The fruit drink which contains 70 % fruit juice will have 120 pints of 65 % pure fruit juice and 20 pints of 100% pure fruit juice.
Given that:-
Two types of juice are 65 % fruit juice and 100 % pure fruit juice.
The company is attempting to produce a fruit drink that contains 70% pure fruit juice.
We have to find the amount of each of 65% pure fruit juice and 100 % pure fruit juice which contains 70 % fruit juice with 140 pints of total juice.
Let the amount of 65 % pure fruit juice be x pints and,
The amount of 100 % pure fruit juice be y pints
We know that,
x + y = 140 ...(1)
Also,
Using weighted mean, we can write,
(65x + 100y)/(x + y) = 70
65x + 100y = 70x + 70y
5x = 30y
x = 6y
Putting x = 6y in (1), we get
6y + y = 140
7y = 140
y =140/7
y = 20 pints
x = 6y = 6*20 = 120 pints
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what is the answer to 6x+4
Answer:
2(3x+2)
Step-by-step explanation:
i think that's what it is
Answer:
What do you need done here?
Step-by-step explanation:
6x + 4 means nothing unless you want to factor the binomial.
I assume you want to factor.
Factor out 2.
2(3x + 2)
Is this what you are looking for?
An arts academy requires there to be 4 teachers for every 68 students and for every 3 tutors for every 36 minutes. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 72 students?
The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.
The given question is solved using the unitary method.
The arts academy requires 4 teacher for every 68 students
The arts academy requires 1 teacher for every 68/4 students
The arts academy requires 1 teacher for every 17 students
The academy has 17 students per teacher
It requires 3 tutors for every 36 students
3 tutor = 36 student
1 tutor = 36 /3 = 12 students
The academy has 12 students per tutor
For 72 students the total number of tutor required are 72/12 = 6
The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.
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create a linear equation that has infinitely many solutions. Must start with 18=
Answer:
Step-by-step explanation:
18=18+x-x*x/x
20.8cm divided by 2.3g
Answer:
9.043
Step-by-step explanation:
i just divide
Answer: 9.043 centimeters/grams
Step-by-step explanation:
All you have to do it divide!
Given the information marked on each figure below, select all classifications that must be true.
Note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers.
If necessary, you may learn what the markings on a figure indicate.
The figure RSTU can represent Quadrilateral, Parallelogram and Rectangle
The figure KLMN represents Quadrilateral and Parallelogram
The figure ABCD represents only Quadrilateral
Given,
The figures;
RSTU, KLMN and ABCD
We have to identify the true facts about the figure.
All figure are drawn like a rectangle.
Quadrilateral;
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Parallelogram;
A quadrilateral is referred to as a parallelogram in geometry. The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.
Now here,
RSTU; This figure can represent all the options.
That is,
Quadrilateral, Parallelogram and Rectangle
KLMN; This figure represents Quadrilateral and Parallelogram
ABCD; This figure represents only Quadrilateral
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please help 8th grade math!
The line parallel to y=-2/5x+7 that passes through the point (-1,3)
Answer:
y=-2/5x +13/5
Step-by-step explanation:
y= -0.4x+b
3=0.4+b
b=2.6
y=-2/5x +13/5
Answer: [tex]\text{y} = -\frac{2}{5}\text{x}+\frac{13}{5}[/tex]
===============================================
Work Shown:
I'll be using point slope form to get these steps
[tex]\text{y}-\text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y}-3 = -\frac{2}{5}(\text{x}-(-1))\\\\\text{y}-3 = -\frac{2}{5}(\text{x}+1)\\\\\text{y}-3 = -\frac{2}{5}\text{x}-\frac{2}{5}*1\\\\\text{y}-3 = -\frac{2}{5}\text{x}-\frac{2}{5}\\\\[/tex]
[tex]\text{y} = -\frac{2}{5}\text{x}-\frac{2}{5}+3\\\\\text{y} = -\frac{2}{5}\text{x}-\frac{2}{5}+\frac{15}{5}\\\\\text{y} = -\frac{2}{5}\text{x}+\frac{-2+15}{5}\\\\\text{y} = -\frac{2}{5}\text{x}+\frac{13}{5}\\\\[/tex]
This answer has a slope of -2/5 and y intercept of 13/5.
Parallel lines have equal slopes but different y intercepts.
To verify this equation, plugging in x = -1 leads to y = 3.
Help with this asap
Please and thank you
a) 7 video games;
26 - x = 40 - 3x
x = 7
( x+5) * (x ^3+6x ^2+18x)
The value of (x + 5) * (x^3 + 6x^2 + 18x) is x^4 + 11x^3 + 48x^2 + 90x
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the polynomial expression?
The polynomial expression is given as
(x + 5) * (x^3 + 6x^2 + 18x)
Express the polynomial expression as a product of factors
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x * (x^3 + 6x^2 + 18x) + 5 * (x^3 + 6x^2 + 18x)
Open the brackets in the polynomial expression
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 18x^2 + 5x^3 + 30x^2 + 90x
Collect the like terms in the polynomial expression
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 5x^3 + 18x^2 + 30x^2 + 90x
Evaluate the like terms in the polynomial expression
So, we have the following equation
(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 11x^3 + 48x^2 + 90x
Hence, the solution is x^4 + 11x^3 + 48x^2 + 90x
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What is the missing angle in the triangle?
A. 25
B.79
C. 126
D. 180
Answer:
25
sum of the interior angles of triangle =180
101+54=155
155-180=25
Solve the simultaneous equations 4 x + 3 y = − 10 4 x + y = − 14
Answer:
x = - 4, y = 2
Step-by-step explanation:
First equation: 4x + 3y = - 10
Second equation: 4x+y= - 14
To solve simultaneously:
Rearrange one of the equations and substitute the equation to another equation, I prefer rearranging the second equation because it is easier.
Rearranging the second equation to get y, and then substitute back to the first equation to find x:
y = - 14 - 4x ------> new second equation
Substitute y (new second equation) into the first equation to find x:
4x +3(-14 -4x) = - 10
4x - 42 - 12 x = - 10
- 8x - 42 = -10
-8x = - 10 + 42
- 8x = 32
8x = - 32
x = - 4
Now we substitute x = - 4 to the second equation to find y:
4x + y = - 14
y = - 14 - 4(-4)
y = - 14 - (-16)
y = - 14 + 16
y = 2
there is a problem with this equation in solving equations in Qhere it is if 1/5x=2
Q is the set of the rational numbers
Rational numbers are all numbers that can be put in the form of a/, where b is not equal to zero.
Examples:
[tex]\frac{3}{4},5\frac{2}{7},5.4,2[/tex]The given equation is
[tex](\frac{1}{5})^x=2[/tex]Insert log on both sides
[tex]log\mleft(\frac{1}{5}\mright)^x=log\mleft(2\mright)[/tex]Use the rule of power with a log
[tex]xlog(\frac{1}{5})=log\mleft(2\mright)[/tex]Divide both sides by log(1/5)
[tex]\begin{gathered} x=\frac{log\mleft(2\mright)}{log\mleft(\frac{1}{5}\mright)} \\ x=-0.43067655 \end{gathered}[/tex]Since we can not put the value of x in the form of a/b, then
The equation has NO solution in Q (or empty set { } or Nul)
A pair of shoes usually sells for $68 if the shoes are 40% off and sales tax is 6% what is the total price of the shoes including tax
Usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.
As given in the question,
Given that:
Usual selling price of shoes = $68
Discount on shoes =40%
Discounts an amount or percentage from something that they are selling, they take the amount or percentage off the usual price.
so, remove 40% from the price and you have left 60%
reduced price = 60% of $68
=60/100 * 68 = $40.8
Sales tax is 6% of reduced price= 6% of $40.8
=$2.448 upto 3 decimal digits
Now , price including tax =$40.8+$2.448 =$43.248
Hence, total price including tax= $43.248
Therefore, usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.
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Step
1
try
Angle
m/IKL=54"
m/
CL
F
H
54°
Reason
Given
Select a Reason
Answer:
<DKF IS 54° BECAUSE IT IS VERTICALLY OPPOSITE ANGLE OF THE<IKL.
Use the graph of y=x^2 to graph the quadratic equation f(x)=(x+4)^2+5
Answer:
shifted 5 up and 4 to the left
Step-by-step explanation:
A rectangle is 8m longer than it is wide. If the length is increased by 2m and the width is increased 2m, the area is
increase by 68m 2. Find the original dimensions.
The original dimensions are 12 m and 20 m.
What is area of rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.
Let x be the width of the rectangle.
Length of the rectangle = x+8
Area of the rectangle = x(x+8)
According to question, new width= x+2
New length = x+2+8 = x+10
New area = (x+2)(x+10)
Area increased = (x+2)(x+10) – x(x+8)
x^2+12x+20-x^2-8x=68
4x-20=68
4x=48
x=12
Hence, the width = 12m and length = 12+8 = 20 m
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Answer quick please. I need to finish this in 5 min
Answer: I got 18
Step-by-step explanation:
Substitute all the variables
18 = 2*3^2
X = 4 * 9^2
X = 4 * 81
X = 324
324/18 = 18
so the is answer is 18.
Also are you going to A+ by any chance?
solve the inequlaity 2(4x+1)<3(2x-3)
Answer:
x<-5.5 or x<-11/2
Step-by-step explanation:
2(4x+1)<3(2x-3)
1. First we need to expand the brackets
8x+2<6x-9
2. get the x on one side so we would -6x and -2 on each side
2x<-11
3. divide by 2 on each side as we want to get the value of x which gives
x<-11/2
the fraction can also be written as a decimal
x<-5.5
4) so, the final answer is
x<-5.5 or <-11/2
how many nonzero complex numbers zz have the property that 0, z,0,z, and z^3,z 3 , when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle?
Consequently, there exist four numbers z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
The three unique vertices of an equilateral triangle are 0, z, and z3: (z^3=0)= e ^iπ/3(z -0 ) ⇔ z^3=e^(±iπ/3)z
=(z^2-e^±iπ/3)z=0⟺z=0
or z^2=e^±iπ/3
Since we have z[tex]\neq[/tex]0, z=e^±iπ/6= ±(√3/2 ± I 1/2 )
There are thus four numbers in z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
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solve the following expression
Answer:
2
Step-by-step explanation:
substitute s for 8
then substitute f for 2
that means 2*2 or 4
8/4 is 2
Answer: the answer would be 2
Step-by-step explanation: since f = 2 you would multiple 2 x2 then you would get 4 then you divid 8 and 4 and you get 2
A bottle of maple syrup in Wayne’s freezer needs to be warmed for breakfast. Sitting on the kitchen counter, the bottle temperature will go up a steady 9.6° C every hour. If the bottle temperature begins at the freezer temperature of –16° C, how many hours will it take to reach 20° C?
Change in temperature: (20 – (–16)) = 20 + 16 = 36
It will take the bottle of maple syrup 3 hours 45 minutes to reach 20° C from –16° C.
How to get the temperature changegiven data
the bottle temperature will go up a steady 9.6° C every hour
freezer temperature = –16° C
final temperature = 20° C
The temperature rise from –16° C to 20° C
from –16° C to 0° C = 16° C
from 0° C to 20° C = 20° C
adding both increments gives = 20 + 16 = 36° C
if every hour we have 9.6° C then how many hours will give 36° C
1 hour = 9.6° C
? hour = 36° C
we cross multiply to have
= 36 * 1 / 9.6
= 3.75
This is 3 hours then a fraction of some minutes, the fraction is gotten by
0.75 * 60 = 45
Therefore the time to reach 20° C is 3 hours 45 minutes
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If £1 is equal to 99.72 rupees and the post office only has 500 rupee papers how much can I change out of £450
£1 = 99.72 rupees -> £450 = 44874 rupees.
As the post office only has 500 rupee papers, once we calculate out the result, we have to round down to the nearest whole number.
The amount of rupee papers we can change out is : 44874 : 500 = 89.748 (papers)
We round down to 89 papers.
In the diagram below, NO is parallel to KL. If KN = 24, NO = 30, and
KL = 48, find the length of N M.
Answer: NM = 40
Step-by-step explanation:
First, we will label everything. See attached.
Next, we will set up a proportion to solve. Let the missing side, ? in the picture, be equal to x.
➜ On the left side will be the "smaller top" triangle
➜ On the right side will be the larger triangle
➜ View the second attachment for a visual explanation of this if you are confused.
[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]
Next, we will cross-multiply and solve.
[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]
48x = 30(x + 24)
48x = 30x + 720
18x = 720
x = 40
if gas is 4.83 per gallon and johnny's car has a 107 gallon tank how much money would it take for him to fill the tank?
Answer:
Step-by-step explanation:
Fuel cost = (Distance / Consumption) × Cost per gallon.
107 X 4.83 = 516.81
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The graph of line p passes through the point (-3,-4) and has a slope of 2. What is the y-coordinate of the y-intercept of line p?
Answer: m= -1/2
Step-by-step explanation: Equation of line in slope intercept form is represented by,. y= mx+c —-(1). Given that the line p passes through A (- 2, 4) and has a slope m= -1/2.
⚠URGENT!!!⚠The larger prism has had two identical holes carved out of it, each of which is a rectangular prism. Find the volume of the remaining solid, writing your answer correct to 2 decimal places. Note that all measurements are in meters.
Volume=_____m^3
The volume of the remaining solid correct to 2 decimal places is 3634.60 m³
Calculating VolumeFrom the question, we are to determine the volume of the remaining solid
Volume of the remaining solid = Volume of the larger prism - Volume of the rectangular prisms carved out
First, we will determine the volume of the larger prism
Volume of the larger prism = 17 × 17 × 17
Volume of the larger prism = 4913 m³
Now, we will determine the volume of one of the rectangular prism that was carved out
Volume = 4 × 9.4 × 17
Volume = 639.2 m³
∴ Volume of the two identical holes carved out = 2 × 639.2 m³
= 1278.4 m³
Thus,
Volume of the remaining solid = 4913 m³ - 1278.4 m³
Volume of the remaining solid = 3634.60 m³
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The Distributive Property- 6( x + 3)
Answer:
-6x-18
Step-by-step explanation:
in class
Answer:-24
Step-by-step explanation: you do -6(x)+(-6)(3) and u get -6+-18 and get -24 hope it helps .
HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT
Based on the equation of the line that is parallel to the first line, the equation of the line in slope-intercept form is y = 3/4x - 6³/₄
How to write the equation?First, find the slope of 3x + 4y = 7:
( 3x + 4y = 7) x 1/4
3/4x + y = 7/4
The slope is therefore 3/4x.
Lines that are parallel to each other have the same slope. You can therefore use this slope to find the formula of the other line by first solving for the y-intercept:
y = Slope(x) + y-intercept
-9 = 3/4(-3) + y-intercept
y-intercept = -6³/₄
The equation of the line is:
y = 3/4x - 6³/₄
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solve for x from the picture please
x = 9
x + 3 + x - 1 = 20
2x + 2 = 20
2x = 18
x = 9
A bracelet is 8.0 inches long. One bead on the bracelet is
0.8 inch long.
One bead is
times the length of the bracelet.
Answer:
8.0/0.8
=10times