The relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the function below
g(x) = (x − 2)^3 + 6
The function compared to f(x) = x^3, shows a translation of f(x) by 2 unit to the right along the horizontal and vertical translation of the function 6 units up
Hence the relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.
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Answer:
g(x) is shifted 6 units to the left and 2 units down.
Step-by-step explanation:
took the test
Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The equation y=60x+30
y=60x+30 represents what Health Club B charges. Health Club A charges a $50 sign-up fee and $27 per month.
Answer:
y = (constant variable x time) + independent variable
y = 60x + 30 ← Health Club B
y = 27x + 50 ← Health Club A
Step-by-step explanation:
I can't see the question at the bottom due to the covering but if you comment I can edit this and give a proper answer. Otherwise this is all I can give you.
2. This month Tania saved
6 times as much money
as last month. Last
month she saved $24.
How much did Tania
save this month?
3.
Answer:
$144
Step-by-step explanation:
24*6 = 144
In a study of 250,178 cell phone users,it was found that 81 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is 0.000412 probability of a person developing cancer of the brain or nervous system. We therefore expect about 104 cases of such cancer in a group of 250,178 people.Estimate the probability of 81 or fewer cases of such cancer in a group of 250,178. What do these results suggest about media reports that all cell phone cause cancer of the brain or nervous system?
P(x≤81)=[tex]P(x\leq 81)\\What do these results suggest about media reports?[/tex]
Using the normal distribution, the probability is given as follows:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For this problem, the proportion and the sample size are given by:
p = 0.000412, n = 250178
Hence the mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 250178 \times 0.000412 = 103.1[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{250178 \times 0.000412 \times (1 - 0.000412)} = 10.15[/tex]The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]
Z = -2.13
Z = -2.13 has a p-value of 0.0158.
Hence:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
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Harry took a loan from the bank.
DDD represents Harry's remaining debt (in dollars) after ttt months.
D=-200t+9000D=−200t+9000D, equals, minus, 200, t, plus, 9000
What was the size of Harry's loan?
The amount of Harry's loan is $9000.
A loan is when money is lent to another person with the understanding that it would be repaid, along with interest.
According to the question,
A bank loan is taken up by Harry.
After t months, D indicates Harry's outstanding debt (in dollars).
D=-200t+9000
In order to find the initial size of Harry's loan, the time(t)=0, that is, the time when no debts had been paid.
The negative sign in the expression of D denotes the payment of debt.
Substituting t=0, we get,
D=-200*0+9000
D=9000
Thus, the amount of loan taken by Harry is $ 9000.
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Use the function f(x) = 4x² - 7x-15 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph
a) The factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).
b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).
c) The function has a minimum and grows in the + y direction.
d) Marking the two x-intercepts, second, generating a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and estimate the location of the vertex and, finally, creating a parabola with a minimum and growing in the + y direction by matching the points.
How to analyze and interpret quadratic functions?
In this problem we have a quadratic function in standard form, that is, an equation of the form f(x) = a · x² + b · x + c, where a, b and c are real coefficients. a) First, we need to complete the square and find the roots to determine the factorized form:
4 · x² - 7 · x - 15 = 0
4 · [x² - (7 / 4) · x - (15 / 4)] = 0
x² - (7 / 4) · x - (15 / 4) = 0
x² - 2 · (7 / 8) · x - (15 / 4) + (289 / 64) = 289 / 64
x² - 2 · (7 / 8) · x + 49 / 64 = 289 / 64
(x - 7 / 8)² = 289 / 64
x - 7 / 8 = ± 17 / 8
x = 7 / 8 ± 17 / 8
Then, the factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).
b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).
c) The end behavior of the graph is inferred from the lead coefficient. A positive coeffcient , which is the case of the function, indicates that vertex of the polynomial is a minimum and parabola grows in the + y direction.
d) In accordance with algebra, we can generate a quadratic equation by knowing three distinct points on Cartesian plane.
First, mark the two x-intercepts, second, generate a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and, finally, generate a parabola with a minimum and growing in the + y direction.
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A baseball travels d meters t seconds after being dropped from the top of the building
Considering the given function, it is found that:
When t = 0, d = 0 meters.When t = 0.5, d = 1.25 meters.When t = 1, d = 5 meters.When t = 1.5, d = 11.25 meters.When t = 2, d = 20 meters.Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.
What is the function for the distance traveled by the ball?The function is:
d = 5t².
Hence:
When t = 0, d = 5 x 0² = 0 meters.When t = 0.5, d = 5 x 0.5² = 1.25 meters.When t = 1, d = 5 x 1 = 5 meters.When t = 1.5, d = 5 x 1.5² = 11.25 meters.When t = 2, d = 5 x 2² = 20 meters.Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.
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How do you compute this? 4(-2, 3) - 2(6, -7)
Step-by-step explanation:
Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))
jake made some tarts. He sold 3/5 of them and gave 1/4 of the remainder to his friends. If he had 150 tarts left, how many did he sell?
Check what other students also ask
Answer:
300 tarts
Step-by-step explanation:
we must solve this equation by going backwards
3/4 of something (as 1/4 was given away) is 150
150 / 3/4 is what you must do
or
150 * 4/3
that is
200
3/5 was sold so 2/5 was left
2/5 of something is 200
200 / 2/5
200 * 5/2
that is
500
3/5 of that was sold
so
500 * 3/5 is 300
300 tarts were sold
Really not sure what is meant by this when I'm only given one number, would appreciate help very much!!!!
Using continuous compounding, it is found that the value of r is of r = 7.7%.
What is continuous compounding?The amount of money after t years in continuous compounding is:
[tex]P(t) = P(0)e^{rt}[/tex]
In which:
P(0) is the initial amount.r is the exponential growth rate.The doubling time of 9 years means that P(9) = 2P(0), which is used to find r, hence:
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]2P(0) = P(0)e^{9r}[/tex]
[tex]e^{9r} = 2[/tex]
[tex]\ln{e^{9r}} = \ln{2}[/tex]
[tex]9r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{9}[/tex]
r = 0.077.
r = 7.7%.
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Jolene set up a retirement account. She arranged to have $350 taken out of each of her monthly checks; the account will earn 2.1 % interest compounded monthly. She just turned 33 and her ordinary annuity comes to term when she turns 60. Find the value of her retirement account at that time
Answer:
$152,419.36
Step-by-step explanation:
The future value of an ordinary annuity is given by the formula ...
FV = P((1 +r/12)^(12t) -1)/(r/12)
where P is the monthly payment, r is the annual interest rate, and t is the number of years.
Annuity valueFor P = 350, r = 0.021, and t = 27 (years to retirement age), the value is ...
FV = 350((1 +0.021/12)^324 -1)/(0.021/12) ≈ $152,419.36
The value of Jolene's retirement account when she turns 60 will be $152,419.36.
Tara cuts a 300 inch long spool of yarn into two pieces of different sizes. The longer piece is three times as long as the shorter piece. How long is the shortest piece?
Answer:
75 inches
Step-by-step explanation:
Let x = the short side
Let y = the long side
x + y = 300
y = 3x
Plug 3x for y into the first equation:
x + 3x = 300
4x = 300 Divide both sides by 4
x = 75
solve the algebraic equation 7 x - 2 equals to 2x + 13
Answer:
x = − 6
Step-by-step explanation:
I have my work
AN ARTICLE IN USA TODAY STATED THAT “INTERNAL SURVEYS PAID FOR BY DIRECTORY ASSISTANCE PROVIDERS SHOW THAT EVEN THE MOST ACCURATE COMPANIES GIVE OUT WRONG NUMBERS 15% OF THE TIME.” ASSUME THAT YOU ARE TESTING SUCH A PROVIDER BY MAKING 10 REQUESTS AND
ALSO ASSUME THAT THE PROVIDER GIVES THE WRONG TELEPHONE NUMBER 15%
OF THE TIME. FIND THE PROBABILITY OF GETTING ONE WRONG NUMBER.
Step-by-step explanation:
I assume this means exactly one wrong number in the 10 attempts.
the probability to get a wrong number is 0.15 (15%).
therefore, the probability to get a correct number is
1 - 0.15 = 0.85
in 10 tries to get 1 wrong number (and 9 correct numbers) looks like this :
0.15×0.85⁹ = 0.034742542...
this would be the probability to e.g. get a wrong number at the first attempt, and all other attempts are correct.
how many different constellations can we have that way ?
10.
because the wrong number could be given at any of the 10 attempts.
so, the probability to get exactly 1 wrong answer is
10×0.15×0.85⁹ = 0.34742542... ≈ 35%
now, if the question is about the probability to get at least one number wrong, then we can say this is the opposite of the probability to get all 10 numbers correctly.
the probability to get all 10 numbers correctly is
0.85¹⁰ = 0.196874404... ≈ 20%
and therefore, the probability to get at least 1 number wrong is
1 - 0.196874404... = 0.803125596... ≈ 80%
FYI :
this would be, of course, also the result of we did it the complex way :
the sum of the probabilities of
exactly 1 number wrong
exactly 2 numbers wrong
...
exactly 9 numbers wrong
all 10 numbers wrong
and for each of the cases of n wrong numbers the probability is
(10! / (n! × (10-n)!)) × 0.15^n × 0.85^(10-n)
this represents the constellation of n numbers wrong (and 10-n numbers right) multiplied by the number of possible combinations of picking n numbers out of 10.
and again, all this summed up (1 <= n <= 10) is the same as
0.803125596...
The probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Now, Let q = probability of giving out wrong number = 15 % = 0.15
And, p = probability of not giving out wrong number = 1 - q
= 1 - 0.15 = 0.75
Hence, For a binomial probability,
P(x) = ⁿCₓ qˣ pⁿ⁻ˣ.
With n = 10 and x = 1, the probability of getting a number wrong
P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹
= 10(0.15)(0.75)⁹
= 1.5(0.0751)
= 0.1126
= 11.26 %
b. At most one wrong is P(x ≤ 1) = P(0) + P(1)
= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹
= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹
= 0.0563 + 0.01126
= 0.06756
= 6.756 %
≅ 6.76 %
Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
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Write a linear function that passes through the points (3, -7) and (0, 15)
Answer:
The linear function for the given pts. will be
[tex]y = \frac{ - 22}{3}x + 15[/tex]
Step-by-step explanation:
Hello!
[tex]first \: find \: the \: slope \: for \: the \: two \: pts. \\ m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{(15 - ( - 7))}{(0 - 3)} where \: y2 = 15 \\ y1 = - 7 \\ x2 = 0 \\ x1 = 3 \\ m = \frac{ - 22}{3} \\ thus \: y = mx + b \: \: solve \: for \: b \: using \: one \: of \: the \: two \: points \\ lets \: take \: the \: second \: point \\ y = mx + b \\ 15 = \frac{ - 22}{3} (0) + b \\ b = 15 \\ therefore \: substitute \: this \: value \: to \: get \: the \: \\ y = \frac{ - 22}{3} x + 15[/tex]
On a coordinate plane, a circle has center (0, 0) and radius 4. A parabola opens down and goes through (3, 0), has vertex (0, 2) and goes through (negative 3, 0). Everything above the parabola and inside of the circle is shaded. Which system has the solution set shown? x squared + y squared greater-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared greater-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2
The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.
How to illustrate the information?It should be noted that inequalities are simply used to compare two expressions that are unequal.
It can be seen that the solution set that's illustrated is:
x² + y² <= 16
-1/4x² + 2 <= y
Therefore, the inequality system that has the solution set shown will be option C.
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what is the solution I need help
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
Square root of numbersThe square root of numbers is is expressed using the square root sign. In order to determine the square root os 0.15 given, we need need to determine the square of perfect square before and after the given number.
For the square root of √0.09
√0.09 = 0.3
Similarly for the square root of √0.16
√0.16 = 0.4
Since the resulting value is 0.3 and 0.4, hence the square root of 0.15 must be between these two values on the number line.
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
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It takes 3 liters of paint to cover an area of 24 square meters. What percentage increase in the quantity of paint would be required to cover an area of 50.4 square meters?
Answer:
110 [%].
Step-by-step explanation:
if the initial area is 24 m² and final area 50.4 m², then the required percentage can be calculated as:
[tex]\frac{50.4}{24}*100-100=110[/tex] ,
where 50.4/24*100 - the final percentage.
P.S. It means, the final value of the paint is 3*2.1=6.3 [liters].
Find the magnitude and direction of each resultant for the given vectors. Round each side to the nearest tenth and round each angle to the nearest degree.
w = < 5, 6 >, x = < -1, 14 >
The magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.
Magnitude of the resultant vector
Sum of vectors in x direction, ∑X = 5 - 1 = 4
Sum of the vectors in y direction, ∑Y = 6 + 14 = 20
Resultant vector = √(∑X² + ∑Y²)
Resultant vector = √(4² + 20²) = 20.4 units
Direction of the vectorθ = arc tan (ΣY/ΣX)
θ = arc tan (20/4)
θ = arc tan (5)
θ = 78.7⁰
θ ≈ 79⁰
Thus, the magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.
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3x - 2(2x - 5) = 2(x + 3) - 8
Answer:
x = 4
Step-by-step explanation:
Hello!
We can solve for x by expanding the parentheses and isolating x.
Solve for x3x - 2(2x - 5) = 2(x + 3)-83x - 4x + 10 = 2x + 6 - 8-x + 10 = 2x - 210 = 3x - 212 = 3xx = 4The value of x is 4.
About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
Given sample size be 300 and about 5% of the population has a particular genetic mutation.
We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.
Sample size=300
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation=[tex]\sqrt{np(1-p)}[/tex]
Use the known values in the above formula.
Standard deviation=[tex]\sqrt{300*0.05(1-0.05)}[/tex]
=[tex]\sqrt{14.25}[/tex]
=3.77
Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
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The controller of MingWare Ceramics Inc. wishes to prepare a cost of goods sold budget for September. The controller assembled the following information for constructing the cost of goods sold budget: Direct materials: Enamel Paint Porcelain Total Total direct materials purchases budgeted for September $35,870 $7,530 $139,890 $183,290 Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 2,980 2,710 7,150 12,840 Direct labor cost: Kiln Department Decorating Department Total Total direct labor cost budgeted for September $51,550 $149,500 $201,050 Finished goods inventories: Dish Bowl Figurine Total Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850 Desired inventory, September 30 3,720 4,590 4,360 12,670 Work in process inventories: Estimated inventory, September 1 $3,540 Desired inventory, September 30 1,980 Budgeted factory overhead costs for September: Indirect factory wages $80,400 Depreciation of plant and equipment 10,550 Power and light 5,110 Indirect materials 3,390 Total 99,450 Use the preceding information to prepare a cost of goods sold budget for September. For those boxes in which you must enter subtracted or negative numbers use a minus sign. MingWare Ceramics Inc. Cost of Goods Sold Budget For the Month Ending September 30 Finished goods inventory, September 1 $Finished goods inventory, September 1 Direct labor $Direct labor Direct materials: $- Select - - Select - $- Select - - Select - $- Select - Direct labor fill in the blank 15 - Select - - Select - $- Select - Work in process inventory, September 30 fill in the blank 22 - Select - $- Select - - Select - $- Select - 4,100
The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:
Cost of Goods Sold Budget:Beginning inventory of finished goods $11,850
Cost of goods manufactured 485,310
Ending inventory of finished goods (12,670)
Cost of Goods Sold $484,490
What is the cost of goods sold budget?The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.
The cost of goods sold budget is based on the cost of goods manufactured budget.
Data and Calculations:Direct materials: Enamel Paint Porcelain Total
Total direct materials purchases
budgeted for September $35,870 $7,530 $139,890 $183,290
Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 (2,980) (2,710) (7,150) (12,840)
Materials used in production $183,250
Direct labor cost: Kiln Department Decorating Department Total
Total direct labor cost
budgeted for September $51,550 $149,500 $201,050
Finished goods inventories: Dish Bowl Figurine Total
Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850
Desired inventory, September 30 3,720 4,590 4,360 12,670
Cost of goods manufactured budget:Work in process inventories:
Estimated inventory, September 1 $3,540
Direct materials used in production $183,250
Direct labor costs $201,050
Total factory overhead costs $99,450
Desired inventory, September 30 (1,980)
Cost of goods manufactured $485,310
Budgeted factory overhead costs for September:Indirect factory wages $80,400
Depreciation of plant and equipment 10,550
Power and light 5,110
Indirect materials 3,390
Total 99,450
Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.
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The following data were accumulated for use in reconciling the bank account of Mathers Co. for July: 1. Cash balance according to the company's records at July 31 $20,010. 2. Cash balance according to the bank statement at July 31, $21,110. 3. Checks outstanding, $4,060. 4. Deposit in transit, not recorded by bank, $3,260. 5. A check for $480 in payment of an account was erroneously recorded in the check register as $840. 6. Bank debit memo for service charges, $60. a. Prepare a bank reconciliation
The preparation of a bank reconciliation statement for Mathers Co. for July is as follows:
Bank Reconciliation StatementAt July 31
Cash balance per bank statement as at July 31, $21,110
Deposit in transit 3,260
Outstanding checks (4,060)
Balance as per adjusted cash balance $20,310
What is bank reconciliation?A bank reconciliation statement is a summary of banking and business cash transactions so that their balances can agree.
Bank reconciliations help the company to reconcile its bank account as per bank statements with its internal financial records.
The steps for preparing a bank reconciliation include:
Discover the discrepancies in both statements.Adjust the cash balance with entries from the bank statement and other accounting errors. Adjust the bank statements with uncredited deposits, checks not yet presented, and accounting errors. Compare the end balances.Data and Calculations:Cash balance per Cash Account at July 31 $20,010
Cash balance per bank statement at July 31, $21,110
Checks outstanding, $4,060
Deposit in transit $3,260
Transposed payment $360 ($840 - $480)
Bank service charges $60
Adjusted Cash Balance per Cash Account:Cash balance per Cash Account as at July 31 $20,010
Transposed payment 360
Bank service charges (60)
Adjusted cash balance per cash account $20,310
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which of the following best describes the graph below?
The correct answer is the option A because in one-to-one functions, each y value corresponds to only one x value.
I need help solving
The graph of the translated function can be seen in the image below.
How to translate the graph of a function?
For a given function f(x), we define a vertical translation of N units as:
g(x) = f(x) + N
Where if N is positive, the translation is upwards. If N is negative, the translation is downwards.
In this case, we have:
y = f(x) - 2
Then we just need to translate the given graph 2 units below, we will get the graph you can see below.
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a number line shows the whole numbers from 0 to 10 describe where you would plot square root 30
what are the 5 different way to solve the quadratic equations
Step-by-step explanation:
A quadratic equation is a equation with a degree of 2. Below are the 5 ways to solve a quadratic equation.
Factoring - First, make sure that one side of the equation is 0. Turn the equation into a product of two binomials and set each one to 0. Solve both to get both solutions.Completing the Square - Add to both sides such that one side becomes a square of a binomial. Square root both sides and solve with algebra.Square Roots - If one side of the equation is a perfect square, square root both sides and solve normally.Graphing - Make one side of the equation 0 and graph. The x-intercepts are the solutions.Quadratic Formula - First, make the equation follow the form [tex]ax^2+bx+c=0[/tex]. Then, use the formula [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] to get the solutions.What is
6/7 of 2/3.
Step-by-step explanation:
[tex] = \frac{6}{7} \times \frac{2}{3} \\ [/tex]
[tex] = \frac{12}{21} \\ [/tex]
Change into lowest term...
[tex] = \frac{4}{7} \\ [/tex]
...
A new baby grew 3/4 of an inch in June and 7/16? 4- in July. How many total inches did the baby grow during these two months?
Answer:
The baby grew 1 3/16 inches
Step-by-step explanation:
A new baby grew:
3/4 of an inch in June,7/16 of an inch in July.Total inches during two months:
3/4 + 7/16 = Fractions with different denominators3*4/(4*4) + 7/16 = Multiply the first fraction by 4 12/16 + 7/16 = Add numerators19/16 = Numerator is greater than denominator(16 + 3)/16 = Convert to mixed fraction16/16 + 3/16 = 1 + 3/16 = 1 3/16 AnswerZA =
Round your answer to the nearest hundredth.
Answer:
Rounded to the nearest tenth would be 75.5 degrees
Step-by-step explanation:
Find the equation of the line parallel to y equals 1 half x plus 2 that passes through the point (4, 5) in slope-intercept form.
Answer: [tex]y=\frac{1}{2}x+3[/tex]
Step-by-step explanation:
We can solve this by using the point-slope form, which can help get the equation of a line given the slope of the line and a point on the line. Slope-intercept form is the form [tex]y=mx+b[/tex], and we can convert from point-slope form to this with simple algebra.
The point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope of the line, and [tex](x_1,y_1)[/tex] is the point.
We know that the line is parallel to [tex]y=\frac{1}{2}x+2[/tex], which means it will have the same slope. The slope of this line is [tex]\frac{1}{2}[/tex], so the slope of any line parallel to it will also be [tex]\frac{1}{2}[/tex].
[tex]y-5=\frac{1}{2}(x-4)\\y-5=\frac{1}{2}x-2\\y=\frac{1}{2}x+3[/tex]
