Answers
2x+2x-8=16
4x-8=16
4x=24
x=6
y=6-4
y=2
Answer is C
Related Questions
Openstudy using synthetic division, what is the quotient (2x3 − 2x − 12) ÷ (x − 2)?
Answers
What is the volume of a right circular cone with a diameter of 21 centimeters and a height of 87 centimeters? Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
Answers
Volume=1/3πr^2h
therefore the volume of our cone will be:
π=3.14
h=87
r=21/2
Volume=1/3*3.14*(21/2)^2*87
=10,039.365 cm^2
930 miles to travel with a car that gets 22 miles per gallon. How much will it cost to travel if gas costs 2.03 a gallon?
Answers
_______________________________________________
Explanation:
_______________________________________________
(1 gal / 22 mi) * (930 mi) =
(1 gal / 22 mi) * (930 mi / 1) = {the units of "mi" ("miles" cancel out} ;
= (1 gal/ 22) * (930 / 1) = (1 gal * 930) ÷ (22 * 1) ;
= (930 gal) ÷ 22 ;
= (465 / 11) gal =
= 42 3/11 gal = 42.2727272727.... gal .
________________________________________________________
(456 /11) gal * ($ 2.03 / gal) =
$85.813636363636363581 -------> round to: $85.81 .
__________________________________________________________
A circle is drawn in the xy-coordinate plane. if there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are
Answers
either x, or y or both must be 0.
So we consider the points of the form (x, 0), (0, y) and (0, 0). These are the x and y intercepts.
A circle can touch the axes at 1, 2, 3 or 4 points but not more.
Check the picture for examples of all the cases.
Answer: n∈{1, 2, 3, 4}
Question 3 (Essay Worth 10 points)
(03.06 MC)
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325.
Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answers
To form the equation to represent total rent, we first need to establish the changing rate and the fixed cost. Changing rate is the fee for every one day the car is rented and fixed cost is the initial cost of the car rental.
To find the changing rate we divide the cost difference between two days by the difference of days
We have
$180 = 4 days
$ 325 = 9 days
The changing rate is [tex] \frac{325-180}{9-4}= \frac{145}{5}=29 [/tex]
The table below shows the working out of the price for each day the car is rented. We work out that day 0 cost $63 which means this is the fixed cost
Hence, the equation of total cost is [tex]y=29x+63[/tex], where [tex]y[/tex] is the total cost and [tex]x[/tex] is the number of days
PART B:
Using the function notation means we will use [tex]f(x)[/tex] instead of [tex]y[/tex], so the equation is
[tex]f(x)=29x+63[/tex]
PART C:
To graph the function, we first need to set the scales on the x-axes and y-axes.
The scale on x-axes could go up in ones but must start from 0
The scale on y-axes, since it is much bigger values, we can go up in 50
We then plot on the graph for each pair of days and cost. The plots should give us a straight line graph
One example of the graph is shown below
f-7 over g equals h, sole for f
Answers
Suppose that f(x)=x^2 and g(x)= -4/5x^2 which statement best compares the graph of g(x) with the graph of f(x)
Answers
Answer: the graph of g(x) is the graph of f(x) compressed vertically
Step-by-step explanation:
If x = 3 is a zero of the polynomial function f(x) = 2x3 + x2 − 25x + 12, which of the following is another zero of f(x)? ASAP
Answers
The other zeros of the polynomial if 3 is a zero is -4 and 1/2
If x = 3 is a zero of the polynomial function f(x) = 2x3 + x2 − 25x + 12, then x - 3 is a factor.
To get the other factor we will take the division of the polynomial and the factor to have:
2x^3 + x^2 − 25x + 12/x - 3 = 2x² + 7x - 4
Factorize 2x² + 7x - 4
2x² + 7x - 4 = 0
2x² + 8x - x- 4 = 0
2x(x+4)-1(x+4) = 0
(x+4)(2x-1) = 0
x = -4 and 1/2
Hence the other zeros of the polynomial if 3 is a zero is -4 and 1/2
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question is in the image
Answers
(x^n)^m = x^mn
This states that the final exponent of the variable or the expression is the product of the exponents.
For this item, we can rewrite the given as,
(1000m³n¹²)^(1/6)
If we multiply the exponents to 1/6, we get
(1000^1/6) x (m^1/2) x (n^2)
Also, it should be noted that 1000 = 10³. Hence, the final answer would be,
(10^1/2) x (m^1/2) x (n^2)
Simplifying this,
ANSWER: n² √10m
The answer is letter A.
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches. The area of the top of the plate is ____ inches squared.
Answers
Answer:
42 Inches squared ( hope that helps) ;)
The area of the top of the plate will be 42 inches squared.
What is the area of the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches.
Then the area of the triangle is given as,
Area = 1/2 x 12 x 7
Area = 6 x 7
Area = 42 square inches
The area of the top of the plate will be 42 inches squared.
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The diameter of a beach ball is 10 inches. How many cubic inches of air can the beach ball hold? Use 3.14 for pie . Round to the nearest tenth of a cubic inch
Answers
volume = 4/3 x PI x r^3
r = 10/2 =5
V = 4/3 x 3.14 x 5^3 = 523.333
523.3 cubic inches
Identify the function that best models the given data.
Answers
B) 3.125x^2 - 14.5x + 208.5
To prove this you plug 6 (which is the number of trees) instead of x
3.125x^2 - 14.5x + 208.5
3.125(6)^2 - 14.5(6) + 208.5
112.5 - 87 + 208.5
=234
Answer: W(i) = 3.125x^2 − 14.5x + 208.5
Step-by-step explanation:
How would you convert the repeating, nonterminating decimal into a fraction? Explain the process as you solve the problem. 0.1515
Answers
Let x = 0.1515..
100x = 15.15..
x = 00.15... Now subtract:-
------ --------
99x = 15
so 99x = 15 giving x = 15/99 answer
Answer:
5/33
Step-by-step explanation:
x = 0.1515
100 x = 15.1515
100 x - x = 15.1515 - 0.1515
99 x = 15
x = 15 / 99 = 3 ∙ 5 / 3 ∙ 33 = 5 / 33
0.15165 = 5 / 33
the polynomial (x - 2) is a factor of the polynomial 3x2 - 8x + 2.
Answers
First, let's factor 3x²-8x+2
Looking at wee can see that the first term is and the last term is where the coefficients are 3 and 2 respectively.
Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient -8? Let's list all of the factors of 6:
Factors of 6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 6
1*6
2*3
(-1)*(-6)
(-2)*(-3)
note: remember two negative numbers multiplied together make a positive number
Now, which of these pairs add to -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8
None of these pairs of factors add to -8.
So the expression 3x²-8x+2 cannot be factored.
So (x - 2) is NOT a factor of 3x²-8x+2
So the statement is false
Answer:
B.false
Step-by-step explanation:
apexs
To which real number subset(s) do the following real numbers belong?
-4, -2, 1, 3, 5
A. whole numbers
B. natural numbers
C. integers and rational numbers
D. natural and irrational numbers
Answers
If the probability of an event is 0.7 repeating, what are the odds against the event
Answers
A grab bag contains 8 football cards and 2 basketball cards. an experiment consists of taking one card out of the bag, replacing it, and then selecting another card. determine whether the events are independent or dependent. what is the probability of selecting a football card and then a basketball card? express your answer as a decimal.
Answers
8 football, 2 basketball...total of 10
P(1st pick is football) = 8/10 which reduces to 4/5
replace
P(2nd pick is basketball) = 2/10 which reduces to 1/5
P (both) = 4/5 * 1/5 = 4/25 = 0.16 <==
Answer:
Independent - 0.16
Step-by-step explanation:
The number of points awarded in each round of a game can be represented by f(x) = 2x, where x represents the number of the round.
What is x when f(x) = 16?
Answers
2x=16 divide both sides by 2
x=8
Answer:
x=4; in round 4, 16 points will be rewarded
How much money will you have at the end of one year if interest is compounded semiannually at 10% on a $600 deposit? A. $661.50 B. $662.00 C. $660.00 D. $659.50
Answers
Compound interest on a principal of $600.00 at a rate of 10% per year compounded twice per year over a period of one year results in an accumulated total of $661.50 (principal plus interest).
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
A = P(1 + r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
P = principal (the initial deposit amount) = $600
r = annual interest rate = 10%
n = the number of compounding periods per unit of time = 2
t = 1
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt}[/tex]
A = 600.00(1 + 0.1/2[tex])^{(2)(1)}[/tex]
A = 600.00(1 + 0.05[tex])^{(2)}[/tex]
A = $661.50
Therefore, the amount is $661.50.
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There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed. Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points) Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points) Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)
Answers
To solve this problem, let us first assign variables. Let us say that:
X = number of marigold plants
Y = number of sunflower plants
n = number of months
We can see that in the given problem, X is decreasing by a percentage, this means that we have to set-up a geometric equation while for Y the decrease is linear so we set-up an arithmetic equation.
Part A.
For marigold plants X, a geometric sequence has a general form of:
X = Xo * (1 + r)^n
where r = -15% = -0.15 (negative since it is decreasing)
Xo = the initial amount of marigold plants = 150
X = 150 * (1 – 0.15)^n
X = 150 (0.85)^n
For the sunflower plants Y, an arithmetic sequence has a general form of:
Y = Yo + d * n
where d = -8 and Yo = 125
Y = 125 – 8 n
Part B. For n = 3
X = 150 (0.85)^3 = 92.12 = 92
Y = 125 – 8 (3) = 101
Part C. From Part B we see that the two values are very far from each other when n = 3, therefore they must be similar when n < 3. So we try n = 2
X = 150 (0.85)^2 = 108.38 = 108
Y = 125 – 8 (2) = 109
Therefore the two plants have approximately similar amount after 2 months.
Given that jklm is a rhombus, find kjm.
a. 37°
c. 106°
b. 74°
d. 143°
Answers
Answer:
C.
Step-by-step explanation:
what is the reciprocal of 8-3i
Answers
The reciprocal of the complex number 8-3i is found by dividing its complex conjugate (8+3i) by the modulus squared of 8-3i, which is 73. The result is 8/73 + 3i/73.
Explanation:The reciprocal of a complex number is the complex conjugate of that number divided by the modulus squared of the original number. In the case of the complex number 8-3i, its complex conjugate is 8+3i. To find the reciprocal of 8-3i, you would divide this complex conjugate by the modulus squared of 8-3i.
First, calculate the modulus squared of 8-3i:
Modulus of 8-3i = sqrt(82 + (-3)2) = sqrt(64 + 9) = sqrt(73).Modulus squared = (sqrt(73))2 = 73.Then, divide the complex conjugate by this modulus squared to get the reciprocal:
Reciprocal of 8-3i = (8+3i) / 73 = 8/73 + 3i/73.
Which of the following is not a way to represent the solution of the inequality 2(x − 1) less than or equal to 10? (1 point)
A. x less than or equal to 6
B. 6 greater than or equal to x
C. A number line with a closed circle on 6 and shading to the left
D. A number line with a closed circle on 6 and shading to the right
Answers
A and B are the same and C is proven wrong due to the equality sign lkeaving only D to be correct
How to algebraically find the limit of a function as x approaches infinity?
Answers
Well... One way you can do this is by testing a set of arrays and see the trend. If I chose to find what y1 is in (100, y1) and what y2 is in (101, y2), I would find the difference between y2 and y1. If y2 - y1 is positive, this means there is a positive relationship and y is also approaching POSITIVE infinity. A negative relation means that it is approaching NEGATIVE infinity. However, it could be approaching a single number like "4" for instance, and you just need to plug in the right number of data sets to make that educated guess.
Formula Example:
5 + 1 / (x + 1) will always approach 5 because "1 / (x + 1) will approach 0".
Hope this helps.
To algebraically find limit of a function as "x" approaches infinity, identify highest degree term, divide by "x", and evaluate the resulting expression.
To algebraically find the limit of a function as x approaches infinity, we can follow the below steps :
(i) Identify the highest degree term: Determine the term with the highest power of x in the function.
(ii) Ignore lower degree terms: If the highest degree term is dominant, ignore lower degree terms and constants.
(iii) Divide by x: Divide every term in the function by x raised to the power of the highest degree.
(iv) Evaluate the limit: Examine the resulting expression as x approaches infinity. If the expression tends to a finite value, that is the limit. If the expression diverges (goes to infinity or negative infinity), then the limit does not exist.
By simplifying the function and observing the behavior of the resulting expression, we can algebraically determine the limit of the function as x approaches infinity.
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find multiplicative inverse of 2+3i / 3-2i
Answers
( 2 + 3 i ) / ( 3 - 2 i ) * ( 3 + 2 i ) / ( 3 + 2 i ) =
= ( 2 + 3 i ) * ( 3 + 2 i ) / ( 9 - 4 i² ) = → we use difference of squares
= ( 6 + 4 i + 9 i + 6 i² ) / ( 9 + 4 ) = → because : i² = - 1
= ( 6 + 13 i - 6 ) / 13 =
= 13 i / 13 = i
Answer: i.
The price of bananas is $6.50 for 5 pounds. What is the price as a unit rate?
$6.50/1lb
$1.30/1lb
$1/30/3lb
$1.05/1lb
Answers
A unit rate is when ratios are expressed as a quantity of one. To change $6.50 for 5 pounds to a unit rate, you must divide everything by 5 in order to get the price for one individual pound. $6.50 / 5 = $1.30, so the price of $6.50 for 5 pounds as a unit rate is $1.30/1 lb.
There are 36 students on the bus. There are 2 times as many girls than boys on the bus. On your paper, write a system of liner equations and solve for the number of girls and boys on bus. How many girls are on the bus. A-12 B-24 C-17 D-19
Answers
y = boys
z = students in the bus
x + y = z
x + y = 36
total girls = 2 * total boys
x = 2 * y
2y + y = 36
3y = 36
y = 12
x = 2y = 24 (B)
Final answer:
To find the number of girls and boys on the bus, create a system of linear equations and solve for the variables. In this case, there are 12 boys and 24 girls on the bus.
Explanation:
To solve for the number of girls and boys on the bus:
Let G represent the number of girls and B represent the number of boys.
From the problem, G = 2B and G + B = 36.
Substitute G = 2B into the second equation to get 2B + B = 36, which gives B = 12. Therefore, there are 12 boys and 24 girls on the bus.
The x-intercept of the graph of f(x)= 3log(x-5)+2 is:
Answers
Answer: [tex]\frac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51
Step-by-step explanation:
The given function : [tex]f(x)= 3\log(x-5)+2[/tex]
We know that , the x-intercept is the point on graph( basically intersection of graph and x-axis) where y coordinate is zero.
I.e. for x-intercept of function , f(x) =0
i.e. [tex]0= 3\log(x-5)+2[/tex]
[tex]\Rightarrow\ \log(x-5)=\dfrac{-2}{3}[/tex]
Taking exponent on both sides , we get
[tex]x-5=e^{\frac{-2}{3}}\\\\\Rightarrow\ x=e^{\frac{-2}{3}}+5\ \ or\ \ x=\dfrac{1}{e^{\frac{2}{3}}}+5[/tex]
On simplification , [tex]\frac{1}{e^{\frac{2}{3}}}+5\approx5.51[/tex].
Hence , the x-intercept of the graph f(x)= [tex]\dfrac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51.
Answer:
10^-2/3 +5
Step-by-step explanation:
Find the value of X and Y. Show your work.
Answers
7x = 31 + 4
7x = 35
x = 35/7
x = 5
4y + 8 = 24
4y = 24 - 8
4y = 16
y = 16/4
y = 4
4/101.78 do long divison for this problem
Answers
✌️ Good luck on your assignment ✌️