A mixed nuts factory makes a 10 pound mixture of almonds, walnuts, and
cashews. Almonds cost $1.25 per pound, walnuts cost $2.75 per pound,
and cashews cost $3.15 per pound. The mixture calls for twice as many
almonds as walnuts. The total cost of the mixture is $18.90. How much of
each ingredient did the store use?
This is a System of equations problem
Answers
Answer
x+y+z=10
1.25x+2.75x+3.15x+18.90
x=2z
Step-by-step explanation:
x=almonds
y=walnuts
z=cashews
9514 1404 393
Answer:
6 pounds almonds3 pounds walnuts1 pound cashewsStep-by-step explanation:
We can let a, w, c represent pounds of almonds, walnuts, and cashews, respectively. Then the given relations are ...
a +w +c = 10 . . . . . total pounds of nut mix
a = 2w . . . . . . . . . twice as many almonds as walnuts
1.25a +2.75w +3.15c = 18.90 . . . . total cost of the mix
__
Solving the system of equations can proceed by any of the methods you have learned for systems of two equations in two unknowns. Substitution, elimination, and matrix methods all work. Graphing methods are also available.
We can easily reduce this system to two equations in two unknowns by using the second equation to substitute for 'a'.
2w +w +c = 10 ⇒ 3w +c = 10
1.25(2w) +2.75w +3.15c = 18.90 ⇒ 5.25w +3.15c = 18.90
Solving the first of these equations for c, then substituting into the second of these equations gives ...
c = 10 -3w
5.25w +3.15(10 -3w) = 18.90
-4.20w +31.50 = 18.90 . . . . simplify
12.60 = 4.20w . . . . . . . . . . . add 4.20w -18.90
3 = w . . . . . . . . . . . . . . . . . . . divide by 4.20
c = 10 -3(3) = 1 . . . . . . . . . . . use the expression for c
a = 2(3) = 6 . . . . . . . . . . . . . use the expression for a
The nut mix used 6 pounds of almonds, 3 pounds of walnuts, and 1 pound of cashews.
_____
Additional comment
The attached graph shows one way to obtain a graphical solution. The first and third equations were solved for c, and those expressions were set equal to obtain the graph for the red line. The blue line is the second equation. Here, we have used (x, y) for (a, w). The solution for these variables is (a, w) = (6, 3). Using the first expression for c gives c = 10 -(6+3) = 1. This is the same solution as above.
Related Questions
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Raquel has to fill-up 5 volleyball with air. Each ball has a radius of 4.5 inches. What is the volume of the 5 volleyballs all together?
WILL MARK BRAINLEST!!
Answers
Answer:
Mate just divide 5 by 4.5 and you got your answer (1.11)
Step-by-step explanation:
If you see any question that has each in its name then its a division question.
WILL GIVE BRAINLIEST!!!!!!!
A surveyor wants to find the distance between peaks A and B. He finds point C, 288 ft from peak A, so that ACB is a right angle. The measure BAC is 89. Find the distance AB
Answers
Hints on solving trigonometry problems:
If no diagram is given, draw one yourself.
Mark the right angles in the diagram.
Show the sizes of the other angles and the lengths of any lines that are known
Mark the angles or sides you have to calculate.
Consider whether you need to create right triangles by drawing extra lines. For example, divide an isosceles triangle into two congruent right triangles.
Decide whether you will need Pythagorean theorem, sine, cosine or tangent.
Check that your answer is reasonable. The hypotenuse is the longest side in a right triangle.
How to use the tangent ratio to find missing sides or angles?
Example:
What is the value of y in (1/2)x + 3 = (1/3)y - 2 if x = 28/3?
Answers
Answer:
y = 29
Step-by-step explanation:
x/2 + 3 = y/3 - 2
28/3 ÷ 2 = 14/3
14/3 + 9/3 = y/3 - 6/3
23/3 + 6/3 = y/3
29/3 = y/3 ∴ y = 29
Find the a. Median b. Median c. Mode and d. Range of the following scores 60, 70, 90, 70, 80, 65, 95, 80, 100, 60
Answers
Answer:
median-75
mode-70
range-40
mean-77
Step-by-step explanation:
In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearest
tenth of a cm, how long is that leg?
Answers
Answer:
36.5 cm
Step-by-step explanation:
The Adjacent leg is 36.5 cm
What are trigonometric functions?"The trigonometric functions (also called circular functions, angle functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths."
What is hypotenuse, opposite and adjacent side of a right angled triangle?"In a right angled triangle, the hypotenuse is the longest side, an opposite side is the one across from a given angle, and an adjacent side is next to a given angle."
We have
Hypotenuse (AB) = 58 cm
Angle θ = 51 degree
From the figure, by using trigonometric functions
Cos θ = [tex]\frac{BC}{AB}[/tex]
we have to find BC
Cos [tex]51^{0}[/tex] = [tex]\frac{BC}{AB}[/tex]
We have, AB = 58 cm
BC = AB cos [tex]51^{0}[/tex]
⇒BC = 58 . cos [tex]51^{0}[/tex]
⇒BC = 36.50 cm
⇒BC = 36.5 cm
Hence, Adjacent leg is 36.5 cm
Learn more about trigonometric functions here
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solve for x. need help pls
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Help! find the area of the parallelogram
Answers
28.2
Step-by-step explanation
A=bh=6·4.7≈28.2
What is the recursive rule for an=4n-3
Answers
Answer:
1
Step-by-step explanation:
n=1
4×1=4
4-3=1
What is the graph of the system y = −2x + 3 and 2x + 4y = −8? Line through point 0, 3 and 1, 1. Line through 0, negative 2 and negative 4, 0. Line through point 0, 3 and 1, 1. Line through 0, 2 and negative 4, 0. Line through point 0, 3 and 1, 1. Line through 0, 2 and 4, 0. Line through point 0, 3 and 1, 1. Line through 0, negative 2 and 4, 0.
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Answer:
X = -4-2y
Step-by-step explanation:
Answer:
Line through point 0, 3 and 1, 1. Line through 0, negative 2 and negative 4, 0.
Step-by-step explanation:
I accidentally got it right
The price of the stereo was $96 the tax rate was 6% what was the tax
Answers
Answer:
101.76
Step-by-step explanation:
What is the volume of the cylinder shown? (Use 3.14 for it.)
6.838.92 in.^3
1.413.56 in^3
1.243.44 in^3
11.190.8 in.^3
Answers
Step-by-step explanation:
11^2= 121
multiply by pi
121×3.14=379.94
then multiply the height
379.94×18=6,838.92
Help please I’m so behind
Answers
Answer: 5 and 27 as remainder
Step-by-step explanation:
Find the volume of the cylinder. Use 3.14 for π.
Round your answers to the nearest tenth.
Answers
Answer:
V≈565.4
Step-by-step explanation:
V=πr2h=π·32·20≈565.48668
HELPP !!! I need help
Answers
Answer:
4. the answer is 5.4 which is between 5 and 6.
5. the answer is C.
Step-by-step explanation:
for #4 you just had to divide 27 by 5, and for #5 both numbers are positive so they are in the first quadrant.
Determine the value of variable in the following
equation:
2x + 40 = 30
Answers
Steps:
2x + 40 = 30
2x = 30 - 40
2x = -10
x = -10 / 2
x = -5
Find the surface area of the cylinder
8 cm
3 cm
The surface area of the cylinder is cm?
(Simplify your answer. Type an exact answer in terms of r.)
Enter your answer in the answer hoy
Answers
Answer:
V=pr²t
=3,14 ×8×8×3
=602.88
Step-by-step explanation:
IVA
Answer: surface area
A = 56 π cm^2
Step-by-step explanation:
A = 56 π cm^2
you can stop here and write our answer as 56π Or we can plug in 3.14 and multiply. 56*3.14 = 175.84cm^2
can someone help me plss
Answers
Find the area of the figure to the nearest hundredth.
Answers
Step-by-step explanation:
We have 2 Semicircular. area of each one :
[tex]\pi \: \times \: r[/tex]
r = 2.5ft and pi=~3 ==> 7.5×2=15ft (area of two Semicircular)
the area of triangle = 5 + 5 + 6 = 16ft
area of the figure = 16 + 15 = 31ft
Jessie saves $6 each week. In how many weeks will she have saved at least $50?
Answers
Answer:
9 weeks at least to have at least 50 dollars.
Step-by-step explanation:
Well 6 dollars each week and to get AT LEAST 50 dollars you need to save for 9 weeks.
Well 9*6=54
If you do it for 8 you’d only get 48 which is not at least 50 but 54 is.
So 9 weeks is the final answer.
50≤54
50 isn’t less then 48
Answer
. . . . . .
Step by step explanation -
Adam is thinking of a mystery number. If he divides it by 9 and then subtracts 7 from it, the result is 1. What is Adam's mystery number?
Answers
Answer:
72
Step-by-step explanation:
1+7=8
8*9+72
PLEASE HELP!! I don't really know how to solve this.
Answers
Answer:
x=13
y=14
Step-by-step explanation:
We know that angle JNK is equal to angle MNL. We also know that angle JNK and angle KNL are supplementary.
Knowing this, we can write two equations: [tex]4x-1=3y+9[/tex] and [tex](4x-1)+(2x+6y+19)=180[/tex]. We can solve for y in the first equation. Subtracting 9 from both sides gives us [tex]4x-10=3y[/tex]. Dividing both sides by 3 gives us [tex]\frac{4x-10}{3} =y[/tex].
We can plug that in to the second equation to get [tex](4x-1)+(2x+6(\frac{4x-10}{3} )+19)=180[/tex]. Expanding the second parenthesis, we get [tex]2x+8x-20+19[/tex] which equals [tex](10x-1)[/tex]. We now have [tex](4x-1)+(10x-1)=180[/tex]. Expanding gives us [tex]14x-2=180[/tex]. Adding 2 to both sides gives us [tex]14x = 182[/tex]. Dividing both sides by 14 gives us [tex]x=13[/tex].
We can now plug 13 into the above equation to solve for y. [tex]y= \frac{4*13-10}{3}[/tex] Solving that gives you [tex]y=14[/tex].
Please help I don't understand this subject in math and my teacher isn't explaining it well. please explain how you find the answer, thanks :)
Answers
Answer:
[tex]in \: this \: shape \: you \: have \: two \: pieces \: one \: square \: ad \: half \: of \: circle \\ area \: of \: circle = 12 \times 12 = 144 \\ area \: of \: hafl \: of \: circle = 12 \times 12 \times 0.25 \times 3.14 = 113.04 \\ whole \: area = 144 + 113.04 = 257.04[/tex]
Answer: E. 200.5 ft
so first you’d find the area of the square which is 12 x 12 = 144 (area = length x width)
next, find the radius of the semi circle which is 12 divided by 2 (because we used the measurements from the square and the diameter is 12 and radius is half of diameter)
pretend your solving for a full circle and then divide it by 2 to get the answer for the semi circle since a semi circle is half of a circle (formula for circle A = pi r^2)
area of circle = 113.04 divided by 2 to get semi circle = 56.5
then add both areas together
56.52 + 144 = 200.5
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Lesson 5.16 - Problem Solving with Mixed Numbers (D)
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Problem Solving with Mixed Numbers
Jada made 3 1/6gallons of lemonade. Jada served 5/6
gallon to her friends.
How much lemonade does Jada have left?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer:
Try Reasearching it! I hope you have a fantastic day/night ;-;
Step-by-step explanation:
Question 6 of 10
A(n) is produced when you slice a cone with a plane that is parallel to
the base of the cone.
A. parabola
Ο Ο Ο
B. circle
C. hyperbola
D. ellipse
SUBMIT
Answers
The correct option is (b) circle .
The conic section formed by the cone and a plane parallel to its base is a circle.The surface of a right-regular cone and a plane parallel to the base of the cone cross to form the closed figure known as a circle. The ellipse, which we'll discuss next, is actually just a special instance of the circle.What is conic?Any curve created by the intersection of a plane and a right circular cone is known in geometry as a conic section, sometimes known as a conic. The intersection can be a circle, an ellipse, a hyperbola, or a parabola, depending on the angle the plane makes with the cone.What conic section is formed from slicing parallel to the base of the cone ?
The resulting curve is a circle if the cone is cut in half parallel to the base. The curve is known as an ellipse if the cone is cut at a modest angle. The curve generated is known as a parabola if the slice is done parallel to the cone's edge.Learn more about Conic brainly.com/question/22337165
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VI.
Molly paid $85 last month for her utilities. 55% of this amount was for electricity
a. How much did Molly pay for electricity?
What percentage of her money did she have left over?
c. What is the amount of leftover money Molly has for last month?
Answers
Answer:
$46.75
0.55 X 85 = $46.75
a trucker hauls citrus fruit from Florida to Montreal. Each crate of oranges is 4 ft3 in volume and weighs 80 lb. Each crate of grapefruit has a volume of 6 ft3 and weighs 100 lb. His truck has a maximum capacity of 300 ft3 and can carry no more than 6800 lb. Moreover, he is not permitted to carry more crates of grapefruit than crates of oranges. If his profit is $2.50 on each crate of oranges and $4 on each crate of grapefruit, how many crates of each fruit should he carry for maximum profit
Answers
answer = 560 profited
4. Calculate the compound interest earned when $8 500 at 8% per year for:
a. 3 years
b. 8 months
Answers
The bus travels 35 blocks in 7 minutes . If the bus travels at a constant speed , how long will it take to travel 50 blocks ?
HELPPP PLEASE NOOO LINKSSS PLEASE
Answers
Answer:
10 min
Step-by-step explanation:
35/7=5 blocks in 1 min
50/5=10
Plz help me I will give you 40 points and Brainly