Man can buy 4 containers of yogurt and 3 boxes of crackers for $9.55. She can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. How much does one box of crackers cost?
Answer:
one box of crackers costs $0.70
Step-by-step explanation:
Let $x be the price of 1 container of yogurt and $y be the price of 1 box of crackers.
1. Man can buy 4 containers of yogurt and 3 boxes of crackers for $9.55. 4 containers of yogurt cost $4x and 3 boxes of crackers cost $3y. In total,
[tex]3x+4y=9.55.[/tex]
2. Man can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. 2 containers of yogurt cost $2x and 2 boxes of crackers cost $2y. In total,
[tex]2x+2y=5.90.[/tex]
3. Solve the system of two equations:
[tex]\left\{\begin{array}{l}3x+4y=9.55\\2x+2y=5.90\end{array}\right.[/tex]
Multiply the second equation by 2 and subtract it from the first equation:
[tex]3x+4y-2(2x+2y)=9.55-5.90\cdot 2,\\ \\3x+4y-4x-4y=9.55-11.80,\\ \\-x=-2.25,\\ \\x=\$2.25.[/tex]
Then
[tex]2\cdot 2.25+2y=5.90,\\ \\2y=5.90-4.50,\\ \\2y=1.40,\\ \\y=\$0.70[/tex]
By setting up a system of equations and using elimination, we find that one box of crackers costs $2.25.
To solve the cost of one box of crackers, we need to set up two equations based on the information given:
4y + 3c = $9.552y + 2c = $5.90We use 'y' to represent the cost of one container of yogurt and 'c' for the cost of one box of crackers. To find the value of 'c', we can use substitution or elimination.
Let's eliminate 'y' by multiplying the second equation by 2, which gives us 4y + 4c = $11.80. Subtracting the first equation from this, we get:
c = $11.80 - $9.55
c = $2.25
So, one box of crackers costs $2.25.
What's the volume of a block of ice measuring 3 meters long, 1.5 meters wide and 2 meters high.
Answer: The volume of a block of ice is 9 meters
You have to LxWxH
so i comeplete a table right ,
number of cuts | number of ballots
1 | 3
2| 9
3| 27
4| 81
5| 243
perhaps I continue this process , how many ballots will I have after 10 cuts ?
how many will I have after n cuts ?
Answer: The number of ballots increases by 3: 3x3=9, 9x3=27, 27x3=81...
After 10 cuts, there will be 59,049 ballots.
I could really use some help with these 4 problems. Any help will be greatly appreciated!
(7) is the same problem with different numbers as (4) in another question you posted: https://brainly.com/question/11799042
(8) is not correct. [tex]\mathbf u\cdot\mathbf v=(12)(-15)+(4)(-5)=-200[/tex]
(9) is not correct. The direction of the vector [tex]\langle3,4\rangle[/tex] is [tex]\theta[/tex] where
[tex]\tan\theta=\dfrac34\implies\theta=\tan^{-1}\dfrac34[/tex]
so the applied force is the vector
[tex]\mathbf F=\langle14\cos\theta,14\sin\theta\rangle=\langle11.2,8.4\rangle[/tex]
(if you're not sure how to compute the (co)sine of the inverse-tangent expression, note that a tangent of 3/4 corresponds to a right triangle with hypotenuse 5)
The object is moved 7 ft in the same direction as [tex]\mathbf F[/tex], so that its displacement is given by the vector
[tex]\mathbf d=\langle7\cos\theta,7\sin\theta\rangle=\langle5.6,4.2\rangle[/tex]
Then the work done on the object is the dot product of these two vectors,
[tex]W=\mathbf F\cdot\mathbf d=(11.2)(5.6)+(8.4)(4.2)=98\approx97[/tex]
(the discrepancy here might be coming from finding a numerical value for [tex]\theta[/tex])
(10) is correct. We can find a unit vector pointing in the direction of any vector [tex]\mathbf v[/tex] by dividing [tex]\mathbf v[/tex] by its magnitude:
[tex]\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\frac23\,\mathbf i-\frac12\,\mathbf j}{\sqrt{\left(\frac23\right)^2+\left(-\frac12\right)^2}}=\dfrac45\,\mathbf i-\dfrac35\,\mathbf j[/tex]
Find the missing number of each unit rate
Answer:
3 and 4
Step-by-step explanation:
21/7 = x/1
x = 21/7*1 = 3
16/4 = y/1
y = 16/4*1 = 4
Given y varies directly as x, use the given x-value and y-value to find an equation that relates x and y. x = 24 and y = 360 A) y = 15x B) x = 15xy C) y = .15x D) y = 15 x
Answer:
A
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the given condition x = 24 and y = 360
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{360}{24}[/tex] = 15
Hence y = 15x is the equation → A
Answer: A
Step-by-step explanation:
Help with question 14!!
Answer: a=2 b=5 c=-7
parabola equation is y = 2x^2+5x-7 = 0
Step-by-step explanation:
Substitute (x,y) into y = a x^2 + b x + c
(2,11) 11 = 4a + 2b + c
(-1,-10) -10 = a - b + c
(-4,5) 5 = 16a -4b + c
Solve the linear system in a, b, c
Det[{{4,2,1},{1,-1,1},{16,-4,1}}] = 54
Det[{{11,2,1},{-10,-1,1},{5,-4,1}}] = 108
Det[{{4,11,1},{1,-10,1},{16,5,1}}] = 270
Det[{{4,2,11},{1,-1,-10},{16,-4,5}}] = -378
a = 108/54 = 2
b = 270/54 = 5
c = -378/54 = -7
parabola equation is y = f(x) = 2x^2+5x-7
f(2) = 8+10-7 = 11 ✔
f(-1) = 2-5-7 = -10 ✔
f(-4) = 32-20-7 = 5 ✔
Show all work 3(x-2)=3x-2
Determine whether the equation has one solution, no solution, or an infinite number of solutions Use words,numbers,and/or symbols to justify your answer
which equation can be used to find the measure of angle LKJ?
Answer:
D
Step-by-step explanation:
use the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8.9}{10.9}[/tex], hence
x = [tex]sin^{-1}[/tex]( [tex]\frac{8.9}{10.9}[/tex] ) → D
Answer:
D
Step-by-step explanation:
After changing its format, a radio station lost 34% of its listeners. If there were an estimated 83,000 listeners orginally, how many listeners does the radio station have now?
Final answer:
The radio station has 54,780 listeners now.
Explanation:
To find the number of listeners the radio station has now, we need to calculate the number of listeners it lost after changing its format. If the station lost 34% of its listeners, we can calculate the number of lost listeners by multiplying the original number of listeners by 0.34 (34%).
Lost Listeners = 83,000 * 0.34 = 28,220 listeners
To find the number of listeners the radio station has now, we subtract the lost listeners from the original number of listeners.
Number of Listeners Now = 83,000 - 28,220 = 54,780 listeners
What Is 7 Rounded To The Nearest Tenth?
Answer:
7.0
Step-by-step explanation:
If we had the number 7.1 the 1 is the tenth digit. .
So 7 to the nearest tenth is written 7.0.
Answer:
7.5 is exactly halfway between 7 and 8. Therefore, 7.5 rounds to 8.
Step-by-step explanation:
To round to the nearest tenth using a number line, look at the tenth place value closest to the number you are rounding.
What is the answer ?
Answer:
2y
Step-by-step explanation:
Simplifying
21x + -42y = 0
Solving
21x + -42y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '42y' to each side of the equation.
21x + -42y + 42y = 0 + 42y
Combine like terms: -42y + 42y = 0
21x + 0 = 0 + 42y
21x = 0 + 42y
Remove the zero:
21x = 42y
Divide each side by '21'.
x = 2y
Simplifying
x = 2y
In the triangle below which of the following is equivalent to the tangent of 52 degrees?
Answer:
Option D. [tex]\frac{24}{7}[/tex].
Step-by-step explanation:
In any right angle triangle tangent of an angle is the ratio of opposite side and adjacent side.
tan x =[tex]\frac{\text{Opposite side (24)}}{\text{Adjacent side (7)}}[/tex]
= [tex]\frac{24}{7}[/tex]
therefore, Option D. [tex]\frac{24}{7}[/tex] is the answer.
The box plot shows the data distributions for the number of laps two students run around a track each day
Answer:
C. The range of Liam's data set is 16
Step-by-step explanation:
Hello, my dear friend, I am sure the question you are intending should be corrected (See below question), as well as the box plot should be uploaded (See attached the image of the box plot I uploaded for you).
Q. The box plots show the data distributions for the number of laps two students run around a track each day. Which statement is true about the data?
Options:
A. The median of both data sets is 10.
B. The median of both data sets is 14.
C. The range of Liam’s data set is 16.
D. The range of Sumat’s data set is 17.
If this is the case, then the box plot shows the following data.
The median of Liam's data is 10, the range is (20-4) =16
The median of Sumat's data is 14, the range is (22-3) =19
The correct answer will therefore be:
C. The range of Liam's data set is 16
Can you answer this:
The box plots show the data distributions for the number of laps two students run around a track each day.
Which statement is true about the data?
The difference between the medians of both data sets is 2.
The difference between the medians of both data sets is 4.
The difference between the ranges of both data sets is 2.
The difference between the ranges of both data sets is 4
Juan has put together 325 pieces of a puzzle that has 500 pieces. He can put together 25 pieces every hour. How long will it take him to finish the puzzle?
Answer:The answer is 7 hours here is how I solved it. If it's out of 500 pieces and you've already done 325 then lets minus that so we only have to deal with the left over pieces. So 500- 325 which will give you 175 from there let's divide it by 25 to see how many hours it will take. Once you divide you will get 7 you can double check by doing 7 times 25 then add that to 325 to get 500 pieces.
Step-by-step explanation:
which is the solution for the equation y=5x+3
Which expression is equivalent to x+x+x+x+2
Answer:
4x+2
Step-by-step explanation:
Answer:
4x + 2
Step-by-step explanation:
The given expression is x + x + x + x + 2
We can add the like terms.
The like terms are the terms having the same variable and the same exponents. The coefficients may vary.
For examples, 3x and -2x
2xy and 3xy
In the given expressions x, x, x, x are the like terms.
So, x + x + x+ x + 2
4x + 2
Therefore, the answer is 4x + 2
I’m doing the Pythagorean Theron in math class an I’m stuck on this question - the base path of a base ball diamond form a square.if it is 90 feet from home to first how far does the catcher have to through to catch someone stealing second base
check the picture below.
How many solutions does this system have?
x + 4y = 6
y = 2x - 3
a. one
b. two
c. an infinite number
d. no solution
There is only one solution to this system of equations. The solution is where the two equations meet, which in this system is (2, 1).
Answer:
One Solution
Step-by-step explanation:
GOT IT RIGHT ON EDGE 2020
PLS ANSWER WILL GIVE BRAINLIEST 2 QUESTIONS
Daniel worked for 213 hours and earned $18.20.
How much would he make if he worked for 514 hours?
The total amount, a, in dollars, that Mitra earns is a = 14.6h, where h is the number of hours that she works.
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answer:
He would make $4391.92
The constant of proportionality is 14.6
Step-by-step explanation:
If Daniel works 213 hours and makes $1820.00
(I assume that is a typo and he made 1820. not 18.20)
How much does he make per hour
$1820/213 = $8.54 per hour
Now if he works 514 hours
514 * 8.54/hour = $4391.92
y = kx, where k is the constant of proportionality
a = 14.6h,
The constant of proportionality is 14.6
zola has 575 beads.She needs 32 beads to make a necklace.How many necklaces
Answer:
17
Step-by-step explanation:
575/32=17.96875 or 17
Answer:
17 necklaces
Step-by-step explanation:
32n=575
n=575/32
n=17.96
Round down to 17, can't make .96 of a necklace.
Solve. 2/3x = -20. A) -60 B) -30 C) -10 D) 10
Simplify 2/3x to 2x/3
2x/3 = -20
Multiply both sides by 3
2x = -20 × 3
Simplify 20 × 3 to 60
2x = -60
Divide both sides by 2
x = -60/2
Simplify 60/2 to 30
x = -30
Answer: B) -30
Answer:
the answer to you question is -30
Step-by-step explanation:
what you have to do is take the fraction and multiply it by its reciprocal to get it away from the x and if you multiply on one side then you have to multiply on the other side also so you would multiply -20 by 3/2 the you would get the answer of -30
Hope this helps!!!:) can I get the Brainliest?
Alonzo describes a histogram as having a cluster from 20–50, a frequency of 0 from 10–20, and a peak at 40–50. Which histogram is he describing?
Answer:
Skewed Left
Step-by-step explanation:
First we will try to draw the histogram in order to interpret its type.
Its given that from 10-20 the frequency is 0
and 20-50 there are clusters in the histogram but the peak is there at 40-50
So by visualizing the histogram which is hereby attached depicts that the histogram is skewed left as skewed histogram is one in which the frequency starts from 0 and the highest frequency occurs at the end so as is in the given problem.
Answer:
The first one.
Step-by-step explanation:
ms. James has a 6 square foot bulletin board and a 12 square food bulletin board. She wants to cover both boards with index cards without gaps or overlaps. Each index card has an area of 1/4 square foot. How many index cards does she need?
Answer:
She need 72 index cards.
Step-by-step explanation:
Ms. James has a 6 square foot bulletin board and a 12 square food bulletin board and she wants to cover both boards with index cards without gaps or overlaps.
Each index card has an area of [tex]\dfrac{1}{4}[/tex] square foot.
Dividing the area of each board with the area of the index card will yield the the number of cards she needs to cover up completely.
Let us assume T₁ and T₂ are the number of cards she needs to cover 6 square feet food bulletin board and 12 square feet food bulletin board respectively. So
[tex]T_1=\dfrac{6}{\frac{1}{4}}=24,\\\\T_2=\dfrac{12}{\frac{1}{4}}=48[/tex]
Therefore, in total she need 24+48=72 index cards.
From 6x2−7xy+8y2 subtract the sum of x2−3xy−y2 and 2x2+5xy−4y2
Every 2 is meant to be the power of 2
Answer:
13 y^2 - 9 x y + 3 x^2
Step-by-step explanation:
Simplify the following:
6 x^2 - 7 x y + 8 y^2 - (x^2 - 3 x y - y^2) - (2 x^2 + 5 x y - 4 y^2)
-(x^2 - 3 x y - y^2) = -x^2 + 3 x y + y^2:
6 x^2 - 7 x y + 8 y^2 + -x^2 + 3 x y + y^2 - (2 x^2 + 5 x y - 4 y^2)
-(2 x^2 + 5 x y - 4 y^2) = -2 x^2 - 5 x y + 4 y^2:
6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 + -2 x^2 - 5 x y + 4 y^2
Grouping like terms, 6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 - 2 x^2 - 5 x y + 4 y^2 = (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2):
(8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)
8 y^2 + y^2 + 4 y^2 = 13 y^2:
13 y^2 + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)
x y (-7) + x y 3 + x y (-5) = -9 x y:
13 y^2 + -9 x y + (6 x^2 - x^2 - 2 x^2)
6 x^2 - x^2 - 2 x^2 = 3 x^2:
Answer: 13 y^2 - 9 x y + 3 x^2
find the values for A and B that would make the equality true
-5(3x^2+5x+b)=ax^2-25x+45
Answer:
a = - 15 and b = - 9
Step-by-step explanation:
distribute the left side
- 15x² - 25x - 5b
For - 15x² - 25x - 5b = ax² - 25x + 45
Then the coefficients of like terms must be equal, hence
comparing coefficients of x² term ⇒ a = - 15
comparing constant term ⇒ - 5b = 45 ⇒ b = - 9
Answer: a = -15, b = -9
Step-by-step explanation:
-5(3x² + 5x + b) = ax² - 25x + 45
-15x² - 25x - 5b = ax² - 25x + 45 distributed -5 on left side
Notice that the middle terms (-25x) are equal, so the the remaining terms will also be equal.
-15x² = ax² ⇒ -15 = a
-5b = 45 ⇒ b = -9
Please help me. I am having trouble. This is for solving x is algebraic expressions.
Answer: a - add 3 to both sides
Step-by-step explanation: you want to have the variable with the number all to itself to solve for x, so you have to add 3 to both sides to get 3/4x=-15. then divide by 3/4 to both sides and you will get a final answer.
Solve for X in the equation below. Show your work.
HI! I REALLY NEEED HELP WITH THIS QUESTION PLEASE SHOW YOUR WORK IF YOU ARE WILLING TO HELP MEH! PLEASE HELP ME!
(x-2)= -1/4(x-8)
Answer:
x = 16/5
Step-by-step explanation:
(x-2)= -1/4(x-8)
Multiply each side by -4 to clear the fraction
-4 (x-2) = -4*-1/4 (x-8)
Distribute
-4x+8 = x-8
Add 4x to each side
-4x+4x+8 = x+4x-8
8 = 5x-8
Add 8 to each side
8+8 = 5x-8+8
16 = 5x
Divide each side by 5
16/5 = 5x/5
16/5 =x
PLEASE HELP ILL GIVE 49 POINTS! THANKS!
Show work
Answer:
y = -2x+11
Step-by-step explanation:
If we have a slope and a line, we can use the slope intercept form of a line
y-y1 = m(x-x1)
where (x1,y1) is the point and m is the slope.
Substitute in what we know
y-5 = -2 (x-3)
We want it in slope intercept form which is y = mx+b
Distribute the -2
y-5 = -2x+6
Add 5 to each side
y-5+5 = -2x +11
ANSWER:
y = -2x + 8
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)Y1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineABOUT SLOPE INTERCEPT FORM:
y = mx + bm represents the slopeb represents the y - intercept AKA the starting pointy - Y1 = m (x - X1)
y - 5 = -2 (x - 3)
y - 5 = -2x + 3
+ 5 + 5
y = -2x + 8 --- IN SLOPE INTERCEPT FORM
Hope this helps you!!! :)
p = 5(2t -20) what is an equivalent form of this rule
Answer:
p = 10t - 100
Step-by-step explanation:
Perform the indicated multiplication: p = 10t - 100.
The equivalent form of the algebraic equation p = 5(2t - 20) is p = 10t - 100, which is a simplified linear representation of the original equation.
The student is looking for an equivalent form of the algebraic equation p = 5(2t - 20). By distributing the 5, we obtain p = 10t - 100. This is now a simplified linear equation representing the same rule as the original equation. It's also similar to manipulating a quadratic equation to find the value of t, as shown in the other examples provided. However, this linear equation doesn't require solving for t; rather, we're simply rewriting it in a more straightforward format.