well, one way to go about it is, to do away with the denominators by using the LCD of all fractions, hmmm let's see, we have denominators of 3,5 and 15, so the LCD will just be 15.
now let's multiply both sides by the LCD of 15 to do away with the denominators,
[tex]\bf \cfrac{2}{3}+\cfrac{3n}{5}=\cfrac{13}{15}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( \cfrac{2}{3}+\cfrac{3n}{5} \right)=15\left( \cfrac{13}{15} \right)}\implies 10+9n=13 \\\\\\ 9n=3\implies n=\cfrac{3}{9}\implies n = \cfrac{1}{3}[/tex]
How many factors of 3 does the number 135 have?
Answer:Prime factorization:
135 = 3 x 3 x 3 x 5, which can also be written 135 = 3³ x 5. 1 + 3 + 5 = 9. Nine is a multiple of both 3 and 9, so this quick divisibility trick lets us know that both 3 and 9 are factors of 135. 135 = 1⁵ x 3³ x 5¹.
Answer:
The answer is three times 3.
Step-by-step explanation:
In order to determine the answer, we have to know about factorization.
Any number can be expressed by prime numbers. The procedure is:
if the number is even, to divide the number by the first prime number, 2.if the number is odd, to divide the number by some odd prime number.In this case, we need to know how many factors of 3 have the number.
[tex]135/3=45\\45/3=15\\15/3=5\\5/5=1\\\\135=3^3*5[/tex]
As we can see, there are three times the factor 3.
Finally, the answer is three times 3.
UITO
11.
The number -1.4 would fall into which sets of numbers?
I. Rational Numbers
II. Integer
III. Whole Number
IV. Counting Number
a) I only
b) I, II, and III
c) I and II
d) II and III
Answer:
C
Step-by-step explanation:
Natural numbers are 1, 2, 3, 4, and so on, whole numbers are 0, 1, 2, 3, and so on, integers are natural and whole numbers and their opposites (for example, the opposite of 2 is negative 2), and rational number all those and fractions and terminating/repeating decimals.
So basically, -1.4 is an integer and a rational number. Hope that helps!
Find the distance between
(3,4) and (-5,7).
Hey!
------------------------------------------
Formula: [tex]\sqrt{(x2 - x1) + (y2 - y1)^{2} }[/tex]
------------------------------------------
Solution:
[tex]= \sqrt{(-5 - 3) + (7 - 4)^{2} }[/tex]
[tex]= \sqrt{(-8) + (3)^{2} }[/tex]
[tex]= \sqrt{-5^{2} }[/tex]
[tex]= \sqrt{-25}[/tex]
= 5
------------------------------------------
Answer:
The distance between both points is 5 units.
------------------------------------------
Hope This Helped! Good Luck!
How many liters are in 14 quarts?
Answer:
13.2 liters
Step-by-step explanation:
Answer:
13.2489412
Step-by-step explanation:
let g(x)=-9x^2-8x and f(x)=x+2 find f(x)+g(x)
the total weight of peter, david and henry is 123 kg. peter is 15 kg heavier than david. david is 3 kg lighter than henry. find henry's weight.
Let me break this down with what we know like:
-David + Henry + Peter = 123kg
-Peter is 15kg heavier than David
-David is 3kg lighter than Henry
Now that we know this we can break things down.
The ratio of the 3 people is this:
- (0:3:15)=(David:Henry:Peter)
And these 3 numbers are equivalent to 18+ start with a increase of 3 every weight plus added to find all 3 of their weights, so if there is an increase of 3 and a start of 18 then we can make an equation for example:
123kg = 3x + 18
105 = 3(35)
105 = 105
So we know all 3 other than the info we knew from before which is about 11.6, So if all of them have about 11.6. So everyone's weight would be:
-David is about 11.6kg
-Henry is about 14.6kg
-Peter is about 26.6kg
Hope this helps ^^
Answer:
P-peter,D-david ,H-henry. ,P+D+H=123Kg. so P=15+D,= 15+D+D+D+3=123. 3D+18=123. .3D=123-18.
D=35
so David(D)=35
Peter(P)= 15 + 35=50
so (P)=50
and henry(H)=D+3= 35+3=38
Henry(H)= 38
Mr. Lawson parked his car in a parking garage 33 feet below street level. He
then got in an elevator and went up 88 feet to his office. How far above street
level is his office?
55
Step-by-step explanation:
Subtraction
Total these measurements?
8.3m
5.2m
4.36m
42.1m
86.0m
Help pls
Answer: 145.96
Step-by-step explanation:
add them to gather8.3+ 5.2+4.36+42.1+86.0
Solve the system. -4= x - y 4= -x + y
Answer:
x-y=-4
y-x=4
y=x+4
(x,y)=(1,5),(2,6),(3,7),...
u see it doesn't have a particular answer any pair of numbers with 4 difference will do
Point I is on line segment HJ. Given H I = x, H J = 3x – 9, and
IJ = x + 5, determine the numerical length of HJ.
Answer:
HJ = 33
Step-by-step explanation:
Given that point I is on segment HJ, then
HJ = HI + IJ ← substitute values
3x - 9 = x + x + 5, that is
3x - 9 = 2x + 5 ( subtract 2x from both sides )
x - 9 = 5 ( add 9 to both sides )
x = 14
Hence
HJ = 3x - 9 = (3 × 14) - 9 = 42 - 9 = 33
The numerical length of HJ is 33
The given parameters;
distance of HI = x
distance of HJ = 3x - 9
distance of IJ = x + 5
To find:
the numerical length of HJA sketch of the positions of the line segments is shown below;
|<-----x------->|<--------------------------x+5------------------------------>|
H---------------I----------------------------------------------------------------J
The value of x will be calculated by setting up the following equation;
HI + IJ = HJ
x + x + 5 = 3x - 9
2x + 5 = 3x - 9
collect similar terms together;
2x - 3x = -9-5
-x = -14
x = 14
The numerical length of HJ is calculated as;
HJ = 3(14) - 9
HJ = 42 - 9
HJ = 33
Thus, the numerical length of HJ is 33
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URGENT!! PLEASE ANSWER!
After completing the wood trim on her kitchen cabinets, Candice has 38 inches of trim left. She decides to make a picture frame out of the wood. She wants to make the frame so that the length is 5 inches less than three times the width. What must the dimensions be?
Answer:
The dimensions of the frame must be 13 inches and 6 inches
Step-by-step explanation:
* Lets explain how to solve the problem
- The perimeter of any quadrilateral is the sum of the lengths of its sides
- The rectangle is a quadrilateral with each two opposite sides are
equal so the perimeter of the rectangle = 2l + 2w, l and w are the
length and the width of it
- Candice has 38 inches of trim
- She wants to make a picture frame
- The frame is shaped a rectangle where its length is 5 inches less
than three times the width
- Assume that the length is l and the width is w are the dimensions
of the frame
∵ l = 3w -5 ⇒ (1)
∵ The perimeter of the frame is the length of trim
∵ The length of the trim is 38 inches
∴ The perimeter of the frame is 38 inches
∵ Perimeter of the frame = 2l + 2w
∴ 2l + 2w = 38 ⇒ (2)
- Substitute equation (1) in equation (2)
∴ 2(3w - 5) + 2w = 38
- Multiply the bracket by 2 and add like terms
∴ 6w - 10 + 2w = 38
∴ 8w - 10 = 38
- Add 10 for both sides
∴ 8w = 48
- divide both sides by 8
∴ w = 6
- Substitute the value of w in equation (1) to find l
∵ l = 3w - 5
∴ l = 3(6) - 5 = 18 - 5 = 13
∴ l = 13
∵ l and w represent the length and the width of the frame
∴ The dimensions of the frame must be 13 inches and 6 inches
what is 8 simplified?
Answer:
8/ 8 is 1 /1
Step-by-step explanation:
8 ÷ 8
8 ÷ 8
Reduced fraction:
1 /1
Robert works at a car dealership. Each month, he receives a base salary of $1,685.00, plus a commission of $465.00 for each vehicle he sells. Which of the following equations could be used to determine Robert's total income each month? (Let x represent the number of cars sold by Robert and y represent his total monthly income.)
A.
$1,685y = $465x
B.
y = $465x + $1,685
C.
y = $465x
D.
y = $1,685x + $465
The answer is choice B.
y = $465x + $1685
...........help pleaseeee
When multiplying more than two integers how can you determine the sign of the product
Maria has 8n-30 marbles, her brother has 5n marbles. How many more marbles does Maria have than her brother
Answer:
3n-30
Step-by-step explanation:
Answer: 3n-30
Step-by-step explanation: plato
Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?
They are independent because P(X) x P(Y) = P(X and Y).
They are independent because P(X) + P(Y) = P(X and Y).
They are dependent because P(X) x P(Y) = P(X and Y).
They are dependent because P(X) + P(Y) = P(X and Y).
Answer: The correct option is
(A) [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]
Step-by-step explanation: We are given to consider a situation in which X and Y are two events such that
[tex]P(X)=\dfrac{4}{5},~P(Y)=\dfrac{1}{4},~P(X\cap Y)=\dfrac{1}{5}.[/tex]
We are to select the statement that best describes the events X and Y.
We know that
any two events A and B are said to be independent if
[tex]P(A)\times P(B)=P(A\cap B).[/tex]
We have, for events X and Y,
[tex]P(X)\times P(Y)=\dfrac{4}{5}\times\dfrac{1}{4}=\dfrac{1}{5}=P(X\cap Y)\\\\\\\Rightarrow P(X)\times P(Y)=P(X\cap Y).[/tex]
Thus, X and Y are independent because [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]
Option (A) is CORRECT.
Which is an algebraic expression for the word phrase "8 less than the product of 12 and a number x"? A. 12x – 8 B. 8 – 12x C. 12 – 8x D. 8x – 12
Answer:
A
Step-by-step explanation:
A product is the answer you get when you multiply 2 numbers together.
So you are starting backwards. Get the product first.
12*x
Now you want to take 8 away from it.
12x - 8 is what you get.
A
Answer:
A
Step-by-step explanation:
Your friend is making a pattern for quilt pieces. Her pattern is a right angle with two acute angles that complementary. The measure of one of the angles is to be 12° more than half the measure of the other angle. Find the measure of each angle of the triangle. Show your work using the format above.
Answer:
The measure of angle 1 is 52° and the measure of angle 2 is 38°
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
Let
x ----> the measure of angle 1
y ----> the measure of angle 2
we know that
[tex]x+y=90\°[/tex] -----> equation A
[tex]y=\frac{x}{2}+12[/tex] ----> equation B
Substitute equation B in equation A and solve for x
[tex]\frac{x}{2}+12+x=90\°[/tex]
[tex]\frac{x}{2}+x=90\°-12\°[/tex]
[tex]\frac{3x}{2}=78\°[/tex]
[tex]x=(2)78/3=52\°[/tex]
Find the measure of y
[tex]y=\frac{52}{2}+12=38\°[/tex]
therefore
The measure of angle 1 is 52° and the measure of angle 2 is 38°
The two acute angles in the triangle are 52° and 38°. This is found by setting up and solving two equations based on the problem's conditions.
Explanation:This question is about solving an equation related to two acute angles in a triangle. Let's denote the smaller angle as 'x' and the larger angle as 'y'. Since the two angles are complementary, we can write an equation like 'x + y = 90'. The problem states that one angle is 12° more than half the other. We can formulate this as 'y = x/2 + 12'. To solve for 'x' and 'y', we need to substitute 'y' from the second equation into the first one to get 'x + x/2 + 12 = 90'. Multiplying through by 2 to eliminate the fraction gives '2x + x + 24 = 180', which simplifies to '3x = 156'. Solving for 'x' gives 'x = 52'. Substitute 'x' into either of the original equations gives 'y = 52/2 + 12 = 38'. Thus, the two acute angles in the triangle are 52° and 38°.
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need an answer for this equation in geometry plz
Answer:
120 degrees
Step-by-step explanation:
These are called supplementary angles. These are angles that add up to 180 degrees.
To solve this, you need to know that a triangle's interior angles should all add up to 180 degrees, no matter how weird the triangle looks.
For squares and other stuff it's 360 degrees
But as shown, all three interior angles of this triangle are the same. This means each of them is 60 degrees.
60 + 60 + 60 = 180
-----------------------------------------------------------------------------------------------------------------
To find X, we know that the angle of a straight line is 180 degrees. Since X and that one interior angle share the same line,
we subtract 60 from 180 to get the remaining angle of X.
180 - 60 = 120 degrees.
9. An Integer is 10 times the difference of a rational number and
what is the value of the rational number?
tonal number and 5. If the value of the integer is 124,
Equation
To find the value of the rational number, set up an equation using the representation of the integer as 10 times the difference of the rational number and 5. Solve the equation to find the value of the rational number, which is 17.4.
Explanation:To find the value of the rational number, we can use the given equation: An Integer = 10 times the difference of the rational number and 5.
Let's denote the rational number as x. According to the equation, the integer can be represented as 10(x - 5).
Since the value of the integer is 124, we can set up the equation: 10(x - 5) = 124.
Solving for x, we can divide both sides of the equation by 10 to isolate x: x - 5 = 12.4.
Finally, add 5 to both sides to find the value of x: x = 17.4.
Therefore, the value of the rational number is 17.4.
Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set
of this problem?
-
Answer:
x-1÷2/5=x+1÷3/5
Step-by-step explanation:
Hint: Is means equals.
"One less than
half a number is
a maximum of 19"
What inequality is graphed below?
x < -4
x ≤ -4
x ≥ -4
x > -4
Answer:
The answer is x>-4
Answer:
2342423
Step-by-step explanation:
asdadadsada
50 pts!!! Given: x - 6 1/3 ≤ 1 1/2. Choose the solution set.
A.{x | x R, x ≤ 7 }
B.{x | x R, x ≤ 7 }
C.{x | x R, x ≤ 5 }
Answer:
{x | x R, x ≤ 7 5/6 }
Step-by-step explanation:
we have
[tex]x-6\frac{1}{3} \leq 1\frac{1}{2}[/tex]
Convert mixed number to an improper fraction first
[tex]6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}[/tex]
[tex]1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}[/tex]
substitute
[tex]x-\frac{19}{3} \leq \frac{3}{2}[/tex]
Multiply by 6 both sides to remove the fractions
[tex]6x-38 \leq 9[/tex]
Adds 38 both sides
[tex]6x \leq 9+38[/tex]
[tex]6x \leq 47[/tex]
Divide by 6 both sides
[tex]x\leq \frac{47}{6}[/tex]
convert to mixed number
[tex]\frac{47}{6}=\frac{42}{6}+\frac{5}{6}=7\frac{5}{6}[/tex]
substitute
[tex]x\leq 7\frac{5}{6}[/tex]
therefore
{x | x R, x ≤ 7 5/6 }
Which table represents a linear function?
The answer would be the fourth option. A linear function would be like a adding rule. For example +4 on the left side and +1 on the other side. In this case the answer would be the fourth option because the adding rule is +1 and +2.
Hope this helps.
Jessica bought a soft drink for 2 dollars and 6 candy bars she spent a total of 14 dollars how much did each candy bar cost?
Answer:2 per candy bar
Step-by-step explanation:
14-2=12 12/6=2
The sum of three integers is 228. The second integer is 1 more than the first,
and the third integer is 2 more than the first. Write an equation to determine
the integers. Solve your equation. Show your work.
Please help
Answer: The integers are 75,76,77
Step-by-step explanation:
Answer: first ingeter is 75, second is 76, and third 77
Step-by-step explanation: 75 + 76 + 77 = 228
Mr. Huynh wrote the sum of 7 fifteens and 38 fifteens on the board. Draw a model, and write the correct expression.
Answer with Step-by-step explanation:
Let one ⊕ represents fifteens.
Mathematically, we assume that
x represents fifteens
So, our equation becomes,
[tex]7x+38x\\\\=45x[/tex]
Model can be represented as :
7×⊕ + 15 ×⊕
=⊕⊕⊕⊕⊕⊕⊕ + ⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕
=⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕
How do u make that into a decimal and js it terminating or repeating ?
Answer:
0.2
Step-by-step explanation:
first you do 1÷5 which is 0.2
and since it has an end it is terminal
examples of terminal decimals: 0.2, 0.34, 0.4356, ect
examples of repeating: 0.3333333333..., 0.4343434343434343434343...,0.25555555555..., ect
To convert into decimals, perform division between the numerator and the denominator. The resulting decimal can either be terminating (ends after a few digits) or repeating (has a pattern that infinitely repeats), based on the values used. Multiply by powers of ten to move the decimal point to the right accordingly.
Explanation:To convert a fraction or a different numerical format into a decimal, we can employ the concept of division. Essentially, you can divide the numerator (top number) by the denominator (the bottom number) to produce a decimal. Now, whether this decimal is terminating or repeating depends on the values of the numerator and denominator.
As an example, let's consider the fraction 1/2. If we do the division, we get 0.5. Since there are no further digits after 0.5, we can say that it is a terminating decimal.
On the other hand, if we consider a fraction like 1/3, the decimal representation will be 0.3333..., and the 3s will continue indefinitely. This is a repeating decimal.
Regarding the pattern you referred to, it's used for multiplying a decimal by powers of ten. Count the zeros in the power of 10 and then move the decimal point in your number that many places to the right.
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