Answers
Answer:
y = 2 3/8
Step-by-step explanation:
Multiply by the denominator. This gives a linear equation that can be solved in the usual way.
... 3 = 8(y -2)
Divide by 8.
... 3/8 = y - 2
Add 2
... 2 3/8 = y
_____
In problems involving rational expressions, it often works well to multiply by the product of the denominators, or by their least common multiple, if that is easy to find. Doing this eliminates fractions. Here there is only one denominator (y-2), so we multiply by that.
Related Questions
The average age of six children is 13 years and 5 months. a seventh child joins the group, increasing the average age by two months. how old is this seventh child
idk
Answers
Answer:
14 years 7 months
Step-by-step explanation:
If the average age was increased by 2 months by adding a 7th child, the total age was increased by 2·7 months = 14 months more than the previous average. That is, the added child's age is 14 months more than the previous average, so is ...
... (13 years + 5 months) + (1 year + 2 months) = 14 years + 7 months
_____
For the non-believers:
The previous total of all ages was ...
... 6 × (13 years 5 months) = 80 years 6 months
The new total of all ages is ...
... 7 × (13 years 7 months) = 95 years 1 month
The amount added to the previous total is ...
... (95 1/12 - 80 6/12) years = 14 7/12 years = 14 years 7 months
To find the age of the seventh child, calculate the total age of the six children and the total age of all seven children.
Explanation:To solve this problem, we can use the concept of the average. Step 1: Calculate the total age of the six children by multiplying the average age (13 years and 5 months) by the number of children (6). Step 2: Calculate the total age of all seven children by multiplying the new average age (13 years and 7 months) by the total number of children (7). Step 3: Subtract the total age of the six children from the total age of all seven children to find the age of the seventh child.
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Fill in the blank: linear functions grow by equal ____________ over equal intervals.
A. expressions
B. variables
C. factors
D. differences
Answers
Answer:
D. differences
Step-by-step explanation:
One way to identify a linear function is by checking the differences over equal intervals. If they are the same, then the function is linear.
Answer:
D. Differences
Step-by-step explanation:
Linear function grow by equal differences over equal intervals as, on a graph, it is shown by a steady increasing line. Exponential functions, on the other hand, do not.
Which expression below gives the average rate of change of the function g(x) = -x2 - 4x on the interval 6 ≤ x ≤ 8 ?
plsss
Answers
Answer:
the first selection (see below)
Step-by-step explanation:
The average rate of change (m) on the interval [x1, x2] is given by ...
... m = (g(x2) -g(x1))/(x2 -x1)
For g(x) = -x²-4x and (x1, x2) = (6, 8), the expression is the one attached.
Answer:
[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]
Step-by-step explanation:
average rate of change of the function g(x) = -x^2 - 4x on the interval 6 ≤ x ≤ 8
To find average rate of change we use formula
Average =[tex]\frac{g(x_2)-g(x_1)}{x^2-x_1}[/tex]
use the given interval 6<=-x<=8
x2=8 and x1= 6
we replace the value in the given formula
g(x) = -x^2 - 4x
[tex]g(8) = -8^2 - 4(8)[/tex]
[tex]g(6) = -6^2 - 4(6)[/tex]
x2-x1 is 8-6
So equation becomes
[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]
Help Now 5 points and will mark brainliest!!! On a trip to his grandparents, Donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes. How many miles did Donny drive? A) 55 miles B) 65 miles C) 70 miles D) 90 miles
Answers
If you travel at a constant speed, you follow this equation:
[tex] d = st [/tex]
where d is the distance, s is the speed and t is the time.
In this example, you first travel 60 miles per hour for 45 minutes. Since 45 minutes are 3/4 of a hour, you will cover a distance of
[tex] d_1 = 60\cdot\dfrac{3}{4} = 45 [/tex]
In the second part, since 30 minutes is half a hour, you will cover a distance of
[tex] d_2 = 50\cdot\dfrac{1}{2}=25 [/tex]
So, in total, you travel
[tex] d=d_1+d_2=45+25 = 70 [/tex] miles
Answer:
C-70 miles
Hope this helped :)
What is the least common multiple of the number 64, 16, 2, and 8?
Answers
Answer:
64
Step-by-step explanation:
Since 64 is a multiple of itself and of all the other numbers, the answer is 64.
Max wants to know if the following is correct.3+5=6+2. Draw and write to tell how you know.
Answers
Answer:
Yes
Step-by-step explanation:
3+5 is 8 and 6+2 is also 8. You can draw 3 apples with 5 other apples, and count that there are 8 of them and draw 6 apples with 2 other apples that make up 8 apples. Or you can rearrange the apples to be 5 and 3 and 6 and 2.
if a polynomial function f(x)has root -2 + square root 8 and 9 what must be a factor of f(x)
Answers
The polynomial function f(x) having roots [tex]-2 + \sqrt(8)[/tex] and 9 would have factors [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9). These roots can be determined by setting the known values equal to x and subtracting from x.
Explanation:In mathematics, specifically in polynomial functions, the roots of a function are values that make the function equal to zero. These roots correspond to the factors of the polynomial function. If a function f(x) has roots -2 + square root 8 and 9, then the factors of f(x) will be those values set equal to x and then subtracted from x.
Therefore, the corresponding factors would be [tex]x - (-2 + \sqrt{8})[/tex] and (x - 9). When you simplify these, they become [tex](x + 2 - \sqrt(8))[/tex] and (x - 9). To further simplify, we know that [tex]\sqrt(8) = 2\times \sqrt(2),[/tex] therefore we get [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9).
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If a polynomial function has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of the polynomial.
Explanation:Polynomial functions are mathematical expressions comprising variables, coefficients, and non-negative integer exponents. They are used in various fields, including mathematics, physics, engineering, and computer science. They model relationships between variables, aiding in solving equations, analyzing data, and predicting outcomes in diverse applications.
If the polynomial function f(x) has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of f(x). This is because if a number is a root of a polynomial, then the polynomial can be divided evenly by the corresponding linear factor.
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Someone please help me
Answers
Step-by-step explanation:
1. See the attachment for the filled-in diagram. Adding the contents of the figure gives the sum at the bottom, matching selection C.
2. If we let "d" represent the length of the second volyage, then the total length of the two voyages is ...
... (d+43) + d = 1003
... 2d = 960 . . . . . . . subtract 43
... d = 480 . . . . . . . . divide by 2
The second voyage lasted 480 days.
3. 1.9% - 1.9/100 = 0.019. Adding this fraction to the original means the original is multiplied by 1 +0.019 = 1.019. Doing this multiplication each year for t years means the multiplier is (1.019)^t.
Since the starting value (in 1975) is 4 (billion), the population t years after that is ...
... P(t) = 4(1.019)^t
The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?
Answers
Answer:
65550 is the population at the end of 2017
Step-by-step explanation:
Population at the beginning of 2106: 60000
Increased 15% in 2016
Increase = 60000*.15 = 9000
New population = 60000+9000 = 69000
The population at the beginning of 2017: 69000
Decrease by 5% in 2017
Decrease 69000*.05 = 69000*.05 = 3450
New population = 69000-3450=65550
The population at the end of 2017 is 65550
One of the same side angles of two parallel lines is three times the other angle. Find the measures of these two angles.
Answers
45° and 135°
Step-by-step explanation:If the smaller is represented by x, then the larger is 3x. The two angles are supplementary, so ...
... x + 3x = 180°
... 4x = 180°
... 180°/4 = x = 45°
... 3x = 135°
The two angles are 45° and 135°.
Answer:
45° and 135°
Step-by-step explanation:
If the smaller is represented by x, then the larger is 3x. The two angles are supplementary, so ...
... x + 3x = 180°
... 4x = 180°
... 180°/4 = x = 45°
... 3x = 135°
The two angles are 45° and 135°.
Step-by-step explanation:
True or false: the variable in an exponential function is always the exponent of the power.
Answers
Answer:
False
Step-by-step explanation:
It is the exponent of a base.
The variable in an exponential function is always the exponent of the power is false.
What are exponential functions?When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.
Their usual form is specified below. They are written in several such equivalent forms.
The variable in an exponential function is always the exponent of the power is false. It is the exponent of a base.
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Given f '(x) = (x − 4)(6 − 2x), find the x-coordinate for the relative minimum on the graph of f(x).
Answers
Answer:
x = 3
Step-by-step explanation:
f'(x) = 0 for x = 3 and x = 4 . . . . by the zero product rule.
The coefficient of x² in f'(x) is negative, so the parabola opens downward.
f''(x) is positive for x < 3.5, so the coordinate x = 3 represents a relative minimum.
The graph shows the distance a cyclist traveled in yards (y) as a function of time in seconds (x). The graph is divided into four segments; labeled P, Q, R, and S, respectively.
Which segment did the cyclist complete before stopping for a drink of water?
P
Q
R
S
Answers
Answer:
P
Step-by-step explanation:
The distance doesn't change during segment Q, so that is when the cyclist is stopped. The segment before that is labeled P.
The question asks the label of the segment before the one where the cyclist was stopped, so the appropriate choice is P.
Answer:
it is Q
Step-by-step explanation:
Because it is stopped and its a strait line making it look like it is taking a brake.
b(1)=-2
b(n)=b(n-1)-7
Find the third term in the sequence
Answers
b(3) = -16
Step-by-step explanation:b(2) = b(1) -7 = -2 -7 = -9
b(3) = b(2) -7 = -9 -7 = -16
Answer: b(3)= -16
Step-by-step explanation:
A salesperson receives a 5% commission on the sale of each car. If the commission on a car is $490, what is the price of the car?
*Please Show Work*
Answers
Answer:
$9800
Step-by-step explanation:
commission = 5% × car price
20 × commission = 100% × car price . . . . . . multiply by 20
20 × $490 = car price = $9800 . . . . . . . . . . fill in given value of commission
The price of a car on which a salesperson earns a 5% commission of $490 is calculated by dividing the commission amount by the commission rate as a decimal (0.05), resulting in a car price of $9,800.
The question is asking to calculate the price of a car based on the commission earned by the salesperson. The salesperson receives a 5% commission on each sale and has earned $490 from the sale of one car.
To find the price of the car, we need to set up a simple equation. If 5% of the price results in a $490 commission, we need to divide the commission by the percentage rate expressed as a decimal.
The calculation will look as follows:
Convert the commission percentage to a decimal: 5% = 0.05.
Divide the commission earned by the decimal rate: $490 ÷ 0.05.
The result is the price of the car.
So, $490 ÷ 0.05 = $9,800.
Therefore, the price of the car is $9,800.
Either Table A or Table B shows a proportional relationship.
Table A:
x −2 −1 0 1
y 2 3 0 5
Table B:
x −1 0 1 2
y −3 0 3 6
nvm you dont have to answer this i just found out the answer
Answers
Answer:
Table B shows a proportional relationship.
Step-by-step explanation:
In a proportional relationship two quantities vary directly with each other. It means
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
Where, k is the constant of variation.
The ordered pairs of table A are (-2,2), (-1,3), (0,0) and (1,5).
From these ordered pairs we can conclude that the value of y-coordinate is not changing according to the x-coordinate because the values of x increased by 1 for each ordered pair but the value of y is not increasing in the same proportion..
The ordered pairs of table B are (-1,-3), (0,0), (1,3) and (2,6). The value of y increasing at a constant rate 3 and the value of y-coordinate is 3 times of x-coordinate.
Choose any two ordered pairs of table B. Let the two points are (0,0) and (1,3), then the constant of variation is
[tex]k=\frac{y_2-y_1}{x_2-x_1}=\frac{3-0}{1-0}=3[/tex]
The proportional relationship is defined as
[tex]y=3x[/tex]
Therefore, 3 is the constant of variation and rate of change.
So, Table B shows a proportional relationship.
Answer:
Table B Shows proportional relationship.
Step-by-step explanation:
Correct answers are the green and yellow dots. Hope this helps. The red dot I got wrong.
Solve the equaton for x.
3x = -4y
A. x = -12y
B. x = -12/y
C. x = -3/4y
D. x = -4y/3
Answers
3x = -4y
To solve for X, divide both sides by 3:
x = -4y / 3
The answer is D.
In the figure below, figure ABCD is similar to figure WXYZ. What is the length of side XY?
Answers
Answer:
XY = 150
Step-by-step explanation:
AB = 8
W Z = 80
SF = 10
8 x 10 = 80
So if BC = 15
XY = 15 x 10 = 150
Answer:
150Step-by-step explanation:
you can solve with a proportion
8 : 15 = 80 : x
x = 15 * 80 : 8
x = 150
or you find the rate from AD and WZ
8 : 80
simplify
1 : 10
15 * 10 = 150
Algebra 2 help!
What are the x and y intercepts of the equation?
Round the answers to the nearest hundredth.
y = log(12x + 7) - 3
Answers
Answer:
x-intercept: 82.75y-intercept: 2.15Step-by-step explanation:
A graphing calculator can show you the intercepts.
___
Or you can figure them out.
The y-intercept is where x=0, so is ...
y = log(12·0 +7) -3 = log(7) -3 ≈ -2.1549 ≈ -2.15
___
The x-intercept is where y = 0, so is ...
0 = log(12x +7) -3
3 = log(12x +7) . . . . . . add 3
10^3 = 12x +7 . . . . . . . take the antilog
993 = 12x . . . . . . . . . . subtract 7
993/12 = x = 82.75 . . . divide by the coefficient of x
Prove that for any value of x the value of the expression x^4–(x^2–7)(x^2+7) is equal to 49.
Answers
Multiplying it out using the distributive property, you have ...
... x^4 -(x^4 -7x^2 +7x^2 -49)
... = x^4 -x^4 +7x^2 -7x^2 +49 . . . . distribute the minus sign
... = x^4(1 -1) +x^2(7 -7) +49 . . . . . . collect like terms
... = 0 +0 + 49 . . . . . . . . . . . . . . . . . .simplify
... = 49
If one card is drawn from a standard 52- card deck and not replaced, what is the probabity of getting an ace on the next draw?
Answers
Answer:
The probability is about 7.7%
Step-by-step explanation:
A probability is the ratio of the number of relevant outcomes and the number of all possible outcomes. To answer this question we do some counting first:
Consider two draws. We are interested in the second draw being an Ace, the first draw can either be an Ace or not, so, there are two cases of a relevant outcomes (all without replacement):
(number of relevant oucomes n ) = (number of cases of Ace-Ace draws) + (number of cases of NonAce-Ace draws):
[tex]n=4\cdot 3+{48\cdot4}= 204[/tex]
(number of possible outcomes) = (number of choices at first draw) * (number of choices at second draw) = 52 * 51 = 2652
The probability is then
P = 204/2652 = 0.0769, or about 7.7%
A small cruising ship that can hold up to 66 people provides three-day excursions to groups of 42 or more. If the group contains 42 people, each person pays $58. The cost per person for all members of the party is reduced by $1 for each person in excess of 42. Find the size of the group that maximizes income for the owners of the ship.
Answers
50 people
Step-by-step explanation:Let x represent the number of people on the cruise. The amount they each must pay is ...
... ($58 -(x -42)) = $100 -x
The revenue from the group is the product of the number of people and the amount each pays:
... r(x) = x·(100 -x)
This describes a downward-opeing parabola with zeros at x=0 and x=100. The vertex (maximum) will be found halfway between those zeros, at x=50.
A group size of 50 maximizes revenue from the cruise.
(3a^2)^3 in simplest form
Answers
Answer:
27 ^6
Step-by-step explanation:
The first step is to split the expression into 2 parts (ab)^x = a^x b^x
(3a^2)^3
3^3 a^2 ^3
27 a^2^3
We can then us the power of power rule to simplify the exponents x^a^b = x^(ab)
27 a^(2*3)
27 ^6
estimate 8 2/9- 3 6/7
Answers
Answer:
4
Step-by-step explanation:
8 2/9 is close to 8
3 6/7 is close to 4
8 2/9 - 3 6/7 is close to 8-4 = 4
My estimate is 4
identifying equation in point slope form for the line perpendicular to y equals negative 1 / 3x - 6 that passes through -1,5
Answers
Answer:
y = 3x +8
Step-by-step explanation:
The slope of the given line is -1/3. The slope of a perpendicular line is the opposite of the reciprocal of that: -1/(-1/3) = 3.
Then, in point-slope form, the equation of the line is ...
... y - k = m(x - h) . . . . . for slope m through point (h, k)
... y - 5 = 3(x -(-1)) . . . . . for line of slope 3 through (-1, 5)
... y = 3x +8 . . . . . . . . . simplify
At the produce counter, 71⁄5 pounds of seedless grapes cost $12.89. How much would 3 pounds cost? A. $3.58 B. $5.16 C. $1.79 D. $5.37
Answers
Answer:
D. $5.37
Step-by-step explanation:
We need to figure out how much grapes cost per pound
Change the mixed number to an improper fraction
7 1/5 = (5*7+1) /5 = 36/5
$12.89 / 36/5
Copy dot flip
12.89 * 5/36 = 1.79 per lb
If we are purchasing 3 pounds, we will multiply by 3
3 lbs * $1.79 / lb = $5.37
convert fractions to a fraction out of 100.
15/60=?
30/60=?
25/75=?
Answers
The numerator can be found by multiplying each of these fractions by 100. It can be helpful to reduce these fractions first.
Here, we calculate those numerators.
a) 15/60 · 100 = 1/4 · 100 = 100/4 = 25
b) 30/60 · 100 = 1/2 · 100 = 100/2 = 50
c) 25/75 · 100 = 1/3 · 100 = 100/3 = 33 1/3
Of course, the denominator is 100, so the fractions are ...
... 15/60 = 25/100
... 30/60 = 50/100
... 25/75 = (33 1/3)/100
_____
Comment on this solution
Effectively, we have multiplied each fraction by 1 = 100/100. That is ...
... fraction × (100/100) = (fraction × 100)/100
This changes the form, but not the value.
Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the same? Yoga Studio A: Membership: $24.00 Monthly Fee: 21.50. Yoga Studio B: Membership: $41.00 Monthly Fee: $17.25
Answers
In 4 months, the total cost of Yoga Studio A would equal that of Yoga Studio B
The cost of Yoga Studio A at any given month can be represented as:
= Membership fee + (Monthly fee x Number of months)
Assuming number of months is x, the formula would be:
= 24 + (21.50 × x)
= 24 + 21.50x
Yoga Studio B would be:
= 41 + (17.25 × x)
= 41 + 17.25x
In order to find the month that these costs would be equal, equate both formulas:
24 + 21.50x = 41 + 17.25x
21.50x - 17.25x = 41 - 24
4.25x = 17
x = 17 / 4.25
x = 4 months
In conclusion, their costs would be the same in the 4th month.
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Kayla ran L laps around a 14-mile track. The equation d = 0.25L gives the number of miles she ran. If d is 1.5, which statement does NOT describe what L is?
A. The unknown in the equation.
B. The number of laps Kayla ran.
C. The length of one lap.
D. The number of laps needed to run 112 miles.
Answers
Answer:
C. The length of one lap.
Step-by-step explanation:
In the first four words, the problem statement tells you that L is the number of laps run. It is not the length of one lap.
_____
Comment on the problem presentation
Appropriate punctuation would be very helpful. Apparently, it is a 1/4-mile track, not a 14-mile track. Apparently, the distance is 1 1/2 miles, not 112 miles. Copying and pasting problem text often leaves out the special symbols used on some web sites. Some editing is usually needed.
i will give brainlest thanks
Answers
Answer:
68
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
... Tan = Opposite/Adjacent
For this geometry, this means ...
... tan(x°) = 5/2
Taking the inverse tangent, we can find x.
... x° = arctan(5/2) ≈ 68.199°
... x ≈ 68