Ok so I need help with multiplying fractions, this is the way my teacher did it but I have no idea how to do it the way he did it so if someone can, please explain to me on how to do it
Answers
example 1: this is basically reducing WHILE multiplying. since 5 and 10 have a greatest common factor and is able to be reduced by each other, we do so. hence the reason 5 went to 1 and 10 went to 2 because 5 goes into 5 once and 5 goes into 10 twice. it was a different case for 3 and 8. 3 obviously cant go into 8 and 3 is prime so nothing can be done with those. ONLY REDUCE WHILE MULTIPLYING DIAGONALLY you CANNOT do up and down or side to side. so our new fractions are [tex]\frac{3}{2}[/tex] and [tex]\frac{1}{8}[/tex] so multiply across and get [tex]\frac{3}{16}[/tex] which cant be reduced more.
example 2: this one in my opinion is pretty easy. you take the two fractions and multiply regularly across. you get [tex]\frac{27}{80}[/tex]. that fraction can be reduced. so we find the prime factorization of each number. 3 is a prime factor. 3x3x3=27 which is our top number. 2 and 5 are all prime numbers used to reach 80. 2x2x2x2x5=80. that's the prime factorization method its an easier way to check your work also.
example 3: this one is practically a combination of the two previous ones. [tex]\frac{16}{21}[/tex] and [tex]\frac{7}{8}[/tex] can be diagonally reduced on both diagonals. 7 goes into 7 once and 7 goes into 21 three times 8 goes into 8 once and 8 goes into 16 twice. now we have [tex]\frac{1}{1}[/tex] and [tex]\frac{2}{3}[/tex] multiply across and get just [tex]\frac{2}{3}[/tex]. prime factorization is the best way to do this but, more effective with larger numbers. [tex]\frac{2*2*2*2*7}{3*7*2*2*2}[/tex] now cross out the numbers that are the same on the top and bottom. three 2's cancel out, one 7 cancels out, and now we're left with [tex]\frac{2}{3}[/tex].
I really hope this helps you!!
Related Questions
someone please help- just look at the picture
Answers
Answer:
30
Step-by-step explanation:
18/60 =.3 x 100 = 30
Angle 1 and Angle 2 are complementary angles. Angle 1 is 5x degrees. Angle 2 is 50 degrees. Find the value of x. Type ONLY the number.
Answers
Answer:
x = 8
Step-by-step explanation:
complementary angles sum to 90°
sum the 2 angles and equate to 90
5x + 50 = 90 ( subtract 50 from both sides )
5x = 40 ( divide both sides by 5 )
x = 8
pls help i’ll give brainliest
Answers
Answer:
A
Step-by-step explanation:
Area of the rectangle is 15*20=300
Area of the triangle is 8*17/2=68
Total area is 300+68=368
Perimeter is 15+20+20+8+17=80
Answer:
[tex]\rm {P = 80 \space\ feet,\space\ A = 360 \space\ square \space\ feet}[/tex]
Step-by-step explanation:
The perimeter of a shape is the sum of all the sides of the shape.
• Perimeter of the polygon = 15 + 20 + 17 + 8 + 20
= 80 feet
To find the area of the polygon, we can separately find the areas of the triangle and the rectangle and then add them together.
• Area of rectangle = length × breadth
= 15 × 20
= 300 square feet
• Area of triangle = [tex]\frac{1}{2}[/tex] × base × height
As the height of the triangle is not provided, we have to calculate it.
Let the height of triangle = [tex]x[/tex]
Using Pythagoras's theorem:
[tex]x^2 + 8^2 = 17^2[/tex]
⇒ [tex]x^2 = 17^2 - 8^2[/tex]
⇒ [tex]x = \sqrt{17^2 - 8^2}[/tex]
⇒ [tex]x=\bf15[/tex]
Now using this value of height, we can find the area of the triangle:
Area of triangle = [tex]\frac{1}{2}[/tex] × 8 × 15
= 60 square feet
• Finally, we can add the areas of the triangle and rectangle together to find the area of the polygon:
Area of polygon = 300 + 60
= 360 square feet
) Suppose that we have a bucket of 30 red balls and 70 blue balls. If we pick 20 balls uniformly out of the bucket, what is the probability of getting exactly k red balls
Answers
Answer: 30%
Step-by-step explanation:
A Delivery service charges $25 per pound for making a delivery. If there is an additional 8% sales tax, what is the cost of delivering an item that weighs 4/5 of a pound?
Answers
The cost of delivering an item that weighs 4/5 of a pound?$21.60.
How to find the delivery cost?Let x = the number of pounds
Thus, we can say that;
Cost = 25x * 1.08
Since we want to find the cost of delivering an item that weighs 4/5 of a pound, the we will put 4/5 for x to get;
Cost = (25 * 4/5) * 1.08
Cost = 20 * 1.08
Cost = 21.6
The delivery cost would be $21.60.
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HELP HELP HELP
HELP HELP HELP
HELP HELP HELP
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
As per the given information ~
The given triangles are similar, so their corresponding sides should be in same ratio :
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x}{4} = \cfrac{5}{x - 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{x}{2} = \cfrac{5}{x - 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: x(x - 3) = 10[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 3x = 10 [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 3x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 5x + 2x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: x(x - 5) + 2(x - 5) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (x + 2)(x - 5) = 0[/tex]
so, x = 5 or -2
but since side length can't be negative, we will take x = 5 neglecting the negative value (-2)
So, side lengths of unknown sides are :
[tex] \qquad \sf \dashrightarrow \: {2x = 2 × 5 = 10 units} [/tex]
and
[tex]\qquad \sf \dashrightarrow \: x - 3 = 5 - 3 = 2 \: \: units[/tex]
A card is chosen at random from a deck of 52 cards. It is then replaced and a
second card is chosen. What is the probability of choosing a jack and then an
ace card?
O 0.077
0.004*
O 0.0059
O 0.001
Answers
Answer: 0.0059 (choice C)
Explanation:
There are 4 jacks out of 52 cards total.
4/52 = 1/13 is the probability of getting a jack.
The same applies to an ace as well.
The probability of a jack followed by an ace is (1/13)*(1/13) = 0.0059 approximately, when we replace the first card. If the replacement wasn't done, then the second probability would be different from 1/13.
How many different teams of 4 can be chosen from a group of 15 adults and 16 children if each team must have at least one child on it?
Answers
The Number of teams is mathematically given as
N= 30100
What is the Number of teams?Generally, the equation for Number of teams is mathematically given as
X items are selected from n items by [tex]^nC_x[/tex] ways
[tex]^nC_x = \frac{n!}{ [ (n-x)! * x! ]}[/tex]
Number of teams
N= n(1 child and 3 adults) + n(2 child and 2 adults) + n(3 child and 1 adults) + n(4 child)
N= 16C1 * 15C3 + 16C2 * 15C2 + 16C3 * 15C1 + 16C4 * 15C0
N= 16 * 455 + 120 * 105 + 560 * 15 + 1820
N= 30100
In conclusion, the Number of teams
N= 30100
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help me I need the good answers!!!?
1) Q.1 Find the equation of a line that passes through (1, 2) and (5, 4).
Answers
equation of a line is y=mx+ c
where m is that gradient and c is y intercept
so first we find the gradient (m)
M= change in y intercept ÷change in x
M=4-2÷5-1
M=2÷4=1/2(as a fraction)(you can also use o.5)
there 1/2is the gradient
then to find the equation of the line
y= 1/2x +c (from coordinates 1,2 we substitute)
2=1/2(1)+c
2-1/2=c
c=1.5
or
from the coordinates 5,4
4=1/2(5) +c
4=5/2+ c
c=4-5/2
c=1.5
equation of the line=y=0.5x + 1.5
or y=1/2x +1.5
hope it helps you^_^
Figure ABCD is a parallelogram.
A
5x + 3
C
B
38
What is the value of x?
6
07
08
09
Answers
Answer:
7
Step-by-step explanation:
5x+3=38 subtract the 3 from the 38 leaving you with 35/5 getting you 7
The value of x in the given parallelogram is 7.
What is Quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles
A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
So 5x+3=38
We need to find the value of x
Subtract 3 from both sides
5x=38-3
5x=35
Five times of x equal to thirty five
Divide both sides by 5
x=7
Hence, the value of x in the given parallelogram is 7.
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Using the net below, find the surface area
of the triangular prism.
7 cm
5 cm
15 cm
4 cm
Surface Area
5 cm
7 cm
[?] cm²
Enter
Answers
Answer:
118
Step-by-step explanation:
The total area is the area of the large rectangle in the middle plus the areas of the two triangles.
The length of the entire rectangle is 5 cm + 5 cm + 4 cm = 14 cm.
The width of the rectangle is 7 cm.
Each triangle has a base of 4 cm and a height of 5 cm.
A = LW + 2 × (1/2)bh
A = (14 cm)(7 cm) + (4 cm)(5 cm)
A = 98 cm² + 20 cm²
A = 118 cm²
Will mark Brainliest. Find x
Answers
the value of 'x' is 0. 9
How to determine the value
For the given triangle, we have the;
Adjacent side = 7Opposite side = 13 + xWe want to find the value of x
Using the tangent ratio
Tan θ = opposite/adjacent
Let's substitute the value of theta, opposite and adjacent
Tan 60 = 13 + x / 7
1. 73 = 13+ x/ 7
cross multiply
1. 73 × 7 = 13 + x
12. 1 = 13 + x
x = 13 - 12. 1
x = 0. 9
We can see that the value of x is 0. 9
Thus, the value of 'x' is 0. 9
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this is a question on a review assignment that i’m stuck on , my summer school teacher said i could get help if i needed. any help would be greatly appreciated
Answers
Answer:
volume = 3549.203
Step-by-step explanation:
you need to subtract the volume of the cylinder from the volume of the box
cylinder:
[tex]vol=\pi r^2h\\V=\pi (5)^2(20)\\V=\pi (25)(20)\\V=500\pi[/tex]
box:
[tex]vol=(length)(width)(height)\\V=(20)(16)(16)\\V=5120[/tex]
subtract:
[tex]5120-500\pi =3549.203[/tex]
The circle below is centered at (3, 1) and has a radius of 2. What is its
equation?
Answers
Answer:
( x-3) ^2 + ( y-1) ^2 = 4
Step-by-step explanation:
The equation for a circle is given by
( x-h)^2 + ( y-k) ^2 = r^2 where (h,k) is the center and r is the radius
( x-3) ^2 + ( y-1) ^2 = 2^2
( x-3) ^2 + ( y-1) ^2 = 4
Which expression is equivalent to startfraction 10 x superscript 6 baseline y superscript 12 baseline over negative 5 x superscript negative 2 baseline y superscript negative 6 baseline endfraction? assume x not-equals 0, y not-equals 0.
Answers
[tex]3/ 5x^6*y^6[/tex] is the solution f the expression [tex](-9x^-1*y^-9) / (-15x^5*y^-3)[/tex]
Given expression:
(-9x^-1*y^-9) / (-15x^5*y^-3)
As we know, any number with negative power can be written in inverse form with positive power.
[tex]x^-a = 1/x^a[/tex]
Two number having same base their powers are added:
[tex]x^a + x^b = x^a+b[/tex]
[tex]= > (-9x^-1*y^-9) / (-15x^5*y^-3)= (-3x^-1*y^-9) / (-5x^5*y^-3)\\=3/(5x^6 y^6)[/tex]
Hence the solution would be [tex]3 (5x^6 y^6)[/tex].
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Answer:
b
Step-by-step explanation:
If you rolled two dice, what is the probability
that you would roll a sum of 9?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
second
first
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3
5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Answers
The probability you will roll a sum of 9 is 1/4.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability you will roll a sum of 9 = total times a sum of 9 is derived / total sample spaces
total times a sum of 9 is derived = (3 + 6) , (6 + 3) , (4 + 5) , (5 + 4) Total sample spaces = 36The probability you will roll a sum of 9 = 4/36 = 1/9
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WILL GIVE BRAINLIEST IF YOU ARE CORRECT
Answers
The choice which best describes how to measure the center of these data is; both centers are best described by the median.
MedianThis is a measure of central tendency which helps determine the middle value in a data by rearranging the data either in an ascending order or a descending order.
Mean on the other hand, is used to find the best average of a data set.
Therefore, the mean cannot be used to find the center of the data.
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We want the following inequality to be
true:
|x| < 9
Which of the following are possible
values for x?
Choose all answers that apply:
A
B
x = -10
x = 7
x = 13
Answers
Answer:
x = 7
Step-by-step explanation:
The integer values of x that satisfy |x| < 9 are ...
{-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7. 8}
Of these values, the only one listed as an answer choice is ...
x = 7
__
Additional comment
The expression |x| means "the absolute value of x". It is the value of x with the sign made positive. That is |-10| = 10, a number greater than 9. Of course, |13| = 13, also a number greater than 9.
Quick algebra 1 question 25 points!
Only answer if you know the answer, quick shout-out to subtomex0, tysm for the help!
Answers
Answer:
1. Translate 5 units up (Fixed after a comment from subtomex0 - Thanks again!)
2. Vertical Compression by a scale factor of 3/8
3. Reflect across the y-axis, and shift 2 units to the left
4. Vertical stretch by a scale factor of 6, and shifting 1 unit up
5. Shifting 11 units to the left
6. Vertical stretch by a scale factor of 8
7. Vertical compression by a scale factor of 1/2, and reflection across the y-axis.
Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answers
[tex]8 \: cars = 120 \: dollars \\ 1 \: car = \frac{120}{8} = 15 \: dollars[/tex]
[tex]m(c) = 15c[/tex]
option dAnswer:
d: m=15c
Step-by-step explanation:
Usually (not always), variable y depends on variable x.
Since in this question, the amount of money Paul can earn changes based on the number of cars he washes, y is the amount of money, and x is the number of cars he washes.
This can be represented as: 120 = 8 times ___
___ is the amount of money Paul earns by cleaning 1 car.
___ is 120 divided by 8, which is 15.
--> Paul earns $15 by cleaning each car.
The new equation will be m = 15c
Simplify the expression 3(x + 2)(x2 − x − 8). (6 points)
Answers
3x^3+3x^2-30x -48
Step-by-step explanation:
we apply distributive property
3(x + 2)(x^2 − x − 8)
so we have:
(3*x+3*2)(x^2 − x − 8)
(3x+6)(x^2 − x − 8)
3x*x^2 - 3x*x -3x*8 + 6*x^2 -6*x -6*8
3x^3-3x^2-24x +6x^2 -6x -48
3x^3+3x^2-30x -48
Answer:
3x³ + 3x² - 30x - 48
Step-by-step explanation:
3(x + 2)(x² - x - 8) ← distribute (x + 2) by 3
= (3x + 6)(x² - x - 8)
each term in the second factor is multiplied by each term in the first factor
= 3x(x² - x - 8) + 6(x² - x - 8) ← distribute both parenthesis
= 3x³ - 3x² - 24x + 6x² - 6x - 48 ← collect like terms
= 3x³ + 3x² - 30x - 48
A compound inequality is shown below.
x ≤ 3 and x ≥ 0
Which graph represents the solution of the inequality?
Answers
Answer:
b
Step-by-step explanation:
edge
Measures of the two triangles DEF and PQR
are shown in the figure. Check if the
triangles are congruent. If congruent, which
of the following statements is true?Justify.
∆DEF ≅ ∆PQR ;
∆ DEF ≅ ∆ QPR ;
∆DEF ≅ ∆RPQ
Answers
Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other. Also, their corresponding angles are congruent to each other.
Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.
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An angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2) What is the exact value of cos(120)
Answers
The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
Solving trigonometry identityIf an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;
Cos120 = cos(90 + 30)
Using the cosine rule of addition
cos(90 + 30) = cos90cos30 - sin90sin30
cos(90 + 30) = 0(√3/2) - 1(0.5)
cos(90 + 30) = 0 - 0.5
cos(90 + 30) = 0.5
Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
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Answer:
It's -0.5
Explanation:
Answered it
please help me, i want now
Answers
The value of angle C in the triangle is 50°.
How to calculate the triangle?From the information given, the angle A = 60° while B is given as 70° and we are told to calculate the value of C.
It should be noted that the sum of angles on a triangle is 180°. Therefore, the value of C will be:
= 180° - (60° + 70°)
= 180° - 130°
= 50°
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Joni and Lori began running from the same point. Joni ran 5 miles west while Lori ran 7 miles north. How far apart were they when they finished
Answers
The distance they finishes is 8.6 miles
Given that miles run by Joni is 5 miles and the miles ran by Lori is 7 miles
We need to find the distance they finished
To calculate the total distance along the diagonal line, the Distance Formula first squares the differences between the two x coordinates and the two y coordinates, then adds those squares, and finally calculates their square root.
We know that
According to the Distance formula
= [tex]\sqrt{(5)2+(7)^2}[/tex]
= [tex]\sqrt{25+49}[/tex]
= [tex]\sqrt{74}[/tex]
= 8.6 miles
Therefore the distance finished is 8.6 miles
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.
If f(x)=3x^2+x-2, then f(-2)=
Answers
A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. Suppose 1 step of the dog covers 1 foot. How many feet would the car cover in taking 12 steps
Answers
Answer:
the cat would take 13 steps
How to determine instantaneous rate of change with pi
Answers
The instantaneous rate of change of the function is 5/π
How to determine the instantaneous rate of change?The function is given as
[tex]f(x) =\cos(x - \pi) + 4[/tex]
Where
[tex]x = \pi[/tex]
Calculate f(π) as follows
[tex]f(\pi) =\cos(\pi - \pi) + 4[/tex]
This gives
[tex]f(\pi) =\cos(0) + 4[/tex]
Evaluate the expression
[tex]f(\pi) =5[/tex]
The instantaneous rate of change is then calculated as;
[tex]f'(x) = \frac{f(\pi)}{\pi}[/tex]
This gives
[tex]f'(x) = \frac{5}{\pi}[/tex]
Hence, the instantaneous rate of change of the function is 5/π
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A survey of 400 nurses yielded the following information: 279 were health club members, 215 were smokers, and 160 of the health club members were smokers. how many of the 400 surveyed nurses were health club members or were smokers?
Answers
Health club members or were smokers is [tex]334[/tex] from a A survey of [tex]400[/tex] nurses yielded.
How can we find the health club members or were smokers ?
Events of health club members is [tex]P(M)=279[/tex]
Events of smokers is [tex]P(S)=215[/tex]
Probability of health club members and smokers is [tex]p(M and S)=160[/tex]
Probability of health club members or were smokers is =?
So we use the formula
[tex]p(M or S)=p(M)+p(S)-p(M and S)\\ = 279+215-160\\ = 334[/tex]
Probability of health club members or were smokers is [tex]334[/tex]
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