The solutions to the given quadratic equation are x = -6 and x = -2
Quadratic equationsFrom the question, we are to solve the given quadratic equation
The given equation is
y = x² + 8x + 12
To solve the equation, we will set it equal to 0
That is,
x² + 8x + 12 = 0
Solving
x² + 8x + 12 = 0
x² + 2x + 6x + 12 = 0
x(x +2) +6(x + 2) = 0
(x +6)(x + 2) = 0
x +6 = 0 OR x +2 = 0
x = -6 OR x = -2
Hence, the solutions to the given quadratic equation are x = -6 and x = -2
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24g ____ 1,679mg?
Complete the inequality statement
Answer:
24g > 1,679mglook at the picture
Answer:
C
Step-by-step explanation:
x²-9x<-8
x²-9x+(-9/2)²<-8+(-9/2)²
(x-9/2)²<-8+81/4
(x-9/2)²<(-32+81)/4
(x-9/2)²<49/4
|x-9/2|<7/2
-7/2<x-9/2<7/2
add 9/2
9/2-7/2<x-9/2+9/2<7/2+9/2
2/2<x<16/2
1<x<8
A random sample of n D 225 and xN D 21 was drawn from a normal population with a known
standard deviation of 26:8: Calculate the 95% confidence interval of the population mean.
Using the z-distribution, the 95% confidence interval of the population mean is: (17.5, 24.5).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the other parameters are:
[tex]\overline{x} = 21, \sigma = 26.8, n = 225[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 21 - 1.96\frac{26.8}{\sqrt{225}} = 17.5[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 21 + 1.96\frac{26.8}{\sqrt{225}} = 24.5[/tex]
The interval is: (17.5, 24.5).
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Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 95%, sample size 10.
Using the t-distribution, the critical value needed is: t = 2.2622.
How to find the critical value for the t-distribution?The critical value is found using a calculator, with two parameters:
The confidence level.The number of degrees of freedom, which is one less than the sample size.For this problem, we have a confidence level of 95% and 10 - 1 = 9 df, hence the critical value is t = 2.2622.
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How many more people attended from the 40-60 class than the 60-80
Answer:7 people
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Please Please Please help with this math problem
Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.
Mathematically, the revenue can be calculated by using the following expression:
R(x) = x × P(x)
Revenue, R(x) = x(-1/20(x) + 920)
Revenue, R(x) = x(-x/20 + 920)
Revenue, R(x) = -x²/20 + 920x.
Expressing the profit as a function of x, we have:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = -x²/20 + 920x - (80x + 6000)
P(x) = -x²/20 + 840x - 6000.
For the value of x which maximizes profit, we would differentiate the profit function with respect to x:
P(x) = -x²/20 + 840x - 6000
P'(x) = -x/10 + 840
x/10 = 840
x = 840 × 10
x = 8,400.
For the maximum profit, we have:
P(x) = -x²/20 + 840x - 6000
P(8400) = -(8400)²/20 + 840(8400) - 6000
P(8400) = -3,528,000 + 7,056,000 - 6000
P(8400) = $3,522,000.
Lastly, we would calculate the price to be charged in order to maximize profit is given by:
P(x) = -1/20(x) + 920
P(x) = -1/20(8400) + 920
P(x) = -420 + 920
P(x) = $500.
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Consider the probability that exactly 90 out of 147 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 56%.
Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answer:
Step-by-step explanation:
i didnt do anything bro why u delete my answer
lim
x →1+. 1- x/x² - 1
Answer: [tex]\displaystyle \boldsymbol{-\frac{1}{2}}[/tex]
================================================
Work Shown:
[tex]\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{1-\text{x}}{\text{x}^2-1}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-(\text{x}-1)}{(\text{x}-1)(\text{x}+1)}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-1}{\text{x}+1}\\\\\\\displaystyle L = \frac{-1}{1+1}\\\\\\\displaystyle L = -\frac{1}{2}\\\\\\[/tex]
In the second step, I used the difference of squares rule to factor.
The (x-1) terms cancel which allows us to plug in x = 1. We plug this value in because x is approaching 1 from the right side.
necesito ayuda con estas operaciones
3x=12
3x= -5=0
x+4=17
9y+3=21
5(x-2)=20
x÷2=4
2x÷=4
5÷x=2
4x+5=3x-6
3(x-2) =0
x÷3-4=0
5(7-x) =31-x
3(2x-2) =2(3x+9)
The expressions are illustrated below.
How to compute the expression?3x = 12
x = 12/3
x = 4
x + 4 = 17
x = 17 - 4
x = 13
9y + 3 = 21
9y = 21 - 3
9y = 18
y = 18/9
y = 2
x ÷ 2 = 4
x = 4 × 2
x = 8
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Suppose Mai places $3500 in an account that pays 19% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
S
(b) Find the amount in the account at the end of 2 years.
Answer:
a.$4165
b.$4956.35
Step-by-step explanation:
a)19% × 3500 = 665.
3500+665 =4165
b)19% × 4165 = 791.35
4165+791.35= 4956.35
The sum of three consecutive integers is -15.
If 1 is added to each integer, what is the product.
of the three resulting integers?
A bank gives an interest of 12% per annum.How long will it take to double one's interest?
Tyler wants to have $250,000 in his retirement account by the time he retires in 30 years. The interest rate is 5%. Use the annuity formula to calculate the amount Tyler needs to deposit on a monthly basis in order to reach his goal. When solving, round numbers to the nearest hundred-thousandth. Round your final answer to the nearest cent.
Using the monthly payment formula, he needs to deposit A = $1,342.12 a month to reach his goal.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are:
P = 250000, r = 0.05, n = 12 x 30 = 360.
Then:
r/12 = 0.05/12 = 0.004167.
Then:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 250000\frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}[/tex]
A = $1,342.12
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Any ideas for this graph
60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER
1. The solution to the first percent puzzle is as follows:
75% 66²/₃ 11¹/₉
33¹/₃% 25% 22¹/₅% 3⁷/₁₀%
50% 37¹/₂% 33¹/₃% 5¹/₂%
50% 37¹/₂% 33¹/₃% 5¹/₂%
2. The solution to the second percent puzzle is as follows:
10% 90%
50% 5% 45%
50% 5% 45%
What is a percent puzzle?A percent puzzle is a puzzle that engages students to practice working with percentages.
The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.
The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.
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I need to see the steps to the problem for me to fully get it
The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
How to find the result of a multiplication of two matrices
In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:
[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex] (1)
Where each element of the resulting matrix is equal to the following expression:
[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex] (2)
Where the operator "[tex]\bullet[/tex]" represents a dot product.
Now we proceed to calculate each element of the matrix:
[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
5 · 1 + 7 · 5 + 3 · (- 1)
37
[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
5 · 7 + 7 · 2 + 3 · 2
55
[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
5 · (- 3) + 7 · 1 + 3 · (- 4)
- 20
[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
(- 3) · 1 + 7 · 5 + 9 · (- 1)
23
[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
(- 3) · 7 + 7 · 2 + 9 · 2
11
[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
(- 3) · (- 3) + 7 · 1 + 9 · (- 4)
- 20
[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
2 · 1 + 5 · 5 + 2 · (- 1)
25
[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
2 · 7 + 5 · 2 + 2 · 2
28
[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
2 · (- 3) + 5 · 1 + 2 · (- 4)
- 9
The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
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Determine the domain and range of the following and show/explain your work.
5 y = - x^4 + 4 Provide a graph to verify your answer.
6 y = 2x^3 - 1 Provide a graph to verify your answer.
7 y = 3√(2x+8) Provide a graph to verify your answer.
See below for how the domain and the range are calculated
How to determine the domain and the range?Function, y = -x^4 + 4
The function is given as:
y = -x^4 + 4
See attachment for the graph
From the attached graph, we have:
Domain = Set of all real numbersRange = Set of real numbers less than or equal to 4Function, y = 2x^3 - 1
The function is given as:
y = 2x^3 - 1
See attachment for the graph
From the attached graph, we have:
Domain = Set of all real numbersRange = Set of all real numbersFunction, y = ∛(2x + 8)
The function is given as:
y = ∛(2x + 8)
See attachment for the graph
From the attached graph, we have:
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root of polynomial function f(x)=(x-3)^4(x+6)^2
20) Chester bought a new car with a sticker price of $18,675. He paid 25% of the cost as a down payment. What
amount did he finance?
O a.) $14,016.25
Ob.) $14,126.25
O c.) $14,006.25
Od.) $14,106.25
Answer:
B is correct
16. Describe the type of solution for the linear system of
equations given below.
2x + 3y = 15
6y=-4x + 12
F.
no solution
G. infinite solutions
H.
one solution
J. two solutions
Answer:
Step-by-step explanation:
2x+3y=15
multiply by 2
4x+6y=30 ...(1)
6y=-4x+12
4x+6y=12 ...(2)
(1) and (2) represent parallel lines.
Hence no solution.
The games have been sorted into video games and board games. The number of video games is 28 less than 6 times the number of board games. The games are 80% video games. How many board games are there?
8
10
13
14
The number of board game sorted is 14
How to find the number of games?The games have been sorted into video games and board games.
The number of video games is 28 less than 6 times the number of board games.
Therefore,
the number of board games = x
number of video game = 6x - 28
The games are 80% video games. Hence,
80 / 100 × x + 6x - 28 = 6x - 28
4 / 5 × 7x - 28 = 6x - 28
4 / 5 (7x - 28) = 6x -28
28 / 5 x - 112 / 5 = 6x - 28
28 / 5 x - 6x = -28 + 112 / 5
28x - 30x / 5 = - 28 + 112 / 5
-2x / 5 = -28 / 5
-10x = -140
x = 14
Therefore, the number of board game sorted is 14.
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Answer:
14
Step-by-step explanation:
80 / 100 × x + 6x - 28 = 6x - 28
4 / 5 × 7x - 28 = 6x - 28
4 / 5 (7x - 28) = 6x -28
28 / 5 x - 112 / 5 = 6x - 28
28 / 5 x - 6x = -28 + 112 / 5
28x - 30x / 5 = - 28 + 112 / 5
-2x / 5 = -28 / 5
-10x = -140
x = 14
The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
The equation that can be used to find the height of the tree is as follows:
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
The height of the tree is 35.6 m
How to use sine rule to find height of the tree?Th equation that can be used to find the height of the tree uses the principle of sine rule.
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin(180-4-29)}[/tex]
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
cross multiply
h sin 147 = 40 sin 29°
h = 40 sin 29° / sin 147
h = 19.3923848099 / 0.54463903501
h = 35.6015636045
h = 35.6 m
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Membership selection. A town council has members, Democrats and Republicans.
(A)
If the president and vice-president are selected at random, what is the probability that they are both Democrats?
(B)
If a 3-person committee is selected at random, what is the probability that Republicans make up the majority?
The probability that they are both Democrats is approximately
enter your response here.
(Type a decimal. Round to three decimal places.)
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.2 = 20%.
b) 0.5539 = 55.39%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.
Item a:
The parameters are:
N = 15, n = 2, k = 7.
The probability is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
Item b:
At most one Democrat, with n = 3, hence:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which:
[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]
[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]
Then:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]
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Will mark brainliest
Find an equation of the tangent line to the function
y = 3x2
at the point P(1, 3).
Solution
We will be able to find an equation of the tangent line ℓ as soon as we know its slope m. The difficulty is that we know only one point, P, on ℓ, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point
Q(x, 3x2)
on the parabola (as in the figure below) and computing the slope mPQ of the secant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.]
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
How to determine the equation of a line tangent to a quadratic equation by algebraic methods
Herein we must determine a line tangent to the quadratic equation y = 3 · x² at the point P(x, y) = (1, 3) by algebraic means. The slope of the line can be found by using the secant line formula and simplify the resulting expression:
m = [3 · (x + Δx)² - 3 · x²] / [(x + Δx) - x]
m = 3 · [(x + Δx)² - x²] / Δx
m = 3 · (x² + 2 · x · Δx + Δx ² - x²) / Δx
m = 3 · (2 · x + Δ x)
If Δx = 0, then the equation of the slope of the tangent line is:
m = 6 · x
If we know that x = 1, then the slope of the tangent line is:
m = 6 · 1
m = 6
Lastly, we find the intercept of the equation of the line: (x, y) = (1, 3), m = 6
b = y - m · x
b = 3 - 6 · 1
b = - 3
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
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What is the volume of this prism if a scale factor of 1.25 is applied to its dimensions?
A. 17.00 cubic units
B. 33.20 cubic units
C. 21.25 cubic units
D. 13.60 cubic units
Answer: B
Step-by-step explanation:
1: 5 × 1.25 = 6.25
2 × 1.25 = 2.5
1.7 × 1.25 = 2.125
2: L × W × H = 6.25 × 2.5 × 2.125 = 33.20 cubic
Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?
–2
–1
1
2
The value for x that is a double root of this function is x = -1
How to determine the double root?The function is given as:
f(x) = x^3 - 3x - 2
From the graph of the above function (see attachment), we have the following highlights:
The curve crosses the x-axis at x = 2The curve touches the x-axis at x = -1The point that it touches the x-axis is the double root point
Hence, the value for x that is a double root of this function is x = -1
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Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
The function is illustrated below based on the information.
How to describe the function?When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.
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Simplify. x^2+5x-/14 x²+8x+7
please send a picture of it
the equation seems a lil bit complicated
the equation y=ax describes the graph of a line.if the value of a is negative,the line
If the value of a is negative, the line is reflected across any of the axis
How to describe the line?The equation is given as:
y = ax
The new line is given as
y = -ax
The above implies that y = ax is transformed to y = -ax
The transformation can be any of:
reflection across the x-axisreflection across the y-axisHence, if the value of a is negative, the line is reflected across any of the axis
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Evaluate bh for b = 12 and h = 2. Type a numerical answer in the space provided.
The value of bh for b =12 and h = 2 is 24
How to evaluate the expression?The expression is given as:
bh
Where
b = 12 and h = 2
So, we have:
bh = 12 * 2
Evaluate
bh = 24
Hence, the value of bh for b =12 and h = 2 is 24
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