Answer:
[tex](a)[/tex] [tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
[tex](b)[/tex] [tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
[tex](c)[/tex] [tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
[tex](d)[/tex] [tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
Step-by-step explanation:
Given
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Solving (a): A common denominator of M and N.
To do this, we simply get the LCM of both denominators
[tex]M = x^2 - 5x - 50[/tex]
[tex]N = x^2 - 14x + 40[/tex]
Factorize both:
[tex]M = (x - 10)(x + 5)[/tex]
[tex]N = (x- 10)(x - 4)[/tex]
The LCM is
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
Hence, the common denominator is:
[tex]Denominator= (x - 10)(x+5)(x-4)[/tex]
Solving (b): Rewrite M
[tex]M = \frac{7x - 5}{x^2 -5x - 50}[/tex]
Factor the denominator:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of M by (x - 4)
The expression becomes:
[tex]M = \frac{7x - 5}{(x+5)(x - 10)} * \frac{x - 4}{x-4}[/tex]
[tex]M = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)}[/tex]
Solving (c): Rewrite N
[tex]N = \frac{3x - 8}{x^2 -14x+ 40}[/tex]
Factor the denominator:
[tex]N = \frac{3x - 8}{(x-4)(x-10)}[/tex]
The LCM calculated in (a) above is:
[tex]LCM= (x - 10)(x+5)(x-4)[/tex]
So, we have to multiply the numerator and denominator of N by (x + 5)
The expression becomes:
[tex]N = \frac{3x - 8}{(x-4)(x-10)} * \frac{x + 5}{x + 5}[/tex]
[tex]N = \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
(d) Solve M + N
[tex]M + N = \frac{(7x - 5)(x-4)}{(x+5)(x - 10)(x-4)} + \frac{(3x - 8)(x + 5)}{(x-4)(x-10)(x + 5)}[/tex]
Take LCM
[tex]M + N = \frac{(7x - 5)(x-4) + (3x - 8)(x + 5)}{(x+5)(x - 10)(x-4)}[/tex]
Open brackets
[tex]M + N = \frac{7x^2 - 28x - 5x + 20 + 3x^2 + 15x - 8x - 40}{(x+5)(x - 10)(x-4)}[/tex]
Collect Like Terms
[tex]M + N = \frac{7x^2 + 3x^2- 28x - 5x + 15x - 8x + 20 - 40}{(x+5)(x - 10)(x-4)}[/tex]
[tex]M + N = \frac{10x^2-26x -20}{(x+5)(x - 10)(x-4)}[/tex]
Joel had a coin collection. He had two hundred coins,
which were dimes and quarters. The total value of his
collection was worth $32.
Remember to define your variables.
Create 2 equations
(Each equation should have a "common theme" for
example in this problem one equation will be the the
total number of coins and the other will be the total
value of the coins)
The next step is to solve the problem. Remember to
think of the best method for problem solving
Answer:
Joel's coin collection had 120 dimes and 80 quarters.
Step-by-step explanation:
Given that Joel had a coin collection of two hundred coins, which were dimes and quarters, and the total value was worth $32, to determine how many coins of each type he had, the following equations must be performed:
0.25 - 0.10 = 0.15
200 x 0.10 = 20
32 - 20 = 12
12 / 0.15 = 80
200 - 80 = 120
(80 x 0.25) + (120 x 0.1) = X
20 + 12 = X
32 = X
Therefore, Joel's coin collection had 120 dimes and 80 quarters.
In the parallelogram below,
y = [?]
5y-20
2y+25
PLEASE HELP
Marta can pick 10 baskets of peaches in one hour. How long will it take her to pick 60 baskets of peaches?
Answer:
It will take her 6 hours for her to pick 60 baskets of peaches.
Step-by-step explanation:
Please help me if you can 10 points if you help
Answer:
C) 0%
Step-by-step explanation:
Let’s give the square sides equaling 4. The area would equal 16.
Decreasing the top by 75% would make it 1. Increasing the bottom by 75% makes it 7.
(1+7)/2=4
The height is still four so 4x4=16
No change in area.
[tex]e + \frac{1}{8} = \frac{3}{8\\}[/tex]
Can y’all please help me out?
Answer:
19.5 degrees
Step-by-step explanation:
180 - (33.5 + 127) =
180 - 160.5 =
19.5
Hope that helps!
difference quotient for f (x) = 2x + 3 /5x
Answer:
1 and -0.6
Step-by-step explanation:
13 in = ___________ ft
Answer:
1.0833333 Feet
Hope this helps! If I could have brainliest im trying to level up.
Step-by-step explanation:
13 Inches =
1.0833333 Feet
(rounded to 8 digits)
Target buys pants for $6.42 and marks up the price for customers by 70%. How much do they sell pants for?
0.7\left(6.42\right)=\$4.490.7(6.42)=$4.49
$4.49 is not the correct answer. What is the mistake? Explain.
180÷(4+16)-8×3+7×(2+3)
Answer:
111
Step-by-step explanation:
Use PEMDAS to solve this equation, so first we have to do parenthesis first. Simplify 4+16 to get 20. Simplify 2+3 to get 5. Therefore, the equation will now look like 180/(20)-8x3+7x(5). Because we can do either division or multiplication first, we have to solve the equation started from the left. Therefore, we do 180/20 which is 90. Then the equation will be 90-8x3+7x5. Multiply -8 and 3 together to get -24. Therefore, the equation will be 90-24+7x5. Because we always do multiplication/division before addition/subtraction. We have to do 7x5 which is equal to 35. Therefore, the equation will look like 90-24+35. Because there is only subtraction and addition now, we should start from the left hand side which is 90-24. Simplify this to get 76. Then the equation will be 76+35. Simplify this to get 111.
If this answer helps, please mark it as brainliest
A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, steamed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular latte and $1.65 on each low-fat latte. Assuming that all lattes that are made can be sold, what would be the ideal mix of regular and low-fat lattes to maximize the profit for the airline?
Answer:
To maximize profit, the amount of each type of coffees made are;
The number of regular latte made = 52 cups
The number of low-fat latte made = 48 cups
Step-by-step explanation:
The given parameters are;
The number of espresso in a regular latte = 1 shot
The number of cups of 2% milk in regular latte = 1 cup
The amount of whipped cream in a regular latte = 0.5 cup
The number of cups of skim milk in the low-fat latte = 1.25 cup
The number of espresso in a low-fat latte = 1 shot
The amount of whipped cream in a low-fat latte = 0 cup
The number of cups of espresso in the journey = 100 shots
The number of cups of skim milk in the journey = 60 cups
The number of cups of 2% milk in the journey = 60 cups
The amount of profit the airline makes on each regular latte = $1.58
The amount of profit the airline makes on each low-fat latte = $1.65
Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;
x ≤ 30/0.5 = 60
x ≤ 60
y ≤ 60
y ≤ 60/1.25 = 48
∴ y ≤ 48
x + y ≤ 100
Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made
Therefore, the number of low-fat latte made, y = 48
Therefore, the number of regular latte made, x ≤ 100 - 48 = 52
For maximum profit, the maximum number of low-fat latte, 'x', should be made
Therefore, x = 52
The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte
What does it mean to evaluate?
Answer:
Evaluate means to assess or determine something.
Step-by-step explanation:
Answer:
Means to simply solve, sometimes you may need to show your thinking, depending on the question.
Step-by-step explanation:
Jacqueline drove 72 km on 6 L of gasoline. Which of the following equations can be used to find how far she can travel on a full tank of 50 L?
Answer:
600 km
Step-by-step explanation:
72 (km on 6 L of gasoline) / 6 (liters of gasoline) = 12 (km per liter)
50 (liters of gasoline) * 12 (km per liter) = 600 (km that Jacqueline can drive using 50L of gasoline)
I hope this helps :)
Answer:
600
Step-by-step explanation:
took the test
The equation a2 + b2 = ca represents the relationship between the three sides of a right triangle.
Hal leans a ladder that is 26 feet long against the side of a building. The base of the ladder is 10 feet from the side of the building.
How high up the side of the building is the top of the ladder?
A 24 feet
B 22 feet
C 28 feet
D 16 feet
Answer:
Step-by-step explanation:
I think you mean a² + b² = c², not ca.
a = 10, c = 26
b² = c² - a² = 26² - 10² = 576
b = √576 = 24 ft
Find the distance between the points (-3, 4) and (-3, -5).
Answer:
[tex]\displaystyle d = 9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-3, 4)
Point (-3, -5)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(-3+3)^2+(-5 - 4)^2}[/tex][Distance] [√Radical] (Parenthesis) Add/Subtract: [tex]\displaystyle d = \sqrt{(0)^2+(-9)^2}[/tex][Distance] [√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{81}[/tex][Distance] [√Radical] Evaluate: [tex]\displaystyle d = 9[/tex]
Mr. Bernstein owns 11 paintings, but has only enough wall space in his home to display five of
them at any one time. How many ways can Mr. Bernstein display three paintings in his home?
Answer:
In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation you’re familiar with where one quantity changes constantly in relation to another quantity. How are the two quantities in the situation related? If you represent the two quantities on a graph, what will it look like?
Step-by-step explanation:
HEY can You help me with this work pls i need help don't put random. if u don't know it pls guys.
1️⃣Remove parentheses
6a+6+3x-2+2a+4
2️⃣Collect like terms
(6a+2a)+(6-2+4)+3x
3️⃣Simplify
8a+8+3x
Answer: 8a+8+3x
QUESTION 21️⃣Remove parentheses.
-2z-3+4c+6y+y+3c
2️⃣Collect like terms.
-2z-3+(4c+3c)+(6y+y)
3️⃣Simplify
-2z-3+7c+7y
Answer: -2z-3+7c+7y
QUESTION 31️⃣Subtracting (7.8 - 5.1t) from (2.8 - 3.2t)
(2.8 - 3.2t) - (7.8 - 5.1t)
2️⃣Remove the parentheses.
2.8 - 3.2t - 7.8 + 5.1t
= 5.1t - 3.2t + 2.8 - 7.8 (we have now shown the difference in another way)
3️⃣Subtracting the like terms, will give:
1.9t - 5
4️⃣Recall
(2.8 - 3.2t) - (7.8 - 5.1t).
(-3.2t + 2.8) - (-5.1t + 7.8)
Answer:
a. (-3.2t + 2.8) - (-5.1t + 7.8)
b. 1.9t - 5
c. (-3.2t + 2.8) - (-5.1t + 7.8)
QUESTION 41️⃣Simplify
1/2p-(1/4p-4)
2️⃣Simplify
p2-(p/4-4)
3️⃣Simplify
p2-p/4+4
4️⃣Combine Terms
(p/2-p/4)+4
5️⃣Combine Terms
p/4+4
Answer: p/4+4
Done ✔
PLEASE HELP 20 POINTS
SHOW ALL WORK
Answer:
Steps below
Step-by-step explanation:
8) x = y²/2 2rcosΘ = r²sin²Θ 2cosΘ = rsin²Θ
r = 2cosΘ/sin²Θ = 2cotΘcscΘ
9) (x+2)²+y²=4 y= rsinΘ x=rcosΘ
(rcosΘ+2)²+y²sin²Θ = 4
r²cos²Θ+4rcosΘ+4+y²sin²Θ=4
r²(sin²Θ+cos²Θ)+4rcosΘ=0
r²+4rcosΘ=0 r+4cosΘ=0
r = - 4cosΘ
10) r = 2sinΘ r=2* y/r r²=2y x²+y²=2y
x² + (y²-2y+4) = 4 x²+(y-2)² = 4
11) r = 3tanΘsecΘ = 3* (y/x) * (r/x)
1 =3y/x²
x² = 3y 3y = x²
what's the domain and range
If Robert buys a candy bar for 78 cents, how much
change does he get back from a one-dollar bill?
32 cents
23 cents
22 cents
33 cents
there are 60 minutes in a hour.how many minutes are there in 24 hours
There are 1440 minutes in 1 hour
Step-by-step explanation:
Since there are 60 minutes in 1 hour multiply 60 by 24, you get 1440.
Please Help, what is the answer
Answer:
The correct option is (2).
Step-by-step explanation:
We need to find the value of the given expression i.e.
[tex]\dfrac{(8x^6)^2}{(4x^2)^3}[/tex]
We can calculate it as follows :
[tex]\dfrac{(8x^6)^2}{(4x^2)^3}=\dfrac{8^2\times (x^6)^2}{(4)^3\times (x^2)^3}\\\\=\dfrac{x^{12}}{x^6}\\\\=x^6[/tex]
So, the final answer is x⁶. The correct option is (2).
natasha has a sales job and receieves $60,440 as her annual pay plus commission. her company pays her a commision of 12% on her total sales if she makes sales of $70,000 in the first 3 months how much will she be paid for those 3 months?
Answer:
$68,840
Step-by-step explanation:
70,000*12%=8,400
8440+64,440=$68,840
how do i solve this 14 − x = 5
Answer:
9
Step-by-step explanation:
because 14-5=9
Write an equation to show how the Distributive Property can help you solve each problem. 3 Kelly signed copies of her new book at a local bookstore. In the morning she signed 36 books, and in the afternoon she signed 51 books. It took her 5 minutes to sign a book. How much time did she spend signing books? Equation: Solution:
Answer:
wouldnt it be 8 im not sure tho
Step-by-step explanation:
Can someone help meee
Answer:
69
the measure of angle will
111 + AXB = 180
AXB = 180 - 111
AXB = 69
hope it helps
Answer:
angle AXB= 180-111=69°
Step-by-step explanation:
find the term to term rules for the following sequences. 28 25 22 19 16 .
Answer:
a) next one is previous one -3
b) next one is 3 times previous one
you want your markup to be 35% of the final selling price. Your cost is $200. For what price should you sell the product
a. $235.00
b. $270.00
c. $279.00
d. $307.69
Josh build a tower using blocks that linked together. I notice that he had 36 block in 3/8 of his tower. Exactly how many blocks were in this entire tower?
A. 96
B. 60
C. 12
D. 13 1/2
Solve the simultaneous equation
4x-y=9
2x-3y= -23
Answer:
x = 5
y = 11
Step-by-step explanation:
y = 4x - 9
2x -3(4x - 9) = -23
2x - 12x + 27 = -23
-10x = -23 -27
-10x = -50
minus cancels out
x = 5
y = 4(5) -9
y = 20 - 9
y = 11