Craig bought 8 folders and notebooks forschool. Folders cost $0.50 and notebooks cost$1.50. Craig spent a total of $6. How manyfolders (f) and how many notebooks (n) did hebuy?f+ n = 80.5f + 1.5n = 6
Answers
We have a sysyem of equations that represent the information we have.
As we have 8 items between the notebooks and folders, we can write:
\(f+n=8\)being f: number of folders, and n: number of notebooks.
Then, as each folder costs $0.50 , the notebooks cost $1.50 each and the total cost was $6 we can write:
\(0.50f+1.50n=6\)We can solve it by substracting 2 times the second equation from the first. This will create a new linear combination of the two equations that will eliminate f and let us solve for n:
\(\begin{gathered} (f+n)-2(0.50f+1.50n)=8-2*6 \\ f+n-2*0.5f-2*1.50n=8-12 \\ f+n-f-3n=-4 \\ 0f-2n=-4 \\ n=\frac{-4}{-2} \\ n=2 \end{gathered}\)We can now use any of the two equations to solve for f. We will use the first one as it is simpler:
\(\begin{gathered} f+n=8 \\ f=8-n \\ f=8-2 \\ f=6 \end{gathered}\)We can check with the second equation to verify the solution:
\(\begin{gathered} 0.5f+1.5n=6 \\ 0.5*6+1.5*2=6 \\ 3+3=6 \\ 6=6\text{ -->Verified} \end{gathered}\)Answer: 6 folders and 2 notebooks.
Related Questions
Which shows 9.635 written in expanded form, using powers of ten
Answers
Step-by-step explanation:
The expanded form of 9.635 is given by :
\(9.635 =9+\dfrac{6}{10}+\dfrac{3}{100}+\dfrac{5}{1000}\)
or
\(9.635 =9+0.6+0.03+0.005\)
We can write it using the powers of ten.
\(9.635 =9.635 \times 10^0\)
10⁰ is equal to 1.
Hence, this is the required solution.
What is the quotient? 3/7 divided by 2/3
Answers
Answer:
3/7 divided by 2/3 is 9/14
Add 3+i and 2 - 3i geometrically in the complex plane.
Answers
The result of the addition of complex numbers 3+i and 2 - 3i will be 5-2i as the rule says "to add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts.".
What is complex number?Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i² = -1.
What is complex plane?The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.
Here,
To add the complex numbers,
To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts.
(3+i)+(2-3i)=5-2i
According to the rule, "to add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts," the sum of the complex numbers 3+i and 2 - 3i will be 5-2i.
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Question 1(Multiple Choice Worth 3 points)
(01.04 LC)
Evaluate the numerical expression
25
O-25
O
1
25
0_1
25
(5+) ².
Answers
The given expression (25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] is equivalent to 217.5.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is the expression as follows -
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]
The given expression is -
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]
Solving further, we get -
(25)2 x 100 ÷ 23 + [24 ÷ 8]
25(2) x 100 ÷ 23
25(2) x 4.35
50 x 4.35
217.5
Therefore, the given expression equivalent to 217.5.
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{
Complete question expression is -
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]
}
Number of Computers
72
60
48
36
24
12
V
1 2 3 4 5 6 7 8 9 10 11 12
Number of Days
The graph shows a proportional relationship between
the number of computers produced at a factory per day.
In three days, 36 computers are produced; 48
computers are produced in 4 days; and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the graph.
Unit rate:
computers per day
Answers
The unit rate of computers per day using the graph is that 12 computers are made per day.
What is a unit rate?The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.
How to find the unit rate of computers per dayTo obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
So, it is given by:
\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)
\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)
\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)
\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)
\(\bold{Slope = 12}\)
Unit rate = 12 computers per day.
The attachment of the graph is given below.
Therefore, the unit rate of computers per day is 12.
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15 points! Please help
Answers
Answer:
I'm pretty sure it's reflection
Step-by-step explanation:
The triangle to the right is basically a reflection of the first triangle
2/5 of the product of 5/6 and 42 equals
Answers
Answer:14
Step-by-step explanation:
Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
Answers
Explanation
The square root of a number is “what number times itself”
2 x 2 = 4
3 x 3 = 9
7 is between 4 and 9 so C is the correct answer
“Please help me I’ll mark u brainly please don’t do this for the points”
Answers
The measure of angle x in each of the triangles is:
1) 20°
2) - 49°
3) 8°
4) 33.33°
5) 10°
6) 3°
7) 1°
8) 2°
9) 6°
1) The measure of the inner angles in the triangle are 100°, 40°, and 2x°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
100° + 40° + 2x = 180°
140° + 2x = 180°
2x = 40°
x = 20°
2) The measure of the inner angles in the triangle are 99°, 37°, and (- x - 5)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
99° + 37° + ( - x - 5 )° = 180°
136° + (- x - 5)° = 180°
( - x - 5 )° = 44°
x = - 49°
3) The measure of the inner angles in the triangle are 60°, 60°, and ( - 12 + 9x)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
60° + 60° - 12 + 9x = 180°
120° - 12° + 9x = 180°
108° + 9x = 180°
9x = 72°
x = 8°
4) The measure of the inner angles in the triangle are 36°, 46°, and ( 2 - 3x)°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
36° + 46° - 2° + 3x° = 180°
82° - 2° + 3x° = 180°
80° + 3x° = 180°
3x = 100°
x = 33.33°
5) The measure of the inner angles in the triangle are 71°, 50°, and ( 6x - 1 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
71° + 50° - 1° + 6x° = 180°
121° - 1° + 6x° = 180°
120° + 6x° = 180°
6x = 60°
x = 10°
6) The measure of the inner angles in the triangle are 45°, 90°, and ( 8x + 21 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
45° + 90° + 21° + 8x° = 180°
156° + 8x° = 180°
8x = 24°
x = 3°
7) The measure of the inner angles in the triangle are 85°, 64°, and ( 4x + 27 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
85° + 64° + 27° + 4x° = 180°
176° + 4x° = 180°
4x = 4°
x = 1°
8) The measure of the inner angles in the triangle are 44°, 104°, and ( 7x + 18 )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
44° + 104° + 18° + 7x° = 180°
166° + 7x° = 180°
7x = 14°
x = 2°
9) The measure of the inner angles in the triangle are 125°, 25°, and ( - 5x )°.
The sum of all angles in the triangle is equal to 180°.
Therefore,
125° + 25° - 5x° = 180°
150° + 5x° = 180°
5x = 30°
x = 6°
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There are 49 non-fiction books on my shelf. The remaining 75% of
books are novels. How many books are on my shelf?
Answers
Step-by-step explanation:
the answer is in the above image
William receives a weekly allowance according to the following formula: For each day that he remembers to do his chores, he eams 51.50, and for each day that he doesn't remember to do his chores, he loses
50.25. What amount of allowance would William receive for a week in which he remembers to do his chores on five days and forgets to do them on two days?
Answers
50.25 * 5 = 251.25
50.25 * 2= 100.5
251.25-100.5= 150.75
What type of angles are ∠4 and∠6?
Question 2 options:
adjacent angles
alternate exterior angles
alternate interior angles
corresponding angles
none of these
Answers
Answer:
None of these
Step-by-step explanation:
For adjacent, they are not next to each other.
For alternate exterior, both are not exterior.
For alternate interior, both are not interior.
For corresponding, they are not along the same line.
That leaves us with the answer none of these.
Hope that helps!
Plz help I need help
Answers
I think it’s y=1.4x, but I don’t really know.
These signs give information about two different towns.
Study these signs carefully. Then, answer the questions and complete the statements
about them below.
Use the drop-down menus to complete each statement.
Answers
Answer:
In which town does the total number have meaning?
Answer: Town B
For Town A, it does not, cannot, does not.
For Town B, does, can, does.
Help I would appreciate it
Answers
Answer:
it is option C
hope it helps
97 And 83
What is the equation of the line that passes through
(-5, 0) and (4, 3)?
Answers
Answer:
\(y=\frac{1}{3}x+\frac{5}{3}\)
Step-by-step explanation:
The point-slope form of an equation for a line is y = mx + b (m is the slope; b is the y-intercept).
First, find the slope using the two given points.
\(m=\frac{y_2 - y_1}{x_2-x_1}=\frac{3-0}{4-(-5)}=\frac{3}{9}=\frac{1}{3}\)
At this stage, you know the slope and need to find the y-intercept. Plug in one of the points (either one) into the equation. Let's use (-5, 0).
\(y=\frac{1}{3}x+b\\0=\frac{1}{3}(-5)+b\\0=-\frac{5}{3}+b\\\frac{5}{3}=b\)
The equation for the line is \(y=\frac{1}{3}x+\frac{5}{3}\).
You can check for errors by putting in the point you didn't use...
Check to make sure the point (4, 3) satisfies the equation.
\(3=\frac{1}{3}(4)+\frac{5}{3}\\3=\frac{4}{3}+\frac{5}{3}\\3=\frac{9}{3}\) True!
log(2)-log(8) check all that apply
Answers
Explanation:
log(1/4)
= log(2^2)
= - 2log(2)
A rectangular room is 4 yards long and 5 yards wide . Lucas is covering the floor with tiles that are 1 square foot . How many tiles will he need ?
Answers
Answer:
I think like 21
Step-by-step explanation:
i think it correct but if it not it okay but alaest I try my best on it
Vladimir hit a home run at the ballpark. A computer tracked the ball's trajectory in feet and modeled its flight path as a
parabola with the equation, y = -0.003(x – 210)2 + 138. Use the equation to complete the statements describing the
path of the ball.
Answers
Answer:
The vertex of the parabola is
✔ (210, 138)
The highest the ball traveled was
✔ 138
feet.
Step-by-step explanation:
Edge 2022
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The highest the ball has travelled is 138 feet.
What is an equation of a parabola?A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower the parabola is, and the "-" or "+" that the parabola will open up or down.
A.) In the given quadratic equation, the vertex of the equation is y=-0.003(x-210)² + 138 is (210,138).
B.) Since the vertex is the highest point, therefore, The highest the ball has travelled is 138 feet.
The complete question is,
Vladimir hit a home run at the ballpark. A computer tracked the ball's trajectory in feet and modelled its flight path as a parabola with the equation, y = -0.003(x – 210)2 + 138. Use the equation to complete the statements describing the
path of the ball.
The vertex of the parabola is ?
The highest the ball travelled was? Feet
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uestion 1:
Damon wants to sell his motorcycle that he paid $4,000 for 3 years ago. The motorcycle depreciated (decreased in value) at a constant rate each month over a 3-year period. If x represents the monthly depreciation amount, write an expression that shows how much Damon can sell his motorcycle for today.
Answers
Answer:
4,000 -x3
Step-by-step explanation:
x times 3 is equal to the decrease so therefore you take the decrease away form 4/oo
Answer:
3y-x=4,000
Step-by-step explanation:
The area of the parallelogram
Answers
Answer:
28
Step-by-step explanation:
a = b * h
a = 4 * 7 = 28
A school keeps track of the percentage of scholars who pack lunch versus buy lunch. On Monday, 80% of scholars packed lunch. On Tuesday, 70% of the scholars who packed lunch do so again, and 50% of those who bought lunch on Monday pack lunch on Tuesday. Assume all scholars either pack lunch or buy lunch. Find the percent change in the number of scholars who bought lunch from Monday to Tuesday, and indicate whether this was an increase or decrease.
Answers
Answer:
Increase by 10% of students that bought lunch.
Step-by-step explanation:
I think the percent change was by 10%. Because 10% of those students who packed lunched on Monday did not pack lunch on Tuesday, and assuming that they either buy or pack it that means that 10% more students bought lunch.
Which of the following are exponential functions? Select all correct answers
Select all that apply:
Please explain how you solve this
f(x)=2(1/2)^x
g(x)=3(−7)^x
j(x)=14(3)^x
k(x)=13(−2)^x
h(x)=9(6.7)^x
Answers
The exponential functions are f(x)=2(1/2)∧x
How to determine an exponential function?We should note that an exponential function is the type of function that is used to find the growth in a function. A good example of an exponential function is the function f(x)=m×, where m>0 and m≠0 and x is a positive or negative integer.
The given parameters are
f(x)=2(1/2)^x
g(x)=3(−7)^x
j(x)=14(3)^x
k(x)=13(−2)^x
h(x)=9(6.7)^x
Among these parameters, the one that is a function is f(x)=2(1/2)∧x because it satisfies the condition of a function.
This function when simplified gives 1ˣ
Therefore f(x)=1ˣ
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Meg is building a rectangular prism with cubes. Which is the volume of Meg's
rectangular prism?
Answers
Answer:
48
Step-by-step explanation: 4x8=32 2x8=16 32+16=48 :)
What is the slope of the line that passes through the points (5, -4) and (7, -4)?
Write your answer in simplest form.
Answers
Answer:
hey so the answer is m=-4
hope this helps!!~~
If 5 pizzas cost 60$, how much will 9 pizzas cost
Answers
Answer:
$108
Step-by-step explanation:
If 5 pizzas cost $60, then each pizza costs $12. 9 x 12 = 108.
Answer:
108
Step-by-step explanation:
if 5 pizzas cost 60,
each pizza cost 60/5= 12dollars
then, 9 pizzas cost 12 x 9 = 108dollars
Image help | b), exercise 74
(this cost me 50 of my 53 points, please don't answer if you don't know)
Answers
Answer:
x = 3Sides are 6, 8 and 10Step-by-step explanation:
Use Pythagorean to find the value of x:
c² = a² + b²Consider:
a = x + 3, b = 3x - 1, c = 4x - 2Substitute and solve for x:
(4x - 2)² = (x + 3)² + (3x - 1)²16x² - 16x + 4 = x² + 6x + 9 + 9x² - 6x + 116x² - 10x² - 16x + 4 - 10 = 06x² - 16x - 6 = 03x² - 8x - 3 = 03x² - 9x + x - 3 = 03x(x - 3) + (x - 3) = 0(x - 3)(3x + 1) = 0x - 3 = 0, 3x + 1 = 0x = 3, x = - 1/3Positive root is accepted only.
Sides of the triangle:
a = x + 3 = 3 + 3 = 6b = 3x - 1 = 3*3 - 1 = 8c = 4x - 2 = 4*3 - 2 = 10The ratio of yellow flowers to the total number in a bucket is 5 to 9. How many flowers are yellow if there are 45 flowers in all
Answers
Answer 25 yellow flowers
Step-by-step explanation:
Let
x -----> the number of yellow flowers
y ----> the total number of flowers
we know that
----> ---> equation A
----> equation B
substitute the value of y in the equation A and solve for x
Is -7/8 equivalent to 8 / -7
Answers
Answer:
No
Step-by-step explanation:
Because -7/8= -0.875, while 8/-7= -1.142
Answer: no
Step-by-step explanation: -7/8= -875 8/-7=1.1428571428571428
n − 2/3 = 25 3/4 help now
Answers
Answer:
26 5/12
Step-by-step explanation:
n − 2/3 = 25 3/4 Add 2/3 to both sides
n - 2/3 + 2/3 = 25 3/4 + 2/3 Combine
n = 25 3/4 + 2/3
Work with the fractions
3/4 + 2/3 The lowest common denominator is 12
(3*3)/(3*4) = 9 / 12
(2*4)/(3*4) = 8/ 12
9/12 + 8/12 = 17/12 = 1 5/12
Now you need to add 1 to 25
1 + 25 = 26
And add the fraction 5/12
The answer is 26 5/12