In the xy-plane, the graph of y = 3x^2 -14x intersects the graph of y = 2 at the points (0,0) and (a, a). What is the value of a?
Answers
We have a parabola
\(y=3x^2-14x\)and a line y=2
If we graph the two functions we obtain
we can obtain the ordered pairs where the equations intercept each other when y=2 in the parabola equation and finding the values of x
\(2=3x^2-14x\)Solving the equation we find two values for x so we have
\(\begin{gathered} x_1=-0.14 \\ x_2=4.8 \end{gathered}\)the ordered pairs are
(-0.14,2) and (4.8,2)
as we can see the points given in the question are wrong because at the points given the value of y will be different to 2, for example in (0,0 ) the line and the parabola do not intersect each other.
Related Questions
Suppose you and a friend form a band. You want to record a demo. Sony Studios rents for $150 plus $20 an hour. Capitol Studios rents for $200 plus $15 an hour. Use a system of equations to help you to determine when the studios charge the same amount.
at what number of hours do the studios charge the same amount?
Answers
Answer:
200 < 225 + 80x < 550
The 200 is the amount the Jenna currently have.
225 + 80x is the amount that Jenna has to pay given x number of hours.
550 is the sum of Jenna's 200 and additional 350 she can get by selling pre-ordered Cds. This is the maximum amount she can pay for the studio rental and sound technicians.
Step-by-step explanation:
225 + 80x < 550
80x < 550 -225
80x < 325
80x / 80 < 325/80
x < 4.06 or 4 hours
225 + 80x → 225 + 80(4) = 225 + 320 = 545
The number of hours for the sound technician will range from 1 hour to 4 hours.
Assuming they will use 6 hours.
225 + 80(6) = 225 + 480 = 705
705 - 550 = 155
Jenna has to raise an additional $155 to pay off the studio rent and 6 hours of sound technicians.
this might be wrong but, i hope it helps
Answer:
Step-by-step explanation: times the hour by four on each and get 60 then it would be an equal pay for the hours.
I don’t understand this I don’t know if I’m supposed to draw or what ?
Answers
Given that p(x)=2(5−x)2+1 , what is the value of p(-4)? Responses
Answers
Answer:
37
Step-by-step explanation:
x=-4
=2(5-(-4)2+1
=2(5+4)2+1
=2(9)2+1
=18(2)+1
=36+1
=37
What is the slant height of the cone?
Answers
The slant height of the cone is 12.6 units
What are solids ?
A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.
h= 12
diameter = d = 8
so, radius, r = d/2 = 8/2 = 4
Formula for slant height , l is:
l = √(h² + r²) = √(12² + 4² )
= √(144 + 16) = √160 = 12.649 ≈ 12.6 units
The slant height of the cone is 12.6 units
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you have been provided the code that generates a list l1. this list will be the input of a function f(x) that you have to write. the function f(x), where x is a numerical list, should return a list with only those elements in l1 that are odd.
Answers
This will only include the odd elements from the input list l1 in the list that is produced.
Here's an example implementation of the function f(x) that takes a list x as input and returns a list with only the odd elements from x:
python
def f(x):
# Initialize an empty list to hold the odd elements
odd_list = []
# Iterate over each element in the input list x
for elem in x:
# Check if the element is odd
if elem % 2 != 0:
# If the element is odd, append it to the odd_list
odd_list.append(elem)
# Return the list containing Only the odd elements
return odd_list
You can call this function by passing the l1 list as an argument, like this:
python
l1 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
odd_elements = f(l1)
print(odd_elements) # Output: [1, 3, 5, 7, 9]
This will output a list with only the odd elements from the input list l1.
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Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is
shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²
= √1 + 4
= √5
-
What error, if any, did Heather make?
A. She substituted incorrectly into the distance formula.
B. She subtracted the coordinates instead of adding them.
C. She made a sign error when simplifying inside the radical.
OD. She made no errors.
Answers
The distance between points R and S is \(\sqrt{ (185)\). The correct answer is D. She made no errors.
Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²= √1 + 4
= √5
The error is with the order of subtraction in the formula for the distance between two points.
Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.
The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;
dAB = \(\sqrt{ ((x^2 - x1)^2 + (y2 - y1)^2)\)
Comparing the given question with the formula above, we have;
A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.
Therefore, we have;
RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)
On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS
= \(\sqrt{ (8^2 + 11^2)RS\)
= \(\sqrt{ (64 + 121)RS\)
= \(\sqrt{ (185)\)
Therefore, the distance between points R and S is \(\sqrt{ (185)\).
From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.
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Sofia proposes that the class decompose the bench into rectangular prisms, calculating the volume of each prism, and then adding up the volumes. Use Sofia’s strategy to determine the volume of the bench.
Answers
Using Sofia's strategy, the volume of the bench is calculated as: 1.404 cubic meter.
Note the following:
The bench is shown in the diagram attached below. The bench is made up of several cubes.1 cube has a side length of is 0.3 meters.Volume of rectangular prism = \(l \times h \times w\)To find the volume of the bench, we would decompose the bench into three rectangular prisms (Sofia's Strategy).
The first rectangular prism has:
length (l) = 1.2 m (4 cubes long)height (h) = 0.6 m (2 cubes high)width (w) = 1.2 m (4 cubes wide)Volume of the first rectangular prism = \(1.2 \times 0.6 \times 1.2 = 0.864 $ m^3\)
The Second rectangular prism has:
length (l) = 0.6 m (2 cubes long)height (h) = 0.6 m (2 cubes high)width (w) = 0.3 m (1 cube wide)Volume of the first rectangular prism = \(0.6 \times 0.6 \times 0.3 = 0.108 $ m^3\)
The Third rectangular prism has:
length (l) = 1.2 m (4 cubes long)height (h) = 0.6 m (2 cubes high)width (w) = 0.6 m (2 cubes wide)Volume of the first rectangular prism = \(1.2 \times 0.6 \times 0.6 = 0.432 $ m^3\)
Volume of the bench will be: 0.864 + 0.108 + 0.432 = 1.404 cubic meter.
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Edwin sells jars of jam for $1.90 each. Determine how many jars of jam Edwin needs to sell to break even if the variable cost per jar is $1.10 and fixed expenses are $35,700.00 per year.
Answers
Edwin needs to sell 44,625 jars of jam to break even.
To determine how many jars of jam Edwin needs to sell to break even, we'll calculate the breakeven point using the following formula:
Breakeven Point = Fixed Expenses / (Selling Price per Unit - Variable Cost per Unit)
Given information:
Selling Price per Unit (SP) = $1.90
Variable Cost per Unit (VC) = $1.10
Fixed Expenses = $35,700.00 per year
Plugging in the values into the formula:
Breakeven Point = $35,700 / ($1.90 - $1.10)
Breakeven Point = $35,700 / $0.80
Breakeven Point = 44,625 jars
Therefore, Edwin needs to sell 44,625 jars of jam to break even.
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Megan's room was remodeled. The new area of the room is 175% of the previous area. Only the length of the room changed. The width of the original room is 4m and the length of the original room is 4m. If the new room adds X to the length, what is the new expression for the new area? How many square meters has Megan's room increased? Explain how you solved the new area.
Answers
Answer:
new area = 7m (length) x 4m (width) = 28; an increase of 12 sq meters
Step-by-step explanation:
Original area must have been 16 because both the length and width were 6 meters.
175% of 16 is 12, meaning the length must be increased from 4 to 7 to get 28 when multiplied by a width of 4m
−0.22+�−0.33−0.22x+x−0.33x?
Answers
The answer to the equation −0.22x + x − 0.33x is 0.11x.
The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:
−0.22x + x − 0.33x = −0.22 + 0.33x
We then subtract x from both sides of the equation, resulting in:
−0.22x − x = −0.22 + 0.33x − x
We then combine like terms on the left side of the equation, resulting in:
−1.22x = −0.55
Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:
x = 0.11
Therefore, the answer is 0.11x.
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Complete question
What is the value of -0.22+−0.33−0.22x+x−0.33x?
What is greater 6ft or 300cm
Answers
I think it; 300cm is greater.
Why; 300 cm make 9 ft.
9 ft > 6 ft
300cm is greater than 6 ft.
What is unit conversion?Unit conversion is a multi-step procedure that includes rounding, selecting the appropriate number of significant digits, and multiplying or dividing by a numerical factor.
For this problem, we need to do a unit conversion between ft and cm. since,
1 ft = 30.48 cm
6 ft = 182.88 cm.
Therefore 300cm is greater than 6 ft.
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D) What is the greatest common factor of 45 and 30?
Answers
Answer:15
Step-by-step explanation:
i did the math
Answer:
15
Step-by-step explanation:
15 x 2=30
15x3=45
What two numbers add up to -2 and multiple to 10
Answers
There are no two Real numbers that add up to -2 and multiply to 10.
The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:
Equation 1: x + y = -2
Equation 2: x * y = 10
To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:
1. Solve Equation 1 for x:
x = -2 - y
2. Substitute the value of x in Equation 2:
(-2 - y) * y = 10
3. Simplify the equation:
-2y - y^2 = 10
4. Rearrange the equation to standard form:
y^2 + 2y + 10 = 0
5. Since the equation is a quadratic equation, we can apply the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 2, and c = 10.
6. Calculate the discriminant: b^2 - 4ac:
2^2 - 4(1)(10) = 4 - 40 = -36
7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.
In conclusion, there are no two real numbers that add up to -2 and multiply to 10.
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Is -8+12i or 12i an imaginary number
Answers
A political scientist surveys 20 of the current 136 representatives in a state's legislature. What is the size of the sample : what is the size of population
Answers
Answer:
The size of the sample is 20.
The size of population is 136.
Step-by-step explanation:
In statistics, a sample is a portion or subset of a larger population. In this case, the political scientist has surveyed 20 of the 136 representatives in the state's legislature, so the size of the sample is 20.
The population is the complete set of individuals or items under consideration. In this case, the population is the entire set of 136 representatives in the state's legislature, so the size of the population is 136.
By surveying a sample of representatives, the political scientist can make inferences or draw conclusions about the population as a whole. However, the sample size will affect the precision and accuracy of these inferences. The larger the sample size, the more likely it is that the sample represents the population well.
I would greatly appreciate Brainliest.
Have a nice day.
slove the equation fully
Answers
Step-by-step explanation:
I solved it in my notebook
solve 1/2x + 6y = 12 y = x + 15
Answers
The value of x is -12.07, and y is 3.07 for equation 1/2x + 6y = 12, y = x + 15.
We have to solve the given equations, 1/2x + 6y = 12 y = x + 15.
Equation; 1/2x + 6y = 12 and y = x + 15.
The given equations are solved by using the elimination method following all the steps given below.
The equations are,
\(\dfrac{1}{2}x + 6y = 12\\\\y = x+15\)
Substitute the value of y in equation 1 from equation 2,
\(\dfrac{1}{2}x + 6(x+15) = 12\\\\\dfrac{1}{2}x + 6x + 90 = 12\\\\\dfrac{x+12x+180}{2} = 12\\\\13x + 181 = 12 \times 2\\\\13x + 181 = 24\\\\12x = 24-181\\\\12x = -157\\\\x = \dfrac{-157}{13}\\\\x = -12.07\)
Substitute the value of x in equation 2,
\(y =- 12.07+15\\\\y = 3.07\)
Hence, The required value of x is -12.07, and y is 3.07 for equation 1/2x + 6y = 12, y = x + 15.
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15 points! please help me out!
Answers
Answer: 260 ft^2
Step-by-step explanation:
Find the area of the triangle: 0.5*height*base = 0.5*10*20 = 100 ft^2
Find the area of the rectangle: 20*8 = 160 ft^2
Add them together: 160+100 = 260 ft^2
Khali has a box with the dimensions shown. He plans to cover the box with glitter What is the total surface area to be covered with glitter? Show your work
Answers
Answer:
162
Step-by-step explanation:
4.5x9x4
What is the difference?
-3 2/3 - (-2 1/4)
Answers
let's firstly convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)
find the equation of the line
Answers
Answer:
y = 1/2x + 1/2
Step-by-step explanation:
I'm going to give me answer is gradient/slope form :
To work out the gradient we make a triangle from the line and do :
change in y / change in x
You should get 1/2
Now we have y=1/2x + c
to work out c we substitute a point from the line and solve for c :
Point (1 , 1)
1 = 1/2(1) + c
1 = 1/2 + c
c = 1/2
So our final answer is y = 1/2x + 1/2
Hope this helped and have a good day
Scupper Molly invested $1,800 semiannually for 23 years at 8% interest compounded semiannually. What is the value of this annuity
due? (Please use the following provided Table.) (Round your answer to the nearest cent.)
Annuity due
Answers
Answer:
the amount of a $3,000.00 annuity due at 12 percent compounded semiannually for 3 years. A. $334,321.00 B. $43,068.93 C. $22,180.50 D. $41,814.50
The amount of the annuity due in 23 years with 8% of interest compounded semiannually is $62053.35.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Scupper Molly invested $1,800 semiannually for 23 years at 8% interest compounded semiannually.
Then the amount of the annuity due will be
\(\rm A = 1800 (1 + 0.08)^{2\times 23}\\\\A = 1800 (1.08)^{46}\\\\A = 1800 \times 34.474\\\\A = 62053.35\)
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Find the surface area of the pyramid represented by the net.
A net showing 4 triangles and a square. The square has a length and width of 4 meters and the triangles have a base of 4 meters and a height of 7 meters.
Answers
Step-by-step explanation:
You have EIGHT triangles that have base 2 and height 7
area of triangle = 1/2 * b * h
eight of them : EIGHT * 1/2 * 2 * 7 = 56 m^2
PLUS one square that is 4 x 4 = 16 m^2
total = 56 + 16 = 72 m^2
What are the factors of 42 to find it’s prime numbers and how do I put it in a factor tree
Answers
To create a factor tree for 42, we start by finding a pair of factors of 42, such as 2 and 21 and factor each branch until we have prime numbers.
Answer:
See below
Step-by-step explanation:
Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.
Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.
OK WHAT IS THE FRACTION FORM OF THE RATIO 1:3
Answers
Answer:
Part A is 1/4
Part B is 3/4
Step-by-step explanation:
1(A):3(B)
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Alexandra is a head librarian in a city with a population of 1.8×106 residents. When her library system conducted a survey, they found that the average resident visits a library 1.5 times per year. How many total library visits per year does that work out to?
Write your answer in standard form. Do not use exponents. THE ANSWER IS 2,700,000 YOUR WELCOME...
Answers
The total number of library visits per year is 2.7 million, written in standard form as 2.7×106.
What is average?Average refers to the central tendency or typical value of a set of numerical data, which is obtained by dividing the sum of the values by the total number of values. It is a commonly used statistical measure that helps to represent the general trend or level of a dataset. The average can be calculated for various types of data, such as income, age, weight, and test scores, among others.
According to the given information:
To calculate the total number of library visits per year, we need to multiply the average number of visits per resident by the total population:
Total number of library visits per year = average visits per resident x total population
Substituting the given values, we get:
Total number of library visits per year = 1.5 x 1.8×106
Multiplying, we get:
Total number of library visits per year = 2.7×106
Therefore, the total number of library visits per year is 2.7 million, written in standard form as 2.7×106.
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Heng tried to define a reflection across line r.
• Any point N on line r maps to itself.
• Any point M not on the line of reflection maps to a point M' such that the midpoint L of MM' is
on liner.
Which counterexample shows that Heng's definition does not fully define a reflection?
Choose 1 answer:
Answers
Answer:
Any point N on line r maps to itself.
Step-by-step explanation:
Reflection is one of the examples of solid transformation in which a given point, segment, or figure is flipped over a reference point or line to produce its image. The distance of the object to the reference point or line is the same as the distance of its image to the point or line. And both have the same size, but different orientation.
The option that does not fully define a reflection is; any point N on line r maps to itself, because no image of point N is produced after the operation.
Answer:
C. This matches Heng's definition, but is not a reflection, because MM'MM
′
M, M, prime is not perpendicular to line rrr.
Step-by-step explanation:
3. In an experiment a scientist mixes together three substances. She mixes 18.42 g of
substance A. _ 5.8 g of substance B and 0.75 g of substance C.
Then she divides the mixture equally into four containers.
What is the mass of the mixtures in each container?
Give your answer correct to two decimal places.
Answers
Answer:
6.24
Step-by-step explanation:
A= 18.42g, B = 5.8g,C = 0.75g
Total = 18.42 + 5.8 + 0.75
= 24.97g
Then divided into four equal parts
= 24.97g/4
= 6.2425g
= 6.24g
Find the sum of the first 8 terms of the fallowing sequence?
3,15,75,375 …
Answers
Answer:
\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)
Three research departments have 6, 9,
and 7 members, respectively. Each
department is to select a delegate
and an alternate to represent the
department at a conference. In how
many ways can this be done?
Answers
Answer:
I don't know because I don't understand what you mean