A vanilla thickshake is $2 more than a fruit juice. If 3 vanilla thickshakes and 5 fruit juices cost $30, determine their individual prices using simultaneous elimination
Answers
Answer:
vanilla thickshake = $5
fruit juice = $3
USING ELIMINATION METHOD
Let the price of vanilla thickshake = x
Let the price of fruit juice = y
Given that a vanilla thickshake is $2 more than a fruit juice.
so
x = 2+y ...... (Equation 1)Given that If 3 vanilla thickshakes and 5 fruit juices cost $30.
3x+5y=30 ...... (Equation 2)So the system of equations
[tex]x = 2+y[/tex]
[tex]3x+5y = 30[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}x-y=2\\ 3x+5y=30\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}x-y=2\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:3x-3y=6[/tex]
[tex]\begin{bmatrix}3x-3y=6\\ 3x+5y=30\end{bmatrix}[/tex]
so
[tex]3x+5y=30[/tex]
[tex]-[/tex]
[tex]\underline{3x-3y=6}[/tex]
[tex]8y=24[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}3x-3y=6\\ 8y=24\end{bmatrix}[/tex]
solve 8y = 24 for y
[tex]8y=24[/tex]
Divide both sides by 2
[tex]\frac{8y}{8}=\frac{24}{8}[/tex]
[tex]y=3[/tex]
[tex]\mathrm{For\:}3x-3y=6\mathrm{\:plug\:in\:}y=3[/tex]
[tex]3x-3\cdot \:3=6[/tex]
[tex]3x-9=6[/tex]
[tex]3x=15[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]
[tex]x=5[/tex]
Therefore,
The price of fruit juice = y = 3The price of vanilla thickshake = x = 5
2ND METHOD
Step-by-step explanation:
Let the price of fruit juice = xAs a vanilla thickshake is $2 more than a fruit juice.
Thus the price of thickshake vanilla = x+2Given that 3 vanilla thickshakes and 5 fruit juices cost $30.
3(Vanilla thickshakes) + 5(fruit juice) = 30
3(x+2) + 5x = 30
3x+6+5x=30
8x+6=30
8x=30-6
8x=24
x = 3
Thus,
The price of fruit juice = x = $3The price of vanilla thickshake = x+2 = 3+2 = $5Related Questions
HELP MEEEEE (find the values of z and y)
Answers
Using Point Slope Formula, write an equation that passes through (-2, 6) and ( 8, 9)
Answers
Answer:
y - 9 = 3/10(x - 8)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Point (-2, 6)
Point (8, 9)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute [SF]: [tex]\displaystyle m=\frac{9-6}{8+2}[/tex]Subtract/Add: [tex]\displaystyle m=\frac{3}{10}[/tex]Step 3: Write Function
Plug in variables into general form.
y - 9 = 3/10(x - 8)
y - 6 = 3/10(x + 2)
The number of girl child per family was recorded for 1000 families with 3 children. The data obtained was as follows: [2] Number of Girls 0 1 2 3 Number of Families 112 314 382 192 Suppose a family is chosen at random, find the probability that it has: (a). At most one girl (b). More girls than boys
Answers
Answer:
[tex]a.\ Probability = 0.426[/tex]
[tex]b.\ Probability = 0.574[/tex]
Step-by-step explanation:
Given
[tex]Total\ Families = 1000[/tex]
Number of Girls : 0 ----> 1 -----> 2 ------->3
Number of Families: 112 -> 314 --> 382 ---> 192
Solving (a): At most one girl
From the table, the number of families with at most one girl is: 112 + 314
i.e.
Number of Girls : 0 ----> 1
Number of Families: 112 -> 314
So, we have:
[tex]At\ Most\ One\ Girl = 112 + 314[/tex]
[tex]At\ Most\ One\ Girl = 426[/tex]
The probability is then calculated as:
[tex]Probability = \frac{At\ Most\ One\ Girl}{Total}[/tex]
[tex]Probability = \frac{426}{1000}[/tex]
[tex]Probability = 0.426[/tex]
Solving (b): More girls
From the table, the number of families with more girl is: 382 + 192
i.e.
Number of Girls : -----> 2 ------->3
Number of Families: --> 382 ---> 192
So, we have:
[tex]More\ Girls = 382 + 192[/tex]
[tex]More\ Girls = 574[/tex]
The probability is then calculated as:
[tex]Probability = \frac{More\ Girls}{Total}[/tex]
[tex]Probability = \frac{574}{1000}[/tex]
[tex]Probability = 0.574[/tex]
In an ordinary annuity, payments or
receipts occur at
a.Beginning of each period
b.End of each period
c.Mid of each period
d. Quarterly basis
Answers
In a candy mix there are 4 green bars for every 3 red bars. How many red bars are there if there are 200 green bars? A. 150 red bar's B. 199 red bars c.201 red bars d. 267 red bars
Answers
Step-by-step explanation:
4 green bars to 3 red bars
=> 200 green bars to 3 * (200/4) = 150 red bars.
There are 150 red bars. (A)
Answer:
Step-by-step explanation:
A - 150 is the a answer
4 green bars for every 3 red bars, take 3 red bars as one bucket so total we have 200/4 buckets which is 50
now 1 bucket has 3 green bars so total we have 3* 50 buckets which is 150
What is (f+g) (x)???
Answers
Answer:
A.
Step-by-step explanation:
To get to the answer, add both f(x) and g(x) together. This would be (2x^2 +3x -4) + (-4x^2 + 5x - 8). Remember that adding a negative number is the same as subtracting the positive of that number, for example, 3 + (-4) is the same as 3 - 4.
can you please show the work on both of them?
Answers
Question 9)
From the line graph, taking two points
(-5, 4) (-6, 7)Finding the slope between (-5, 4) and (-6, 7)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:4\right),\:\left(x_2,\:y_2\right)=\left(-6,\:7\right)[/tex]
[tex]m=\frac{7-4}{-6-\left(-5\right)}[/tex]
[tex]m=-3[/tex]
We know that the slope-intercept of the line equation is
y = mx+b
where m is the slope and b is the y-intercept
substituting (-5, 4) and m = -3 in the slope-intercept of the line
y = mx+b
4 = -3(-5)+b
4 = 15+b
b = 4-15
b = -11
substituting b = -10 and m = -3 in the slope-intercept of the line
y = mx+b
y = -3x+(-11)
y = -3x - 11
Thus, equation is slope-intercept form will be:
y = -3x - 11
Hence, option B is true.
Question 10)
From the line graph, taking two points
(4, 7) (-8, 1)Finding the slope between (4, 7) and (-8, 1)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(4,\:7\right),\:\left(x_2,\:y_2\right)=\left(-8,\:1\right)[/tex]
[tex]m=\frac{1-7}{-8-4}[/tex]
[tex]m=\frac{1}{2}[/tex]
We know that the slope-intercept of the line equation is
y = mx+b
where m is the slope and b is the y-intercept
substituting (4, 7) and m = 1/2 in the slope-intercept of the line
y = mx+b
7 = 1/2(4)+b
7 = 2+b
b = 5
substituting b = 5 and m = 1/2 in the slope-intercept of the line
y = mx+b
y = 1/2x + 5
Thus, the equation is slope-intercept form will be:
y = 1/2x + 5
Hence, option C is true.
[tex] {x}^{3} - 4x + \sqrt{{x}^{3} - 4x + 9 } = 3[/tex]
Help me please
Answers
For this question, you need to isolate all terms under the square root, so you need to move x^3 and -4x to the right. Then you would square both sides, and combine like terms.
A plane travels north for 2.5 h at a velocity of 100 km/h. Another plane travels east for 4 hours at a velocity of 62.5 km/h. Which plane traveled the longer distance? Show all calculations
Answers
Answer:
The two planes have traveled the same distance.
Step-by-step explanation:
Given that:
Velocity of first plane traveling north = 100 km/h
Time taken by the plane = 2.5 hours
Velocity of second plane traveling north = 62.5 km/h
Time taken by the plane = 4 hours
To find:
Which plane traveled longer distance?
Solution:
First of all, let us have a look at the formula for finding the distance using velocity and time.
Formula is:
[tex]Distance = Velocity \times Time[/tex]
Distance traveled by first plane:
[tex]Distance_1 = 100\times 2.5\\\Rightarrow Distance_1 = 250 \ km[/tex]
Distance traveled by second plane:
[tex]Distance_2 = 62.5\times 4\\\Rightarrow Distance_2 = 250 \ km[/tex]
Here, we can clearly see that:
[tex]Distance _1 = Distance _2[/tex]
Therefore, the two planes have traveled the same distance.
B Print
Find the slope of the line.
12
11
10
9
4
2
ol
5
9 10
The slope is
Answers
Giving brainliest help I need it, ignore answers I put unless their right
Answers
Answer:
For the middle one 20 /9 or 2 and 2/9
Step-by-step explanation:
20 /9 or 2 and 2/9
Do you need help with the rest or no?
In the equation 5x-2=-x-20, What is the value of x?
a. 2
b. -1
c. -3
d. -2
Answers
Answer:
C choice.
Step-by-step explanation:
[tex]5x - 2 = - x - 20 \\ [/tex]
First, we move the same terms to the same side.
[tex]5x + x = - 20 + 2 \\ 6x = - 18[/tex]
Then we move 6 to divide - 18.
[tex]x = \frac{ - 18}{6} \\ x = - 3[/tex]
The figure shows triangle ABC inscribed in circle D.
If the measure of angle CBD = 44°, find the measure of angle BAC, in degrees. Explain each
step you take to solve using proper math vocabulary.
Unit 4a Question
B
Answers
Answer: 46
Step-by-step explanation:
Just got it on a test so I wanted to help you guys out. Thank you guys in the comment section of the other answer. That one is wrong.
Find the equation of the line that is parallel to the given line and passes through the given points Y=0.1 X -2;(-4,8)
The equation is y=
Please help it’s very urgent
Answers
Answer:
y=0.1x + 8.4
I hope it will be useful.
plz give answer and explanation
i will give 24 points
Answers
Answer:
please refer to the above attachment.
Step-by-step explanation:
a. 3800 + 2.5%3800 = 3895
3895 - 3800 = 95 is the interest
b. there are 12 months in a year so...
95 x 12 = 1140 is the total interest
Please help :((( will mark brainliest !
Answers
Answer: i think its c
hope its right
:)
3.3 repeating as a fraction
Answers
Answer:
The correct answer is 33/100.
Step-by-step explanation:
To transform a decimal into a fraction, follow the steps below:
Step 1: Change the Fraction into a Decimal:
3.30 = 33/100
Step 2: Find the GCF of both numbers:
The GCF (Greatest Common Factor) of 33 and 10 is 1.
Step 3: Divide both numbers by the GCF:
3.30 =
33/1 ÷ 100/1 =
33/100
Therefore, the correct answer is 33/100.
Hope this helps! :D
3.3 repeating in fraction form will be 33/100.
The correct answer is 33/100.
Given, 3.3 in repeating form.
To transform a decimal into a fraction, follow the steps below:
Change the Fraction into a Decimal:
3.30 = 33/100
Find the GCF of both numbers:
The GCF (Greatest Common Factor) of 33 and 10 is 1.
Divide both numbers by the GCF:
3.30 = 33/1 ÷ 100/1
= 33/100
Therefore, the correct answer is 33/100.
Know more about fraction,
https://brainly.com/question/8482939
#SPJ6
Red snapper cost $4.15 per pound find the cost of 3.5 pound round to the nearest cent
Answers
Answer:
$14.53 for 3.5 pounds of red snapper
Step-by-step explanation:
Answer:
14.52?
Step-by-step explanation:
i multiplied 4.15 by 3.5
Please HELP ASSSP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
There are 96 more freshmen than juniors. the answer is D: 96
Step-by-step explanation:
28% and 22%
28 - 22 = 6
6% of 1,600 = 96
6% = 0.06
0.06 x 1,600 = 96
There are 96 more freshmen than juniors.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
please help! (One question)
Answers
Answer:
An equilateral triangle is never similar to a scalene triangle, because you can never map one onto the other using only dilations and using rigid transformations
Step-by-step explanation:
What value of x is in the solution set of 8x - 6 > 12 + 2x?
O-1
O0
O3
O5
Answers
The answer of X will be equal (3)
MATH PLS HELPPP BRANLIETS 5 POINTS!!!!!!!!!!
Answers
Answer:
A?
Step-by-step explanation:
I think it is A but I'm not 100% sure
Answer:
The total cost of riding in the taxi
Step-by-step explanation:
What is 3 2/5 / 6 plz help!!!
Answers
Answer:
The answer is 0.56 the 6 is repeating
Step-by-step explanation:
Answer:
0.56666666666
The diffrence between 9 and half of a number is 16 what is the number?
Answers
Answer:
is this how the question is really wrote out. it doesn't look like english
Step-by-step explanation:
half of 9 is 4.5
Half of 50 is 25, and the difference between 25 and 9 is 16. I hope this helps! :)
please help will mark brainliest
Answers
Answer:
y = 5.5
Step-by-step explanation:
y = 22 * 0.5^2
=> 22* 0.25
=> 5.5
Hope this helps! :3
plz mark as brainliest!
Express the ratio 12:3:9 in its simplest form
Answers
Answer:
4:1:3
Step-by-step explanation:
its all in the picture v
Answers
F(x) = -2x^2 +32
F(3) =-2(3)^2 +32
F(3)=-2(9)+32
F(3) =-18+32
F(3) = 14
X=14
Answer:
lynns is correct
Step-by-step explanation:
hduydgdgdududuegegdhdudggrhr
Please help me choose the right equation!!! I’m a taking a test and really want to pass!!!
Answers
Answer:
Step-by-step explanation:
The conservation club has 32 members. There are 18 girls in the club. What is the ratio of girls to boys in simplest form?
79
916
97
716
Answers
Answer:
9:7
Step-by-step explanation:
number of boys is 32 - 18 = 14
ratio will be 18:14
then 9:7
Answer: 9:7 hope this help i did the quiz so i know answer
Step-by-step explanation:
2 integers with a sum of 0 and product of -16
Answers
Answer:
-4 and + 4
Step-by-step explanation:
Two integers with a sum of 0 and product of - 16
Let the two digits = a and b
a + b = 0
a * b = - 16
If a = 4 and b = - 4 ;
CHECK:
4 + (-4) = 4 - 4 = 0
4 * (-4) = - 16
HENCE, the two integers are 4 and - 4 or - 4 and 4