Rachel and Frank spends $10.5 and $5.25 respectively.
It is given to us that
f is the amount of money that Frank spent and
r is the amount of money that Rachel spent.
Frank and Rachel together spent a total of $15.75.
Rachel spends twice as compare to Frank
The equation that represents this situation:
1. f + r = $15.75
2. r = 2f
Substituting r = 2f in equation 1.
f + r = 15.75
f + 2f = 15.75
3f = 15.75
f = 5.25
Substituting f = 5.25 in equation 2.
r = 2f
r = 2(5.25)
r = 10.5
Thus, Rachel spends $10.5 and Frank spends $5.25.
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The graph below shows a line segment PQ:
Graph of line segment PQ with endpoints at negative 2 comma 1 and 4 comma 4
What is the slope of the line segment PQ?
−2
−1 over 2
1 over 2
2
which relation is a function?
morris rarely arrives home before 4:00 p.m. it is now 3:20 p.m. estimate the probability that morris will arrive home in the next 30 minutes
2. PB and J Array Ken has made a selection of square jam sandwiches for party, which he arranges in a single layer on the table in perfect rectangle. Sarah has brought along the same number of square peanut butter sandwiches, which she puts out, also as a single layer, to form a border vA (one sandwich wide) around Ken's Given that all of the sandwiches are the same size and they are all used, how many sandwiches could each person possibly have made?
Let's assume Ken arranged his sandwiches in a rectangular shape with length 'L' and width 'W'. Now Sarah arranged her sandwiches to form a border around Ken's rectangle. The solution diagram is attached below.
Ken needs as much sandwiches as area of rectangle i.e. number of Ken's sandwiches would be = LW.
It is clear that Sarah needs as much sandwiches as perimeter of rectangle and extra four sandwiches to put on corners. It means number of Sarah's sandwiches would be = 2·(L+W) + 4.
Given that all of the sandwiches are the same size and they are all used.
Ken and Sarah bought same number of sandwiches. So we need to solve the following equation :-
Number of Ken's sandwiches = Number of Sarah's sandwiches
LW = 2·(L+W) + 4
Using trial and error approach, we get 6 x 4 = 2 x (6 + 4) + 4.
So number of Ken's sandwiches would be LW = 6 x 4 = 24 sandwiches.
Hence, final answer is "Each person could have 24 sandwiches".
Which expressions are polynomials? Select each correct answer.
20x2y
20x²
20x² + y
20x2+y12
These expressions satisfy the criteria for being polynomials based on their structure and components.
[tex]\( 20x^2y \)[/tex]
[tex]\( 20x^2 \)[/tex]
[tex]\( 20x^2 + y \)[/tex]
Let's analyze each expression:
1. [tex]20x^2y[/tex]
This expression can be rewritten as [tex]\( 20x^2y \).[/tex]
It consists of variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], coefficients ([tex]20[/tex]), and exponents ([tex]2[/tex] on [tex]\( x \))[/tex]
It involves multiplication and addition (implied by the terms).
Conclusion: This expression is a polynomial.
2. [tex]20x^2[/tex]
This expression can be rewritten as [tex]\( 20x^2 \)[/tex].
It consists of variable [tex]\( x \)[/tex], coefficient ([tex]20[/tex]), and exponent ([tex]2[/tex]).
It involves multiplication and addition (implied by the term).
Conclusion: This expression is a polynomial.
3. [tex]20x^2+ y[/tex]
This expression consists of two terms: [tex]\( 20x^2 \)[/tex] and [tex]\( y \)[/tex]
[tex]\( 20x^2 \)[/tex] is a polynomial (as identified above).
[tex]\( y \)[/tex] is also a polynomial (since it can be seen as [tex]\( 1y^1 \)[/tex], where the coefficient is [tex]1[/tex] and the exponent is [tex]1[/tex]).
The expression involves addition and multiplication.
Conclusion: This expression is a polynomial.
4. [tex]20x^2+y^{12[/tex]
This expression is not standard notation and appears to be incorrectly formatted:
It lacks clear separation between terms.
It combines numeric digits directly without appropriate variables and exponents.
Conclusion: This expression is not a polynomial.
graph the line whose x-intercept is -8 and whose y-intercept is 9
The graph of the line whose y intercept is 8 and whose x intercept is 9 is given below.
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Given:
An intercept form of the standard line is,
x/a + y/b = 1, where a and b are x-intercept and y-intercept form of the line.
So, the equation is,
x/-8 + y/9 = 1
And the graph is given in the attached image.
Therefore, the graph is given.
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Need help with 3 and 4.
Please help me I don't know this
Two angles are complementary. If one angle measures 32 degrees, what is the measure of the second angle?
Select one:
A. 48 degrees
B. 148 degrees
C. 58 degrees
D. 68 degrees
Two angles are complementary if they add up to 90 degrees. If one angle measures 32 degrees, the other angle measures 58 degrees, which is found by subtracting 32 from 90.
Explanation:The question is asking about complementary angles, which are two angles that add up to 90 degrees. If one angle measures 32 degrees, we can find the measure of the second angle by subtracting 32 degrees from 90 degrees since the two angles must sum to 90 degrees.
The calculation would be: 90 degrees - 32 degrees = 58 degrees.
Therefore, the measure of the second angle is 58 degrees, making the correct answer:
C. 58 degrees
George has to pay $30 in taxes for every $100 that he earns .Last summer he earned $3,680. How much did he pay in taxes
Can you tell me how to do this?
Dave walked a distance of 40 meters to the north. It took him 50 seconds. What was his velocity?
A. 1.25 m/s north
B. 5 m/s north
C. 4 m/s north
D. 0.8 m/s north
The perimeter of a rectangle is 80x. The base is two times the height. In terms of x, what are the dimensions of the rectangle?
a.
h = 10x; b = 10x
c.
h = 10.3x, b = 20.6x
b.
h = 13.3x; b = 26.6x
d.
h = 5x; b = 25x
y-2y8y-6 is equivalent to:
How do I graph this ?
if you pay $8.50 per square yard of carpeting,what is your total cost for 27.5 square yards?
What must be done before adding or subtracting fractions
The absolute ______ of 2 is 2.
1.) absolute value
2.)sign
3.)opposite
Pepper’s dog pen measures 4 meters wide and has an area of 20 square meters. What is the perimeter of the pen in meters?
Sally surveyed 20 of her friends to determine their favorite color. Her data shows that 25% said blue, 15% said green, 10% said yellow, and the rest said red.
Which circle graph best represents Sally's data?
Answer:
The circle graph that represents Sally's data in the attahed figure
Step-by-step explanation:
we know that
The color blue represent [tex]25\%[/tex]------> Is a quarter of circle
The color yellow plus the color green represent [tex]10\%+15\%=25\%[/tex] -----> Is a quarter of circle
The color red represent [tex]100\%-50\%=50\%[/tex]------> Is a half circle
therefore
The answer in the attached figure
The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh a total of 249 ounces. Which value could replace x in the table?
Solving the system of linear equations, we found that there are 12 hardcover books and 33 paperback books, making the value that could replace 'x' is 12.
The question involves solving a system of linear equations to find the number of hardcover and paperback versions of a book that together weigh 249 ounces. Since the hardcover version weighs 7 ounces and the paperback weighs 5 ounces, we can create two equations based on the given information. If we let x represent the number of hardcover books and y represent the number of paperback books, the equations would be:
x + y = 45 (since there are 45 copies in total)
7x + 5y = 249 (since the total weight is 249 ounces)
Solving this system, we can multiply the first equation by 5, which gives us 5x + 5y = 225, and subtract this from the second equation to find the value of x. This yields 2x = 24, so x = 12. Therefore, there are 12 hardcover books and the rest are paperbacks. To find the number of paperbacks, we substitute x back into the first equation and get 12 + y = 45, which means y = 33. Hence, the number that could replace x in the table is 12.
If you can buy one can of pineapple chunks for $2 then how many can you buy with $10
Michael’s grandmother made two pies for Thanksgiving, a sweet potato pie and a chocolate pie. Each pie had 8 slices. All of the sweet potato pie and 2 slices of the chocolate pie were eaten. How much pie did Michael’s family eat on Thanksgiving? A) 5 8 pie B) 10 16 pie C) 1 1 4 pies Eliminate D) 1 3 8 pies
two attendants earn $6240 and $6220 per annum, respectively, exclusive of a bonus of $2640 per annum.
if both have a pension deduction of 20%,the difference in the pension deduction of the two attendants on a semimonthly basis is..........?
If a + 4b = 33 and 6a + 3b = 51, what is the value of a + b?
(I got 5 but it was wrong)
Answer:
12
Step-by-step explanation:
Since the problem asks for $a+b$, we look for a way to isolate $a+b$ from the given equations.
Notice that $a + 6a = 7a$ and $4b + 3b = 7b$. This gives us the key to isolating $a + b$. We simply add the two equations together:\begin{align*}
7a + 7b &= 84 \\
7(a + b) &= 84 \\
a + b &= \frac{84}{7} \\
a + b &= \boxed{12}
\end{align*}
Bill pays $49 for an item after it has been discounted 30%. What was the original price of the item?
Which line is the best model for the data in the scatter plot?
i.e. the points are closely related to the line.
Also, the other properties of a trend line are--The magnitude of the negative and positive residual values must be same.
( i.e. Not all point could lie above the line and not all points could lie below the line )
( In graph A most of the points lie below the line.
Hence, Graph A is not the correct answer.
In graph most of the points lie above the line.
Hence, Graph C could not be the best model.
In graph D most of the points lie above the line and hence it could not be the best model)
whereas in Graph B there are equal number of points above and below the line.
Rick shared his bag of grapes with his friends. He gave 2/10 of the bag to Melissa and 4/10 of the bag to Ryan. What fraction of the bag of grapes does Rick have left?
After giving away 2/10 of his grapes to Melissa and 4/10 to Ryan, Rick has 4/10 of his bag of grapes left.
Explanation:Rick gave away part of his bag of grapes to his friends: 2/10 to Melissa and 4/10 to Ryan. To find out what fraction of the bag he has left, we need to add together the fractions that he gave away and then subtract this from the whole bag, which is represented by the fraction 1 (or 10/10).
Rick gave away:
Melissa: 2/10
Ryan: 4/10
Total given away: 2/10 + 4/10 = 6/10
Fraction of the bag Rick has left:
1 (or 10/10) - 6/10 = 4/10
Therefore, Rick has 4/10 of the bag of grapes left after sharing with his friends.
To find out how much of the bag of grapes Rick has left, we need to subtract the fractions that he gave to Melissa and Ryan from 1. Rick has 2/5 of the bag of grapes left.
Explanation:To find out how much of the bag of grapes Rick has left, we need to subtract the fractions that he gave to Melissa and Ryan from 1.
Given that Rick gave 2/10 of the bag to Melissa and 4/10 of the bag to Ryan, we can calculate the fraction of the bag he has left by subtracting these two fractions from 1:
1 - 2/10 - 4/10 = 1 - 6/10 = 4/10 = 2/5
Therefore, Rick has 2/5 of the bag of grapes left.
Can someone help me!! I’m trying to find equivalent measures! 15!points if you can help!
What are three rational numbers between 0.2 and 0.3 (one must be a fraction)?