equations, as follows:
x² - 9y² = 72.x + 3y = 9.From the second equation, we have that:
x = 9 - 3y.
Replacing in the first, we have that:
(9 - 3y)² - 9y² = 72.
9y² - 54y + 81 = 72.
54y = 9.
y = 9/54
y = 1/6, as 9/9 = 1, 54/9 = 6.
Hence the solution for x of the system of equations is found by replacement, as follows:
x = 9 - 3y = 9 - 3/6 = 9 - 1/2 = 18/2 - 1/2 = 17/2.
The solution is x = 17/2.
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A solid lies between planes perpendicular to the y-axis at [tex]y=0[/tex] and [tex]y=4[/tex]. The cross-sections perpendicular to the y-axis are circular disks with diameters running from the y-axis to the parabola [tex]x=\sqrt{10} y^2[/tex]. Find the volume of the solid.
For any given [tex]0\le y\le4[/tex], a cross section in that plane is a circle whose diameter is [tex]x=\sqrt{10}\,y^2[/tex] with thickness [tex]\Delta y[/tex]. Such a cross section contributes a volume of [tex]\pi \left(\frac x2\right)^2 \, \Delta y = \frac{5\pi}2 y^4 \, \Delta y[/tex].
As [tex]\Delta y\to0[/tex] and the number of cross sectional cylindrical disks increases without bound, the infinite sum of their volumes converge to the volume of the solid, given by the definite integral
[tex]\displaystyle \frac{5\pi}2 \int_0^4 y^4 \, dy = \frac{5\pi}2 \cdot \frac{4^5}5 = \boxed{512\pi}[/tex]
Solve the system by back substitution.
-4x - 8y - 2z - 6w = 5
3y + 18z + 6w = 24
z + w =2
-2w = -6
Solution should be set like {( _ , _ , _ , _ )}
The values of all the variables are:
w = -3z = 5y = -16x = 33 approxWhat are equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.Given equations:
-4x - 8y - 2z - 6w = 53y + 18z + 6w = 24z + w =2-2w = -6To find the values of x, y, w, and z:
-2w = -6w = -6/2w = -3Substitute (w = -3) in z + w = 2:
z + w = 2z -3 = 2z = 2 + 3z = 5Substitute (w = -3) and (z = 5) in 3y + 18z + 6w = 24:
3y + 18z + 6w = 243y + 18(5) + 6(-3) = 243y + 90 - 18 = 243y + 72 = 243y = 24 - 723y = - 48y = - 16Substitute (y = - 16), (w = -3) and (z = 5) in -4x - 8y - 2z - 6w = 5
-4x - 8y - 2z - 6w = 5-4x - 8(-16) - 2(5) - 6(-3) = 5-4x + 128 - 10 + 18 = 5-4x + 118 + 18 = 5-4x + 136 = 5-4x = 5 - 136-4x = - 131x = 131/4x = 32.75Rounding off: x = 33Therefore, the values of all the variables are:
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rewrite this expression using a positive exponent
[tex]\frac{1}{2^{-6} }[/tex]
Answer:
1/5 needs to be 20 words long
Evaluate the expression 3.8 +0+ y for the given values of y value value of expression -4.3 -1.6 0 5.2 -0.5
The answers are -0.5, 2.2, 3.8, and 9.0
We need to evaluate the expression 3.8 + 0 + y for the given values of y.
Let x = 3.8 + 0 + y
The values of y are -4.3, -1.6, 0, and 5.2
Let's substitute the value of y in the expression and calculate the values of x.
When y = -4.3, x = 3.8 + 0 + (-4.3) = 3.8 - 4.3 = -0.5When y = -1.6, x = 3.8 + 0 + (-1.6) = 3.8 - 1.6 = 2.2When y = 0, x = 3.8 + 0 + 0 = 3.8When y = 5.2, x = 3.8 + 0 + 5.2 = 3.8 + 5.2 = 9.0Refer to the attached image for the values of the expression corresponding to the values of y.
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Answer:
-0.5, 2.2, 3.8, and 9.0
Step-by-step explanation:
SOMEONE HELP WITH THIS PROBLEM
Answer:
y < 3x + 2
y> -2x + 2 The symbol should be > with a line under it to show greater than or equal to
Step-by-step explanation:
3x+18+4x+15=180 what is x
Answer:
x = 21
Step-by-step explanation:
Adding numbers:
3x+ 18 + 4x + 15 = 180
3x + 33 + 4x = 180
Combine Like terms:
3x + 33 + 4x = 180
7x + 33 = 180
Subtract:
7x + 33 - 33 = 180-33
7x = 147
Divide:
[tex] \frac{7x}{7} = \frac{147}{7} [/tex] x = 21I need help asap please!
Answer:
5x+10
Step-by-step explanation:
[tex](f \circ g)(x)=f(g(x)) \\ \\ =f(-5x-6) \\ \\ =-(-5x-6)+4 \\ \\ =5x+6+4 \\ \\ =5x+10[/tex]
If f(x)=3x-2 determine the value of y for each x value -4, 2, 3
Answer:
Step-by-step explanation:
y = f(x) = 3x -2
When x = -4,
y = 3(-4) -2 = -12-2 = -14
When x = 2,
y = 3(2) -2 = 6-2 = 4
When x = 3,
y = 3(3) -2 = 9-2 = 7
R6000 is deposited into a savings account. Four years later, R7000 is added to the savings. The interest rate for the first three years is 8% per annum compounded annually. Thereafter, the interest rate changes to 9% per annum compounded annually. Calculate the value of the savings at the end of the seventh year.
Answer:
R 19734.32
Step-by-step explanation:
If an amount P is deposited at R% interest compounded annually for n years, the amount at the end of n years is given by the formula
[tex]P = P(1 + r)^t[/tex]
r = R/100
Note
Interest rate 8% = 8/100 =0.08 for computation
Interest rate 9% = 8/100 =0.09 for computation
Since the interest rate changes after 3 years, the first thing to do is to find out how much the value is after 3 years
[tex]V(3 years) = 6000(1 + 0.08)^3[/tex] = 6000 x1.08³ = 6000 x 1.259712 = 7558.27
After 3rd year interest changes to 9%(0..09) but an additional amount is deposited
Let's find the value after the 4th year at 9% compounded annually using the general formula with r = 0.09 and t =1
V (after 4th year) = 7558.27(1.09)¹ = 7558.27 x 1.09 = 8238.51
We are depositing 7000 at the end of the 4th year so the principal becomes 8238.51 + 7000 = 15,238.51
This new amount accrues interest at 9% for 3 more years (7-4)
So value of savings at end of 7th year is
V = 15238.51(1+0.09)³ = 15238.51 x 1.259712 = 19734.32
Answer:
R19734.32
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Years 1-3Given:
P = R6000r = 8% = 0.08t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=6000(1+0.08)^3[/tex]
[tex]\implies \sf A=6000(1.08)^3[/tex]
[tex]\implies \sf A=6000(1.259712)[/tex]
[tex]\implies \sf A=7558.272[/tex]
Therefore, the amount in the account after 3 years was R7558.272.
Year 4The interest rate changed to 9%.
Given:
P = R7558.272r = 9% = 0.09t = 1Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=7558.272(1+0.09)^1[/tex]
[tex]\implies \sf A=7558.272(1.09)[/tex]
[tex]\implies \sf A=8238.51648[/tex]
Therefore, the value of savings at the end of the 4th year was R8238.51648.
Years 5-7After four years, R7000 was added to the account.
Given:
P = R8238.21648 + R7000 = R15238.21648r = 9% = 0.09t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=15238.21648(1+0.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.295029)[/tex]
[tex]\implies \sf A=19734.3207...[/tex]
Therefore, the value of the savings at the end of the seventh year is R19734.32.
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Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = 0.5 x + 2 intersect the circle with radius 5 and center (0, 2)?
At (4.472 , 4.236) in the first quadrant , the line with equation y = 0.5 x + 2 intersect the circle with radius 5 and center (0, 2) .
The equation of circle with center (h,k) and radius r can be written as
(x-h)²+(y-k)²=r²
In the given question
the center of the circle is (0,2) and the radius of the circle is 5 .
So the equation of circle become
(x-0)²+(y-2)²=5²
x²+(y-2)²=25 ...(i)
It is given that y=0.5x+2 intersects the circle
y = 0.5x+2
Rewriting the equation we get
y-2=0.5x
(y-2)=0.5x
x=(y-2)/0.5
x = 2(y-2) ...(as 0.5=1/2) ....(ii)
Squaring both sides
x² = (2(y-2))²
x² = 2²(y-2)²
x² = 4(y-2)² ...(iii)
Substituting the value of equation (iii) in equation (i) we get ,
4(y-2)²+(y-2)²=25
5(y-2)²=25
(y-2)²=25/5
(y-2)²=5
Taking Square root both the sides , we get
√(y-2)²=√5
y-2 = √5
y=(√5)+2
y=2.236+2
y=4.236
Substituting the value of y in (ii) we get
x=2(4.236-2)
x=2*2.236
x=4.472
Therefore , the circle with radius 5 and center (0, 2) will intersect the line with equation y = 0.5 x + 2 in the first quadrant at (4.472 , 4.236).
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What is the MEDIAN of this set of data?
10, 90, 80, 60, 50, 40, 70, 30, 20, 100
Answer:
your answer is 55 as shown by above photo ^^
Answer:
55
Step-by-step explanation:
1)
**
16 yd
A
8 yd
12 yd What is the area of the shape
Answer:
35 yd
Step-by-step explanation:
Right angle ABC is taken by a dilation with center P and scale factor 1/2 to angle A'B'C'. What is the measure of angle A'B'C'?
Answer: 90 degrees
Step-by-step explanation:
Dilations preserve angle measure.