Devon and his friends bought strawberry wafers for $3 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $30 to buy a total of 22 packets of wafers of the two varieties.
Part A: Write a system of equations that can be solved to find the number of packets of strawberry wafers and the number of packets of chocolate wafers that Devon and his friends bought at the carnival. Define the variables used in the equations. (5 points)
Part B: How many packets of chocolate wafers and strawberry wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)
A)
S = Strawberry wafer packets
c = chocolate wafer packets
s +c = 22
3.00s +1.00c = 30.00
B)
s + c = 22
s = 22-c
3.00(22-c) + 1.00c = 30.00
66.00 - 3.00c +1.00c = 30.00
66.00 -2.00c =30.00
-2.00c = -36.00
c = -36.00 / -2.00 = 18
18 packets of chocolate wafers
4 packets of strawberry wafers
ray bought 5 lemons and 3 limes for $7.20. Lia bought 4 lemons and 6 limes for the same price. How much would it cost to buy 1 lemon and 1 lime?
Answer: The cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.
Step-by-step explanation:
Let x be the cost of 1 lemon and y be the cost of 1 lime.
Then for Ray, the equation representing total price will be :-
[tex]5x+3y=7.20[/tex]................................(1)
For Lia, the equation representing total price will be :-
[tex]4x+6y=7.20[/tex]..................................(2)
Dividing 2 on the both sides of equation (2), we get
[tex]2x+3y=3.60[/tex]...............................(3)
Subtracting (3) from (1), we get
[tex]3x=3.6\\\\\Rightarrow x=1.2[/tex]
Substitute value of x in (3), we get
[tex]2(1.2)+3y=3.6\\\\\Rightarrow2.4+3y=3.6\\\\\Rightarrow3y=1.2\\\\\Rightarrow y=0.4[/tex]
Thus, the cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.
Find the slope of the line passing through points q(8, 7) and p(4, 1).
Hi there! :)
Step-by-step explanation:
[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{1-7}{4-8}=\frac{-6}{-4}=\frac{-6/2}{-4/2}=\frac{-3}{-2}=\frac{3}{2}[/tex]
Slope is 3/2.
Final answer is 3/2.
Hope this helps!
Thanks!
Have a nice day! :)
:D
Which of the following illustrates the truth value of the given statements? A square root of 16 is 4, and the only square root of 9 is -3.
T F → F
T T → T
F T → F
F F → F
The intersection of two planes is a point, and two lines intersect in a point.
T T → T
F T → F
T F → F
F F → F
The alphabet has 28 letters, and a week has seven days.
T T → T
T F → F
F F → F
F T → F
a law clerk has earned more than $20000 since being hired (it's a math inequality problem)
The measure of an exterior angle of a regular polygon is 72 degrees. Find the measure of an interior angle.
write an equation in slope intercept form, passes through (-1,-10), parallel to y=7
An equation in slope intercept form, passes through (-1,-10), parallel to y=7 is y = -10 .
What is slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the steepness and the direction of the line.
What is standard form of slope for line and point ?The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
According to the question
An equation in slope intercept form,
passes through (-1,-10), parallel to y = 7
now,
When line is y = 7
that means , x = 0
and it is also a horizontal line , i.e slope (m) = 0
As, Parallel lines have same slope .
By using slope intercept formula for (-1,-10)
y = mx + b
substituting the value
-10 = 0 + b
b = -10
Therefore, putting values in general equation of slope intercept for any point
y = mx + b
y = -10
Hence, an equation in slope intercept form, passes through (-1,-10), parallel to y=7 is y = -10 .
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The difference between the roots of the quadratic equation x2+x+c=0 is 6. Find c.
To solve this question:
First, we compare with the standard quadratic equation to find a, b and c.Then, we apply Bhaskara to find the roots, as function of c.Then, since the difference is 6, we use this to find c.Doing this, we get that: [tex]c = -\frac{35}{4}[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
x²+x+c=0
Comparing with the standard second order equation, which is:
[tex]ax^2 + bx + c = 0[/tex]
We get that:
[tex]a = 1, b = 1[/tex]
Finding the roots:
[tex]\Delta = b^{2} - 4ac = 1^2 - 4(1)(c) = 1 - 4c[/tex]
[tex]x_{1} = \frac{-1 + \sqrt{1 - 4c}}{2}[/tex]
[tex]x_{2} = \frac{-1 - \sqrt{1 - 4c}}{2}[/tex]
Difference of 6
Thus:
[tex]x_1 - x_2 = 6[/tex]
[tex]\frac{-1 + \sqrt{1 - 4c}}{2} - \frac{-1 - \sqrt{1 - 4c}}{2} = 6[/tex]
[tex]-\frac{1}{2} + \frac{\sqrt{1 - 4c}}{2} + \frac{1}{2} + \frac{\sqrt{1 - 4c}}{2} = 6[/tex]
[tex]\frac{2\sqrt{1 - 4c}}{2} = 6[/tex]
[tex]\sqrt{1 - 4c} = 6[/tex]
[tex](\sqrt{1 - 4c})^2 = 6^2[/tex]
[tex]1 - 4c = 36[/tex]
[tex]-4c = 35[/tex]
[tex]4c = -35[/tex]
[tex]c = -\frac{35}{4}[/tex]
Thus, [tex]c = -\frac{35}{4}[/tex] is the value.
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The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 5:18. There are 36 gallons of gasoline. How many ounces of oil are there?
16 ounces
10 ounces
129.6 ounces
2.5 ounces
The amount of oil, in ounces, in the fuel mix can be found using a proportion with the given ratio and the amount of gasoline.
Explanation:To find the number of ounces of oil, we need to use the given ratio and the amount of gasoline. The ratio of oil to gasoline is 5:18, meaning that for every 5 ounces of oil, there are 18 gallons of gasoline. Since we know that there are 36 gallons of gasoline, we can set up a proportion to find the number of ounces of oil:
5 ounces / 18 gallons = x ounces / 36 gallons
Cross multiplying, we get:
18x = 5 * 36
Simplifying further:
18x = 180
Dividing both sides by 18, we get:
x = 10 ounces
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A jar of coins contains dimes, pennies, and quarters. There are 220 pennies in the jar. There are 3 quarters for every 4 pennies, and there is 1 dime for every 3 quarters. How many dimes and quarters are in the jar?
A.55 dimes and 165 quarters
B.98 dimes and 293 quarters
C.73 dimes and 98 quarters
D.165 dimes and 55 quarters
Answer:
A. 55 dimes and 165 quarters
Step-by-step explanation:
Given,
The number of pennies in the Jar = 220,
∵ There are 3 quarters for every 4 pennies,
i.e. 4 pennies = 3 quarters,
⇒ 1 penny = [tex]\frac{3}{4}[/tex] quarter
⇒ 220 pennies = [tex]220\times \frac{3}{4}[/tex]
[tex]=\frac{660}{4}[/tex]
= 165 quarter.
Therefore, there are 165 quarters.
Now, there is 1 dime for every 3 quarters,
i.e. 3 quarters = 1 dime
⇒ 1 quarter = [tex]\frac{1}{3}[/tex] dime,
⇒ 165 quarters = [tex]\frac{165}{3}[/tex] = 55 dimes.
Therefore, there are 55 dimes.
Option 'A' is correct.
A rectangle has a perimeter of 60 inches and length of 22 what is the width of the rectangle
perimeter = 2l +2w
length = 22
perimeter = 60
60 = 2(22) +2w
60 = 44 +2w
subtract 44 from both sides
16 = 2w
w = 16/2
w = 8
width is 8 inches
The length of a rectangle is 2 cm longer than its width. if the perimeter of the rectangle is 36 cm , find its area.
The area of the rectangle is 80 square cm.
Explanation:To find the area of a rectangle, we need to know the length and width. Let's denote the width of the rectangle as 'w'. As given, the length of the rectangle is 2 cm longer than its width, so the length can be represented as 'w + 2'.
The perimeter of a rectangle is the sum of all four sides. In this case, it is given as 36 cm. Using the formula for the perimeter of a rectangle, we can set up the equation:
2(w + w + 2) = 36
Simplifying the equation:
4w + 4 = 36
4w = 32
w = 8
Substituting the value of 'w' back into the expression for length:
Length = 8 + 2 = 10
The area of a rectangle is given by the formula: area = length × width. So, the area of this rectangle is:
Area = 10 × 8 = 80 square cm
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For any distribution, what is the z-score corresponding to the median? 0 1 n cannot be determined from the information given
find sin x if cos x= 2/3 and x is in quadrant 4
I need to know this answer ?
combine all the like terms
4x^3 + 2x^2
then you have -6x-6x which = -12x and -10+4 = -6
so it becomes 4x^3+2x^2-12x-6
Answer is A
Write the slope-intercept form of the equation for the line.
A. y= -3x - 1
B. y= 1/3x - 1
C. y= 3x - 1
D. y= 1/3x + 1
(Picture is shown below)
Distributive property to simplify 39x5
what are the Answer choices
if tan(145) = -1/1.43 , what is tan(-125) A. -1.43, B. 1.43, C. 1/1.43, D. -1/1.43
Answer:
B. 1.43
Step-by-step explanation:
Because tan (180-θ)=-tan θ
[tex]tan (145) = tan (180 -35)= -tan 35 = -\frac{1}{1.43}\\tan 35 =\frac{1}{1.43}[/tex]
Because tan (90+θ) = -cot θ
tan (-125) can be written as:
[tex] tan(-125)=-tan (125) = - tan (90+35) = cot 35[/tex]
tan θ x cot θ =1
⇒tan 35 x cot 35 = 1
⇒[tex]\frac{1}{1.43} \times cot 35 =1 \\ cot 35 = 1.43[/tex]
⇒[tex] tan(-125)= cot 35 = 1.43[/tex]
Which killed the greatest number of American soldiers during the Spanish-American war?
A) yellow fever
B) invasion of Puerto Rico
C) battle of Manila Bay
D) battle of San Juan Hill
How many terms are there in a geometric series if the first term is 7, the common ratio is 2, and the sum of the series is 105?
Hint: (image attached below) r ≠ 1, where a1 is the first term and r is the common ratio.
OPTIONS
A) n = 3
B) n = 4
C) n = 5
D) n = 6
Answer:
the answer would be B. N=4
a basketball court measures 94 feet in length and w feet in width. it's perimeter is 288 feet. which value of w makes the equation 2(94) + 2w = 288 true? A.50ft B. 55 feet C. 65 feet D. 60 feet
Write the number 2174 to the nearest hundred
A turtle walked 1/8 of a mile in 1/2 of an hour. How many miles will he turtle walk in one hour?
What is the equation, in point-slope form, for a line that goes through (2, −6) and has a slope of −3/4 ? y−6=3/4(x−2) y+6=−3/4(x−2) y+6=−3/4(x+2) y−6=−3/4(x+2)
Answer:
option 3 aka c
Step-by-step explanation:
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value. G(x) = 2 sin (x-π) F(x) = 3x^2 + 12x + 16
The minimum of G(x) is -2 and of F(x) is 4 So, G(x) has the smallest minimum y-value.
The function G(x) is a sine function. The sine function, sin(x), has a range of -1 to 1. The minimum value of sin(x) is -1. Since G(x) = 2 sin(x - π), we multiply the minimum value of sin(x) by 2.
The minimum value of sin(x - π) is:
sin(x - π) = -1
Thus, the minimum value of G(x) is:
2 * (-1) = -2
To find the minimum value of a quadratic function, we use the vertex formula, x = -b / 2a. For F(x), a = 3, b = 12, and c = 16.
The x-coordinate of the vertex is:
x = -12 / (2 * 3) = -12 / 6 = -2
Substitute x = -2 into the function to find the minimum y-value:
F(-2) = 3(-2)² + 12(-2) + 16
F(-2) = 3(4) - 24 + 16 = 12 - 24 + 16 = 4
A kitten grows from 5oz at birth to 3lb 5oz at 6 months (find the rate of change)
One positive integer is 6 less than twice another. the sum of their squares is 569. find the integers.
#12 if measure of angle 1 = 19x +1 and measure of angle 5 = 15x +13 then measure of angle 1 =? X=?
In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year? (Round your answer to the nearest cent
What is the 1st term when 3x3 − 7x + 6x4 − 2x2 is arranged in descending order?
3x3
−7x
6x4
−2x2