Answer:
[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex].
Step-by-step explanation:
To find [tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}[/tex] using synthetic division you must:
Write the problem in a division-like format. To do this:
Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right.
[tex]\begin{array}{c|cccc}&x^{3}&x^{2}&x^{1}&x^{0}\\-1&1&2&-5&-6\\&&\\\hline&\end{array}[/tex]
Step 1: Write down the first coefficient without changes:
[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\\\hline&\1\end{array}[/tex]
Step 2:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\left(-1\right) \cdot 1=-1\\\hline&{1}&{2}+\left({-1}\right)={1}\end{array}[/tex]
Step 3:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}{-1}&1&2&{-5}&-6\\&&-1&\left({-1}\right) \cdot {1}={-1}\\\hline&1&{1}&\left({-5}\right)+\left({-1}\right)={-6}\end{array}[/tex]
Step 4:
Multiply the entry in the left part of the table by the last entry in the result row.
Add the obtained result to the next coefficient of the dividend, and write down the sum.
[tex]\begin{array}{c|rrrr}{-1}&1&2&-5&{-6}\\&&-1&-1&\left({-1}\right) \cdot \left({-6}\right)={6}\\\hline&1&1&{-6}&\left({-6}\right)+{6}={0}\end{array}[/tex]
We have completed the table and have obtained the following resulting coefficients: 1, 1, −6, 0.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is [tex]x^{2}+x-6[/tex], and the remainder is 0.
[tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}=x^{2} + x - 6+\frac{0}{x + 1}=x^{2} + x - 6[/tex]
Now, we factor [tex]x^{2}+x-6[/tex]
[tex]\left(x^2-2x\right)+\left(3x-6\right)\\x\left(x-2\right)+3\left(x-2\right)\\\left(x-2\right)\left(x+3\right)[/tex]
Therefore,
[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex]
After sales tax your brand new car is $17,300. What is the total price of the car with DMV fees of 1.25% of the purchase price of the car?
A. $261.25
B. $17,516.25
C. $216.25
D. $17,561.25
The right answer is Option B.
Step-by-step explanation:
Given,
Purchase price of car = $17,300
DMV fees = 1.25% of purchase price
DMV fees = [tex]\frac{1.25}{100}*17300=\frac{21625}{100}[/tex]
DMV fees = $216.25
Total price of car = Purchase price + DMV fees
Total price of car = 17300 + 216.25 = $17516.25
The total price of car is $17,516.25
The right answer is Option B.
Keywords: percentage, division
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Let f be the function given by the sum of the first three nonzero terms of this series. The maximum value of |lnx-f(x)| for .3<=x<=1.7 is:__________
Answer:
Step-by-step explanation:
f(x) = sin(4x)f' = 4 cos(4x)f'' = -16 sin(4x)f''' = -64 cos(4x)f⁽⁴⁾ = 256 sin(4x)f⁽⁵⁾ = 1024 cos(4x)The 4-th order Taylor series expansion isf(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4!)f⁽⁴⁾(x) + ...The Maclaurin series is obtained by setting x = 0.Note that sin(0) = 0 and cos(0) = 1.The non zero terms aref(h) = 4h - (4h)³/3! + (4h)⁵/5! - (4h)⁷/7! + ...Answer: f(x) =4x- 4/3+4x/5+4x7
HOPE THIS HELPED ;3 please mark Brainliest
Assuming that the roots of the given qudratic equation are a,b find the sum and product of the roots.
Answer: Sum of root a+b = -c/d
Product of root ab= e/d
Step-by-step explanation:
Let the general quadratic equation be dx² + cx + e = 0
And the root of the equation be
'a' and 'b'
Using the general formula to find the solution to the quadratic equation
a = -c+√c²- 4de/2d
b = -c-√c²- 4de/2d
Taking the sum of the roots
a+b = (-c+√c²- 4de/2d) + (-c-√c²- 4de/2d)
a+b = (-c-c+√c²- 4de/2d - √c²- 4de/2d)/2d
a+b = -2c/2d
a+b = -c/d
The sum of the root of the quadratic equation will be -c/d
Product of roots
ab = (-c+√c²- 4de/2d)(-c-√c²- 4de/2d)
= {c² +(c√c²- 4de)- (c√c²- 4de) -(c²-4de)}/4d²
= {c²-c²+4de}/4d²
= 4de/4d²
= e/d
The product of the above quadratic equation will be e/d
PLZZ HELPP!!! WILL GIVE BRAINLIEST!!!
Let f(x) = 8x^3 + 18x^2 − 10 and g(x) = 4x + 1. Find f(x)/g(x).
A. 2x^2 + 4x - 1 + 9/4x + 1
B. 2x^2 + 4x - 1 - 9/4x + 1
C. 2x^2 + 4x + 1 + 9/4x + 1
D. 2x^2 + 4x + 1 - 9/4x + 1
Answer:B. 2x^2 + 4x - 1 - 9/4x + 1
Step-by-step explanation:
f(x) = 8x^3 + 18x^2 − 10
g(x) = 4x + 1
We want to determine f(x)/g(x). We would apply the long division method. The steps are shown in the attached photo.
The correct answer is
2x^2 + 4x - 1 - 9/4x + 1
Answer:
[tex]\text{B. }2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]
Step-by-step explanation:
One way is to use long division.
2x² + 4x - 1
4x + 1) 8x³ + 18x² - 10
8x³ + 2x²
16x²
16x² + 4x
-4x - 10
-4x - 1
- 9
[tex]\dfrac{8x^{3} + 18x^{2} - 10} {4x+1} = 2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]
A reciepe uses 1 1/4 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can you use for 1 gallon of milk?
Answer:
128 servings
Step-by-step explanation:
16 cups in a gallon
16/1.25 = 12.8
12.8 * 10 = 128
128 servings
An airline has six flights from New York to California and seven flights from California to Hawaii per day. If the flights are to be made on separate days, how many different flight arrangements can the airline offer from New York to Hawaii?
a) 6*7=42
b) 6+7=13
c) 67 = 279936
d) 76 = 117649
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
Number of flights from New York to California = 6
Number of flights from California to New York = 7
Since if the flights are to be made on separate days,
So, they are independent events.
So, the number of different flight arrangements that can be made offer from New York to Hawaii would be
[tex]6\times 7\\\\=42[/tex]
Hence, Option 'a' is correct.
This is a Mathematics problem about combinations, specifically calculating the total number of possible flight arrangements from New York to Hawaii, given the number of flights per day on two separate routes. The answer is found by multiplying the number of flights from New York to California (6) by the number of flights from California to Hawaii (7), which equals 42 arrangements.
Explanation:The subject of this question is Mathematics, specifically involving the concept of combinations and arrangements. The total number of flight arrangements from New York to Hawaii can be calculated by simply multiplying the number of flights from New York to California by the number of flights from California to Hawaii. Therefore, the correct answer would be a) 6*7=42.
Conceptually, this is because for each of the 6 flights from New York to California, there are 7 possible continuing flights to Hawaii. To find all possible combinations, you would multiply the two numbers together. Through visualization, this could be seen as having 6 'branches' from New York to California, then 7 'branches' from California to Hawaii for each initial branch, giving a total of 42 possible routes.
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What time is it?
A. 11:10
B. 9:11
C. 11:09
D. 10:55
E. 9:55
Answer:
10:55
Step-by-step explanation:
Hour hand is at the 10, minute hand at the 11 (which means 11 * 5 = 55)
Write an equation of the line containing the given point and perpendicular to the given line:
(7,- 4); 9x+7y=4
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
9x+7y=4
7y = - 9x + 4
y = -9x/7 + 4/7
Comparing with the slope intercept form, slope = - 9/7
If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (7,-4) is 7/9
To determine the intercept, we would substitute m = 7/9, x = 7 and y = -4 into y = mx + c. It becomes
- 4 = 7/9×7 + c = 49/9 + c
c = - 4 - 49/9 = -85/9
The equation becomes
y = 7x/9 - 85/9
Answer:
Step-by-step explanation:
any eq. of line perpendicular to 9x+7y=4 is
7x-9y=a
it passes through (7,-4)
7(7)-9(-4)=a
49+36=a
a=85
reqd. eq. is 7x-9y=85
When analyzing related data variables, how can one tell which one is the independent variable and which one is the dependent variable?
Answer:
Dependent and independent Variable.
Step-by-step explanation:
Dependent and independent Variable.
The two variables in an experiment are independent and dependent variable. Usually, the dependent variable is denoted by y and the independent variable a re denoted by [tex]x_i[/tex]The dependent variable depends on independent variable in an experiment and thus cannot be controlled.On the other hand we can change or control the independent variables to test effect on dependent variable.As the independent variable are changed, we observe corresponding changes in the dependent variable.Example: Let money spend be the dependent variable. It depends on an independent variable of shopping. We may control or change or shopping habits to see the changes in the money spent. Money spent totally depends in the amount f shopping done.A student wanted to estimate the number of chocolate chips in a commercial brand of cookie. He sampled 100 cookies and found an average of 10.5 chips per cookie. If we assume the standard deviation is 8, what is a 99% confidence interval for the average number of chips per cookie?A. (8.4,12.6)B. (8.9,12.1)C. (5.3,10.7)
Answer:
The 99% confidence interval is given by (8.4;12.6)
A. (8.4,12.6)
Step-by-step explanation:
1) Notation and definitions
n=100 represent the sample size
[tex]\bar X= 10.5[/tex] represent the sample mean
[tex]\sigma=8[/tex] represent the population standard deviation assumed
m represent the margin of error
Confidence =99% or 0.99
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
2) Calculate the critical value zc
On this case we can to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=NORM.INV(0.005,0,1)" for [tex]z_{\alpha/2}=-2.58[/tex]
"=NORM.INV(1-0.005,0,1)" for [tex]z_{1-\alpha/2}=2.58[/tex]
The critical value [tex]zc=\pm 2.74[/tex]
3) Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
[tex]m=z_c \frac{\sigma}{\sqrt{n}}[/tex]
[tex]m=2.58 \frac{8}{\sqrt{100}}=2.064[/tex]
4) Calculate the confidence interval
The interval for the mean is given by this formula:
[tex]\bar X \pm z_{c} \frac{\sigma}{\sqrt{n}}[/tex]
And calculating the limits we got:
[tex]10.5 - 2.58 \frac{8}{\sqrt{100}}=8.4[/tex]
[tex]10.5 + 2.58 \frac{8}{\sqrt{100}}=12.6[/tex]
The 99% confidence interval is given by (8.4;12.6)
A. (8.4,12.6)
The manager of a supermarket wants to obtain information about the proportion of customers who dislike a new policy on cashing checks. How many customers should he sample if he wants the sample fraction to be within .15 of the true fraction, with probability .98
Answer:
n = 61 costumers
Step-by-step explanation:
For calculating the number of costumers he should sample we use the next equation:
[tex]n = \frac{z_{1-\alpha/2}^{2}p(1-p)}{E^{2} }[/tex]
Where E is the error that we are prepared to accept, in this case E = 0.15
How we don't know the value of p, we can estimate it like p = 0.5
∝ = 1-0.98 = 0.02
1-∝/2 = 0.99
[tex]z_{0.99} = 2.33[/tex]
[tex]n = \frac{(2.33^{2})(0.5)(1-0.5)}{0.15^{2} }[/tex]
n = 60.32 costumers
n ≈ 61 costumers
Final answer:
To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula: n = (Z^2 * p' * (1-p')) / E^2. The manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98.
Explanation:
To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula:
n = (Z^2 * p' * (1-p')) / E^2
Where:
n is the sample size
Z is the z-score corresponding to the desired confidence level
p' is the estimated proportion
E is the maximum error or margin of error
In this case, the manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98. Assuming p' is 0.5, we can calculate the required sample size.
Determine whether the following statement regarding the hypothesistest for two population proportions is true or false.
However small the difference between two population proportion ,for sufficiently large sample size, the null hypothesis of equalpopulation proportions is likely to be rejected.
The statement is true; as sample size increases, even small differences between two population proportions can lead to the rejection of the null hypothesis. The decreasing standard error with larger samples increases the test statistic, leading to smaller p-values. However, practical significance should also be considered alongside statistical significance.
Explanation:The statement regarding the hypothesis test for two population proportions is true. As the sample size increases, even a very small difference between the two population proportions becomes significant. This is because with larger sample sizes, the standard error of the difference between the two proportions decreases, which increases the test statistic used in hypothesis testing. As a result, we are more likely to reject the null hypothesis of equal population proportions if the sample size is sufficiently large, assuming there is indeed a small actual difference.
The null hypothesis typically states that there is no effect or no difference, and in the case of two population proportions, it states that the proportions are equal. When we conduct a hypothesis test, we calculate the probability of observing our sample data, or something more extreme, given that the null hypothesis is true. This probability is known as the p-value. A small p-value indicates that the observed data is unlikely under the null hypothesis, leading to its rejection.
However, it's important to note that the ability to detect small differences with large samples does not imply that those differences are practically significant, only statistically so. Therefore, in addition to hypothesis testing, it's essential to consider effect size and practical significance when interpreting results.
30 Points!!
Juan solves the system of equations by forming a matrix equation.
−4x+y=9
3x+2y=7
He multiplies the left side of the coefficient matrix by the inverse matrix.
How does he proceed to the solution?
Answer:
multiply the left side of the constant vector by the inverse matrix
Step-by-step explanation:
The matrix equation ...
AX = B
is solved by left-multiplying by the inverse of A:
A⁻¹AX = A⁻¹B
IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix
X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix
[tex]\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^{-1}\left[\begin{array}{c}9&7\end{array}\right]=\dfrac{1}{11}\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right][/tex]
Answer:
I used the above answer and got it wrong. Hope this helps! (Sorry it looks a little weird... just look at whta is in the boxes)
Step-by-step explanation:
True or False: The following pair of ratios are equivalent ratios.8/9 and 72/81
A circle is shown. Secants E G and D G intersect at point G outside of the circle. Secant E G intersects the circle at point F and secant D G intersects the circle at point H. The length of E F is x, the length of F G is 6, the length of D H is x + 3, and the length of H G is 5. What is the length of line segment DG? 4 units 7 units 12 units 23 units
Answer:
Step-by-step explanation:
The formula we need here is
[tex]6(6+x)=5(5+x+3)[/tex]
which simplifies to
[tex]6(6+x)=5(8+x)[/tex]
which simplifies to
36 + 6x = 40 + 5x and
x = 4
So DG = 5 + 4 + 3 which is 12
Answer:
The correct answer is C. 12
Step-by-step explanation:
I just took the test
The width of a rectangle is 4 more than half the length.
If the perimeter of the rectangle is 74, what is the width?
Perimeter of rectangle: P = 2l + 2w
Width= ? Length= ?
Answer:
The answer to your question is L = 22; w = 15
Step-by-step explanation:
Data
length = L
width = w
Perimeter = 74
Condition
w = L/2 + 4
Formula
P = 2L + 2w
Substitution
74 = 2L + 2(L/2 + 4)
Simplification
74 = 2L + L + 8
74 = 3L + 8
74 - 8 = 3L
3L = 66
L = 66/3
L = 22
w = 22/2 + 4
w = 11 + 4
w = 15
Evaluate.
43 – 4:25
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This is an improper. Perhaps you can fix it, so that I can assist you with it? I apologise.
to prove that triangle age and triangle old are congruent by sas what other information is needed
Answer:
Congruency of triangle by SAS rule.
Step-by-step explanation:
We have to prove that [tex]\triangle AGE \text{ and } \triangle OLD[/tex] are congruent to each other by SAS congruency rule.
Thus, we need the following information to do so:
A pair of equal corresponding side.An equal pair of equal corresponding angle.A second pair of equal corresponding side.Corresponding sides are:
AG and OLGE and LDAE and ADCorresponding angles are:
[tex]\angle AGE \text{ and } \angle OLD\\\angle GEA \text{ and } \angle LDO\\\angle GAE \text{ and } \angle LOD[/tex]
Decide which trigonometric ratio to use. Solve for x in the triangle below. Round your answer to the hundredths place.
4.59
0.07
6.55
5.60
(I have more questions in my recently asked too that I could really use help with as soon as possible.) Thank you.
Answer:
4.59
Step-by-step explanation:
sin(angle) = opposite / hypotenus
Logan borrowed some money from his friend in order to help buy a new video game system and agreed to pay the friend back a constant amount each week. Logan originally borrowed $40 from his friend and after 7 weeks, he still owed his friend $26. Write an equation for the function L(t),L(t),representing the amount Logan owes his friend after tt weeks.
Answer:L(t) = 40 - 2t
Step-by-step explanation:
Total amount of money that Logan borrowed from his friend to buy the video game system is $40
Let x represent the constant amount that he agreed to pay the friend back each week.
After 7 weeks, he still owed his friend $26. This means that the amount that he paid in 7 weeks is 7×x = $7x
He still owed his friend $26.
This means that amount paid in 7 weeks would be 40 - 26 = $14
Therefore
7x = 14
x = 14/7 = 2
He pays $2 each week.
Let t represent the number of weeks, the equation for the function L(t),representing the amount Logan owes his friend after t weeks would be
L(t) = 40 - 2t
Graph the system of linear equations. negative StartFraction one-half EndFraction y equals StartFraction one-half EndFraction x plus 5 and y equals 2 x plus 2.y = x + 5 and y = 2x + 2. The solution to the system is (, ).
Answer:
It is (-4,-6)
Step-by-step explanation:
I just did it on E2020 ur welcome
To graph a system of linear equations, start at the y-intercept and use the slope to plot the next points. The solution to the system of equations is the point where the lines intersect, and can be found by setting the equations equal to each other and solving.
Explanation:The problem involves graphing a system of linear equations, which are y = x + 5 and y = 2x + 2.
Each equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. For the first equation, the slope is 1 and the y-intercept is 5. For the second equation, the slope is 2 and the y-intercept is 2.
To graph these, you typically start at the y-intercept (where the line crosses the y-axis) and use the slope to determine the next points on the graph - you rise/run according to the slope.
The solution to the system of equations is the point where the two lines intersect. To find this point, you need to solve the system of equations either graphically or algebraically. This would involve setting the equations equal to each other and solving for x, and then substituting that value of x into either of the original equations to solve for y.
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Your mother takes you to your grandparents house for dinner. She drives 60 minutes at a constant speed of 40 miles per hour. She reaches the highway, quickly speeds up, and drives another 30 minutes at constant speed for 70 miles per hour. How far did you and your mother travel altogether? How long did the trip take?
Answer:
Step-by-step explanation:
We will separate our trips as "slow" and "fast". Filling in a motion table:
d = r x t
slow
fast
We know that the slow rate is 40 mph and the time is, in hours (because the time has to match the rate. We can't say "40 mph" and then state the time in minutes), 1 hour.
We know that the fast rate is 70 mph and the time in hours is .5 hours.
If distance = rate times time, then the distance traveled at the slow speed is 40 * 1 = 40 miles
The distance traveled at the fast speed is 70 * .5 = 35 miles.
The trip was 40 + 35 = 75 miles total, and the time it took was 1 + .5 = 1.5 hours.
Please answer with how you did it
Answer:
B) 0.11
Step-by-step explanation:
Use the conditional probability formula.
P(transfer | never graduated) = P(transfer & never graduated) / P(never graduated)
__
Denominator
But the P(never graduated) is made of two parts:
P(never graduated) = P(transfer & never graduated) + P(freshman & never graduated)
= (1 -0.80)×(1 -0.85) + (0.80)×(1 -0.70)
= (0.20)(0.15) + (0.80)(0.30)
= 0.0300 +0.2400 = 0.2700
__
Numerator
The numerator of our fraction is one of the components we just calculated:
P(transfer & never graduated) = (1 -0.80)×(1 -0.85) = 0.0300
__
Conditional Probability
So ...
P(transfer | never graduated) = 0.0300/0.2700 = 1/9 ≈ 0.11
.
What is the twentieth term of the arithmetic sequence 21, 18, 15, 12, ... ?
78
-39
-36
1
Answer:
-36.
Step-by-step explanation:
First term a1 = 21.
Common difference d = 18 - 21 = -3 (15-18 = -3)
nth term an = a1 + (n - 1)d
So 20th term = 21 + (20-1) -3
= 21 - 3 * 19
= 21 - 57
= -36.
The 20th term of the arithmetic sequence will be -36.
The nth teem of an arithmetic sequence is calculated by using the formula: a + (n - 1) d.
The 20th term will be:
= a + (n - 1) d.
= a + (20 - 1)d
= a + 19d
where,
a = first term = 21
d = common difference = 2nd term - 1st term = 18 - 21 = -3
Therefore, 20th term will be:
= a + 19d
= 21 + 19(-3)
= 21 - 57
= -36
Therefore, the 20th term is -36
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A line passes through the points
(P,a) and (P,-a) where p and a are real numbers and p=/0.
Describe each of the following and explain your reasoning please.
1. slope of the line
2. equation of the line
3. Y-intercept
4. slope of a line perpendicular to the given line
Answer:
Step-by-step explanation:
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the information given,
y2 = - a
y1 = a
x2 = 0
x1 = 0
Slope = (- a - a)/0-0 = -2a/0 = 0
2) equation of the line is represented in the slope intercept form as y = mx + c
Where
m = slope
c = intercept.
To determine c, we would substitute y = a, x = p and m = 0 into y= mx + c. It becomes
a = 0×p + c
c = a
The equation becomes
y = a
3) y intercept,c = a
4) the slope of a line perpendicular to the given line is a negative reciprocal of the slope of the given line. Therefore,
Slope = - 0 = 0
WILL GIVE BRAINLIEST
1. Given the function P(x)= (x+3)^2 +2 Write the new function after a translation of 3 units UP. Q(x)= ___
Answer:
Q(x) = [tex](x+3)^{2}+5[/tex] is the final equation.
Step-by-step explanation:
By translation of the graph 3 units upward direction, it means that the y-value of the function is increased by 3 unit at each value of x.
Given , P(x) = [tex](x+3)^{2}+2[/tex]
We can actually translate the graph in any direction, and for that we have to make the necessary changes. If we translate the graph in the positive x direction, then we have to substitute (x - 3) instead of x in the equation.
Since we are translating the graph upwards ,
Q(x) = [tex](x+3)^{2}+2[/tex] + 3
Q(x) = [tex](x+3)^{2}+5[/tex]
This is the final equation of the graph after translation.
An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
a. 16/43
b. 16/44
c. 17/43
d. 17/44
Answer:
The probability is [tex]\frac{16}{43}[/tex]
Step-by-step explanation:
The psychology class has 9 freshman male, 15 freshman females, 8 sophomore male and 12 sophomore female.
Total population constitution of the class=
17 males and 27 females and 44 students in total.
If on selecting on the first attempt, a male has been picked up then the number of males for the picking up in the second attempt has to decrease by one.
Also, the total number of students from which it has to be selected also decreases by 1, because one child has already been selected.
Therefore for Second Attempt, Total 43 students and 16 males.
Probability=[tex]\frac{No.OfFavorableOutcomes}{TotalNo.OfOutcomes}[/tex]
Probability=[tex]\frac{16}{43}[/tex]
Final answer:
The probability that the second student will also be a male, given that the first student is a male, is 16/43.
Explanation:
To find the probability that the second student will also be a male, given that the first student is a male, we need to determine the number of males left in the sample space after choosing the first male student. In the class, there are 9 freshman males and 8 sophomore males, making a total of 17 males. However, since we are choosing 2 students, the total sample space decreases by 1 after choosing the first male student.
Therefore, the probability of choosing a male as the second student, given that the first student is a male, is:
P(second student is male | first student is male) = (number of males left in sample space after choosing first male) / (total sample space after choosing first male)
P(second student is male | first student is male) = 16/43
12) Oliver is not allowed to watch more than 4 hours of television a week. He watched his favorite show on Monday which was 1 hour long and his favorite Tuesday show which was 1.5 hours long. How many more hours of television can he watch? Set up an equation and solve. A) 2.5x = 4; Oliver can watch 1.6 more hours this week. B) x + 1 + 1.5 = 4; Oliver can watch 1.5 more hours this week. C) x + 4 = 1 + 1.5; Oliver can watch 1.5 more hours this week.
Answer:
B. Oliver can watch TV for 1.5 hours more this week.
Step-by-step explanation:
Oliver is not allowed to watch more than 4 hours of television a week. He watched his favorite show on Monday which was 1 hour long and his favorite Tuesday show which was 1.5 hours long.
So he has already finished 2.5 hours of watching . He can watch only for 4 hours for the total week.
Let x be the number of more hours for which he can watch television.
Then ,
x + 1 + 1.5 = 4
x + 2.5 = 4
x = 4 - 2.5
x = 1.5 hours.
So Oliver can watch television for at most 1.5 hours for the rest of the week.
Then the correct option is B.
Julia is going to the store to buy candies. Small candies cost $4 and extra-large candies cost $12.She needs to purchase at least 20 candies, but she cannot spend any more than$180.
Answer:
Small candies [tex]=9[/tex]
Extra large candies [tex]=12[/tex]
Step-by-step explanation:
Let small candies [tex]=x[/tex]
Extra large candies [tex]=y[/tex]
the number of candies is at least [tex]20[/tex].
[tex]x+y\geq20[/tex]
Cost of [tex]1[/tex] small candy [tex]=\$4[/tex]
Cost of [tex]1[/tex] extra large candy [tex]=\$12[/tex]
but she has only [tex]\$180[/tex] to spend
[tex]4x+12y\leq180[/tex]
Solve for
[tex]x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)\times4\\8y=100\\y=\frac{100}{8} \\y=\frac{25}{8} \\from\ eqn(1)\\x+\frac{25}{2}=20\\ x=20-\frac{25}{2} \\x=\frac{15}{2}[/tex]
Since number of candies should be integer.
let [tex]x=7,y=13[/tex]
total spend [tex]4\times7+12\times13=184 [/tex] which is more than [tex]\$180[/tex], so this combination is not possible.
[tex]let\ x=8,y=12\\8\times4+12\times12=176<180[/tex]
She has [tex]\$4[/tex] more so she can buy [tex]1[/tex] more small candy.
Hence small candy [tex]=9[/tex]
extra large candy [tex]=12[/tex]
PLEASE HELP WILL MARK AS BRAINLIEST 50 POINTS
After sales tax your brand new car is $17,300. What is the total price of the car with DMV fees of 1.25% of the purchase price of the car?
A. $261.25
B. $17,516.25
C. $216.25
D. $17,561.25
Answer:B
Step-by-step explanation:
17, 300+ 1.25% You can take the decimal and move it to the other side then start doing the math
Answer:
C; 21625
Step-by-step explanation: