Using a system of equations, it is found that Sana's mother bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Number of pounds of peaches.Variable y: Number of pounds of tomatoes.Variable z: Number of pounds of mushrooms.She bought one more pound of peaches than pounds of tomatoes, hence:
x = y + 1.
y = x - 1.
She bought 3 times as many pounds of tomatoes as pounds of mushrooms, hence:
x = 3z.
y = x - 1 = 3z - 1.
She spent a total of $80, hence considering the cost per pound of each product we have that:
6x + 3y + 10z = 80.
Considering the values of x and y as function of z and replacing in the equation, we have that:
6(3z) + 3(3z - 1) + 10z = 80
18z + 9z - 3 + 10z = 80.
37z = 83.
z = 83/37
z = 2.24.
Then:
x = 3z = 3 x 2.24 = 6.72.
y = x - 1 = 3z - 1 = 6.72 - 1 = 5.72.
Hence, she bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.
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7 lbs peaches, 6 lbs tomatoes, 2 lbs mushrooms
yum!
Why is y=-2x considered a function?
because there are values of y that correspond to more than one value of x.
because x is bigger than y.
because the value of y corresponds only to one value of x.
because y is bigger than x.
Yes
Step-by-step explanation:
its a direct-variation function
Find the value for x: 5, 14, 12, x, 10, 4 average =9
Answer:
14
Step-by-step explanation:
i think 14 because you have to times two answers and add them form each number
Kevin bought 6lbs of jelly beans. Antonio bought 66oz of jelly beans.
How many more did Kevin buy than Antonio?
Answer:
30 ounces (1 pound 14 ounces)
Please give brainliest!
Hope this helps:)
To find this, we first need to convert 6 lbs into ounces
lb = 16 ounce
6 lbs = 96 ounces!
96-66 = 30
Kevin bought 30 more ounces, or 1 pound and 14 ounces more jelly beans than antonio.
Vassil rounded to the nearest half to estimate the product of Five-eighths and StartFraction 8 over 9 EndFraction. How do the estimated and actual products compare?
(Hint: use 18 for the denominator when comparing.)
The actual product is about StartFraction 1 over 18 EndFraction greater than the estimate.
The actual product is about StartFraction 1 over 18 EndFraction less than the estimate.
The actual product is about StartFraction 1 over 9 EndFraction greater than the estimate.
The actual product is about StartFraction 1 over 9 EndFraction less than the estimate.
The correct answer is option B which is the actual product is about StartFraction 1 over 18 EndFraction less than the estimate.
What are fractions?The fraction is defined as the division of the whole part into an equal number of parts. here we have the following information Vassil rounded to the nearest half to estimate the product of Five-eighths and StartFraction 8 over 9 EndFraction.
E = [tex]\dfrac{5}{8}\times \dfrac{8}{9}[/tex] = 0.55
Thus the product of the fraction estimated in the nearest half is,
0.5×1= 0.50
Therefore the correct answer is option B which is the actual product is about StartFraction 1 over 18 EndFraction less than the estimate.
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Answer: B
Step-by-step explanation: took test/quiz
The difference between two trinomials is 5x2 + 11x − 16. If one of the trinomials is 3x2 − 2x + 7, then which expression could be the other trinomial?
Applying the difference, it is found that the other trinomial could be given by: 8x² + 9x - 9.
What are the trinomials?We are working with second degree trinomials, hence:
One is 3x² - 2x + 7.The other is ax² + bx + c.The difference is 5x² + 11x - 16.Hence:
ax² + bx + c - (3x² - 2x + 7) = 5x² + 11x - 16.
(a - 3)x² + (b + 2)x + c - 7 = 5x² + 11x - 16.
Then:
a - 3 = 5 -> a = 8.b + 2 = 11 -> b = 9.c - 7 = -16 -> c = -9Then, the trinomial is:
8x² + 9x - 9.
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what is the diameter of the cylinder
Given :-
Volume of cylinder = 245π cubic unitsHeight of cylinder = 5 unitsTo Find :-
Diameter of cylinder?Solution :-
Firstly lets calculate radius of cylinder by using formula of volume of cylinder, as we know that;
Volume of cylinder = πr²hPutting all values we get;
➸ 245π = π × r² × 5
By cutting 'π' with 'π' we get;
➸ 245 = r² × 5
➸ 245/5 = r²
➸ 49 = r²
➸ √(49) = r²
➸ √(7 × 7) = r²
➸ 7 = r
➸ r = 7 units
Hence, radius of cylinder is 7 units.Now lets calculate its diameter, as we know that;
Diameter = Radius × 2Putting all values we get;
➸ Diameter = 7 × 2
➸ Diameter = 14 units
Hence, diameter of cylinder is 14 units.1PLEASE HELP!!! Need to finish
Answer: Heyaa! ~
Your Answer is... -32
Step-by-step explanation:
Simplify the expression. [7-3(-8+5)]Your input: evaluate −2(7−3(−8+5)) when x=1, y=2, z=5.Hopefully this helps you! ^
Question content area top
Part 1
A cake has two layers. Each layer is a regular hexagonal prism. You cut and remove a slice that takes away one face of each prism as shown. What is the volume of the slice? What is the volume of the remaining cake? Use pencil and paper. Describe two ways to find the volume of the slice.
5 in.
3 in.
2.6 in.
4.3 in.
2 in.
3 in.
(The figure is not to scale.)
Question content area bottom
Part 1
The volume of the slice is
40 in..
(Round to the nearest whole number as needed.)
Part 2
The volume of the remaining cake is
enter your response here in..
The volume of the slice is 40 in³. The volume of the remaining cake would be 197.014 in³.
What is a regular hexagon?A regular hexagon can be defined as a closed shape consisting of six equal sides and six equal angles.
Here we have two regular hexagons
one top small hexagon cake with a side of length = 3 in, height = 3 in
One big hexagon cake, side of length = 4 in, Height = 4 in
A slice cut such that it removes a side segment is equivalent to an equilateral triangle with a side
length = length of hexagon side
The length of the side of the removed equilateral triangle side
Top small cake slice triangle side = 3 in.
Area of surface of small slice = 1/2 x b x h = 1/2 x 3 x 3 x sin 60
= 9√3/ 4
The volume of a small slice
= Area of surface small slice × Height of small cake
= 9√3/ 4 x 3
= 11. 69
Big cake slice triangle side = 4 in.
Area of the surface of big slice = 1/2 x 4 x 4 x sin 60
= 4√3
The volume of big slice = Area of the surface of big slice × Height of big slice
= 16√3
= 28
The total volume of slice = Volume of small slice + Volume of big slice
Total volume of slice = 12 in³ +28 in³ = 40 in³
For the small cake,
the remaining volume = 5 x 11.69 = 58.45
For the big cake
the remaining volume = 5 x 27.71 = 138.56
Total volume remaining cake
= 58.45 in³ + 138.56 in³ = 197.014 in³
a = Length of side
h = Height of hexagon
The volume of each slice is,
= a^2 x h x √3/4
For the small cake, we have
a = 3 in.
h = 3 in.
The volume of small slice = a^2 x h x √3/4
= 9 x 3 x √3/4
= 27√3/4
For the big cake, we have
a = 4 in.
h = 4 in.
Volume of big slice = a^2 x h x √3/4
= 16 √3
The total volume of slice = Volume of small slice + Volume of a big slice
Total volume of slice = 27√3/4 + 16 √3
The total volume of the slice = 39404 in³.
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In the xy-plane, The line P is perpendicular to the graph of the equation 4x+3y=12. Which of the following is the slope of line P? A. -4 B.-3 C. 3/4 D.12
A slope is also known as the gradient of a line. The slope of line P is 3/4.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
As it is known that for two perpendicular lines the slope of the lines will be negative reciprocal of each other. The slope of line 4x+3y=12 can be written as,
y = 4 - (4/3)x
m₁ = -1/m₂
-(4/3) = -1/m₂
m₂ = 3/4
Hence, the slope of line P is 3/4.
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what is the surface area of the triangular prism? 15ft 9ft 24ft 40ft 15ft PLEASE BE FAST ILL GIVE BRAINLIESTTT TODAYS MY LAST DAY AG SCHOOL TO AHH
Answer:
B. 2376 Square feet
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Statistics from the past ten years predict that the chance of rain on any single day in April in Asha’s hometown is 41%. If Asha’s birthday is April 10, what is the chance of it not raining on Asha’s birthday?
Answer:
59% chance
Step-by-step explanation:
Statistics from the past ten years predict that the chance of rain on any single day in April in Asha’s hometown is 41%. If Asha’s birthday is April 10, what is the chance of it not raining on Asha’s birthday?
Asha's birthday in in April. The chance of rain on any single day in April is 41%. So, there is a 41% chance of rain.
But, that's not what the problem is asking for. The problem is asking for the chance of not raining. To solve for this, we use simple algebra.
100%(all of the time) - 41%(how much it happens) = 59%
The 59% is the chance of it not raining on Asha's birthday.
Hope this helps! Happy birthday, Asha!
What is the sphere's volume?
Answer:
[tex]972\pi~ \text{in}^3[/tex]
Step-by-step explanation:
[tex]\text{Volume of sphere} = \dfrac 43 \pi r^3 \\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=\dfrac 43 \pi \left( \dfrac d{2} \right)^3\\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=\dfrac 43 \pi \cdot \left(\dfrac{18}{2}\right)^3\\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=\dfrac{4\pi}3 \cdot 9^3 \\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=972\pi~ \text{in}^3[/tex]
Given: The two functions below, f(x) and g(x). Find: How do the value of each functions outputs compare when x=0?
f(x)< g(x).
g(x)=f(x)
f(x)> g(x)
We will see that, when evaluated in x = 0, g(x) is larger than f(x).
How to compare the functions when x = 0?First, we can see that:
g(x) = x + 3
Then, evaluating it in x = 0 we get:
g(0) = 0 + 3 = 3
Now, if we go to the table that represents f(x), we can see that it has the point (0, -6).
Then we can get:
f(0) = -6
With that, we can conclude that: g(0) > f(0), so the correct option is the first one.
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can you find a five digit number which has no zeros, and no digit is repeated, and where:
the first digit is a prime number
the second digit is the fith digit minus the first digit.
the third digit is twice the first digit
the forth digit is the third digit plus 3
the fith digit is the diffrence between the first digit and the fourth digit
Answer:
13,254
hope this helps :)
please crown me brainliest!
4 people completed their work in one hours how will it take 3 peoples to finish it give your answer in minutes
60/4= 15
15 x 3 =45 minutes
please help i have no idea how to do this
Answer (Step-by-step explanation):
so X is horizontal and Y is vertical. (X,Y) because X comes first and Y comes last and all you need to do is make sure your points are correct and that the best of my ability, you can also try drawing lines to each pin point and you can estimate these (X,Y) because X=? and Y=? so good luck i hope that helps! (:
3) show that the two lines with the given slopes are parallel, perpendicular neither. My₁ = 3/4 M₂ = 12/16 . solve it by showing step by step
Parallel lines have equal slope so
M1-M2=0Lets check
M1=3/4M2=12/16=3/4Now
M1-M23/4-3/40Lines are parallel
Answer:
The two lines are parallel
Step-by-step explanation:
If two lines are parallel, they have the same slope.
If two lines are perpendicular, the slopes will be negative reciprocals (the product of the slopes will be -1).
Given slopes:
[tex]\sf m_1=\dfrac{3}{4}[/tex]
[tex]\sf m_2=\dfrac{12}{16}[/tex]
Reduce m₂ to its simplest form by dividing the numerator and denominator by the largest common factor:
[tex]\sf m_2=\dfrac{12 \div 4}{16\div 4}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\sf as \quad \dfrac{3}{4}=\dfrac{3}{4} \implies m_1=m_2 \quad[/tex]
As the given slopes are the same, the two lines are parallel.
Simplify & Please show all work
Answer:
8/m^3nStep-by-step explanation:
f(a)=a^3-10a^2+28a-17 at a=6
Evaluate function using the
Remainder theorem
Show work
I give Brainliest. :)
Answer:
727
Step-by-step explanation:
6^3-106^2=216+360=576+168=744-17=727
The following scatter plot represents the height of a basketball in seconds during a free throw shot.
Evaluate. (-5)² A. -52 B. -25 C. -10 D. 10 E. 25
(-5)²
= (-5)×(-5)
= 25
-> E
Answer:
E. 25
Step-by-step explanation:
A negative times a negative equals a positive. And a squared number is the number inside the parentheses time that number.
Example:
-5×-5=25
A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
108π m³
216π m³
972π m³
1296π m³
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=9 \end{cases}\implies V=\pi (12)^2(9)\implies V=1296\pi ~m^3[/tex]
5. Find the equation of the line in slope-intercept form.
a. (1,-6) and (-7, 2)
Step-by-step explanation:
y=1x-(-6)
y=-7x-2
follow and label y and x inside the equation
make sure you draw a graph to help you find the intercept form.
Help please!
preform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use size for measurements of very large or very small quantities (e.g use kilometers per year for sea floor apeading.) intercept scientific notation that has been generated by technology
Scientific Notation is EASY.
Just move the decimal to the right if it is positive:
6.2 x 10¹ = 62
6.2 x 10² = 620
6.2 x 10³ = 6,200
6.2 x 10⁴ = 62,000
6.2 x 10⁵ = 620,000
6.2 x 10⁶ = 6,200,000
Move the decimal to the left if it is negative:
6.2 x 10⁻¹ .62
6.2 x 10⁻² = .062
6.2 x 10⁻³ = .0062
6.2 x 10⁻⁴ = .00062
6.2 x 10⁻⁵ = .000062
6.2 x 10⁻⁶ = .0000062
What about about 6.2 x 10⁰?
6.2 It wouldn't change location.
I hope this helps!
I WILL GIVE BRAINLIEST look at the right angled triangle abc
the square fits exactly inside the triangle
work out the sizes of angles x y and z
Answer:
(a) y = 25°
(b) x = 90°
(c) z = 25°
Step by step explanation:
Part A
z + 90° + 65° = 180°
z = 180° - 65° - 90°
z = 25°
Part B
x + 90° = 180°
x = 90°
Part C
x + 65° + y = 180°
90° + 65° + y = 180°
y = 25°
Additional:A straight line has total 180° angle. A square has 4 sides of each 90° angle. A triangle is build up of 180° interior angle.
How many ways can you choose 3 dishes from a menu of 8?
a. 24
b. 336
c. 144
d. 56
The volume of a rectangular pyramid is 220 units^3
3
. If the length of the rectangular base measures 6 units and the width of the rectangular base measures 10 units, find the height of the pyramid.
Answer:
h = 11 units
Step-by-step explanation:
Volume of a Rectangular Pyramid = lwh/3
220 = 6*10*h/3
(220) * (3) = ((6)*(10)*(h) / 3) * 3
660 = (6) (10) (h)
Simplify both sides of the equation.
660 = 60h
h = 11 units
Evaluate:
[tex]\bf{\sum^{32}_{n=1}\:(2n+8)[/tex]
Please help A.S.A.P., thank you guys!
Please show work as well.
[tex]\bigstar[/tex]
Explanation:
[tex]\boxed{\sf \sum _{n=1}^{32}\left(2n+8\right)}[/tex]
Formula Required:
[tex]\sf sum \ of \ arithmetic \ series = \dfrac{n}{2} (2a \ + \ (n-1) \ d)[/tex]
Identify the following's:
First Term (a) = (2(1) + 8) = 10Common Difference (d) = 2nd term - first term = (2(2) + 8) - (2(1) + 8) = 2Total Terms (n) = 32Insert variables:
[tex]\rightarrow \ \sf S_{32} = \dfrac{32}{2} (2(10) + (32-1) 2) \quad \xrightarrow{\text{Simplify} } \quad 1312[/tex]
Daisy is making an abstract painting with two triangles. The dimensions of the painting are shown below:
Two triangles share the same height of 10 inches. One triangle has a base of 8 inches, and the other is 12 inches.
The total area of the two triangles is _____ square inches.
Answer:
The total area of the two triangles is 100 square inches.
Step-by-step explanation:
Solution:
Area of one triangle:
Height = 10 inches
Base = 8 inches
Area of triangle =
= 40 square inches
Area of another triangle:
Height = 10 inches
Base = 12 inches
Area of triangle =
= 60 square inches
Total area of the two triangles = 40 square inches + 60 square inches
= 100 square inches
The total area of the two triangles is 100 square inches.
hope that helped:)
In a random population, out of 500 people, 160 had blue eyes. In a group of 2500 people, how many would have blue eyes?
======================================================
Work Shown:
(160 with blue eyes)/(500 total) = (x with blue eyes)/(2500 total)
160/500 = x/2500
x = 2500*(160/500)
x = 800
------------
Another approach:
160/500 = 0.32 = 32% of the first group has blue eyes
Assuming this percentage is the same for any group, then,
32% of 2500 = 0.32*2500 = 800 people of the second group are estimated to have blue eyes, of the 2500 total.