The table shows the number of apples needed to make apple pies and applesauce sold at a farm
store. During a recent picking at the farm, 169 Granny Smith apples and 95 Red Delicious apples
were picked. Write and solve a system to determine how many apple pies and how many batches
of applesauce can be made if every apple is used. (Hint: read across each row to create your equations!)
# Needed # Needed Total
Type of Apple for 1 (Pie) for Sauce
Granny Smith 5
4
169
Red Delicious
3
2
95
Answers
Answer:
pie - 38
sauce - 37.5
Step-by-step explanation:
For the Red Delicious apples you keep subtracting 5 from the total (95) and adding 1 to both of the total numbers of pies and apple-sauce. For the Granny Smith apples you keep subtracting 9 from the total and adding 1 to both of the total numbers of pies and apple-sauce until you get to 7 then you subtract 5 and 1 to the total of pies then you only have 2 left and that is half of the appl-sauce.
The value of x from the equation is 21 pies and the value of y from the equation is 16 batches of apple sauces
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of apple pies be x
Let the number of batches of apple sauce be y
Now , the system of equations are
5x + 4y = 169 be equation (1)
3x + 2y = 95 be equation (2)
Multiply equation (2) by 2 , we get
6x + 4y = 190 be equation (3)
Subtracting equation (1) from equation (3) , we get
x = 190 - 169
x = 21
Substitute the value of x in equation (2) , we get
3x + 2y = 95
3 ( 21 ) + 2y = 95
63 + 2y = 95
Subtracting 63 on both sides of the equation , we get
2y = 32
Divide by 2 on both sides of the equation , we get
y = 16
Therefore , the value of x and y are 21 and 16 respectively
Hence , the number of apple pies and apple sauces are 21 and 16 respectively
To learn more about equations click :
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Related Questions
!!!20 points and Brainliest please help!!!!
Which of the following is a difference of cubes?
A)3x^9 - 64y^3
B)125x^21 - 64y^3
C)27x^15 - 9y^3
D)x^6 + 27y^9
Answers
Answer:
B) 125x^21 -64y^3
Step-by-step explanation:
You want to identify the difference of cubes among the expressions given.
A)The coefficient 3 is not a cube.
B)125x^21 -64y^3 = (5x^7)^3 -(4y)^3 . . . . . a difference of cubes
C)The coefficient 9 is not a cube.
D)The expression is not a difference.
<95141404393>
An equilateral triangle with side lengths of 8. 7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true? Select three options. The apothem can be found using the Pythagorean theorem. The apothem can be found using the tangent ratio. The perimeter of the equilateral triangle is 15 cm. The length of the apothem is approximately 2. 5 cm. The area of the equilateral triangle is approximately 65 cm2.
Answers
The image of the triangle is missing, so i have attached it.
Also, the options are;
A) The apothem can be found using the Pythagorean theorem.
B) The apothem can be found using the tangent ratio.
C) The perimeter of the equilateral triangle is 15 cm.
D) The length of the apothem is approximately 2.5 cm.
E) The area of the equilateral triangle is approximately 65 cm².
Answer:
Options A, B & D are true
Step-by-step explanation:
A) We are told that the triangle is an equilateral triangle.
Thus, the 3 sides equal 8.7 cm.
Now from the image, b is half of one of the sides.
Thus, b = 8.7/2 = 4.35 cm
Now, we want to find the apothem "a".
Using Pythagoras theorem, we have;
a² + 4.35² = 5²
a² = 25 - 18.9225
a² = 6.0775
a = √6.0775
a ≈ 2.5 cm.
Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"
B) since the main triangle is equilateral, it means each angle is 60°.
Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.
Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°
Now, from tangent ratios, we know that;
Opposite/Adjacent = tan θ
In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm
Thus;
a/4.35 = tan 30
a = 4.35 tan 30
a ≈ 2.5 cm.
Thus, option B is correct as Tangent ratio can be used to find the apothem
C) The perimeter of equilateral triangle = 3x
Where x is length of one side.
One side is 8.7 cm
Thus, perimeter = 3 × 8.7 = 26.1 cm
Thus option C is not correct.
D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.
Thus, option D is true.
E) Area of triangle is;
A = ½ × base × height
Base = 8.7 cm
To get height, we will use trigonometric ratio. Thus;
h/8.7 = sin 60°
h = 8.7 sin 60°
Thus;
A = ½ × 8.7 × 8.7 sin 60°
A = 32.77 cm²
Thus is not equal to 65 cm². Thus, option E is not correct.
The statements that are true for the considered equilateral triangle are:
Option A: The apothem can be found using the Pythagorean theorem.Option B: The apothem can be found using the tangent ratio.Option D: The length of the apothem is approximately 2. 5 cm.What is apothem?
For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.
For this case, referring to the figure attached below, we have:
Length of the apothem = x (assume)The triangle ABC is equilateralLength of line segment from vertex to center (radius) = 5 cmLength of each side of the triangle = 8.7 cmSince the triangle is equilateral, there can be 6 congruent triangles like BOD.
Thus, Area of triangle ABC = 6 × Area of triangle BOD
Area of BOD = [tex]\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2[/tex]
Area of ABC = [tex]6 \times 2.175x = 13.05x \: \rm cm^2[/tex]
The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.
We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).
[tex]tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm[/tex]
Using Pythagoras theorem too, we can get the value of x as:
[tex]5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm[/tex]
Thus, area of the equilateral triangle ≈ [tex]13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2[/tex]
This isn't 65 sq. cm.
Thus, the statements that are true for the considered equilateral triangle are:
Option A: The apothem can be found using the Pythagorean theorem.Option B: The apothem can be found using the tangent ratio.Option D: The length of the apothem is approximately 2. 5 cm.Learn more about tangent ratio here:
https://brainly.com/question/14169279
Brainliest if correct
Answers
Answer:
[tex]\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6 }=\frac{2}{6} =\frac{1}{3}[/tex]
Step-by-step explanation:
To complete the steps:
[tex]\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6 }=\frac{2}{6} =\frac{1}{3}[/tex]
I think the question you are answering a question that does not require simplification so ignore the last bit (= 1/3)
Write the slope-intercept form of the equation of the line that is perpendicular to AB and passes through Point X Show
all work for full credit.
Answers
System of Equations- pls help with the following problem
Solve the System of equations x = -2 ; y = 3 .(Choose from a,b, or c. Show your work step by step).
a) x+y=1
2x+y=5
b) x+2y = 4
x +y = 1
c) x-y=-5
x+y= 11
Pls show your work as I want to understand how to solve this type of equation.
Answers
Answer:
please mark me as brainlest
Step-by-step explanation:
b is the answers for the question
What does (2x−2)(3x+5) equal?
Answers
Answer:
6x² + 4x + 10
Step-by-step explanation:
(2x - 2)(3x + 5)
2x(3x + 5) - 2(3x + 5)
6x² + 10x - 6x + 10
6x² + 4x + 10 ans.
hope this helps you !
Answer number 8 please. Thank you.
Answers
Answer:
The answer is C. A triangle is made up of a total angle of 180°, therefore C. is more than 180°
Annie wants to use the problem-cause-solution order to organize a persuasive speech to reduce violence on campus. she begins by offering statistics of incidents to show that there is a need for action. what is a possible next step
Answers
The possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.
What is a persuasive speech?It should be noted that a persuasive speech simply means a speech that is used to convince an individual to agree to a particular perspective.
In this case, the possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.
Learn more about speech on:
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PLEASE ACTUALLY HELP AND NOT JUST ANSWER CUZ YOU WANT POINTS! Can you please write the inequalities in algebraic form. EX: the sum of 92 and Z is less than 100 90+Z < 100
1. 24 less than Z is less than 12
2. the difference when you subtract 12.65 from A is less than or equal to 26,000
3. 999 less than Z is less than 500
4. the product of -10 and X is 25 or more
5. f minus -1 is less than 0
6. Y over 14 is 0.5 or more
Answers
Answer:
1. Z-24 < 12
2. A-12.65 ≤ 26,000
3. Z-999 < 500
4. -10x ≥ 25
5. f - -1 < 0 or f+1 < 0
6. y/14 ≥ 0.5
The volume of a sphere is 75716 cm3.
Work out the radius of the sphere.
Answers
Answer:
Step-by-step explanation:
Givens
V = 75716
pi = 3.14
r = ?
Formula
V = (4/3) pi * r^3
Solution
75716 = (4/3) * 3.14 * r^3 Multiply both sides by 3/4
75716 * 3/4 = 3.14 * r^3
56787 = 3.14 r^3 Divide by 3.14
56787 / 3.14 = 3.14 * r^3/3.14
18085 = r^3
∛18985 = ∛ r^3
r = 26.25
Simplify
3k - (2m + 5K) - m
Answers
Answer:
[tex]-3m-2k[/tex]
Step-by-step explanation:
Given to simplify : 3k - (2m + 5K) - m
Solution :
[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]
[tex]-\left(2m+5k\right)=-2m-5k[/tex]
[tex]=3k-2m-5k-m[/tex]
[tex]\mathrm{Group\;like\;terms}[/tex]
[tex]=-2m-m+3k-5k[/tex]
[tex]\mathrm{Group\;like\;terms}[/tex]
[tex]=-3m+3k-5k[/tex]
[tex]\mathrm{Group\;like\;terms}[/tex]
[tex]=-3m-2k[/tex]
[RevyBreeze]
Use the distributive property:-
-(2m+5k) = -2m-5k [tex]\checkmark[/tex]
[tex]\rule{270}{1}[/tex]
Let's simplify this expression by combining like terms:-
[tex]\bigstar[/tex] The like terms are:-
3k, -5k
and
-2m, -m
[tex]\bigstar{[/tex] Combine Like terms:-
3k-5k=-2k
-2m-m=-3m
Hence, we have:-
[tex]\bigstar{\boxed{\pmb{-2k-3m}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Which expression represents 4 fifths t(negative 10 t)? –8t 46 over 5 46 over 5 –8t2
Answers
Answer:
is this a multiple choice question? if so can you retype it out to show the separate answer choices because im having trouble reading your question.
Step-by-step explanation:
Answer:
–8t^2 or DStep-by-step explanation:
Took the test and got it right.
WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER
Answers
Answer:
(3,5)
Step-by-step explanation:
We first need to substitute x for 3 in the equation :)
y = 2(3) - 1
y = 6 - 1
y = 5
The cordinate will be (3,5)
Have an amazing day!!
Please rate and mark brainliest!!
When 0.3(4x – 8) – 0.5(–2.4x + 4) is simplified, what is the resulting expressions
-4.4
1.2x-2.4+1.2x-2
2.4x-0.4
2.4x-4.4
Answers
Answer:
[tex]2.4x-4.4[/tex]
Step-by-step explanation:
Given the following question:
[tex]0.3(4x-8)-0.5(-2.4x+4)[/tex]
To simplify the expression, we are going to need to rewrite the expression by expanding the terms and then solve by using the distributive property. Then we combine like terms in till the expression can no longer be simplified to find our answer.
[tex]0.3(4x-8)-0.5(-2.4x+4)[/tex]
[tex]0.3(4x-8)[/tex]
[tex]0.3\times4=1.2x[/tex]
[tex]0.3\times4=2.4[/tex]
[tex]1.2x-1.2-0.5(-2.4x+4)[/tex]
[tex]-0.5(-2.4x+4)[/tex]
[tex]-0.5\times-2.4=1.2[/tex]
[tex]-0.5\times4=-2[/tex]
[tex]1.2-2[/tex]
[tex]1.2x-2.4+1.2x-2[/tex]
[tex]1.2+1.2=2.4x[/tex]
[tex]-2.4+-2=-4.4[/tex]
[tex]=2.4x-4.4[/tex]
Your answer is "2.4x - 4.4."
Hope this helps.
The figure shown is composed of 4 identical cubes.
Find the surface area.
the only thing that they show me was that on the bottom of a cube was 2 in
Answers
Answer:
i think the surface would be 2
What is the value of x? If necessary express your answer in simplest radical form.
A. 18
B. 20
C.4✔️2
D. 4✔️3
Answers
Answer:
B, 20
Step-by-step explanation:
The Pythagorean Theorem states that the two shortest lengths in a right triangle (in our case, 12 and 16), is equal to the longest length in a right triangle (c). So,
a²+b²=c²
Substitute 12 and 16 for a and b, our side lengths
12²+16²=c²
144+256=400
400=c²
Square root both c and 400, which gives us...
20=c
So, the value of x is 20.
Round each decimal to the nearest tenth.
A. 1.65
B. 1.83
C. 2.17
D. 2.42
Answers
Step-by-step explanation:
1.7
1.8
2.2
2.4
The other person got no 1 wrong take note
if the sum of two consecutive even number is 22 , find the number
Answers
According to the question,
x+x+2=22
or,2x+2=22
or,2x=22-2
or,2x=20
or,x=20/2
therefore x=10
now x+2 = 10 + 2 = 12
Therefore the numbers are 10 and 12
What is the value of X
Answers
Answer:
x ≈ 23.31
Step-by-step explanation:
We can use the law of cosines because we know 2 sides and 1 angle.
The general formula for the law of cosines if the triangle sides are a, b,c and α is the angle between sides a and b. c is the missing side.
[tex]c = \sqrt{a^{2} +b^{2} -2*a*b* cos \alpha }[/tex]
In our problem the law of cosines is
x = [tex]\sqrt{21^{2} +13^{2} - 2*21*13 *cos 83}[/tex]
x ≈ 23.31
∠A and ∠B are corresponding angles, the measure of \angle ∠A is 110
Answers
Answer:
Step-by-step explanation:
if the measure of <A is 110°
Then the measure of <B is also 110°
help..
Priya bought these items at the grocery store. Find each unit price.
12 eggs for $3. How much is the cost per egg?
3 pounds of peanuts for $7.50. How much is the cost per pound?
4 rolls of toilet paper for $2. How much is the cost per roll?
10 apples for $3.50. How much is the cost per apple?
Answers
Answer:
egg: 4 eggs per dollar
peanuts: 0.4 pounds per dollar
t p: 2 rolls for a dollar
apples: 3 apples per dollar
The seventh and eighth-grade bands held a joint concert. Together, there were 188 band members. If the eighth-grade band is 3 times as big as the seventh-grade band, how big is the eighth-grade?
Let x=7th band and let y=8th band.
a. 47 eighth-grade band students
b. 63 eighth-grade band students
c. 141 eighth-grade band students
Part B:
Write the two equations for this situation.
Answers
Answer:
c. 141 eighth-grade band students
Part B:
y = 3x
1/3y = x
help pls asap
answer:
explain:
Answers
rate of change:
[tex]\sf \bold{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
coordinates taken: (0, 0), (2, 1)
[tex]\rightarrow \dfrac{1-0}{2-0}[/tex]
[tex]\rightarrow \dfrac{1}{2}[/tex]
Take 2 points
(-2,-1)(2,1)[tex]\\ \rm\rightarrowtail m=\dfrac{1+1}{2+2}[/tex]
[tex]\\ \rm\rightarrowtail m=\dfrac{2}{4}[/tex]
[tex]\\ \rm\rightarrowtail m=\dfrac{1}{2}[/tex]
Write an equation to represent the following statement. The product of 7 and j is 91. Solve for j. j
Answers
Answer:
13
Step-by-step explanation:
7j=91
91/7=j
13
hope that helps:)
The two figures shown below are similar. What is the value of x?
12
24
19
30
Answers
Answer: 24
Step-by-step explanation:
Corresponding sides of similar figures are proportional.
3. A hot air balloon travels 18 miles in 3 hours. At this rate, how many miles will the
3
hot air balloon travel in 2 hour?
4
A. 4.5 miles
B. 6 miles
C. 11.5 miles
D. 13.5 m
Answers
Answer:
B: 6 miles
Step-by-step explanation:
You divide 18 by 3 and get 6.
A triangle has angles measureing 40 and 30. What is the measure of the third angle
Answers
Answer: 110 degrees
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees, so the third angle is 180-40-30=110 degrees.
Hyperbolas are confusingggg
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 60); y equals one over two hundred forty times x squared minus 60
(0, 60); y equals one over two hundred forty times x squared plus 60
(0, 15); y equals one over sixty times x square minus 15
(0, 15); y equals one over sixty times x squared plus 15
Answers
Answer:
I think the answer is A but im not sure
what is the area of the triangle in square yards 10 3/4 yards and 7 yards
Answers
A=hbb
2
A clothing store is having a sale where all items are 60% off. What is the sale price of a $260 wool
coat?
Answers
Answer:
$104
Step-by-step explanation:
$260 - 60% = $104