The speed for maximum car mileage will be 48 mph. The maximum gas mileage will be 29.5 mpg.
We are provided with an equation for mileage of car as
m(x) = -0.028x² + 2.688x -35.012
here , variable 'x' is the speed of the car.
Now
for the maximum speed of the car we have to first take the derivative of m(x) and then for the boundary value condition by putting the derivative equal to zero.
comparing to the equation ax² + bx + c , if the value of
'a' is positive, then we have minimum value at 1st derivative = 0
'a' is negative we have maximum value .
in this case a = -0.028 ( -ve) so we will have a maxima at 1st derivative.
so, dm/dx = -0.056x + 2.688
putting the 1st derivative = 0 , we have
x = 48
therefore , car gets maximum gas mileage at speed of 48 mph.
Also , putting this value in equation (1) we will get max. mileage.
so max. mileage = -0.028 (48)² + 2.688 x 48 - 35.012
= -64.512 + 129.024 - 35.012
= 29.5
so the maximum gas mileage will be 29.5 mpg .
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Type the correct answer in the box. Use numbers instead of words. An expression is shown. 36 ÷ (4 + 2) What is the value of the expression?
The result of the expression 36 ÷ (4+2) is 6
The expression is
36 ÷ (4+2)
To solve this expression, we have to apply the arithmetic operations in the given expression
An arithmetic operation is the operation specified by combining number or variable with one arithmetic operator. The basic arithmetic operations are addition, subtraction, division and multiplication.
First do the arithmetic operations in the bracket
Add 4 and 2 in the expression
36 ÷ (4+2) = 36 ÷ 6
Divide the number 36 by 6 in the expression
36 ÷ 6 = 6
Hence, the result of the expression 36 ÷ (4+2) is 6
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Mike Lasueze is a salesperson in the appliance department at Wicklow Appliance Inc. He is guaranteed a minimum salary of $220 per week or 5.5% of his total sales, whichever is greater. What is his gross pay for a week in which his total sales were $8,400?
For a sale of $8400 made his gross pay is $373.21
In this question, we have been given Mike Lasueze is guaranteed a minimum salary of $220 per week or 5.5 percent of his total sales, whichever is greater.
We need to find his gross pay for a week in which his total sales were $8,400
weekly pay = $220
commission = 5.5% of sales
= 0.055 of sales
let m be the total sale and his gross pay be represented by y
So, we get an equation for the total/gross pay:
y = 0.055x + 220
Required is the gross pay y for x = 8400
y = 0.055(8400) + 220
y = 682
Therefore, for a sale of $8400 made his gross pay is $373.21
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Find the measure of 44.
H
130⁰
50°
44
130⁰
50°
44 = [?]° i’m slow someone help
Answer:
Find the measure of each angle. 1. 23. =70°. 2. 45. 5. 24. 9.48 ... Exterior. ANGLE. ¥180-50=130. 6. 213 2106°. =106°. 44-10+42=180. 44 = 148
Step-by-step explanation:
In Figure 1, a parallelogram is drawn in a trapezium. If the area of the parallelogram is 390 cm², find the area of the trapezium.
Step-by-step explanation:
the area of the parallelogram is
baseline × height.
we know the baseline (15 cm), because as parallelogram it must have 2 pays off equal sides. so, the bottom side must be 15 cm too.
15×height = 390
height = 390/15 = 26 cm
now, the height of the triangle on the right is the same height.
and the baseline of this triangle is 25 - 15 = 10 cm.
the area of a triangle is
baseline × height / 2
so, in our case
10 × 26 / 2 = 10×13 = 130 cm²
therefore the area of the trapezium is the area of the parallelogram plus the area of the triangle :
390 + 130 = 520 cm²
What is the solution to -5 < 9 - 6x
Answer:
x < 7/3
Step-by-step explanation:
[tex] - 5 < 9 - 6x[/tex]
[tex] - 14 < - 6x[/tex]
[tex] \frac{7}{3} > x[/tex]
[tex]x < \frac{7}{3} [/tex]
helppppp me please with this question
The total weight is 57kg
The perimeter = 2×(8+6)
= 2(14) = 28m
The diagonal = √8²+6²
= √64+36
100 = 10m
The total length of the frame =
28+10 = 38 m
Therefore the total Weight =
38× 1.5 kg = 57 kg
What is the formula for weight?
The force of gravity acting on an item is known as its weight, and it can be determined using the formula w = mg, which equals the mass times the acceleration of gravity.
You must multiply the sectional area, length, and density collectively to determine the weight of your metal. The product must then be divided by 1,000 in order to convert the weight to kilograms. There are several online metal weight calculators that you may use to figure out the weight of your metal product.
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Suppose point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5. Describe the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3.
Using proportions, the coordinates of point P that divides the directed line segment YX in the given ratio are found according to the following rule:
P - X = 3/8(Y - X).
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem relating the variables.
One example of application is for the coordinates of a point dividing a segment, as the distance between one end point and the dividing point is a fraction of the total length of the segment.
In the context of this problem, we have that point P divides segment XY in a 3:5 ratio, meaning that PX is 3/8 of the total distance y/x, hence the following proportional equation is built:
P - X = 3/8(Y - X).
In which:
X represents the coordinates of point X.Y represents the coordinates of point Y.This equation is used to find both the x-coordinate and the y-coordinate of P, as follows:
For the x-coordinate, P is replaced by x, while X and Y are replaced by it's respective x-coordinates.For the y-coordinate, P is replaced by y, while X and Y are replaced by it's respective y-coordinates.More can be learned about proportions at https://brainly.com/question/24372153
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✨Hello! I need some help it's very urgent I will be marking brainliest✨
first blank: never, sometimes, always
second blank: less than or equal to negative 3, between -3 and 3, greater than or equal to 3, greater than or equal to -3, less than or equal to 3.
third blank: positive number, less than or equal to zero, negative number, negative number, a number greater than or equal to zero.
Answer:
Sometimes, Never, and Always.
(Sounds like a good movie title).
Step-by-step explanation:
See attached image.
Which two transformations can be used to obtain the graph of G(x) = -4√x , from the graph of F(x)=√x?
Given: The base function
[tex]F(x)=\sqrt{x}[/tex]To Determine: The transformation that would give the function G(x)
[tex]G(x)=-4\sqrt{x}[/tex]Solution
Let us plot the graph of the base function and the new function as shown below
It can be observed that there exist a reflection across the x-axis, also a vertical stetch by a factor of 4
Hence, the correct answer is a vertical stretch by a factor of 4, followed by a reflection across the x-axis, OPTION A
A. 20 B. 30 C. 23 D. 39 I need a little help with this question
Given: A table that shows the result of a survey from 35 randomly selected students at Courtney's school.
Required: To determine the number of votes Rockzilla is expected to receive from a population of 115 students at Courtney's school.
This is achieved thus:
First, we determine the probability of Rockzilla's votes as follows:
[tex]\begin{gathered} Prob.=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }total\text{ }outcome} \\ Prob.=\frac{6}{35} \end{gathered}[/tex]Next, we determine the number of votes Rockzilla is expected to receive as follows:
[tex]\begin{gathered} Expected\text{ }votes=\frac{6}{35}\times115 \\ Expected\text{ }votes\approx20 \end{gathered}[/tex]Hence, the answer is:
[tex]20[/tex]Pls help I need work and a answer I have given an exsample
The original price of the jacket before sale amount is $45.
Original price of the jacket will be calculated by forming the expression relating mentioned price. Let us assume the original price of the jacket to be x.
Writing the equation representing original price, percentage and price after sale
80%×x = 36
Converting percentage to fraction
80/100×x = 36
Shifting the fraction to Right Hand Side of the equation
x = 36×100/80
Cancelling zero as it is common in numerator and denominator and performing division
x = 45
Therefore, according to the sale price, the original price of jacket is $45.
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A family drives 4 1/2 miles in 1/10 of an hour. How many miles will they drive in 3/4 hours?
URGENT NEED!
Consider the conjecture, "Any number divisible by 2 is also divisible by 4" Is each number a counterexample of the conjecture? Select yes or no
12 yes or no
19 yes or no
22 yes or no
28 yes or no
30 yes or no
Which number is next in the following sequence?
1,2,2,4,8,32
The classification of the numbers as counterexamples of the conjecture is given as follows:
12: no.19: no.22: yes.28: no.30: yes.The next number in the sequence is of 256.
Which numbers are counter example of the conjecture?The conjecture is defined as follows:
"Any number divisible by 2 is also divisible by 4"
Hence the counterexamples are the numbers that are divisible by 2 but not by 4, then they are classified as follows:
12: no. (divisible by both 2 and 4).19: no. (not divisible by 2, hence it cannot be a counterexample of the conjecture).22: yes. (divisible by 2 but not by 4).28: no. (divisible by both 2 and 4).30: yes. (divisible by 2 but not by 4).SequenceEach number in the sequence is given by the multiplication of the two previous terms, as:
1 x 2 = 2.2 x 2 = 4.4 x 2 = 8.8 x 4 = 32.Then the next number is calculated as follows:
32 x 8 = 256.
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simplify the following expression
The value of solution of expression is,
⇒ (3⁵)
We have to given that;
The expression is,
⇒ (3³ × 3⁴) ÷ 3²
Now, We can simplify by rule of exponent as;
⇒ (3³ × 3⁴) ÷ 3²
⇒ (3³ ⁺ ⁴) ÷ 3²
⇒ (3⁷) ÷ 3²
⇒ (3⁷⁻²)
⇒ (3⁵)
Thus, The value of solution of expression is,
⇒ (3⁵)
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The total cost of a jacket and a pair of shoes was $91.43. if the price of the jacket was $7.65 less than the pair of shoes, what was the price of the jacket? express your answer as a simplified fraction or a decimal rounded to two places.
The price of the jacket in decimals is $ 41.89
The decimal numeral system is widely used to express both integer and non-integer numbers.
The Hindu-Arabic number system has been expanded to include non-integer values. The term "decimal notation" is used to refer to the way that numbers are represented using the decimal system.The decimal system has been developed to represent any real number in an endless number of decimals by using any number of digits after the decimal separator (see decimal representation). Since there are only a few non-zero digits beyond the decimal separator, the decimal numerals in this context are sometimes referred to as terminating decimals. An unending decimal that, at a given point, continues to use the same set of digits repeatedly is said to be recurrent.Let the price of the jacket be x.
Price of the pair of shoes = x + 7.65
Total cost of both the pieces = x + x + 7.65 = 2x+7.65
But the total cost is $91.43
Hence forming a linear equation we get :
$91.43= 2x+7.65
solving the linear equation for x we get :
x=$ 41.89
hence the cost of the jacket is $ 41.89 .
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You and your family went out to dinner if the dinner was $52 and you left a 25% tip how much did your dinner cost altogether
Using percentages we can conclude that the total cost of the dinner was $65.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the total cost of dinner:
The dinner cost was $52.The tip was 25% of the dinner, then we need to find the 25% of 52 as follows:
52/100 × 25 = 13So, the tip was $13.The total cost of the diner was $52 + $13 which is $65.
Therefore, using percentages we can conclude that the total cost of the dinner was $65.
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What is the minimum value of the function g(x) = |x – 4| + 8 on the interval [-2, 1]?
A. 14
B. 5
C. -2
D. 11
[tex]|x-4|[/tex] is non-negative, and vanishes when [tex]x=4[/tex].
For all [tex]x\in[-2,1][/tex], we have [tex]x<4[/tex], so by definition of absolute value,
[tex]g(x) = |x-4| + 8 = -(x-4)+8 = -x+4[/tex]
which is strictly decreasing on [-2, 1] since [tex]g'(x)=-1<0[/tex]. Then the minimum value of [tex]g[/tex] on [-2, 1] occurs at the endpoint [tex]x=1[/tex], so that
[tex]\min\left\{g(x) \mid -2\le x\le1\right\} = g(1) = |1-4| + 8 = \boxed{11}[/tex]
a sunflower is planted in a garden and the height of the sunflower increases by 11% per day. 2.53 days after being planted the sunflower is 13 inches tall.
The sunflower had a height of 13 inches on day 0 and 13.91 inches on day 1.
Because sunflowers are big feeders and require a slightly alkaline soil (pH 6.0 to 7.5), make sure we put them in nutrient-rich soil. Before planting, we should also make sure the soil is weed-free. Since a sunflower is cultivated in a garden, its height grows by 7% every day. The sunflower is 15.7 inches tall 2.79 days after being planted. To get the sunflower's 1-day growth factor, apply the following calculation:
X x (1 + 0.07) ^ 2.79 = 15.7
X x 1.07 ^ 2.79 = 15.7
1.2077X = 15.7
X = 15.7 / 1.2077
X = 13
13 x 1.07 = 13.91
The sunflower therefore measured 13 inches on day 0 and 13.91 inches on day 1.
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Shirley assumes that none of the marks had rubbed off between Monday and Tuesday.
(b) If Shirley's assumption is wrong, explain what effect this would have on your answer
to part (a).
Using algebra, we know that the total number of bees in her hive is 540.
What is Algebra?One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
So,
Total no. of bees caught on Monday = 90Total no. of bees caught on Tuesday = 120The bees she marked = 20Then,
(A) Work out an estimate for the total number of bees in her hive
90 / x = 20 / 12090 / x = 1 / 690 x 6 = x540 = xThe estimated total no. of bees will be 540 bees.
(B) If Shirley’s assumption is wrong, explain what effect this would have on your answer to part (A).If Shirley's assumption is wrong, the answer would be too high and it would be overestimated.If the marks are rubbed off Shirley will have overestimated the number of bees (there will be fewer bees).Therefore, using algebra, we know that the total number of bees in her hive is 540.
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Amy has 4 pound of ground pork to make meatballs she uses 3/8 pound per meatball to make 9 meatballs.how many 1/8 pound meatballs can Amy make with the remaining turkey ?
Amy can make 29 meatballs from the remaining beef.
What are mathematics operations?
An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.A zero-arity operation, also known as a nullary operation, is a constant.The mixed product is an example of an arity 3 operation, also known as a ternary operation.Amy has 4 pounds of ground beef to make meatballs and he uses 3/8 pound per meatball to make 9 meatballs
We have to subtract 3/8 from 4
= 4 - 3/8
= 29/8
There are 29/8 pounds of ground beef left
Therefore the number of 1/8 pound meatball that can be produced from 29/8 pounds of ground beef can be calculated as follows;
= 29/8 ÷ 1/8
= 29
Hence Amy can make 29 meatballs
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suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?
I would tell her that out of all the people who took the verbal section, 23% scored higher than she did and 77% scored at or below her score. For the math section, 94% of those who took the exam scored at or below her score and 6% scored higher than she did.
Here's the complete question:
Suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?
I would tell her that out of all the people who took the verbal section, ___% scored higher than she did and ___ % scored at or below her score. For the math section, ___ % of those who took the exam scored at or below her score and ____ % scored higher than she did.
For the Verbal section: 100 - 77 = 23
For the Maths section: 100 - 94 = 6
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-13x-2x + 3 = -5x - 17
Answer:
-15x - 3
I hope this helps :)
Solve the equation for v.
v over 8 minus 4 equals negative 12
v = −128
v = −64
v = 16
v = 92
[tex] \frac{v}{8} - 4 = - 12 \\ \frac{v}{8} = - 12 + 4 \\ \frac{v}{8} = - 8[/tex]
Now I will use CROSS MULTIPLICATION
[tex]v = 8( - 8) \\ v = -6 4[/tex]
ATTACHED IS THE SOLUTION
Answer: v/8 - 4 = (-12)
-12 + 4 = (-8)
what divided by 8 is 8?
8/8 = 1 so 8 x 8 = 64
this means v = -64
64/8 - 4 = -12
- 64/8 is -8 and that minus 4 is -12
A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is more than 8. 42?.
A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. Then the probability that the sample is more than 8.42 is 0.0029 or 0.29%.
Using the normal distribution and the central limit theorem,
The mean is μ = 8.5
The standard deviation is σ = 0.22 .
A sample of 37 is taken, hence n = 37, s = 0.22/√37 i.e. s = 0.0362
The probability that the sample average is more than 8.40 is the p-value of Z when X = 8.4, hence:
Z = X - μ/σ
Z = 8.4 - 8.5/0.0362
Z = 2.76
Z = -2.76 has a p-value 0.0029
0.0029 = 0.29% probability that the sample average is more than 8.40.
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which equation is equivalent to the equation 5x + 30 = 45
Answer:
A answer is A brainly helps you
Which one is it help
Answer:
c the last 1
Step-by-step explanation:
bc y where the line ends on y is more than 30 and only 1 line is 5 so 35
Answer:
I think its the last one but it could also be the first
help me, i need the answers quickly
Answer:
#7 m∠4 = 30°
#8. m∠5 = 150
#22. A'(-6, -3), B'(-3, 4), C'(3, 5)
*** You may just want to put the coordinate points: (-6, -3), (-3, 4), (3, 5) without the A', B', C'. ***
#23. A'(6, -3), B'(3, 4), C'(-3, 5)
Step-by-step explanation:
#7 Angles 30° and ∠4 are corresponding angles and hence equal
#8 ∠4 and ∠5 are supplementary linear angles and add up to 180° So m∠5 = 180 - m∠4 = 180 - 30 = 150°
#22 Reflection about the x-axis means the x-coordinates do not change but the new y-coordinate is the negative of the original y coordinate
In other words, a point(x, y) in the pre-image becomes (x, -y) in the image
#23 With a 180° rotation both x and y axes change signs. (x, y) becomes (-x, -y)
help help me pleaseeee pleaseeeee.
WITH SOLUTION.
Answer:
[tex]1) \:\:\: \dfrac{14x}{y}[/tex]
[tex]2) \:\:\:\dfrac{16x^2}{9y^2}[/tex]
[tex]3)\:\:\:10[/tex]
[tex]4)\:\:\:\dfrac{x-2}{x+4}[/tex]
Step-by-step explanation:
I will provide detailed explanation for the first problem and quicker steps to solve the others. You should be able to figure them out
Dividing a number(integer or fraction) by a fraction is equivalent to multiplying that number by the reciprocal of the divisor fraction
So if you have an expression
[tex]\dfrac{a}{b} \div \dfrac{c}{d}\\\\\implies \dfrac{a}{b} \times \dfrac{d}{c}[/tex]
Question 1
[tex]\dfrac{14x^5}{5y^2}\:\div \dfrac{2x^4}{10y}\\\\= \dfrac{14x^5}{5y^2} \times \dfrac{10y}{2x^4}\\\\[/tex]
[tex]=\dfrac{14x^5\cdot \:10y}{10y^2x^4}[/tex]
10 in the numerator and 10 in the denominator cancel:
[tex]=\dfrac{14x^5y}{y^2x^4}[/tex]
[tex]\dfrac{x^5}{x^4} = x^{5-4} = x \;\;\;\;\;\;\text{Since }\dfrac{x^a}{x^b}=x^{a-b}}[/tex]
Likewise
[tex]\dfrac{y}{y^2} = y^{1-2} = y ^{-1} = \dfrac{1}{y}[/tex]
Therefore
[tex]=\dfrac{14x^5\cdot \:10y}{10y^2x^4} = 14 \dfrac{x}{y} = \dfrac{14x}{y}[/tex]
Answer: Question 1
Question 2
[tex]\left(\dfrac{x}{y}\right)\left(\dfrac{4y}{3x}\right)\:\div \dfrac{6y^2}{8x^2}[/tex]
[tex]\dfrac{x}{y} \cdot \dfrac{4y}{3x} = \dfrac{4}{3}[/tex]
[tex]\dfrac{6y^2}{8x^2} = \dfrac{4y^2}{3x^2}[/tex]'
[tex]\left(\dfrac{x}{y}\right)\left(\dfrac{4y}{3x}\right)\:\div \dfrac{6y^2}{8x^2} \\\\= \dfrac{4}{3} \times \dfrac{3x^2}{4y^2}\\\\= \dfrac{16x^2}{9y^2}[/tex]
Question 3
[tex]\dfrac{\left(5\left(y+6\right)\right)}{2\left(xy-3\right)}\:\div \dfrac{\left(y\:+\:6\right)}{4\left(xy\:-\:3\right)}\\\\\\\dfrac{5(y + 6)}{2(xy-3)} \times \dfrac{4(xy-3)}{y+ 6}\\\\[/tex]
The y + 6 terms cancel out from numerator and denominator as do the xy - 3terms
[tex]= \dfrac{5}{2} \times \dfrac{4}{1}\\\\= \dfrac{20}{2} \\\\= 10[/tex]
Question 4
[tex]\dfrac{x^2-4}{x^2+5x+4}\:\div \dfrac{x+2}{x+1}\\\\=\dfrac{x^2-4}{x^2+5x+4}\:\times \dfrac{x+1}{x+2}[/tex]
[tex]x^2-4 = (x + 2)(x-2) \;\;\;\; \text{Since $a^2-b^2 = (a +b)(a-b)$}[/tex]
[tex]x^2 + 5x + 4\;\;\; \text{can be factored as: }\\\\(x + 1)(x + 4)[/tex]
Therefore
[tex]\dfrac{x^2-4}{x^2+5x+4}\:\div \dfrac{x+2}{x+1}\\\\\\=\dfrac{x^2-4}{x^2+5x+4}\:\times \dfrac{x+1}{x+2}\\\\\\= \dfrac{(x+2)(x-2)}{(x+1)(x+4)} \times \dfrac{x+1}{x+2}\\\\\\\\[/tex]
The x+2 terms cancel out as do the x + 1 terms giving the result
[tex]\dfrac{x-2}{x+4}[/tex]
Answer:
[tex]\textsf{1. \quad $\dfrac{14x}{y}$}[/tex]
[tex]\textsf{2. \quad $\dfrac{16x^3}{9y^2}$}[/tex]
[tex]\textsf{3. \quad $10$}[/tex]
[tex]\textsf{4. \quad $\dfrac{x-2}{x+4}$}[/tex]
Step-by-step explanation:
When dividing two fractions, multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of a fraction is its inverse (swap the numerator and denominator).
Question 1[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$\dfrac{a^b}{a^c}=a^{b-c}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\dfrac{14x^5}{5y^2} \div \dfrac{2x^4}{10y} & = \dfrac{14x^5}{5y^2} \times \dfrac{10y}{2x^4}\\\\& = \dfrac{14x^5 \times 10y}{5y^2\times 2x^4}\\\\& = \dfrac{140x^5y}{10x^4y^2}\\\\& = \dfrac{14x^5y}{x^4y^2}\\\\& = 14x^{5-4}y^{1-2}\\\\& = 14x^1y^{-1}\\\\& = \dfrac{14x}{y}\end{aligned}[/tex]
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Question 2[tex]\begin{aligned}\left(\dfrac{x}{y} \right)\left(\dfrac{4y}{3x} \right) \div \dfrac{6y^2}{8x^3}&=\dfrac{4xy}{3xy} \div \dfrac{6y^2}{8x^3}\\\\&=\dfrac{4}{3} \div \dfrac{6y^2}{8x^3}\\\\&=\dfrac{4}{3} \times \dfrac{8x^3}{6y^2}\\\\&=\dfrac{4 \times 8x^3}{3 \times 6y^2}\\\\&=\dfrac{32x^3}{18y^2}\\\\&=\dfrac{16x^3}{9y^2}\end{aligned}[/tex]
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Question 3[tex]\begin{aligned}\left[\dfrac{5(y+6)}{2(xy-3)} \right] \div \left(\dfrac{y+6}{4(xy-3)}\right) & = \left[\dfrac{5(y+6)}{2(xy-3)} \right] \times \left(\dfrac{4(xy-3)}{y+6}\right)\\\\& = \dfrac{5(y+6) \times 4(xy-3)}{2(xy-3) \times (y+6)}\\\\& = \dfrac{20(y+6)(xy-3)}{2(xy-3)(y+6)}\\\\& = \dfrac{20}{2}\\\\&=10\end{aligned}[/tex]
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Question 4Factor the numerator and denominator of the first fraction.
Apply the Difference of Two Squares to the numerator:
[tex]\implies x^2-4=x^2-2^2=(x-2)(x+2)[/tex]
Factor the denominator:
[tex]\begin{aligned}\implies x^2+5x+4 & =x^2+x+4x+4\\ & =x(x+1)+4(x+1)\\ & =(x+1)(x+4)\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\left(\dfrac{x^2-4}{x^2+5x+4}\right) \div \left( \dfrac{x+2}{x+1} \right) & = \left(\dfrac{x^2-4}{x^2+5x+4}\right) \times \left( \dfrac{x+1}{x+2} \right)\\\\& = \left( \dfrac{(x-2)(x+2)}{(x+1)(x+4)} \right) \times \left( \dfrac{x+1}{x+2} \right)\\\\& = \dfrac{(x-2)(x+2)(x+1)}{(x+1)(x+4)(x+2)}\\\\& = \dfrac{x-2}{x+4}\\\\\end{aligned}[/tex]
What percent would you receive if you earned 8 out of 12 on a quiz?
A- 96%
B- 82%
C- 67%
Answer:
C
Step-by-step explanation:
[tex]\frac{8}{12} \times 100 \approx 67[/tex]
MATHHHHHHHHHHHHHHHHHHHHHH LOOK AT PHOTO
Answer:
9/25
0.36
Step-by-step explanation:
Part 1:
You divide 36 by 100 to find the fraction:
36/100
Then, simplify:
36/100 = 9/25
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Part 2:
To find the decimal of a percentage, divide the percent by 100. When dividing by 100, you get the answer by moving the decimal point two spaces to the left.
36% = 0.36