Answer:
(x + 6y)(x - 6y)
Step-by-step explanation:
The expression x² - 36y² can be factored.
Since the expression is a difference (subtraction) between two numbers that are square (x² = x*x and 36y² = 6y*6y), the factoring can be done as a "difference of squares".
The rules is generalized as: [tex]x^{2} - y^{2} = (x - y)(x+y)[/tex]
To factor x² - 36y², take each square roots for each of the numbers and add and subtract between them.
x² - 36y²
= (√x² + √36y²)(√x² - √36y²)
= (x + 6y)(x - 6y)
Line 1 passes through the points -2,7 and 3,3. Line 2 passes through the points 5,1 and 9,1. Find the slope of each line. Which line has the greater slope?
Answer:
The slope of the given line 1 is -4/5.
The slope of the given line 2 is 0.
The line 2 has a greater slope then line 1.
Step-by-step explanation:
The slope of a line with points (x1,y1) and (x2,y2) is given as:
[tex]m = \frac{y_2- y_1}{x_2-x_1}[/tex]
Now, Here the, points of the line 1 are A (-2,7) and B (3,3)
So, here, the slope of line AB is [tex]m = \frac{3 -7}{3-(-2)} = \frac{-4}{3 +2} = \frac{-4}{5}[/tex]
Hence, the slope of the given line 1 is -4/5.
Now, Here the, points of the line 2 are P (5,1) and Q (9,1)
So, here, the slope of line PQ is [tex]m = \frac{1-1}{9-5} = \frac{0}{4} = 0[/tex]
Hence, the slope of the given line 2 is 0.
Now, as we can see 0 > ( -4 / 5)
So, the line 2 has a greater slope then line 1.
State under which condition the original and the simplified expressions are equivalent.
The expressions are equivalent if...
a) a≠0
b) a≠x
c) a≠-x
[tex]\frac{a^2}{ax-x^2} +\frac{x}{x-a}[/tex]
Answer:
a doesn't equal 0
Step-by-step explanation:
State under which condition the original and the simplified expressions are equivalent
On a certain hot summer's day, 643 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled
$1161.50. How many children and how many adults swam at the public pool that day?
249 children and 394 adults swam at the public pool.
Step-by-step explanation:
Number of people swam at pool = 643
Receipts = $1161.50
Cost for one child = $1.50
Cost for one adult = $2.00
Let,
x be the number of children
y be the number of adults
According to given statement;
x+y=643 Eqn 1
1.50x+2.00y = 1161.50 Eqn 2
Multiplying Eqn 1 by 2
[tex]2(x+y=643)\\2x+2y=1286\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](2x+2y)-(1.50x+2.00y)=1286-1161.50\\2x+2y-1.50x-2.00y=124.50\\0.5x=124.50[/tex]
Dividing both sides by 0.5
[tex]\frac{0.5x}{0.5}=\frac{124.50}{0.5}\\x=249[/tex]
Putting x=249 in Eqn 1
[tex]249+y=643\\y=643-249\\y=394[/tex]
249 children and 394 adults swam at the public pool.
Keywords: linear equation, subtraction
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[tex]5x - 15 + 130 = x - 2 [/tex]
Answer:
x=-117/4
Step-by-step explanation:
5x-15+130=x-2
5x-x+115=-2
4x+115=-2
4x=-2-115
4x=-117
x=-117/4
What is another way to write this number:
300+70+5/10+8/100
Answer:
18529/50 or 370.58
Step-by-step explanation:
5/10=1/2
8/100=2/25
300+70+1/2+2/25
370+1/2+2/25
370+29/50
18529/50 or 370.58
Step-by-step explanation:
370 + 50/100 + 8/100
37000/100 + 58/100
37058/100 = 370 58/100 = 370 29/50
Swami packed 28 oranges and 52 apples in boxes. He packed oranges and apples in separate boxes. If he put equal number of fruits in each box, find the maximum number of fruits he put in
each box.
Answer:
4
Step-by-step explanation:
Find the greatest common factor (GCF) of 28 and 52. First, write the prime factorization of each:
28 = 2² × 7
52 = 2² × 13
The GCF is 2² or 4. So the most fruits per box is 4.
Which choice is a factor of 62?
A.13
B.20
C.62
D.3
Answer:
C, the answer is 62.
Step-by-step explanation:
Well, 1 x 62 is 62 so that's the only factor of 62 out of all of them.
1. y = 4x + 3 for x = -1, 0,1
Answer:
-1, 3, 7
Step-by-step explanation:
y = 4(-1) + 3
y = -4 + 3
y = -1
y = 4(0) + 3
y = 0 + 3
y = 3
y = 4(1) + 3
y = 4 + 3
y = 7
To solve the linear equation y = 4x + 3, substitute the given x values (-1, 0, 1) into the equation to find the corresponding y values. The results are -1, 3, and 7 respectively.
Explanation:The question asks to solve the equation y = 4x + 3, for the values of x being -1, 0, and 1. This is a linear equation where y depends on x. To find the corresponding y values for each x value:
Substitute x = -1 into the equation. The calculation becomes: y = 4(-1) + 3 = -4 + 3 = -1.Substitute x = 0 into the equation. The calculation becomes: y = 4(0) + 3 = 0 + 3 = 3.Substitute x = 1 into the equation. The calculation becomes: y = 4(1) + 3 = 4 + 3 = 7.Hence, the values for y when x equals -1, 0, and 1 respectively are -1, 3, and 7.
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11. The distance from Mac's house to school
is 575 yards. Mac's goal is to walk to
school in 5 minutes. How many yards
does Mac need to walk each minute to
meet his goal?
Answer:
115 yards per minute
Step-by-step explanation:
575/5= 115
Answer:
115 yds per minute
The drawing will help
Prove that using: X ∩ (Y ∪ Z ) =(X∩Y) ∪ (Y ∩ Z )
Listing Method; or
Membership Table.
Given
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
X = {2, 5, 8, 9}
Y = {1, 4, 6, 7, 8}
Z = {5, 7, 9}
There should be a typo in the question: the correct formula would be
[tex]X\cap(Y\cup Z)=(X\cap Y)\cup (X\cap Z)[/tex]
Let's compute [tex]X\cap (Y\cup Z)[/tex] first. We have
[tex](Y\cup Z)=\{1, 4, 5, 6, 7, 8, 9\}[/tex]
If we intersect this set with X, we have
[tex]X\cap (Y\cup Z) = \{5, 8, 9\}[/tex]
So, that would be the left hand side. For the right hand side, we have
[tex]X\cap Y = \{8\},\quad X\cap Z = \{5,9\}[/tex]
And their union is again [tex]\{5,8,9\}[/tex]
Final answer:
The intersection of two sets can be proven using a membership table for the given sets X, Y, and Z.
Explanation:
The intersection of two sets, written as AnB, is a set consisting of all elements that are both in A and B. We can use a membership table to prove the following equation: X ∩ (Y ∪ Z) = (X ∩ Y) ∪ (Y ∩ Z).
f the chance of rain for tomorrow is 30%, what is the chance that it will NOT rain?
A. 70%
B. 0%
C. 50%
D. 30%
Select EACH correct answer!
If there is a 30% chance of it raining, then that means there is a 70% chance of it not raining.
100%-30%=70%
Answer: 70%
Step-by-step explanation: In terms of probability, 100% is the maximum which means something is certain. There are some occasions where it can be higher than 100% like dealing with percent increase or decrease, but in this case, we're talking about 100%.
In this problem, we're given that the probability of rain for tomorrow is 30% and we're asked to find the probability that it will not rain.
Since 100% will be the maximum when dealing with probability, we will subtract the chance it will rain tomorrow which is 30% from 100%.
100% - 30% = 70%.
Therefore, the probability/chance it will not rain is 70% which means it's likely it will not rain.
A cookie recipe calls for 6 cups of flour
and 2 cups of sugar. What is the ratio of
the amount of sugar to the amount of
flour?
Answer:
1:3
Step-by-step explanation:
Sugar : Flour
2 : 6 (substitute the numbers of cups)
1 : 3 (simplify by reducing. divide both sides by 2)
The ratio is 1:3.
Answer:
1:3
Step-by-step explanation:
2:6[sugar is to flour]
1:3[to simplify divide both sides by two]
a store in Rogers's neighborhood sells boxes of pencils that have 6 pencils in each box. roger bought several boxes of pencils at the store. which could be the number of pencils he bought?
Answer:
Step-by-step explanation:
It could be 42 pencils
what is 3.1n - 1.1n =
At one of the warehouse stores, paper towels cost $10.48 for a package of 8 rolls. What is the unit price?
Answer:
Unit price = $1.31/roll
Step-by-step explanation:
Divide total cost by number of units:
$10.48 / 8 rolls = $1.31/roll
Priya and Han are biking in the same direction on the same path.
Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after hours.
Priya started riding a half hour before Han. If Han has been riding for hours, how long has Priya been riding?
Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for hours.
Use your expressions to find when Han and Priya meet.
I copy the complete questions again to make them clearer:
Priya and Han are biking in the same direction on the same path.
a. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after [tex]t[/tex] hours.
b. Priya started riding a half hour before Han. If Han has been riding for [tex]t[/tex] hours, how long has Priya been riding?
c. Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for [tex]t[/tex] hours.
d. Use your expressions to find when Han and Priya meet.
Answer:
a) [tex]H=16t[/tex]b) [tex]t+0.5[/tex]c) [tex]P=12(t+0.5)[/tex]d) Han and Priya meet 1.5 hours after Han started riding.Explanation:
a. Since Han is riding at a constant speed of 16 miles per hour, the number of miles that he has gone is proportional to the number of hours, t, that he has been riding, the constant of variation is 16, and the expression for the number of miles he has gone is:
[tex]H=16\times t=16t[/tex]Where, H is the number of miles Han has gone, and t is the number of hours.
b. Since Priya started riding a half hour before Han, you have to add 1/2 or 0.5 to the time of Han, which is t, to express how long Priya has been riding:
[tex]t+0.5[/tex]c. Since, Priya is riding at a constant speed of 12 miles per hour, the number of miles that she has gone is proportional to the number of hours, t + 0.5, that she has been riding, the constant of variation is 12, and the expression for the number of miles she has gone is:
[tex]P=12\times (t+0.5)=12(t+0.5)[/tex]Where P is the number of miles Priya has gone, and t is the number of hours since Han is riding.
d. To find when Han and Priya meet, you just need to solve the sytem of equations, making H = P, which means that the number of miles that both Han and Priya rides is equal:
[tex]H=P\\ \\ 16t=12(t+0.5)\\ \\ 16t=12t+6\\ \\ 4t=6\\ \\ t=6/4=3/2=1.5[/tex]
Which means that they meet when it has passed 1.5 hours since Han started riding.
what is slope of a line that passes through (1,4) (-2,6) awarding more points
Answer:
-2/3
Step-by-step explanation:
m=(6-4)/(-2-1)=2/-3=-2/3
Answer:
[tex]\large\boxed{m=-\dfrac{2}{3}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, 4) and (-2, 6).
Substitute:
[tex]m=\dfrac{6-4}{-2-1}=\dfrac{2}{-3}=-\dfrac{2}{3}}[/tex]
Write the decimal as a fraction or a mixed number in simplest form.
5.76
Answer:
Step-by-step explanation:
it is 145/25 which is reduced to 29/5
Answer:
5 19/25
Step-by-step explanation:
Marcela estimates the distance between the library and town hall is 735 ft. The actual distance is 612 ft.
What is the percent error in Marcela's estimate?
Round your answer to the nearest tenth of a percent.
Enter your answer in the box.
Answer:
The error percentage in estimation is 20 %
Step-by-step explanation:
The estimated distance between library and town = 735 ft
The actual distance = 612 ft
The Error in estimation = Estimated Distance - Actual Distance
= 735 ft - 612 ft = 123 ft
So, the error in the estimation is 123 ft.
Now, [tex]\textrm{ Percentage in Error Estimation} = \frac{\textrm{The estimated Error}}{\textrm{The estimated value}} \times 100[/tex]
= [tex]\frac{123}{612} \times 100 = 20.098[/tex]
or, The error percentage in estimation is 20.09%
Now, rounding off the value to the nearest tenths of a %, we get:
The error percentage in estimation is 20 %
Which of the following is the perimeter of a triangle with side lengths of 7 inches, 8 inches, and 13 inches?
15 inches
13 inches
28 inches
27 inches
Answer: 28 inches
Step-by-step explanation:
Side1 + side 2 + side 3 =
7 inches + 8 inches + 13 inches =
28 inches
There are 482 studemts in the school and there are two Grade 4 classes: Ms.Ashley's and Mr.Ben's classes. Mrs. Aheley's class had 15 boays and 6 girls. Mr Ben's class ahd 14 girls and 10 boys. In Ms. Ashley's class, 2/3 of the students wear glasses.
In Mr. Ben's class, 1/4 of the kids have others siblings in the school.
1. What fraction of the students in the school are in grade 4?
2. What fraction of the grade 4 students are boys?
3. What fraction of the grade 4 students are in Ms. Ashley's class?
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
Answer:
1. 45/482 of the students are in grade 4.
2. 5/9 of the students of the grade 4 are boys.
3. 7/15 of the grade 4 students are in Ms. Ashley's class
4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.
5. There are 14 students with glasses and 7 without glasses.
Step-by-step explanation:
1. Let's review the information given to us for solving the questions:
Number of students in the school = 482
Ms. Ashley's Grade 4 class = 21 students
Ms. Ashley's Grade 4 class boys = 15 students
Ms. Ashley's Grade 4 class girls = 6 students
Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students
Mr. Ben's Grade 4 class = 24 students
Mr. Ben's Grade 4 class boys = 10 students
Mr. Ben's Grade 4 class girls = 14 students
Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students
2. Let's answer all the questions:
1. What fraction of the students in the school are in grade 4?
(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school
21 + 24 / 482 = 45/482
2. What fraction of the grade 4 students are boys?
(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
15 + 10 / 21 + 24
25 / 45 = 5/9
3. What fraction of the grade 4 students are in Ms. Ashley's class?
Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
21 / 21 + 24
21 / 45 = 7/15
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class
24 - 6 / 24
18 / 24 = 3/4
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
There are 14 students with glasses and 7 without glasses.
What is the constant of proportionality in the equation y=0.41x
Answer:
0.41
Step-by-step explanation:
formula; y = kx (where k is the constant variation)
the standard equation representing direct variation
y = 0.41 x is the equation to find the constant of proportionality
so, K = 0.41
A new car is listed at 27,000. A prospective buyer would incur initial expenses that consist of 4%. sales tax and a license fee of $36. what would the total amount in dollars of the incurred initial expenses be?
Answer:
$28,116
Step-by-step explanation:
27,000/100*104 = 28,080 + 36 = $28,116
The price of peaches at Al’s supermarket can be determined by the equation p=0.28n, where P is the price and n is the number of pounds of peaches what is the constant of proportionality
Answer:
k = 0.28
Step-by-step explanation:
The price of peaches at Al's supermarket can be determined by the equation P = 0.28n ........... (1)
where P is the price and n is the number of pounds of peaches.
Now, it is clear that the price of peaches is proportional to the number of pounds of peaches.
So, we can write,
P ∝ n
⇒ P = kn ............. (2) where k is the constant which we have to multiply to covert from proportionality to equation form.
Now, comparing equations (1) and (2) we get k = 0.28 which is the value of the constant of proportionality. (Answer)
Final answer:
The constant of proportionality in the equation p = 0.28n is 0.28, representing the price per pound of peaches at Al's supermarket.
Explanation:
The constant of proportionality in the equation p = 0.28n, where P is the price and n is the number of pounds of peaches, is 0.28. This constant represents the price per pound of peaches at Al's supermarket. When you want to compute the amount spent on peaches, you multiply the quantity (in pounds) by this constant of proportionality, which is the price per pound. As an example, if you have 10 pounds of peaches, the total cost would be calculated as 10 pounds × $0.28 per pound, resulting in a total of $2.80 for the peaches.
abraham lincoln declared thanksgiving a holiday in 1863 what is the prime factorization of 1863
3 x 3 x 3 x 3 x 23 = 1,863. It can also be written in exponential form as 3 to the power of four times 23.
Answer:
1863 = 3 · 3 · 3 · 3 · 23Step-by-step explanation:
[tex]\begin{array}{c|cc}1863&3\\621&3\\207&3\\69&3\\23&23\\1\end{array}[/tex]
8 1/3 s for s = 4 1/2
Answer:
75/2 (or 37 1/2)
Step-by-step explanation:
Here we're multiplying 4 1/2 by 8 1/3.
Converting both numbers to improper fractions:
9/2 times 25/3, or
9 25
---- * ------
2 3
Reducing the fractions, we get:
3 25
---- * ------ = 75/2 (answer)
2 1
The value of the given expression is 36.
Use the concept of fraction defined as:
A fraction is part of a whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that,
[tex]s = 4\dfrac{1}{2}[/tex]
We have to calculate [tex]8\dfrac{1}{3} \test{s}[/tex]
Now convert both fractions into improper fractions,
[tex]4\dfrac{1}2} = \dfrac{8 + 1}{2}\\\\4\dfrac{1}{2} = \dfrac{9}{2}\\\\[/tex]
And [tex]8\dfrac{1}{3} = \dfrac{24}{3}[/tex]
Now we have,
s = 9/2
Therefore,
[tex]8\dfrac{1}{3}s = \dfrac{24}{3}s\\\\8\dfrac{1}{3}s = \dfrac{24}{3}\times\dfrac{9}{2}\\\\[/tex]
Simplifying we get,
[tex]8\dfrac{1}{3}s = 12 \times 3\\\\ 8\dfrac{1}{3}s = 36[/tex]
Hence the value of the expression is 36.
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What is the length of the side opposite angle B?
3 units
4 units
5 units
6 units
Answer:
B
Step-by-step explanation:
4 units is the answer. i got an 100% on the quiz
The triangle missing from the question has attached and the opposite side of angle B is 4 units.
What is a traingle?A triangle is a three sides lines geometry in which the sum of all angles is 180°.
Given that a triangle ABC and has sides as
AB = 4
BC = 3
AB = 5
It's clearly visible that the opposite side of angle B is AC which has length as 4 units.
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A basketball arena can hold approximately 7,000 people. Fans bought 5,134 tickets before the game. About how many more seats are left to fill before the game.
To determine the number of seats left in the basketball arena, the number of tickets sold (5,134) is subtracted from the total arena capacity (7,000), resulting in 1,866 seats remaining available.
A basketball arena can hold approximately 7,000 people.
Fans bought 5,134 tickets before the game.
The number of seats left to fill before the game can be calculated by subtracting the tickets bought from the total arena capacity: 7,000 - 5,134 = 1,866 seats left to fill.
If 3(r+300)=6, then what would be the value of r+300-2?
Answer:
The value of r+300-2 is 0.
Step-by-step explanation:
3(r+300)=6
r+300=6/3
r+300=2
r=2-300
r=-298
---------------
r+300-2=-298+300-2=2-2=0
Use Newton's method to approximate the roots
of f(x) = 3x3 – 4x2 + 1 to six digits.
Answer:
Step-by-step explanation:
14