Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a
2x^2 - 3x = 12
2x^2 - 3x - 12 = 0
a = 2
b = -3
c = -12
(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)
3 +/- sqrt( 9 + 96 ) / 4
3 +/- sqrt(105) / 4
Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]
Hope this helps!
Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-12x^2+2160x-59000 To maximize the monthly rental profit, how many units should be rented out? units What is the maximum monthly profit realizable?
Answer:
To maximize the monthly rental profit, 90 units should be rented out.
The maximum monthly profit realizable is $38,200.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]
To maximize the monthly rental profit, how many units should be rented out?
This is the x-value of the vertex, so:
[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]
To maximize the monthly rental profit, 90 units should be rented out.
What is the maximum monthly profit realizable?
This is p(90). So
[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]
The maximum monthly profit realizable is $38,200.
Given a committee of 8 women and 11 men, how many different ways are there to pick a female president, a male treasurer, and a secretary of either gender if one of the men, Pete, says that he cannot be the treasurer? Assume that none can hold more than one office.
Answer: 1360 ways.
Step-by-step explanation:
Number of men = 11
Number of women = 8
Total members = 8 + 11 = 19
Firstly, the number of ways of selecting 1 woman for female president out of 8 will be:
= 8C1
= 8
Since Pete can not be a treasurer, then the treasurer will then be selected from the remaining 10(11 - 1). The number of ways of selecting 1 treasurer out of 10 will be:
= 10C1
= 10
Thirdly, since none can hold more then one office, in this case, the selection will be done by selecting 1 person out of 7 women and 10 men. Therefore, the number of ways of selecting 1 person out of 17 will be:
= 17C1
= 17
Therefore, the total number of ways will then be:
= 8 × 10 × 17
= 1360
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose from, 33 types of sandwiches, and 44 types of chips. How many different value meal packages are possible
36 different value meal packages are possible
Step-by-step explanation:
To answer this question, multiply all given numbers together.
4*3*3
12*3
36
Ivan invests $5,000 into an account with a 3.5% interest that is compounded semi-annually.
How much money will he have in this account if he keeps it for 15 years?
9514 1404 393
Answer:
$8414
Step-by-step explanation:
The compound interest formula is useful for this.
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years. A is the ending balance.
A = $5000(1 +0.035/2)^(2·15) = $5000·1.0175^30 ≈ $8414.00
Ivan will have $8414 in his account after 15 years.
190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is
Answer:slope 2/3
Y-int 6
Step-by-step explanation:
What is the image of (3, -12) after a dilation by a scale factor of į centered
at the origin?
Answer:
9 is. ................m.m..mk
About 3% of the population has a particular genetic mutation. 200 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 200
Answer:
6
Step-by-step explanation:
200. Move decimal twice to the left. 1% of 200 is 2. 2*3 is 6.
the mean of 200 item was 50 later on it was found that two items were wrongly taken as 92 and 8 instead of 192 and 88 find the correct mean.
Answer:
Since, mean of 200 items was 50 and number of items =200
So, mean =50
Also, we know mean = number of itemssum of items
∴50=200sum of items
Sum of items = 200×50=10000
Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88 respectively
Then misread instead Correct item
92 192 192-92=100
8 88 88-8=80
∴ Correct sum of items =10000+180=10180
∴ Correct mean = number of items/sum of items
=10180/200 =50.9
Answer:
Hello,
203.6
Step-by-step explanation:
Sum of the item first= 50*200=10000
new sum is 10000+(192-92)+(88-8)=10180
New mean=10180/200=50.9
Write the equation in slope-intercept form.
y+3 - 2(x-1)
Answer:
y = 2x - 5
Step-by-step explanation:
[tex]y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5[/tex]
Can someone help me with this plz
Answer:
170.7
Step-by-step explanation:
We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.438.43 and a standard deviation of 1.51.5. Using the empirical rule, what percentage of American women have shoe sizes that are between 6.936.93 and 9.939.93
Answer:
The right solution is "68%".
Step-by-step explanation:
The empirical rule is:
[tex]X\sim N(8.43, 1.5)[/tex]
According to the question,
= [tex]P(6.93< \mu < 9.93)[/tex]
= [tex]P(\frac{6.93-8.43}{1.5} < \frac{\mu -8.43}{1.5} < \frac{9.93-8.43}{1.5} )[/tex]
= [tex]P(z(1)-P(z(-1))[/tex]
= [tex]68[/tex] (%)
Thus the above is the right solution.
What is the extreme value of the polynomial function f(x)= x2 - 4?
Answer:
+∞.
Step-by-step explanation:
That would be positive infinity.
The extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
What is extreme value of a polynomial?Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes.
What are the steps of finding the extreme value of any polynomial?The following steps which are required to find the extreme value of polynomial are:
Arrange the polynomial into the the form of [tex]ax^{2} +bs+c[/tex] where a, b and c are numbers.Determine whether a, the coefficient of the [tex]x^{2}[/tex] term, is positive or negative.If the term is positive, the extreme value will be the infinity because the value will continue to grow as x increases.If it is negative, use the formula [tex]\frac{-b}{2a}[/tex] to find the value for extreme. And then plug [tex]x = \frac{-b}{2a}[/tex] in the original polynomial to calculate the extreme value of the polynomial.According to the given question.
We have a polynomial
[tex]f(x) = x^{2} -4[/tex]
Since, in the given polynomial the coefficient of [tex]x^{2}[/tex] is positive . Therefore, the extreme value of the given polynomial is infinity because the value will continue to grow as x increases.
Hence, the extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
Find out more information about extreme value of a polynomial here:
https://brainly.com/question/16597253
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Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)
compute T(3,3) pls help me
Answer:
(-4,-1)
Step-by-step explanation:
We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.
This implies for scalars a and b that
T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)
T((a,2a)+(-b,b))=a(-1,1)+b(2,3)
T((a-b,2a+b))=(-a,a)+(2b,3b)
T((a-b,2a+b))=(-a+2b,a+3b)
This means we should be able to solve the system below to find a and b for T(3,3):
a-b=3 and 2a+b=3
Add equations to eliminate b and solve for a:
3a=6
Divide 3 on both sides:
a=2
If a-b=3 and a=2, then b=-1.
Plug in a=2, b=-1:
T((a-b,2a+b))=(-a+2b,a+3b)
T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)
T(3,3)=(-4,-1).
Find the missing side lengths leave your answer as a racials simplest form
Answer:
x = 20
y = 10
Answered by Gauthmat
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Susan has calculated that she needs $58000 her first year of retirement to maintain her standard of living. She expects to receive
$1000 per month from her employer defined-benefit pension and $1500 per month from Social Security. What is her annual
retirement income shortfall?
answer options:
28,000
40,000
58,000
150,000
Answer:
$28000
Step-by-step explanation:
12×1000 + 12×1500 = 12000 + 18000 = $30000
the shortfall is the difference between $58000 and $30000
58000 - 30000 = $28000
The temperature in Kansas City varies greatly some days. One day in January, the temperature was 16 degrees but then the temperature decreased by 23 degrees by midnight. What was the temperature at midnight?
Answer:
-7 degrees
Step-by-step explanation:
the temperature was 16 degrees then was the decrease by 23 degrees so subtract 23 from 16 and the answer is -7
Find the integer pair that has the given product and sum. The product is 28 The sum is 11
Answer:
7 and 4
Step-by-step explanation:
when you multiply 7×4 the answer is 28 and when you add them the answer is 11.
I hope this helps
Answer:
4 and 7
Step-by-step explanation:
xy = 28 ..........1
x + y = 11........2
x = 11 - y.........3
substitute 3 in 1:
(11 - y)*y = 28
-y² + 11y - 28 = 0
y² - 11y + 28 = 0
( y - 7)( y - 4) = 0
y = 7 or y = 4
subs in 2:
x = 4 or x = 7
pairs: (4 ; 7) and (7 ; 4)
Factorize:
3a^2 + 10a + 3
Answer: (3a + 1) (a + 3)
Step-by-step explanation:
Concept:
Here, we need to know the idea of factorization.
It is like "splitting" an expression into a multiplication of simpler expressions. Factoring is also the opposite of Expanding.
Solve:
Given = 3a² + 10a + 3
STEP ONE: separate 3a² into two terms
3a
a
STEP TWO: separate 3 into two terms
3
1
STEP THREE: match the four terms in ways that when doing cross-multiplication, the result will give us 10a.
3a 1
a 3
When cross multiply, 3a × 3 + 1 × a = 10a
STEP FOUR: combine the expression horizontally to get the final factorized expression.
3a ⇒ 1
a ⇒ 3
(3a + 1) (a + 3)
Hope this helps!! :)
Please let me know if you have any questions
Estimating Mean SAT Math Score
Type numbers in the boxes.
aby Part 1: 5 points
The SAT is the most widely used college admission exam. (Most community
aby Part 2: 5 points
colleges do not require students to take this exam.) The mean SAT math score
varies by state and by year, so the value of u depends on the state and the year. 10 points
But let's assume that the shape and spread of the distribution of individual SAT math scores in each
state is the same each year. More specifically, assume that individual SAT math scores consistently
have a normal distribution with a standard deviation of 100. An educational researcher wants to
estimate the mean SAT math score (u) for his state this year. The researcher chooses a random
sample of 661 exams in his state. The sample mean for the test is 494.
Find the 99% confidence interval to estimate the mean SAT math score in this state for this year.
(Note: The critical z-value to use, zc, is: 2.576.)
Your answer should be rounded to 3 decimal places.
Answer:
(483.981 ; 504.019)
Step-by-step explanation:
Given :
σ = 100
Sample size, n = 661
xbar = 494
We use the Z distribution since we are working with the population standard deviation ;
C.I = xbar ± (Zcritical * σ/√n)
Zcritical at 99% = 2.576
C.I = 494 ± (2.576 * 100/√661)
C.I = 494 ± 10.019
Lower boundary = (494−10.019) = 483.981
Upper boundary = (494+10.019) = 504.019
C.I = (483.981 ; 504.019)
Five subtracted from seven times a number is 9. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is _____________
B) Solve your equation in part [A] for
Answer:
x=
Answer:
18
Step-by-step explanation:
7-5=2
2x9=18
WILL GIVE 25 POINTS FOR ANSWERING AND BRAINIER!!!
Which answer choice correctly complete the sentence?
Asking the “Did you Check” questions is an important step in the Problem Solving Plan because you can
A. determine if your answers are reasonable.
B. organize your thoughts.
C. understand the problem better.
D. define your strategy easier.
Answer:
A
Step-by-step explanation:
It just makes the most sense
PLZ HELP ASAP
A student poll on campus wanted to analyze the correlation of the Number of calories consumed per day to the weight of a student. in the form of a paragraph describe which visual display is most appropriate to represent the data. explain your reasons for choosing this type of visual display.
Answer:
Each kids weight in a chart
Step-by-step explanation:
I chose this because its the most organized way of doing that
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
b?
a=
b =
Answers:
a = 2
b = 3
=======================================================
Explanation:
Plug in x = 0 and y = 2 to find that
y = a*b^x
2 = a*b^0
2 = a*1
2 = a
a = 2
Then plug in x = 3 and y = 54 to determine the value of b
y = a*b^x
y = 2*b^x
54 = 2*b^3
2b^3 = 54
b^3 = 54/2
b^3 = 27
b = (27)^(1/3)
b = 3
So we have y = a*b^x update to y = 2*3^x
Given f (x) = 4x - 3,g(2) = x3 + 2x
Find (f - g) (4)
Factor the trinomial. Write the answer in binomial fctor form.
2x^2– 13x + 11
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Answer:
(2x -11)(x -1)
Step-by-step explanation:
The middle term can be rewritten as a sum using the coefficients of the first and last terms. Then the expression can be factored by pairs of terms.
2x^2 -13x +11 = 2x^2 -2x -11x +11 = 2x(x -1) -11(x -1)
= (2x -11)(x -1)
[{66 +1} 2-6].7
I need help ASAP please due Monday pre-algebra show work
Ans; 7× [2-6 { 1+66}] —> 7× [2 - 6 { 67} ] —> 7× [2-402] —> 7×[- 400] —> = – 2800
I hope I helped you ^_^
A force of 18 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it from its natural length to 10 in. beyond its natural length
Answer: 18.75 lb.ft
Step-by-step explanation:
Given
Force required to stretch spring 8 in. is 18 lb
it can be written
[tex]\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.[/tex]
Work done in stretching from its natural length to 10 in.
[tex]\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft[/tex]
square root of v-5=6
[tex] \sqrt{x - 5 = 6}[/tex]
Answer:
I think you mean this :
[tex] \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41[/tex]
Or,
Square root of x-5=6 is :
[tex] \sqrt{x - 5} \:=\:\sqrt{6} [/tex]
find b for (b-1)/4=(7b+2)/12
Answer:
-1.25
Step-by-step explanation:
you first have to cross multiply
12(b-1)=4(7b+2)
12b-12=28b+8
group the like terms
12b-28b=8+12
-16b/-16=20/-16
b= -1.25
I hope it helps
Step-by-step explanation:
Answer is in the picture..
hope it helps
