What is the graph of the function f(x) = the quantity of x plus 4, all over x plus 6?
Answers
1. The denominator gives a discontinuity point at (x = - 6). You can tell that is happening just by looking at the graph at x = - 6. The range at that point is - infinity to plus infinity. Other critical points are much better behaved. The y intercept is when x = 0 or 4/6 = 2/3. So the point is (0,2/3)
There is one x intercept at y = 0. When that happens
x + 4 = 0
x = - 4
Point (-4,0)
Notice the whole denominator gets multiplied out. 0 * (x + 6) = 0
Related Questions
The table shows the percentage of students in each of three grade levels who list soccer as their favorite sport. Soccer Sophomores (35%) 50%
Juniors (33%) 45%
Seniors (32%) 30%
Total (100%) (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 or about 42%
Find the probability that the student is a junior, given that soccer is the favorite sport listed.
P(junior | soccer) = ???%
Answers
You can obtain this answer by looking at the percentage of each subgrouping. For instance, 33% of the class in juniors and 45% of them list soccer as their favorites. Thus showing that 14.85% of the entire school is made up of juniors that enjoy soccer.
If you do the totaling for all soccer lovers, you get a total of 41.95% of the school. By dividing the two numbers you get the answer above.
The probability that the student is a junior, given that soccer is the favorite sport listed is 0.354.
How to calculate the probability?The percentage of student on Junior level who like soccer will be:
= 33% × 45%
= 0.1485
The total percentage of students who like soccer is 42%. Therefore, probability that the student is a junior, given that soccer is the favorite sport listed will be:
= 0.1485/0.42
= 0.354
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The diagram shows a line with intercepts 3 and 9 and one of many rectangles which can be inscribed under this line and within the first quadrant.
a. Write an equation for the line.
b. Determine if the rectangle can have x = 4 and y = 2 as its dimensions.
c. Find x and y if the rectangle is a square.
d. Write an expression for A, the area of the rectangle, using x as the only variable.
e. Find x if the area of the rectangle is 6.
f. Which x gives the rectangle its largest area?
Answers
.. x/x-intercept +y/y-intercept = 1
.. x/9 +y/3 = 1
b) The point (x, y) = (4, 2) does not satisfy the equation. (see the graph) These cannot be the dimensions of an inscribed rectangle.
c) The intersection with the line y=x is (x, y) = (2.25, 2.25). These are the dimensions of an inscribed square.
d) The equation can be rewritten as
.. x +3y = 9
.. y = 3 -(x/3)
Then the area can be written as
.. A = xy = x(3 -x/3)
e) For x=6, the area is
.. A = 6(3 -6/3) = 6*1 = 6 . . . . square units
f) The parabola described by A has zeros at x=0 and x=9. The vertex of that parabola is on the line of symmetry, at x = 4.5. That value of x gives the maximum area.
What is the probability that a point chosen at random in the rectangle is also in the blue triangle
Answers
Answer:
The probability that a point chosen at random in the rectangle is also in the blue triangle is:
1/2
Step-by-step explanation:
We are given a figure
We have to find the probability that a point chosen at random in the rectangle is also in the blue triangle.
Area of rectangle= 4×5 sq. in.
= 20 sq. in.
The area of blue triangle=[tex]\dfrac{1}{2}\times 4\times 5[/tex]
= 10 sq. in.
P(that a point chosen at random in the rectangle is also in the blue triangle)
= area of blue triangle/whole area of the rectangle
= 10/20
= 1/2
Answer: the answer is 1/2
Step-by-step explanation:
The relationship between the monthly fee that the cable company charges for internet service and the fee for downloading over 32KB of information is modeled by the linear function f (x) = 1.25x + 45, where x is the number of KB over 32. If the total bill for a month is $170, how many KB was in excess of 32 KB that month?
Answers
Because if the total is 170, then
1.25x = 170-45
1.25x = 125
x = 100
1.25x = 125
x = 100
helppppppppppppppppppppppppppppppp
Answers
8 < 2b
2b > 8
b > 8 ÷ 2
b > 4
2b + 15 < 5
2b < 5 - 15
2b < -10
b < -10 ÷ 2
b < -5
Ans: b > 4 or b < - 5 (Answer A)
True or False. (0,0) is a solution to problem #1. This means that (0,0) is in the solution region.
Answers
A point that is a solution is in the solution region.
Simone is buying 10 bracelets for her friends. Each bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10
Answers
that is $100 so I'm assuming the extra $2 is because of taxes
=98 which mean simone is right
A spinner with
9
equally sized slices is shown below. The dial is spun and stops on a slice at random. What are the odds in favor of landing on a white slice?
note their are 7 white and 2 black
Answers
Rosen 15 how many solutions are there to the equation x1 x2 x3 x4 x5
Answers
Therefore, if x⁵ is the highest exponent, then there are 5 possible answers.
However, it is important to note that not all of these have real answers for each one. In some cases, an x⁵ equation will have a number of real answers and a number of imaginary answers. Nevertheless, they will always add to 5.
I need help ASAP. I don't understand how to solve this
3. Your fixed expenses are $1,500.45/month. Your emergency fund has 4 month’s worth of coverage. You invest half in a savings account with an interest rate of 3.15% APR and the other half in a 45 day CD with an interest rate of 4.65% APR. How much is your total interest in 45 days?
4. If you had invested only 1 month’s worth of the emergency fund in the saving account at a 3.15% APR and the remainder in the 45 day CD at a 4.65% APR, what is the difference in the interest earned in 45 days when compared with question #3?
Answers
3. Your emergency fund is 4 times your expenses so is
.. emergency fund = 4*(1500.45) = 6001.80
Half that amount is 3000.90.
The interest earned at 3.15% for 45 days on 3000.90 is
.. I = Prt = 3000.90*.0315*(45/365) = 11.65
The interest earned at 4.65% for 45 days on 3000.90 is
.. I = Prt = 3000.90*.0465*(45/365) = 17.20
Your total interest in 45 days is $11.65 +17.20 = $28.85
4. The calculation is the same, only the amounts are different.
The interest earned at 3.15% for 45 days on 1500.45 is
.. I = Prt = 1500.45*.0315*(45/365) = 5.83
The interest earned at 4.65% for 45 days on 4501.35 is
.. I = Prt = 4501.35*.0465*(45/365) = 25.81
The total interest earned in this scenario is $5.83 +25.81 = $31.64
This is $31.64 -28.85 = $2.79 more than the interest earned in question 3.
_____
You could work this using weighted average interest rates.
3. The rate earned is (3.15 +4.65)/2 = 3.90% for 45 days, or 0.480822% of the 6001.80 balance, about $28.86
4. The rate earned is (3.15 +3*4.65)/4 = 4.275% for 45 days, or 0.527055% of the balance. The difference is 0.046233% of the balance, or $2.77.
Note the pennies difference from the numbers above. The differences are due to the way the numbers round off when there are two accounts. The numbers above would better match what you would see at your bank.
The total interest earned in 45 days when the emergency fund is evenly split between a savings account and a CD is approximately $29.17. If 1 month's worth of emergency funds were in the savings account and the rest in a CD, the total interest would be approximately $38.05. The difference between the two scenarios is approximately $8.88.
Calculating Interest for Emergency Funds in Savings and CDs
To answer the student's question about the interest earned in 45 days on the emergency fund invested half in a savings account and half in a 45-day CD, as well as the comparison with an alternative investment scenario, we need to perform several calculations using the given interest rates and time periods.
Answer to Question 3
Firstly, the student's fixed expenses are $1,500.45/month, so for a 4-month emergency fund coverage, the total amount saved would be $1,500.45 x 4 = $6,001.80.
Half of this amount goes into the savings account and the other half into the CD, so each gets $3,000.90.
The interest in the savings account with an APR of 3.15% for 45 days (1.5 months) would be calculated using the formula for simple interest: Interest = Principal x Rate x Time.
So the interest earned on the savings account would be: $3,000.90 x (3.15% per year / 12 months) x 1.5 months ≈ $11.85.
The interest in the 45-day CD with an APR of 4.65% would be calculated similarly: $3,000.90 x (4.65% per year / 12 months) x 1.5 months ≈ $17.32.
Therefore, the total interest earned in 45 days would be approximately $11.85 + $17.32 = $29.17.
Answer to Question 4
If only 1 month's worth of emergency fund ($1,500.45) was invested in the savings account and the remainder in the CD, the interest from the savings account would not change, but the interest from the CD would, as it would be calculated on a larger principal of $4,501.35.
The new interest for the CD investment would be $4,501.35 x (4.65% per year / 12 months) x 1.5 months ≈ $26.20.
So the new total interest would be $11.85 (from savings) + $26.20 (from CD) = $38.05.
The difference in interest between the two scenarios would be $38.05 - $29.17 = $8.88.
z varies jointly with x and y. when x=2 and y=3, z=60. what is the value of z when x=4 and y=9?
A. 360
B. 60
C. 90
D. 40,
Answers
Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280lb mixture that is 8% protein?
How many pounds of the cornmeal should be in mixture?
How many pounds of the soybean meal should be in mixture? 50 POINTS!!!!
Answers
0.14x + 19.6-0.07x = 22.4
0.07x + 19.6 = 22.4
0.07x = 2.8
x = 2.8 / 0.07 = 40
x = 40 pounds of Soybean
280 -40 = 240 of cornmeal
15p for an answer please
Answers
9/8
Hope this helps!
commet if i am incorrect
The owners want to hire a contractor to build a porch along side the parlor. The parlor is rectangular with width Of 32 feet and length of 50 feet. The porch will have the same width that on each side of the house. See design plans.
Answers
a) Basically, you are adding the length of porch to the original length of the parlor.
Let's say that the newly added porch is x.
(50 + x)(32 + x)
1600 + 50x + 32x + x²
x² + 82x + 1600
b) Just make the polynomial x² + 82x + 1600 equal to 2320.
x² + 82x + 1600 = 2320
subtract 2320 on both sides to make the polynomial equal to 0.
x² + 82x - 720 = 0
factor this
(x - 8)(x + 90) = 0
(x - 8) =0 (x + 90) = 0
x = 8 x = - 90
(-90ft doesn't make sense. So don't mind about this.)
So the porch should be 8ft.
Hope this helped!
The width of the porch will be 32 feet, the same as the parlor. However, to calculate the amount of building materials needed, additional specifics are required such as the porch's length, location of posts, and number of boards.
Explanation:To answer the question related to designing a porch that matches the width of the parlor, we first understand that the parlor is of a rectangular shape with a width of 32 feet. Considering that the porch will have the same width, it means the porch will also have a width of 32 feet.
From this point, specifics such as the desired length of the porch, location of posts, number of boards or rails, and other related factors would come into play in the calculating of building materials needed for the construction. There may also be the need to consider factors like the ratio of width to length in the design, akin to the mathematical relation mentioned in the statement 'X = Y x 2 + 1'.
So, while we know the width of the porch because it matches the parlor, the exact amount of materials that will be required would depend on further specifics of the porch design, similar to the steps in a stoichiometry problem in chemistry where one calculates the amount of reactants or products in a chemical reaction based on known ratios.
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The volumes of two similar solids are 53cm³ and 1113cm³. Which is the ratio of the corresponding sides?
A. 7
B. 21
C. √21
D. ³√21
Answers
Cube Root 53 = 3.76
The ratio is 10.36/3.76 = 2.76
Cube Root (21) = 2.76 to 3 places.
D <<<<<<<answer.
There is another way to do this (much better I think).
1113/53 = 21
A solid has 3 dimensions. Each dimension of the big solid will be k times bigger than the little one.
Therefore the volumes are related by a factor of cube root(large one ) to small one = cube root (21)
Kana earns a $25,000 salary in the first year of her career. Each year, she gets a 4% raise. How much does Kana earn in the first 10 year of her career? (Round the final answer to the nearest dollar)
Answers
Explanation:
This can be represented as a geometric sequence, with a common ratio of 1.04. This is because she earns 100% of her previous salary plus an extra 4% each year; 104%=104/100 = 1.04.
The explicit form of the sequence would be
25000(1.04)ⁿ⁻¹,
where n is the number of years. We want the sum of the first ten years, so we want
[tex]\Sigma_{n=1}^{10}25000(1.04)^{n-1}[/tex]
Using technology, this comes out to $300,152.68.
if 7(t-4)-2t=4(t-3), what is the value of t?
Answers
multiply 7 and 4 by all in parentheses
(7*t) + (7*-4) - 2t= (4*t) + (4*-3)
7t -28 - 2t= 4t - 12
combine like factors
5t - 28= 4t - 12
add 28 to both sides
5t= 4t + 16
subtract 4t from both sides
t= 16
CHECK:
7(t-4)-2t=4(t-3)
7(16-4) - 2(16)= 4(16-3)
7(12) - 32= 4(13)
84 - 32= 52
52= 52
ANSWER: t= 16
Hope this helps! :)
Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (2,4) and has the origin as its vertex. what is the standard form of the equation
Answers
.. f(x) = a(x -0)^2 +0
.. f(x) = ax^2
For the given point,
.. f(2) = 4 = a*2^2 = 4a
Then a=1 and your equation is
.. f(x) = x^2
Y= v^2/2a solve for v
Answers
Y = (a v^2)/2
Y = (a v^2)/2 is equivalent to (a v^2)/2 = Y:
(a v^2)/2 = Y
Divide both sides by a/2:
v^2 = (2 Y)/a
Take the square root of both sides:
Answer: v = sqrt(2) sqrt(Y/a) or v = -sqrt(2) sqrt(Y/a)
Final answer:
To solve for v in the equation y = v²/2a, multiply both sides by 2a and then take the square root of both sides which gives v = √(2ay).
Explanation:
The question requires us to solve the equation y = v²/2a for the velocity v. To isolate v, we multiply both sides of the equation by 2a, then take the square root of both sides.
Multiply both sides of the equation by 2a: 2ay = v²Take the square root of both sides to solve for v: v = √(2ay)This mathematical process makes v the subject of the equation based on the given formula from kinematics. It's important to note that v will have two values, one positive and one negative, since taking the square root of a number yields both a positive and negative result.
How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
Answers
Since Y and Z are on the same horizontal line, the distance between them is the difference of their x-coordinates: 6 - 1 = 5.
The segment XZ is the hypotenuse of a right triangle with sides 3 and 5, so its length is
.. XZ = √(3^2 +5^2) = √34
XY = 3
YZ = 5
XZ = √34 ≈ 5.83095
.please help me thank you you will be given brainley
Answers
Hope this helps!
This is when one word has more than one definition and its 15 letters
Answers
Select all of the potential solution(s) of the equation 2log5x=log54.
Answers
Given :[tex] 2log_{5} x^{2} =log_{5} 2^{2} [/tex]
To solve for x we use the logarithm rule for powers.
The log rule for powers states:
[tex] mlog_{a}n =log_{a} n^{m} [/tex]
We apply this rule to the left side of the equation.
[tex] log_{5} x^{2} =log_{5} 4
Both sides have log with same base so it can be eliminated.
Eliminating log from both sides we have:
[tex] x^{2} =4
To solve for x we take root of both sides
x=2,-2.
The measure of angle x is 25 more than 4 times the measure of its complement. find the measure of x. x= degrees
Answers
x = 385 -4x . . . . . . . . . eliminate parentheses
5x = 385 . . . . . . . . . . . .add 4x
x = 77 . . . . . . . . . . . . . . divide by 5
The measue of angle x is 77°.
A knife is 3 times the cost of the spoon 9 spoons and 12 knives costs £82.80 work out the cost of 1 knife
Answers
Hope this helped!
The cost of spoon is £1.84 and therefore the cost of one knife is £5.52.
Given :
A knife is 3 times the cost of the spoon.9 spoons and 12 knives costs £82.80.Solution :
This question is solve by creating a linear equation and linear equations are nothing but yet another subset of "equations". Linear calculations that requires more than one variable can be done with the help of linear equations.The standard form of a linear equation in one variable is ax + b = 0.Now let x be the cost of spoon. Than the cost knife is 3x. It is given that 9 spoons and 12 knives costs £82.80.
[tex]9x + 12\times(3x)= 82.80[/tex]
[tex]9x + 36x = 82.80[/tex]
[tex]45x =82.80[/tex]
[tex]x = 1.84[/tex]
Therefore the cost of 1 knife = [tex]1.84\times 3 = 5.52[/tex].
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Please help and show all work. 20 points.
Answers
.. Asector = (1/2)r^2*θ . . . . . . . angle in radians
.. = (1/2)*(24 m)^2*(2π/3)
.. = 192π m^2
The area of the white triangle in that sector is
.. Atriangle = (1/2)r^2*sin(θ)
.. = (1/2)*(24 m)^2*(√3)/2
.. = 144√3 m^2
The area of the shaded segment is the difference of these
.. Asegment = Asector -Atriangle
.. = (192π -144√3) m^2
The 2nd selection is appropriate.
Find the average rate of change of the function over the given interval. f(x) = 3x − 2; [0, 5]
Answers
This brings us to our first step: filling in the x-coordinates (of the domain) in the formula.
f(0) = 3*0 - 2 = -2
f(5) = 3*5 - 2 = 15- 2 = 13
We now have found the following coordinates
(0,-2) and (5,13).
To find the avarage rate of change we need to use the following formula:
rate of change = Δy / Δx
With Δ representing the change of coordinates. Filling in this formula, gives us:
rate of change = [tex] \frac{13 - -2}{5 - 0} = \frac{15}{5} = 3 [/tex]
So our answer: the average rate of change on the interval (domain) [0,5] is 3.
The average rate of change of the function over the given interval is 3.
Explanation:To find the average rate of change of the function over the given interval, we need to calculate the change in the function values and divide it by the change in the input values.
Step 1: Calculate the function values for the two endpoints of the interval.
f(0) = 3(0) - 2 = -2
f(5) = 3(5) - 2 = 13
Step 2: Calculate the change in the function values.
Change in function values = f(5) - f(0) = 13 - (-2) = 15
Step 3: Calculate the change in the input values.
Change in input values = 5 - 0 = 5
Step 4: Divide the change in function values by the change in input values.
Average rate of change = (Change in function values) / (Change in input values) = 15 / 5 = 3
This is embarrassing.. went to a Hobby Lobby job interview.. and flunked the math test.. ack! this involved percentages..how do you get 66% off of a total, and like tax % 7.5 we are not allowed to use a calculator
Answers
To get a percentage off of a total without a calculator, multiply the total by the percentage as a decimal. To calculate the total amount including tax, multiply the total by the tax percentage as a decimal and then add the result to the total.
Explanation:To calculate a percentage off a total without using a calculator, you can multiply the total by the percentage as a decimal. For example, to find 66% off of a total, multiply the total by 0.66. To calculate the total amount including tax, you can add the tax amount to the original total. For a 7.5% tax, multiply the total by 0.075 and then add the result to the total.
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Which properties of equality justify steps b and d?
1. Multiplication Property of Equality; Subtraction Property of Equality
2. Subtraction Property of Equality; Division Property of Equality
3. Subtraction Property of Equality; Multiplication Property of Equality
4. Subtraction Property of Equality; Subtraction Property of Equality
Answers
Subtracting seven from both sides is the justification for step b to get rid of the positive seven on both sides. Multiplying by 2 on both sides to get rid of the fraction on the left side of the equation is the justification for step d.
The properties that justify steps b and d, is 1. Multiplication Property of Equality; Subtraction Property of Equality.
Understanding these properties is crucial in solving equations properly.
Key Properties of Equality:
Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex], then [tex]a \times c = b \times c[/tex].
Subtraction Property of Equality: This property indicates that if you subtract the same number from both sides of an equation, the two sides will also remain equal.
Example: If [tex]a = b[/tex], then (a - c = b - c.
Division Property of Equality: Similar to multiplication, this property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex] and [tex]c \neq 0[/tex], then [tex]\frac{a}{c} = \frac{b}{c}[/tex].
Justification Steps b and d:
Given the context, let's assume step b involves subtracting a term from both sides of an equation, and step d involves multiplying both sides by a number.
For step b (subtracting x):
This step is justified by the Subtraction Property of Equality because the same amount [tex]x[/tex] is subtracted from both sides, which keeps the equality balanced.
For step d (multiplying by a number):
This step is justified by the Multiplication Property of Equality as you are multiplying both sides of the equation by the same non-zero number, thus preserving the equality.
Three brothers have ages that are consecutive even integers. the product of the first and third boys' ages is 20 more than wice the second boy's age. find the age of each of the three boys.
Answers
second brother = x + 2
third brother = x + 4
The product of the first and third boys' ages is 20 more than twice the second boy's age:
x(x+4) = 2(x+2) + 20
x² + 4x = 2x + 4 + 20
x² + 4x - 2x - 24 = 0
x² + 2x - 24 = 0
(x - 4)(x + 6) = 0
x = 4 or -6 (rejected, age cannot be negative)
First brother = 4
Second brother = 4 + 2 = 6
Third brother = 4 + 4 = 8
The three boys are 4, 6, and 8 years old.
Let x be the age of the first boy, snce they are consecutive even integers, they will be 2 way from each other.
1st boy= x
2nd boy= x+2
3rd boy = x+4
"product means the answer to a multiplication problem;
x(x+4)=20+2(x+2)
x%5E2+4x=20+2x+4
x%5E2+4x-2x=20+4
x%5E2+2x=24
x%5E2+2x-24=0
(x+6)(x-4)=0
x+6=0
x=-6
x-4=0
x=4
SInce we know they are even integers, the answerhas to be;
x=4
so the first boys age = 4
2nd boy= 4+2=6
3rd boy= 4+4=8
Hope this helps you