Answers
The system of equations has the solution:
x = 111/42
y = 27/14
z = -15/6
How to solve the system of linear equations?We start with 3 linear equations:
2x+y-z=8
x+4y+z=7
-3x+2y-3z=21
To solve this, first we need to isolate one of the variables. I will isolate x on the second one:
x = 7 - 4y - z
Now we can replace that in the other two:
2*( 7 - 4y - z) + y - z = 8
-3*(7 - 4y - z) + 2y - 3z = 21
Now we need to isolate other variable, let's isolate y on the above one:
14 - 8y - 2z + y - z = 8
-7y - 3z = 8 - 14 = -6
z = (-6 + 7y)/-3 = 2 - (7/3)*y
Now we replace this on the last equation:
-21 + 12y -3z + 2y - 3z = 21
14y - 6z = 42
14y - 6*(2 - (7/3)*y) = 42
14y - 12 + 14y = 42
28y = 42 + 12 = 54
y = 54/28 = 27/14
Now that we know the value of y, we can find the value of z:
z = 2 - (7/3)*y = 2 - (7/3)*27/14 = 2 - 27/6 = -15/6
And the value of x:
x = 7 - 4y - z = 7 - 4*(27/14) + 15/6 = 7 - 48/7 + 15/6 = 111/42
So the solution is:
x = 111/42
y = 27/14
z = -15/6
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Related Questions
KAJE PIERS' basketball court is rectangular with a length of 8x feet and a width of (x + 3) feet.
• Determine the perimeter of the basketball court.
• Determine the area of the basketball court.
Answers
The perimeter and area of the basketball court is 18x + 6 and 8x² + 24x respectively.
perimeter of a rectangleLength = 8xWidth = (x + 3)Perimeter of basketball court = 2(length + width)
= 2(8x + x + 3)
= 2(9x + 3)
= 18x + 6
Perimeter of basketball court = 18x + 6
Area of basketball court = length × width
= 8x × (x + 3)
= 8x² + 24x
Area of basketball court = 8x² + 24x
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a. single $80,602
Determine the tax for each filing status and taxable income amount listed.
a. single $80,602
0/ 50000
b. head of household $83,572
0/ 50000
c. married filing jointly $77,777
0/ 50000
d. married filing separately $83,050
Answers
Based on the filing status and the taxable income, the tax for the following people are:
a single earning $80,602 is $15,950.head of household earning $83,572 is $15,216.married filing jointly earning $77,777 - $11,031.married filing separately $83,050 - $16,773.What are the taxes these people should pay?Based on the tax table, a single in the $80,600 - $80,650 bracket should pay $15,950.
A head of household in the $83,550 to $83,600 bracket would pay $15,216 and a married flling jointly in the $77,750 to $77,800 would pay $11,031.
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Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
Answers
Answer:
the solution is (7,-1)
Step-by-step explanation:
if you dont trust your boy look below
4x + 8(-2x+13)=20
4x -16x + 104 = 20
-12x + 104 *-104* = 20 -104
-12x/-12 = -84/-12
x = 7
y = -2(7) + 13
y = -14 + 13
y = -1
A student is reading a newspaper article about a new playground being built in the community. The article says that the playground will benefit the community for a number of reasons. The student wants to figure out whether the author’s claims are strong. In 1–2 sentences, explain how the student could analyze and evaluate the author’s claims.
Answers
The student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.
How to verify a claim?
We are told that the author of the article is making a claim that a playground will benefit a particular community.
Now, when trying to verify a claim by someone it is very important to try to get facts and figures about that fact to start with before asking for opinions.
Thus, what the student do is that he should look for opinions, the student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.
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Try: Re-reading the question.
Answer: The student should check if the author's article provides more facts or evidence than opinions.
What is the difference between facts and opinions? Facts provide real statements that have been proved with solid evidence by experts. Meanwhile, on the other hand, opinions are what people think. It is more like thinking than something with evidence. It hasn't or can't be proved. If it includes more facts then the author's claims are strong with solid evidence. If it includes more opinions then the author's claims are not strong, they are weak. Since it's only the author's point of view.
Which is a solution for the equation 2x - 4y = 12?
Answers
Answer:
So basically you solve for y
so its gonna be -4y = 12-2x, then divide everything by -4 to solve for y which will be equal to -3 + 1/2x
just write it as 1/2x -3 cause its better
Hope that answers your question
Step-by-step explanation:
Answer:
y = -3 +1x/2
Step-by-step explanation:
2x - 4y = 12
-4y = 12 -2x
y = 12/-4 - 2x/-4
y = -3 +x/2
Find the slope please
Answers
If a dress costs $27.00 when it’s on sale for 10% off, what is its original cost?
Answers
Answer:
the answer is $24.3
Step-by-step explanation:
Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triangle DEC. Which statements about the two triangles must be true? Select three options.
△ABC ~ △DEC
∠B ≅ ∠E
3BC = 2EC
3DE = 2AB
3m∠A = 2m∠D
2m∠A = 3m∠D
Answers
The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
Right triangle ABC is reflected over AC.
Then dilated by a scale factor of Two-thirds to form triangle DEC.
The triangle △ABC and △DEC are similar to each other.
△ABC ≅ △DEC
The dilation is 2/3. Then we have
DE / AB = 2 / 3
3AB = 2DE
∠B ≅ ∠E = 90
There is no effect of dilation on angle.
Then the correct option is A, B, and D.
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Answer:
A. △ABC ~ △DEC
B. ∠B ≅ ∠E
D. 3DE = 2AB
Step-by-step explanation:
got it right on edge 23
if you want to calculate your take home pay you will need to determine the amount of taxes that will be taken out of your paycheck to do this you will:
a. subtract your gross income by your net pay.
b. multiply your gross income by the percent of taxes then subtract the amount to find your net pay.
c. multiply your net income by the number of taxes then subtract the amount to find your net pay?
Answers
In order to determine your take home pay, multiply your gross income by the percent of taxes then subtract the amount to find your net pay.
How to determine the net pay?
Gross pay is the total income earned before any deductions. Net pay is the gross income less any deductions.
Assume your net pay is $10000 and tax is 10%, net pay is:
$10,000 - (0.1 x 10,000) = $9,000
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find X if X is equal to 9x=6
Answers
It continues are you sure this is the equation also if you need it rounded up
X= .667
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
[tex]\textsc{heya!}[/tex]
[tex]\square\!\!\!\!\checkmark[/tex]what we need to do:
find x if 9x=6[tex]\square\!\!\!\!\!\checkmark[/tex] what we are provided with:
9x=6[tex]\textsc{solution:}[/tex]
[tex]\bold{x=\frac{2}{3}}[/tex][tex]\textsc{explanation:}[/tex]
divide both sides by 9; after performing this operation, we obtain:
[tex]\bold{x=\frac{6}{9}}[/tex]
divide top & bottom by 3; we obtain the solution
[tex]\bold{x=\frac{2}{3}}[/tex]
[tex]\textsc{hopefully\;helpful!}[/tex]
by: [tex]^da_n^cIn_g}[/tex]
have a great rest of your day ahead ~ = )
~
make mathematical expression and simplify. The sum of 4 and 5 is subtracted form one-third of the difference of 40 and 4.
Answers
Answer:
X= -3
Step-by-step explanation:
(4+5)-1/3(40-4)=X
X=9- 1/3(36)
X=9-12
please help me I'm almost done
Answers
Answer:
[tex]\mathsf {SA = 112 in.^{2} }[/tex]
Step-by-step explanation:
[tex]\textsf {Formula used :}\\\implies \textsf {SA = 2(length * width + width * height + length * height) }[/tex]
[tex]\textsf {Given :}\\\textsf {Length = 5 in.}\\\textsf {Width = 4 in.}\\\textsf {Height = 4 in.}[/tex]
[tex]\textsf {Solving :}[/tex]
[tex]\implies \mathsf {SA = 2 (5 * 4 + 4 * 4 + 5 * 4)}[/tex]
[tex]\implies \mathsf {SA = 2 (20 + 16 + 20)}[/tex]
[tex]\implies \mathsf {SA = 2 (56)}[/tex]
[tex]\implies \mathsf {SA = 112 in.^{2} }[/tex]
What's the least common
denominator of ¾,
⅘, and ⅔?
O A. 15
O B. 12
O c.20
O D. 60
Answers
Answer:
D. 60
Step-by-step explanation:
60 is the only number that 3 and 4 and 5 all go into.
4 does not go into 15, so not answer A.
5 does not go into 12, so not answer B
3 does not go into 20, so not answer C
D is correct. 4 and 5 and 3 all go into 60.
A minivan with a gross weight of 5700 pounds is parked on a street with a slope of 5°. Find the magnitude of the force required to keep the vehicle from rolling
down the hill. What is the magnitude of the force perpendicular to the hill?
Answers
Answer:
The minivan must keep a thrust of 496.79 pounds from rolling down the hill while the perpendicular force to the hill would be 5678.31 pounds. The picture illustrates the solutions to the problem.
The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.
What is a vector?The quantity which has magnitude, direction, and follows the law of vector addition is called a vector.
A minivan with a gross load of 5700 pounds is stopped on a road with a slant of 5°.
Balance the force along the hill. Then the value of the force is given as,
F = W sin θ
F = 5700 x sin 5°
F = 5700 x 0.087
F = 496.79 pounds
The magnitude of the force perpendicular to the hill will be given as,
N = W cos θ
N = 5700 x cos 5°
N = 5700 x 0.9962
N = 5678.31 pounds
The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.
The diagram is given below.
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-2
Mark all of the statements that are true.
-2
A. The domain for this function is all
real numbers.
B. The domain for this function is
the set {3}.
+2
C. All real numbers are in the range of this function.
D. This graph is not a function because the value of y is the same for
every value of x.
E. The range for this function is the set (3).
Answers
Hope that helps!!
The volume of a water tank is 396 m^3. If it is 7.2 m long and 5.5 m wide. what is the depth of the tank ?
Answers
Answer :
Depth of the tank is of 10mStep-by-step explanation :
We have been provided with the volume of water tank , it's length and breadth. We are asked to calculate the depth of tank (height), so we all know that water tank is always is in the shape of cuboid.
We would be using the formula of calculating the volume of cuboid and substitute the values in it.
V = l × b × hHere,
l is length b is breadth h is heightWe have :
Volume (V) = 396m³length (l) = 7.2mbreadth (b) = 5.5m height (h) = ?Substituting the values :
>> 396 = 7.2 × 5.5 × h
>> 396 = (72 / 10) × (55 / 10) × h
>> 396 = 72 × 55 × h / 100
>> 396 = 3960 × h / 100
>> 396 × 100 = 3960 × h
>> 39600 = 3960h
>> h = 39600 / 3960
>> h = 3960 / 396
>> h = 10
__________________________
find the size of an angle which is five times its supplement
Answers
Two supplementary angles when addd together equal 180.
let one angle = x
The second angle is 5 times that so would be 5x
x + 5x = 180
Simplify:
6x = 180
Divide both sides by 6:
X = 30
One angle is 30, the second angle would be 150
The answer is 150
can you figure thus out?
A number is between 300 and 400. If it is divided by 2, the remainder is 1. If it is divided by 4, 6, or 8, the remainder is 3. If it is divided by 10, the remainder is 5. If it is divided by 3, 5, 7, or 9, the remainder is zero. What is the number?
Answers
Answer:
315
Step-by-step explanation:
The number is divisible by 3,5,7 and 9. Since 3 is a factor of 9, this number is divisible by 5,7, and 9.
5x7x9= 315.
Give the degree measure of the arc intercepted by the chord described. Round to the nearest tenth if necessary:
A chord congruent to the radius.
Answers
Answer: 60 degrees
Step-by-step explanation:
1. Make a right triangle where the right angle is and label the hypotenuse r.
2. Since the chord is equal to r and a 90-degree angle is formed at the intersection, the chord is bisected. Therefore, the chord segment is 1/2 r.
3. Since we have to solve for the intercepted arc, we must find the central angle ( the angle of the right triangle closest to the dot/center) of the arc, which in this case is the sin, or 0.5r/r.
4. We must get rid of the fraction in the numerator, so multiply both the numerator and denominator by 2 which gets you 1r/2r.
5. The r's cancel out, leaving you with 1/2.
6. Since we have to find the angle measure, you must take the negative sin of 1/2 which is 30 degrees.
7. Finally multiply by 2 since you only solved one bisected portion to get 60 degrees.
Answer:
Step-by-step explanation:
60
If a fission reaction yields 4.50×10^9 kJ of energy, then how much mass was lost?
1.50×10^−6 kg
5.00×10^−2 kg
5.00×10^−5 kg
1.50×10^−3 kg
Answers
Answer:
(c) 5.00×10^-5 kg
Step-by-step explanation:
The mass and energy are related by Einstein's formula E = mc².
__
Solving for mass in kg, we find it to be ...
m = E/c² . . . . . . . . where E is in joules, and c is in meters/second
m = (4.50×10^12 J)/(3×10^8 m/s)² = 5.00×10^-5 kg
The lost mass was about 5.00×10^-5 kg.
Answer:
5.00×10^−5 kg
Step-by-step explanation:
I took the test and it was correct! PLEASE LIKE and have a wonderful day!
Situation:
A 8 gram sample of a substance that's a
by-product of fireworks has a k-value of
0.1001.
N = Noe-kt
No = initial mass (at time t = 0)
N = mass at time t
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answers
The half life of the substance is 6.92 days.
What is the Half life ?Half life can be defined as the time required to reduce the concentration to half of its initial value.
Here the equation given is
[tex]\rm N = N_o e^{-kt}[/tex]
The concentration will reduce to half therefore
[tex]\rm N= \dfrac{N_o}{2}[/tex]
so,
[tex]\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}[/tex]
ln 0.5 = - 0.1001 * t(1/2)
-0.693 = -.1001 * t(1/2)
t(1/2) = 6.92 days.
Therefore the half life of the substance is 6.92 days.
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Common Core Performance Assessment.
The Name Game
Pairs of students in Mr. Kuan's class are playing the
Name Game. One team member is given a list of attributes
and has to draw a shape to match the description. The other
team member must then name the shape. The first pair to
complete the task wins.
Wilfredo was given a list with the information at the right.
He drew a shape and his partner, Olivia, named it. What shape
did Wilfredo draw? Answer Exercises 4-7 to solve the problem.
.
•
4. MP.1 Make Sense and Persevere What are you asked to do?
What can you do to persevere when solving the problem?
5. MP.6 Be Precise What math terms and numbers can help you
solve the problem?
6. MP.7 Use Structure What do you know about a quadrilateral?
Use what you know to draw and name a shape that matches
the information in the list.
. MP.3 Construct Arguments Is there more than one possible
way for Wilfredo to draw the shape? Explain.
A quadrilateral
2 sides are parallel
2 sides are equal
2 right angles
Attend to precision by
identifying words and
numbers that can help you
solve the problem.
.
.
Answers
Answer: Common Core Performance Assessment.
The Name Game
Pairs of students in Mr. Kuan's class are playing the
Name Game. One team member is given a list of attributes
and has to draw a shape to match the description. The other
team member must then name the shape. The first pair to
complete the task wins.
Wilfredo was given a list with the information at the right.
He drew a shape and his partner, Olivia, named it. What shape
did Wilfredo draw? Answer Exercises 4-7 to solve the problem.
.
•
4. MP.1 Make Sense and Persevere What are you asked to do?
What can you do to persevere when solving the problem?
5. MP.6 Be Precise What math terms and numbers can help you
solve the problem?
6. MP.7 Use Structure What do you know about a quadrilateral?
Use what you know to draw and name a shape that matches
the information in the list.
. MP.3 Construct Arguments Is there more than one possible
way for Wilfredo to draw the shape? Explain.
A quadrilateral
2 sides are parallel
2 sides are equal
2 right angles
Attend to precision by
identifying words and
numbers that can help you
solve the problem.
Step-by-step explanation:
Draw and set up the integrals for the area enclosed by the y–axis, the curve y = (x + 1)1/2 and y = 2. Compute one of them.
Region II only please
Answers
If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set
[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]
and as a type II region,
[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]
where we solve y = √(x + 1) for x to get x as a function of y.
A. The area of the type I region is
[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]
B. The area of the type II region is of course also
[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]
I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).
Which is a zero of the function f(x)=3x−12?
Answers
==================================================
Explanation:
Replace f(x) with 0 and solve for x.
f(x) = 3x-12
0 = 3x-12
3x-12 = 0
3x = 12
x = 12/3
x = 4 is a zero, aka root, of the function
---------------
Check:
f(x) = 3x-12
f(4) = 3(4)-12
f(4) = 12-12
f(4) = 0
The answer is confirmed.
how to Find the number of ways to distribute 5 bananas and 7 different books to 3 person
empty allowed
Answers
Answer:
In order for each child to receive a book, first distribute one book to each.
This can be done in [math] 5\times 4\times 3 = 60 [/math] ways.
The remaining two books can be distributed in [math] 3^2 [/math] ways.
Total number of ways[math] = 60 \ times 9 = 540 [/ math]
what is 6 divided by a number that will give you 12
Answers
▶︎◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◀︎
[tex]Hello[/tex] [tex]There![/tex]
We need to find what number, if 6 is divided by it, gives us 12.
This isn't hard, I promise! I am going to take you through a few steps, and we'll find the answer.
Are you ready? Then let's begin...:)
[tex]Procedure:[/tex]
✦ We can think about it as: 6 divided by what number gives us 12?
(let the number be z)
[tex]^6/_z=12[/tex]
Multiply both sides by z
[tex]6=12z[/tex]
Divide both sides by z
[tex]z=^6/_{12}[/tex]
Which is the same as
[tex]z=^1/_2[/tex]
hope it's helpful!wishing you a great day![tex]Greetings![/tex]
--
What is the pre-image of vertex A' if the image shown
on the graph was created by a reflection across the line
y=x?
O (10,-2)
O (-10, 2)
O (-2,-10)
O (2, 10)
Answers
Answer:
it is b
Step-by-step explanation:
The solution is Option A.
The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the coordinates of the point A be A ( x , y )
Now , the vertex A is reflected over the line y = x
When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )
So , the coordinates of the point A' ( -2 , 10 )
Now , the coordinates of the point A will be
A ( x , y ) = A ( 10 , -2 )
Therefore , the value of A is A ( 10 , -2 )
Hence , the coordinates of the point before reflection is A ( 10 , -2 )
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At a swimming pool the ratio of children to adults was 3 : 2
Out of 930 people, how many were adults?
Answers
Answer:
372
Step-by-step explanation:
We know that a ratio of 3 : 2 has 5 people, so figuring out how many times that ratio goes into our total number helps us find the value of the total number of adults.
930 / 5 = 186
This means that there are 186 groups of 3 children to 2 adults
So, in each of the 186 groups, there are 2 adults.
Therefore, we can multiply (186)(2)
to find the total number of adults: 372
The number of the children and adult will be 558 and 372.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
At a swimming pool, the ratio of children to adults was 3 : 2.
C / A = 3 / 2
Then solve the equation for C, then the equation will be
C = (3/2)A
The total number of the people is 930. Then the equation will be
C + A = 930
Substitute the value of C in the above equation. Then the equation will be
(3/2)A + A = 930
(5/2)A = 930
A = 930 x (2/5)
A = 372
The number of the adult will be 372.
Then the number of the children will be
C + 372 = 930
C = 930 – 372
C = 558
The number of the children will be 558.
Thus, the number of the children and adult will be 558 and 372.
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E Homework: 3.1 Homework
Evaluate the function f(z) = 3z-8 at the indicated values.
a) Find f(-4).
1
b) Find f
2
c) Find f(z-7).
a) f(-4)=
(Simplify your answer. Type an integer or a simplified fraction.)
THINGS
Answers
The given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
The given function is f(z)=3z-8.
We need to find the value of f(-4), f(2), f(z-7).
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Now to find f(-4), replace z from -4.
f(-4)=3(-4)-8=-12-8=-20
Now to find f(2), replace z from 2.
f(2)=3(2)-8=6-8=-2
Now to find f(z-7), replace z from z-7.
f(z-7)=3(z-7)-8=3z-21-8=3z-29.
Therefore, the given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
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Mr. Garcia had some blueberries. He sold 2 3/4 kilograms of the blueberries and packed the rest equally into 9 bags. Each bag contained 1/4 kilogram of blueberries. Find the mass of blueberries that mr. Garcia had at first
Answers
Answer:
Mr. Garcia had 5 kilograms of blueberries at first
Step-by-step explanation:
to make this easiest, we can imagine that we're undoing mr. garcia's actions.
So, we can start by 'unpacking' mr garcia's bags
we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags
(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)
so,
1/4 x 9 = 9/4
(9 = 9/1 [if that is how you're used to multiplying a fraction])
Then, he also sold 2 3/4 kilograms
so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first
2 3/4 + 9/4 = 2 + 12/4
(12/4 = 3)
2 + 3 = 5
So, Mr. Garcia had 5 kilograms of blueberries at first