Brian is making 12 pounds of nut mixture with almonds and hazelnut. almonds cost $10.80 per pound and hazel nuts cost $10.20 per pound. How many pounds of almonds and how many pounds of hazelnut should Brian use for the mixture to cost $10.35 per pound to make?
Answers
Using a system of equations, Brian should use 3 pounds of almonds and 9 pounds of hazelnut to make the mixture.
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:
Variable x: Number of pounds of almonds.Variable y: Number of pounds of hazelnut.Considering that he makes 12 pounds, at a price of 12 x 10.35 = $124.2, the equations are given as follows:
x + y = 12.10.8x + 10.2y = 124.2.From the first equation, y = 12 - x, hence, replacing in the second:
10.8x + 10.2y = 124.2
10.8x + 10.2(12 - x) = 124.2
0.6x = 1.8
x = 1.8/0.6
x = 3
y = 12 - x = 12 - 3 = 9.
Brian should use 3 pounds of almonds and 9 pounds of hazelnut to make the mixture.
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Related Questions
which equation is equivalent to 4(a-3)
Answers
Answer:
12-4
Step-by-step explanation:
So the equivalent expression would be:
4a-12
The equation of a parabola is (x−3)2=16(y+7) . What are the coordinates of the vertex and focus of the parabola? What is the equation of the directrix?
Answers
The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.
The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.
Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).
The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).
To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.
In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.
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Which expression simplifies to 41? Choose all that apply!
10+ 2.4-1
10+ 2.(4 - 1)
(10 + 2). 4 - 1
10+ (22.4) - 1
Answers
Answer:
A
Step-by-step explanation:
I took the test so yeah hope this helps
In what quadrant would the triangle be if rotated 90 degrees
Answers
I strongly believe the answer is 2, if it isnt that it must be 3.
"Rotated around the origin", as the question actually says, puts it in Quadrant-II (2).
But the way you put the question, just saying the triangle is rotated 90°, leaves it right where it is, in Quadrant-I, with vertex-H on the bottom.
Which of these shapes have rectangular cross sections options. Orectangular prism O triangular prism cylinder D cone ✔cy Osquare pyramid triangular pyramid
Answers
The correct options are rectangular prism, square pyramid.
What are the shapes have rectangular cross sections?When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.
The shapes that have rectangular cross sections when they are cut perpendicular to the base are:
Rectangular prism
Square pyramid
Therefore, the correct options are rectangular prism, square pyramid.
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Complete question:
It is given that m ∠ AOB = 42 ∘ and m ∠ EOF = 66 ∘ . By the ___________, ∠ EOF ≅ ∠ BOC . Therefore, m ∠ BOC = 66 ∘ . By the ________ , m ∠ AOC = 108 ∘ , and by ________ the , m ∠ AOC + m ∠ COD = 180 ∘ . After application of the ___________, m ∠ COD = 72 ∘ .
Answers
The required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
It is given that m ∠ AOB = 42 ∘ and m ∠ EOF = 66 ∘ . By the definition of congruent angles, ∠ EOF ≅ ∠ BOC. Therefore, m ∠ BOC = 66 ∘ . In the addition, m ∠ AOC = 108 ∘ , and by definition of the straight angle, m ∠ AOC + m ∠ COD = 180 ∘ . After application of the subtraction of the angle, m ∠ COD = 72 ∘ .
Thus, the required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.
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Answer:
It is given that m∠AOB = 42º and m∠EOF = 66º. By the vertical angles theorem, ∠EOF ≅ ∠BOC. By the angle addition postulate, m∠AOC = 108º, and by the linear pair theorem, m∠AOC + m∠COD = 108º. After the application of the subtraction property of equality, m∠ COD = 72º.
Step - by - step
first box: vertical angles theorem
second box: angle addition postulate
third box: linear pair theorem
fourth box: subtraction property of equality
Write 90,403
in expanded form and using
number names.
Answers
Answer:
Ninety thousand, four hundred and three.
An English teacher reviewed 2 3 of an essay in 1 4 of an hour. At this rate, how many essays can she review in 1 hour? Simplify your answer and write it as a proper fraction, mixed number, or whole number. essays
Answers
The essays that she can review in 1 hour would be; 2 2/3.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.
Thus, Fraction of the essay reviewed = 2/3
Amount of time used = 1/4
Therefore, the fraction of essay for an hour can be calculated as;
= Fraction of the essay reviewed / Amount of time used
= 2/3 ÷ 1/4
= 2/3 × 4
= 8/3
= 2 2/3
Hence, She will review 2 2/3 essay.
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Use the table below to answer #3
What is the difference between the total amount of bags of box tops collected by 4th grade to 5th grade
Answers
The difference between the total amount of bags of box tops collected by 4th grade to 5th grade is 2 (1/16). Option D
How to find the difference?The given parameters that will help us to get the difference are
The fractions,
We shall be solving the fractions in pars then later we find the difference.
[4 3/12 +5 5/16 +3 3/8} - {3 1/4 +4 1/2 + 3 1/8}
Simplify by find the LCM of each side
[12{12+15+18}/48 ] - {10 (2+4+1)/8
Simplify to get
12 (45/48) - 10[7/8]
subtracting the fractions to have
2 [45 - 42]/48
Making it more simpler to get
2 1/16
Therefore the difference between the two fractions is 2 1/16
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Select the correct answer.
Answers
Answer:it might be A
Provide me three coordinate points for the following, given the Slope and Y-intercept. 4. Slope = 15, Y intercept = -1 (give me 3 coordinate points)
Answers
The coordinates can be
\((1,14)(2,29)(3,44)\)Here is a picture of some sea animals. The number line on the left shows the vertical position of each animal above or below sea level, in meters.
1. How far above or below sea level is each animal? Measure to their eye level.
2. A mobula ray is 3 meters above the surface of the ocean. How does its vertical position compare to the
height or depth of:
The jumping dolphin?
The flying seagull?
The octopus?
3. An albatross is 5 meters above the surface of the ocean. How does its vertical position compare to the
height or depth of:
The jumping dolphin?
The flying seagull?
The octopus?
4. A clownfish is 2 meters below the surface of the ocean. How does its vertical position compare to the
height or depth of:
The jumping dolphin?
The flying seagull?
The octopus?
5. The vertical distance of a new dolphin from the dolphin in the picture is 3 meters. What is its distance from the surface of the ocean?
Answers
Answer:
How far above or below sea level is each animal? Measure to their eye level.The jumping dolphin is approx. 6 meters under sea level
The flying seagull is approx. 8 meters under sea level
The mobula ray is approx. 2 meters under sea level
The clownfish is approx.t 4 meters under sea level
The octopus is approx. 8 meters under sea level
A mobula ray is 3 meters above the surface of the ocean. How does its vertical position compare to the height or depth of:The jumping dolphin: The mobula ray is 9 meters lower than the jumping dolphin.
The flying seagull: The mobula ray is 11 meters lower than the flying seagull.
The octopus: The mobula ray is 11 meters higher than the octopus.
An albatross is 5 meters above the surface of the ocean. How does its vertical position compare to the height or depth of:The jumping dolphin: The albatross is 1 meter lower than the jumping dolphin.
The flying seagull: The albatross is 3 meters lower than the flying seagull.
The octopus: The albatross is 13 meters higher than the octopus.
A clownfish is 2 meters below the surface of the ocean. How does its vertical position compare to the height or depth of:The jumping dolphin: The clownfish is 8 meters lower than the jumping dolphin.
The flying seagull: The clownfish is 10 meters lower than the flying seagull.
The octopus: The clownfish is 6 meters higher than the octopus.
The vertical distance of a new dolphin from the dolphin in the picture is 3 meters. What is its distance from the surface of the ocean?If the new dolphin is above the dolphin in the picture, then its distance from the surface of the ocean is 6 - 3 = 3 meters.
If the new dolphin is below the dolphin in the picture, then its distance from the surface of the ocean is 6 + 3 = 9 meters.
✧☆*: .｡. Hope this helps, happy learning! (✧×✧) .｡.:*☆✧
HELP!
Do units affect significant figures? For example, I know that the number 5600 has two significant figures. But if I wrote it as 5600 L, would the unit "L" count as a sig fig? Please help me!!
Answers
The number is less than 6,000.
The number is odd.
2/4 of the digits are even.
The digit in the thousand's place is the number
of days in a typical school week.
The digit in the ten's place is twice the value of the
digit in the hundred's place.
The digit in the one's place is the number of sides on a nonagon.
The digital root of the number is the number of sides on a stop sign.
Answers
The number is 4,175.
How do we explain?points to note:
The number is less than 6,000.The number is odd.2/4 of the digits are even means that even digits can only be 4 and 6.The digit in the thousand's place is the number of days in a typical school week and we have 7 days in a typical school week.The digit in the ten's place is twice the value of the digit in the hundred's place and we have the only even digit left as 6, to be the hundreds place. The ten's place digit is 2 * 6 = 12, hence the ten's digit is 2.The digit in the one's place is the number of sides on a nonagon which is equal to 9.The digital root of the number is the number of sides on a stop sign means that the sum of the digits in the number is 4 + 1 + 7 + 5 = 17, which reduces to a digital root of 1 + 7 = 8. A stop sign has 8 sides, so the digital root matches.Learn more about digital root at: https://brainly.com/question/24487815
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Find the slope for the line that passes thru the points (-2, 7) and (4, 18)
Answers
Answer:
\(m=\frac{11}{6}\)
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Point (-2, 7)
Point (4, 18)
Step 2: Solve for slope m
Substitute: \(m=\frac{18-7}{4+2}\)Subtract/Add: \(m=\frac{11}{6}\)Answer:
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Find a formula for the linear function depicted in the following graph.
f(x)=
Answers
The formula for the linear function in the graph is f(x) = -2x + 4.
What is graph?The graph is a data structure that is used to represent relationships between objects. It is composed of nodes (or vertices) that are connected by edges (or lines). Graphs can be used to represent many types of data, such as networks of people, roads, and even abstract concepts like language. Graphs are used in a variety of fields, such as computer science, mathematics, and sociology. They allow for efficient storage and retrieval of data, as well as efficient traversal of the data.
The graph shown below is a linear graph with a slope of -2 and a y-intercept of 4.
To find the formula for the linear function, we can use the slope-intercept form, which is y = mx + b. In this equation, m is the slope of the line and b is the y-intercept.
Therefore, the formula for the linear function in the graph is f(x) = -2x + 4.
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complete question:
Find a formula for the linear function depicted in the following graph.
f(x)=
12. The circle graph represents the jobs at a digital
animation company with 1540 employees
How many more story artists are there
than interns?
Answers
Answer:
231
Step-by-step explanation:
From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number
In actual values
Number of story artists = 1540 x 20% = 1540 x 20/100 = 308
Number of interns = 1540 x 5% = 1540 x 5/100 = 77
Difference = 308 - 77 = 231
Yesterday it took 40 minutes to drive to school. Today is took 32 minutes to drive to
school. What is the amount of percent decrease?
Answers
Answer:
20%
Step-by-step explanation:
To find the percent decrease, we do old number subtracted from the new numbers over old.
We do
40 - 32 = 8
Then we put the 8 over the old and get
8/40
In percentage form it would be 20%
Which set of numbers is arranged from least to greatest?
Answers
Answer:
The correct answer is option B
I NEEDD HELPPP ASAPPPPPPPP
Answers
The value of sin (α + β) is,
⇒ sin (α + β) = - 135/377
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Angle α in quadrant 3:
y = opposite = 21 and x = adjacent = 20
Then, hypotenuse = √( 21² + 20²)
= √ ( 441 + 400)
= sqrt( 881)
So, sin α = 21/√881
= 21 × sqrt(881)/881
And, cos α = 20/sqrt(881) = 20sqrt(881) / 881
Since, Angle β in Quadrant 2:
Hence, adjacent = -5 and hypotenuse = 13
Then, by Pythagorean,
y = opposite = 12
So, sin β = 12/13, cos β = -5/13
as given,
And, tan β = -13/12
Since, We know that;
sin (α + β) = sin α cos β + cos α sin β
= 21/√881 × - 5/13 + 20/√881 × 12/13
= 1/√881 (- 105/13 + 240/13)
= - 1/√881 (135/13)
= - 135/377
Hence, The value of sin (α + β) is,
sin (α + β) = - 135/377
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What is the volume of this figure?
Enter your answer in the box.
yd³
Answers
The volume of the composite figure is
4095 cubic ydHow to find the volume of the composite figureThe volume is calculated by dividing the figure into simpler shapes. and adding the individual volumes
The simple shapes used here include
trapezoid andrectangleVolume of rectangle = length x width x depth
= 30 * 9 * 7
= 1890 cubic yd
Volume of trapezoid = 1/2 (sum of parallel lines) x height x depth
= 1/2 (30 + 19) x 10 x 9
= 2205 cubic yd
Total volume
= 1890 cubic yd + 2205 cubic yd
= 4095 cubic yd
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A scientist has two solutions what she has labeled solution a and solution b each contains salt she knows that solution a is 60% salt and solution b is 85% salt she wants to obtain 70 ounces of a mixture that is 80% salt how many ounces of each solution should she use
Answers
Solving a system of equations we can see that:
She needs to use 56 oz of the 85% solution.She needs to use 14 oz of the 60% solution.How many ounces of each solution should she use?We can use the variables:
x = mass of the 60% solution.
y = mass of the 85% solution.
We can write a system of equations.
x + y = 70
x*0.6 + y*0.85 = 70*0.8
We can isolate x on the first equation to get:
x = 70 - y
Replace that in the other one:
(70 - y)*0.6 + y*0.85 = 70*0.8
Now we can solve this for y.
y*0.25 = 70*0.8 - 70*0.6
y = 14/0.25 = 56
Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.
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A baker has 4 3/4 pounds of cookie dough. He uses 1/16 pound of dough for each cookie. How many cookies can he make? Simplify the answer.
Answers
This shows that 76 cookies will be made with the total pounds of cookies
Ratio and proportionFractions are written as a ratio of two integers. Given the following parameters
Total pounds of cookies made = 4 3/4 pounds
Total pounds of cookies made = 19/4 pounds
If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;
Number of cookies = 19/4 ÷ 1/16
Number of cookies = 19/4 * 16/1
Number of cookies = 19 * 4
Number of cookies = 76
This shows that 76 cookies will be made with the total pounds of cookies
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What is the range of the function? f(x)=3^x−1−2
Answers
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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What’s the answer please I need help.
Answers
Answer:
less than
Step-by-step explanation:
What is the volume of this object?
__u3
Answers
Answer:
15u³
Step-by-step explanation:
To find volume ↓
Volume
= length × width × height
= 2u × 2½u × 3u
= 15u³
Hope this helps =)
HELP ME. I HATE MATH DUDE.
Answers
If 32 + 8x is 20 more than 28, what is the value of 4x?
Answers
Answer
32+8x=28+20
32+8x=48
-32 -32
8x=16
/2 /2
4x=8
(Brainlest PLz and rate 5 stars plz) I would appreciate it.
Step-by-step explanation:
Determine (-4)(-2)+5
Answers
Answer:
13
Step-by-step explanation:
The first part, -4 x -2 = 8. Add 5 to eight and you get 13
hopefully i helped
Car dealership pays a wholesale price of $10,000 to purchase a vehicle if they mark up the price 20% what is the retail price of the car
Answers
Answer:
8000
Step-by-step explanation:
10000 x 20% = 2000
10000-2000= 8000