Answer:
d = 49
Step-by-step explanation:
Given that the expression is a perfect square of the form
(ay - b)² = a²y² - 2aby + b²
Then comparing like terms
a²y² = 25y², that is
a² = 25 ⇒ a = 5
and -2aby = - 70y, thus
2ab = 70, that is
2(5)b = 70
10b = 70 ⇒ b = 7
b² = 7² = 49
Hence
25y² - 70y + d = (5y - 7)² = 25y² - 70y + 49
Thus d = 49
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
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
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).
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
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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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.
Explain how you could convert 152 cups into gallons.
Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.
Step-by-step explanation:
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.
What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?
Answer: C
Step-by-step explanation:
The answer is C because it says 360 and 300. If you do a problem solve for that one on a peace of paper I think it would be 16.7%
Answer:
Step-by-step explanation:
Change in number = number visited in 1st week - number visited in 2nd week
= 360-300 = 60
So percentage change in number= 60/360×100=16.67
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:
33. Sarah has $200 in her bank account now. If she
deposits $10 weekly, which of the following formulas
will show her deposits (D) at the end of h weeks?
(1) D=200+ 10
in
(2) D = (200)(10n)
(3) D = 200 + 10
(4) D = 200 + 10
(5) D = 200n + 10
Answer:2
Step-by-step explanation:if she deposits 10 dollars every week she would be adding 10 dollars which means we have to multiply 10 by however many weeks she saves
Sarah's weekly deposits after h weeks can be calculated using the linear equation D = 200 + 10h. This equation includes her starting balance of $200 and adds $10 for each week.
Explanation:The subject of this question is Mathematics, specifically focusing on the concept of linear equations.
The correct formula to show Sarah's deposits at the end of h weeks would be (3) D = 200 + 10h. This formula works by establishing 200 as her starting amount (her current bank balance), and adding $10 for each week (h).
For instance, if h was 5 weeks, Sarah would have D = 200 + 10 * 5 = 200 + 50 = $250 in her bank account. This demonstrates how the formula allows you to calculate her weekly deposits effectively.
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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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Latisha has two pieces of ribbon she plans
to cut. One piece of ribbon is 48 inches and
the other is 80 inches. She plans to cut
all the ribbon into pieces of equal lengths.
What is the greatest possible length of each
piece?
The greatest possible length of each piece is 16 inches
Solution:Latisha has two pieces of ribbon. One piece of ribbon is 48 inches and the other is 80 inches
Ribbon is to be cut into pieces of equal length
To find the greatest possible length of each piece, we have to find greatest common divisor of 48 and 80
The greatest common factor, or GCF, is the greatest factor that divides two numbers
Steps to find G.C.F of 48 and 80
1) Find the prime factorization of 48
[tex]48 = 2 \times 2 \times 2 \times 2 \times 3[/tex]
2) Find the prime factorization of 80
[tex]80 = 2 \times 2 \times 2 \times 2 \times 5[/tex]
3) To find the GCF, multiply all the prime factors common to both numbers:
Therefore, [tex]GCF = 2 \times 2 \times 2 \times 2 = 16[/tex]
So, 16 inches is the greatest possible length to cut so that every piece is of equal length.
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
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.
[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
25 + 11/12b =47 please answer
Answer:
The answer is b = 1/24.
Step-by-step explanation:
Given:
25+11/12b=47.
Now, to solve the equation to get the value of b:
[tex]25+\frac{11}{12b}=47[/tex]
Subtracting both sides with 25 we get:
[tex]\frac{11}{12b}=22[/tex]
Multiplying both sides by 12b we get:
[tex]11=264b[/tex]
Dividing both sides by 264 we get:
[tex]\frac{1}{24}=b[/tex]
Therefore, the answer is b = 1/24.
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]
Rachel has 8/12 of a fun of frosting. If she used 1/4 of it, how much was left?
Answer:
6/12
Step-by-step explanation:
A fourth of 8 is 2, so there would be 6/12 of the tub of frosting left.
Answer:
5/12
Step-by-step explanation:
8/12=2/3
2/3-1/4=8/12-3/12=5/12
which graph represents a function?
Answer:
This graph does not represent a function.
Step-by-step explanation:
This graph does not pass the vertical line test. The vertical line test states that if a vertical line drawn intersects the graph of the relation more than once, then the relation is a NOT a function.
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.
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.
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
Factor 3x2 - 18x + 27 completely.
Answer:
3(x - 3)²
Step-by-step explanation:
Given
3x² - 18x + 27 ← factor out 3 from each term
= 3(x² - 6x + 9)
= 3(x - 3)² ← in factored form
what is 3.1n - 1.1n =
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]
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
How do I solve this? ( explanation with answer)
Answer:
a.) x= 11
d.) -7
g.) -5
Step-by-step explanation:
a.) x+1 = 4*3
x=12-1
d.)3x+1=-4*5
3x+1=-20
x=-7
g.)11x-1=-8*7
11x-1=-56
11x=-56+1
x=-5
Answer:
a) x = 11, d) x = -7, g) x = -5Step-by-step explanation:
[tex]a)\\\dfrac{x+1}{3}=4\\\\\dfrac{x+1}{3}=\dfrac{4}{1}\qquad\text{cross multiply}\\\\(x+1)(1)=(3)(4)\\\\x+1=12\qquad\text{subtract 1 from both sides}\\\\x+1-1=12-1\\\\\boxed{x=11}[/tex]
[tex]d)\\\\\dfrac{3x+1}{4}=-5\\\\\dfrac{3x+1}{4}=\dfrac{-5}{1}\qquad\text{cross multiply}\\\\(3x+1)(1)=(4)(-5)\\\\3x+1=-20\qquad\text{subtract 1 from both sides}\\\\3x+1-1=-20-1\\\\3x=-21\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{-21}{3}\\\\\boxed{x=-7}[/tex]
[tex]g)\\\dfrac{11x-1}{8}=-7\\\\\dfrac{11x-1}{8}=\dfrac{-7}{1}\qquad\text{cross multiply}\\\\(11x-1)(1)=(8)(-7)\\\\11x-1=-56\qquad\text{add 1 to both sides}\\\\11x-1+1=-56+1\\\\11x=-55\qquad\text{divide both sides by 11}\\\\\dfrac{11x}{11}=\dfrac{-55}{11}\\\\\boxed{x=-5}[/tex]
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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