Two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.
Which functions could be the result of the combinations? Select two options.
A. 16x – 12
B. 17x – 12
C. 72x2 – 96x
D. 72x2 + 108x
E. 72x2 – 204x + 144
Answers
Answer:
Step-by-step explanation:
We can eliminate options C and D quite quickly because factoring either one would have one equation be y = x and the other either y = 72x - 96 or y = 72x + 108. Neither of these added to x will give either option A or B
so that leaves E.
72x² – 204x + 144 = 0
we can find the zeros
x = (204 ± √(204² - 4(72)(144))) / (2(72))
x = (204 ± 12) / 144
x = 1.5
x = 4/3
so the equation has factors
(x - 1.5)(x - 4/3)
and therefore also a factor in their product
x² - (\(\frac{17}{6}\))x + 2
which is 1/72 of the original quadratic
so all factors of E are
72(x - 1.5)(x - 4/3)
now we need to distribute factors of 72 among the other two factors so that when we add them together the x¹ terms are either 16 or 17 and the x⁰ terms sum to -12. let "a" and "b" be the factors of 72.
ab = 72
a = 72/b
-1.5a - 4b/3 = -12
1.5a + 4b/3 = 12
1.5(72/b) + 4b/3 = 12
108/b + 4b/3 = 12
324/b + 4b = 36
324 + 4b² = 36b
81 + b² = 9b
b² - 9b + 81 = 0
b = (9 ±√(9² - 4(1)(81))) / 2(1))
b = (9 ± √-243) / 2
as both of these roots are imaginary numbers
there is no valid solution to this problem as posed
IF we allow a slight edit to answer B, we can factor 72 into 9•8
y = 8(x - 1.5) y = 9(x - 4/3)
y = 8x - 12 y = 9x - 12
so the sum of the two would be 17x - 24
Related Questions
Can someone please help, ty!!
Will mark brainliest!
Answers
Answer:
34
Step-by-step explanation:
The sum of the angles of a triangle is 180
26x+6 + 21x-1 +11x+1 = 180
Combine like terms
58x +6 = 180
Subtract 6 from each side
58x = 180-6
58x = 174
Divide by 58
58x/58 =174/58
x=3
We want <C
<C = 11x+1 = 11*3+1 = 33+1 = 34
Billy plotted −3 4 and −1 4 on a number line to determine that −3 4 is smaller than −1 4 . A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. A point is 1 mark to the right of negative 1, and another point is 1 mark to the left of 0. Is he correct? Explain why or why not.
Answers
Answer:
Sample Response: Yes, Billy is correct. The fractions are placed on the correct tick marks. The smaller fraction is located to the left of the larger fraction.
Step-by-step explanation:
Find the lateral surface area below given prism:
Answers
Answer:
the answer should be 158 but I'm not a hundred percent sure
Which sequence shows the numbers in order from least to greatest?
A. -2.14<3.16227766017<2.8
B. 2.8<3.16227766017<2.14
C. 2.14<3.16227766017 <2.8
D. 2.14<2.8<3.16227766017
Answers
The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.
The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.
They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:
< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?
A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.
The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.
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If an orthocenter lies inside of a triangle, then the triangle must be O isosceles. O acute. obtuse. o right
Answers
If an orthocenter lies inside of a triangle, then the triangle must be acute.
Orthocenter of a triangle is the intersection of any two of three altitudes of a triangle. The third altitude usually pass through the point of the first two altitudes.
When the orthocenter lies inside a triangle, the angles formed by the intersection of the three altitudes is less than 90 degrees.An acute triangle is a type of triangle whose angles are less than 90 degrees.Thus, If an orthocenter lies inside of a triangle, then the triangle must be acute.
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Answer:D ( acute)
Step-by-step explanation:
edg
What is the value of x?
P
80°
x+84°
3x
R
Q
Answers
Answer:
x = 49
Step-by-step explanation:
The sum of angles is 360
(x + 84) + 80 + 3x = 360
x + 3x = 360 - 84 - 80
4x = 196
x = 196/4 = 49
reduce to simplest form
-3/2 - 3/8
Answers
Answer:
To add or subtract fractions, they must have a common denominator. In this case, the denominators of the fractions are 2 and 8, which are not the same. To find the least common multiple of 2 and 8, we can list the multiples of each number and find the smallest one that is common to both:
2: 2, 4, 6, 8, 10, 12, 14, ...
8: 8, 16, 24, 32, ...
The least common multiple of 2 and 8 is 8. Therefore, to add or subtract the fractions, we must convert them to have a denominator of 8.
-3/2 = -12/8 and 3/8 = 3/8
So, -3/2 - 3/8 = -12/8 - 3/8
Now we can subtract the fractions directly:
-12/8 - 3/8 = -12 - 3 / 8
= -15/8
Therefore, the simplified form of -3/2 - 3/8 is -15/8
Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
Answers
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot.
In 2019, 147,400 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was Xbar=282. We want to estimate the mean score in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation =40.
If we take many samples, the sample mean Xbar varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score in the population. What is the standard deviation of this sampling distribution?
Give your answer to four decimal places.
Answers
The standard deviation of the sampling distribution is approximately 0.3292.
What is central limit theorem?The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.
Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.
The standard deviation is given by the formula:
SD = σ/√(n)
Now, substituting the value of σ = 40, n = 147,400 we have:
SD = σ/√(n) = 40/√(147400) ≈ 0.3292
Hence, the standard deviation of the sampling distribution is approximately 0.3292.
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find the area of a polygon with the given vertices W (3,4), X (7,4), Y (7,1), Z (3,1)
Answers
Answer: 12 units²
Finding what formula to use:
I can see that we have pairs of points with the same x-coordinate values and the same y-coordinate values. This leads me to believe the polygon given is a rectangle. To check, I will graph the points given. After graphing, it appears I was correct! Now we can solve this problem.
-> See attached
Step-by-step explanation:
Since this is a rectangle, we will use A = L * W
A = L * W
A = 4 * 3
A = 12
A = 12 units²
The area of the given polygon is 12 units².
PLEASE HELP ME ITS DUE TODAY!!!
Answers
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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What is 1-1/2? Savas Realize math problem
Answers
\( \frac{1 - 1}{2} = \frac{0}{2} \)
the result is 0
Help please...............
Answers
Caleb brought groceries and paid $1.60 in sales tax. The sales tax rate is 2.5%. What was the price of caleb’s groceries, before tax?
Answers
Answer:
$64
Step-by-step explanation:
We can set up a percentage proportion to find the value Caleb's groceries before tax.
\(\frac{1.60}{x} = \frac{2.5}{100}\)
We can cross multiply to find the value of x.
\(100\cdot1.60=160\\\\160\div2.5=64\)
So the original cost before tax was $64.
Hope this helped!
Answer:
$1.64
Step-by-step explanation:
We need to find the before tax price so let that be x
100-2.5% = 97.5% (since this is the reduction before the sale)
Turn this percentage into a decimal so 0.975
To find x we must remember this price multiples 0.975 to give us $1.60
x * 0.975 = 1.60
x = 1.60 / 0.975
x = 1.64 (2dp)
Makayla invested $130. She earned a simple interest of 4% per year on the initial investment.
If no money was added or removed from the investment, what was the amount of interest Makayla received at the end of two years? Formula I=PRT
Answers
The answer is $10.4
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: Makayla invested $130. She earned a simple interest of 4% per year on the initial investment.
Then SI = 130×4×2 /100
=$10.4
Hence, Simple Interest recieved is $10.4
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The graph shows how far Katie walked over a 4 minute time interval.
Distance
(in feet)
240
200
160-
120-
80-
40-
1
2 3 4
Time
(in minutes)
OA 40 fumin
OB. 50 fumin
OC. 60 ft/min
D. 80 ft/min
How fast was Katie walking?
4
Answers
Answer:500 ft
Step-by-step explanation:
El punto P está en el exterior de una circunferencia C en el plano. ¿Cuál es el número máximo
de puntos de C que se encuentran a 3 cm de P?
A) 1
B) 2
C) 3
D) 4
E) 8
Answers
The correct response is 4. We can consider the following construction to understand why: We drew a 3 cm radio circle with the center located at P. Llamemoso C1.
What exactly is a circle's radio?Half of a circle's diameter corresponds to its radius. The radius equals 5 cm for a 10 cm diameter.
So, in order for C2 to intersect C, the straight line connecting P and C's center must be contained within C2, that is, it must be separated from C's center by a distance less than r. In other words, we need that:
r > d + 3
the distance between the center of C and the straight line connecting P and the center of C is where d. Its distance, d, is same to that between P and the center of C, minus C1's radio. Defined as,
d = PC - 3
where PC denotes the distance between P and C's center.
Thus, we require that:
r > PC - 3 + 3 = PC
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4. Amy, Betty and Carol have 96 books altogether. Betty has 6 books less than Amy and Carol has half as many as Betty. How many books does each girl have?
Answers
The Amy has 42 books, Betty has 36 books, and Carol has 18 books.
Let's set up equations to represent the given information:
Let A represent the number of books Amy has.
Let B represent the number of books Betty has.
Let C represent the number of books Carol has.
Let's say Amy has x books.
Betty has 6 books less than Amy, so Betty has (x - 6) books.
Carol has half as many books as Betty, so Carol has (x - 6)/2 books.
According to the problem, the total number of books they have is 96.
So, we can write the equation:
x + (x - 6) + (x - 6)/2 = 96
To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:
2x + 2(x - 6) + (x - 6) = 192
2x + 2x - 12 + x - 6 = 192
5x - 18 = 192
5x = 210
x = 42
Amy has 42 books.
Betty has (42 - 6) = 36 books.
Carol has (36)/2 = 18 books.
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List the sample space for the experiment.
S = {Q, R, R, T}
S = {Q, R, S, T}
S = {R, A, T}
S = {S, Q, Q}
Answers
Answer:
The second one S= {Q,R,S,T}
Step-by-step explanation:
The sample space is S = {Q, R, S, T}.
What is set?Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
From the diagram,
There are 4 quarters of the circle.
And in each quarter have representation.
And the representation are;
{Q, R, S, T}
Therefore, {Q, R, S, T} is the sample space.
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solve (x-4)^2=5.
Answers:
A. x=9 and x=1
B. x=5+(square root)4
C. x=-4+(square root)5
D. x=4+(square root)5
Answers
Answer:
don't dout yourself
Step-by-step explanation:
never give up thanks for the free points
find the value of x
Answers
Therefore, the value of x in the right triangle is 24 cm.
What is triangle?A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and the measure of each angle depends on the lengths of the sides and the type of triangle. There are different types of triangles based on their side and angle measures, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have various properties and formulas that are used in geometry and other fields.
Here,
In a right triangle, the side opposite to the right angle is the longest side and is called the hypotenuse. Therefore, in this case, 25 cm is the hypotenuse of the triangle.
Using the Pythagorean Theorem, we can find the missing length x:
a² + b² = c²
where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.
In this case, a = 7 cm, b = x, and c = 25 cm.
Substituting these values into the Pythagorean Theorem, we get:
7² + x² = 25²
49 + x² = 625
x² = 625 - 49
x² = 576
x = √576
x = 24
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A bakery baked two types of cakes, chocolate cake and vanilla cake, Given 30% of the cakes are vanilla cakes and only half of the vanilla cakes was sold. State each of the following ratios in the form of a : b. Given the answers in simplest form. The ratio of the number of chocolate cakes to the number of vanilla cakes
Answers
The ratio of the number of chocolate cakes to the number of vanilla cakes is 14:3
How to determine the ratio of the number of chocolate cakes to the number of vanilla cakes?To find the ratio of the number of chocolate cakes to the number of vanilla cakes, we can first find the total number of cakes baked and then the number of vanilla cakes.
Since 30% of the cakes are vanilla cakes. Let the total number of cakes baked be x.
Thus, the number of vanilla cakes is 0.30x.
Since only half of the vanilla cakes were sold, the number of vanilla cakes remaining is 0.5 × 0.30x = 0.15x.
Since the total number of cakes baked is x, the number of chocolate cakes is x - 0.30x = 0.70x
Thus, the ratio of the number of chocolate cakes to the number of vanilla cakes is:
0.70x : 0.15x
14 : 3
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Use an associative law to find an expression equivalent to
s + (r + 75)
Answers
As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.
The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.
Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:
s + (r + 75) = (s + r) + 75
The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.
Let's take an example to illustrate this:
Suppose s = 10 and r = 20.
Using the original expression:
s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105
Using the expression with regrouped terms:
(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105
As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.
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Find the interquartile range for the data set. 11, 5, 16, 20, 31, 27, 9, 15, 26
Answers
Step 1: Put the data set in order from least to greatest:
5, 9, 11, 15, 16, 20, 26, 27, 31
Step 2: Find the median. The median is the middle value in the data set.
Median = 16
Step 3: Find the first quartile (Q1). Q1 is the median of the lower half of the data set (i.e., the median of the data set below the median).
Lower half of the data set: 5, 9, 11, 15
Q1 = median of the lower half of the data set = 10
Step 4: Find the third quartile (Q3). Q3 is the median of the upper half of the data set (i.e., the median of the data set above the median).
Upper half of the data set: 20, 26, 27, 31
Q3 = median of the upper half of the data set = 26.5
Step 5: Calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 26.5 - 10 = 16.5
Therefore, the interquartile range for the data set is 16.5.
Show how you arrived at your solution on the answer sheet for full credit. Write neatly, clearly and be organized.
11. A maker of frozen meals claims that the average caloric content of its meals is 800. A
researcher tested 12 meals and found that a sample mean was 815 calories and the sample
standard deviation 25. Is there enough evidence to reject the claim at a =0.02? Assume the
variable is normally distributed. Use p-value method or traditional method. (hint: two-tail
test) write your answer three decimal places (8 points)
Answers
Step-by-step explanation:
A car is on a slope of 10degree above the horizontal . a force 1000N is applied to the car up the line of the slope. the car has amass of 500 kg . what is the acceleration of the car
what is a case control study
Answers
Answer:
A study that compares two groups of people: those with the disease or condition under study (cases) and a very similar group of people who do not have the disease or condition (controls). Researchers study the medical and lifestyle histories of the people in each group to learn what factors may be associated with the disease or condition. For example, one group may have been exposed to a particular substance that the other was not. Also called retrospective study.
Step-by-step explanation:
Answer:
A case-control study is designed to help determine if an exposure is associated with an outcome (i.e., disease or condition of interest).
Step-by-step explanation:
do similar triangles always have equal lengths of corresponding sides?
Answers
Answer:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
Answer:
No. Similar triangles only have equivalent angles. Congruent triangles have equal side lengths.
Step-by-step explanation:
Solve using substitution.
- x - y = -1
X = 2
Answers
Add 2
-y = 1
Y = -1
Answer:
x = 2
y = -1
Step-by-step explanation:
-(2) - y = -1
add 2
-y = 1
divide by -1
y = -1
The graph of the equation x + 3y = 6 intersects the y-axis at what the point?
Answers
Answer:
It intersects the y-axis at point (0, 2).
Step-by-step explanation:
x + 3y = 6
3y = -x + 6
y = -1/3x + 2
Answer:
4. (6,0)
Step-by-step explanation:
Plug the points into the equation.
6+3(0)=6
6+0=6
6=6
There are 15 rows of seats in a theater. If each row has 26 seats, how
many seats are there in the theater?
Answers
Answer:
390
Step-by-step explanation:
There are 15 rows of 26. This can be expressed as 15 x 26, which is equal to 390.
Answer: 390
In order to solve the total number of seats, we must do rows times column. Our row is 15, our column is 26. This means our equation is 15 times 26. 15 times 26 is 390.
This means 390 seats are in the theater.
Hope this helps. Good Luck.
