Answer:
(a) To determine the linear function that predicts the number of calculators sold at a given price, we need to find the equation of the line that passes through the points (98, 11,000) and (93, 13,150).First, we can find the slope of the line using the formula:slope = (change in y) / (change in x)slope = (13,150 - 11,000) / (93 - 98)slope = -430 per 1 dollar decrease in price(Note that we can interpret the negative slope as an inverse relationship between price and quantity demanded. As price decreases, the quantity demanded increases.)Next, we can use the point-slope form of a line to find the equation of the line:y - y1 = m(x - x1)where y1 = 11,000, x1 = 98, and m = -430.y - 11,000 = -430(x - 98)Simplifying and solving for y, we get:y = -430x + 51,340Therefore, the linear function that predicts the number of calculators sold at a given price is:y = -430x + 51,340(b) To predict the number of calculators that would be sold each week at a price of $73, we can substitute x = 73 into the linear function we found in part (a):y = -430(73) + 51,340y = 18,140Therefore, we predict that 18,140 calculators would be sold each week at a price of $73.
What is the area if the triangle.. 3" by 5" and base is 4"
Answer:
A = 6"^2
Step-by-step explanation:
the measurements are a Pythagorean triple, therefore it is a right triangle, where 3 and 4 are the legs and 5 is the hypotenuse, we use the formula 1/2 × b × h
A = 1/2 × b × h.
A = 1.5 × 4
A = 6"^2
Write each expression as a product.
(a+1)^3+x^3
We can write this expression as a product of two factors:
(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)
HOW TO WRITE expression as a product.?
To write an expression as a product means to represent the expression as the multiplication of two or more factors. The process of writing an expression as a product depends on the type of expression and the algebraic techniques that are available.
Here are some general steps that can be followed to write an expression as a product:
Look for common factors: If there are common factors in the expression, they can be factored out using the distributive property. For example, in the expression 3x + 6, we can factor out 3 to get 3(x + 2).
Use algebraic identities: There are many algebraic identities that can be used to factor expressions. For example, the difference of squares identity (a² - b²= (a + b)(a - b)) can be used to factor expressions that are in the form of a difference of squares.
Look for patterns: Sometimes, expressions can be factored by recognizing patterns. For example, the expression x² + 2x + 1 can be factored as (x + 1)²by recognizing that it is a perfect square trinomial.
Use polynomial division: If the expression is a polynomial with higher degree, polynomial division can be used to factor it into linear and quadratic factors.
Use the quadratic formula: If the expression is a quadratic trinomial that cannot be factored easily, the quadratic formula can be used to find the roots of the equation, which can then be used to write the expression as a product of linear factors.
Overall, writing an expression as a product requires a good understanding of algebraic techniques and a lot of practice.
We can use the formula for the sum of cubes to write the expression as a product:
(a + 1) + x³ = (a + 1 + x)(a² - a x + x²) + x³
Expanding the first factor on the right-hand side using the distributive property, we get:
(a + 1 + x)(a²- a x + x²) + x^3 = a³- a² x + a x² + a² + a x + x²+ x³
Collecting like terms, we can write this expression as a product of two factors:
(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)
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Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochet at a rate of 1/15 of a blanket per day. She has 60 days until she wants to donate the blankets, but she also wants to skip crocheting some day so she can volunteer in other ways. Write and solve an inequality for how many days she can skip and still finish the blankets.
If Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie can skip up to 15 days and still finish crocheting at least 3 blankets before she wants to donate them to the homeless shelter.
How many days she can skip and still finish the blankets?Let's first calculate how much of a blanket Darcie can crochet in 60 days if she works every day:
1/15 blanket per day * 60 days = 4 blankets
Since Darcie wants to crochet a minimum of 3 blankets, we know that she needs to work for at least 3/4 of 60 days. Let x be the number of days Darcie can skip and still finish the blankets:
(60 - x) * 1/15 >= 3
Simplifying this inequality, we get:
4 - 1/15x >= 3
1/15x <= 1
x <= 15
Therefore, Darcie can skip up to 15 days and still finish crocheting at least 3 blankets before she wants to donate them to the homeless shelter.
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6
Determine if the triangles are congruent and if so,
why. (1 Point)
Congruent by SAS
Congruent by SSS
Congruent by HL
Not Congruent
C
B
A
U
A
W
The triangle congruency postulate that proves both triangles are congruent is: SSS
How to identify the congruency postulate?There are different triangle congruence postulates such as:
SSS: This denotes Side Side Side Congruency Postulate
SAS: Side angle Side Congruency Postulate
ASA: Angle Side Angle Congruency Postulate
AAS: Angle Angle Side Congruency Postulate
HL: Hypotenuse Leg Congruency Postulate
Now, from the given two triangles, we can see the following:
BC ≅ UW
AC ≅ UV
AB ≅ VW
Thus, the three sides are congruent and as such it is congruent by SSS congruency postulate
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What does factoring mean?
pls help me i need this by TODAY and whomever gives the most explanation will get brain points.
Answer: variables
Step-by-step explanation:
mathmeticians made this to where it would leave things out of questions, so factoring would just be your variables my guy
Five number summary
of 72,60,64,75,79,63,70,61,78
The five number summary is: Minimum: 60 Q1 (first quartile): 63 ,Median: 70Q3 (third quartile): 75, Maximum: 79
To find the five number summary of the data set 72, 60, 64, 75, 79, 63, 70, 61, 78, follow these steps:
1. Arrange the data in ascending order: 60, 61, 63, 64, 70, 72, 75, 78, 79
2. Identify the minimum value (smallest number): 60
3. Identify the maximum value (largest number): 79
4. Calculate the median (middle number): There are 9 data points, so the median is the 5th number: 70
5. Calculate the first quartile (Q1): The lower half of the data set is 60, 61, 63, 64, 70. The median of this lower half is the
middle number, which is 63.
6. Calculate the third quartile (Q3): The upper half of the data set is 70, 72, 75, 78, 79. The median of this upper half is
the middle number, which is 75.
The five number summary is:
Minimum: 60
Q1 (first quartile): 63
Median: 70
Q3 (third quartile): 75
Maximum: 79
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Which graph represents the solution to this inequality?
-1/4 (12x+8) ≤ -2x+11
A. a straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passes through minus 5
B.
A straight line passing from minus 17 to minus 5. A ray with a red line starts at point minus 13 and passes through minus 17
C.
A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5
D.
A straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passes through minus 17
A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.
This graph represents the solution to this inequality.
What is inequality?
An inequality in mathematics is a relation that compares two integers or other mathematical statements in an unequal way. The majority of the time, height comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
Given inequality:
(-1/4)*(12x + 8) < -2x + 11
First, we need to solve it for knowing the value of x,
So,
(-1/4)*(12x + 8) < -2x + 11
Or, -3x - 2 < -2x + 11
Or, -2 - 11 < -2x + 3x
Or, -13 < x
A ray with a red dot at minus 13, and it passes through minus 5.
Hence the correct answer is C; a straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.
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When examining the plots, only one displays a straight line going from -17 to -5 and a ray going from -13 to -5. (indicating that x can be any value greater than or equal to -13) Thus, option C is correct.
What is the inequality?To solve the inequality, we can simplify it by first distributing the -1/4 on the left side:
[tex]-3x - 2 ≤ -2x + 11[/tex]
Next, we can isolate the variable on one side by subtracting -2x from both sides:
[tex]-x - 2 ≤ 11[/tex]
Finally, we can isolate the variable by adding 2 to both sides:
[tex]-x ≤ 13[/tex]
And since we want to solve for x, we need to multiply both sides by -1, which will flip the direction of the inequality:
[tex]x ≥ -13[/tex]
This means that x can be any value greater than or equal to [tex]-13[/tex] .
Therefore, Looking at the graphs, the only one that shows a straight line passing from -17 to -5 and a ray starting at -13 and passing through -5 (indicating that x can be any value greater than or equal to -13)
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A plumber charges $50 to make a house call. He also charges $25.00 per hour for labor. What is the slope in this
situation?
[tex]\text{t = total}[/tex]
[tex]\text{equation:} \ t = 25x + 50[/tex]
[tex]m=25[/tex]
[tex]\text{The slope is} \ \bold{25}[/tex]
The area of a rectangle is represented by x^2 + 7x - 18. Factor to find binomial expressions representing the length and width. What is the difference between the length and width?
Answer:
x^2 + 7x - 18 = (x + 9)(x - 2)
The difference between length and width is x + 9 - (x - 2) = x + 9 - x + 2 = 11.
I HAVE 5 MINS Select the expression that makes the equation true.
5.5 x (4 ÷ 2) + 3.8 = ___
3.2 x (8 ÷ 4) + 10
4.6 + (6 ÷ 2) x 2
6.4 + (10 − 3) + 4
7.8 x (12 ÷ 6) − 0.8
Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.
What is the Pythagorean theorem?
The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.
Now,
In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.
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Hep me please I absolutely need help in math
Step-by-step explanation:
Step 1 :
Break down the fraction with the H.C.F of the numerator and the denominator.
For instance, in Question 5 , the HCF of 20 and 8 is 4. So, 4 will go into 20 five(5) times and 4 will go into 8 two(2) times, leaving 5/2.
Step 2 :
Then 2 (denominator) will go into 5(numerator) two(2) times.
So, you'll get 2 as the whole number .
Step 3:
Multiply the denominator by the whole number (2×2) to get 4.
Then subtract 4 from 5 to get 1 and to form a proper fraction by making 1 the numerator and the 2 the denominator to get 1/ 2
Step 4 :
Then put the 2( whole number) and the 1/2 ( proper fraction) together to get the mixed fraction
what is 7 times 3 plus 10
Answer:
31
Use Bodmas to solve it
7*3 + 10
21 +10
31
31
You can use BODMAS by arranging it multiplication comes first so 7 times 3 which is 21 so agter that addition comes next so that will be 21 plus 10 which gives 31
Find the 8th term of the following sequence. Round to the nearest thousandth if necessary.
216, 36, 6
Answer: is it an A.P or G.P
from a point 100m from a building the angles of elevation to the top and the bottom of a flagpole atop the building are 54.5 degrees and 51.8 degrees. how tall is the flagpole?
From a point 100m from a building the angles of elevation to the top and the bottom of a flagpole atop the building are 54.5 degrees and 51.8 degrees. Therefore, the height of the flagpole is 125.6m.
we can use the trigonometric ratios of Sine, Cosine, and Tangent.
First, we need to draw a right triangle with the given information.
The triangle will have two sides:
the 100m side and the side to the flagpole. We can use the angle of elevation of 54.5 degrees to calculate the side of the triangle opposite the flagpole.
To do this, we use the Tangent ratio and solve for the side opposite the flagpole (the height of the flagpole):
Tangent(54.5) = Height/100
Height = 100*Tangent(54.5)
Height = 100*1.256
Height = 125.6m
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6. Keela was making a flag of Ireland for St. Patrick's Day. She knew that the flag was exactly twice
as long as it was tall and that there were three equally sized vertical bars in green, white and orange
(from left to right). She used 9" x 12" construction paper to make her flag. The width of the green
bar was exactly two short sides of the construction paper across minus a overlap. What were the
dimensions of the final flag and how many pieces of construction paper did it take?
hat only had
The dimensions of the final flag and the number of pieces of construction paper it took would be 9 inches tall and 18 inches long.
Three (3) pieces of 9" x 12" construction paper are needed.
How to find the dimensions of the flagFirst, let's find out the dimensions of the flag. The flag is twice as long as it is tall. If the height of the flag is H, then the length L would be 2H.
Since there are three equally sized vertical bars, the length of the flag would be 3 times the width of the green bar:
L = 3(18 - a)
Now, we know that L = 2H. So,
2H = 3(18 - a)
Given that the construction paper is 9" x 12", we can try to create the flag with the minimum amount of overlap a. Since the height of the flag should be equal to the short side of the construction paper, H = 9 inches.
Now we can plug in the value of H in the equation we derived above:
2(9) = 3(18 - a)
18 = 54 - 3a
3a = 36
a = 12
Now we can calculate the dimensions of the final flag:
H = 9 inches
L = 2H = 2(9) = 18 inches
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what is 16 to 1 decimal place
Answer:
What is 16.00 to 1 decimal place?" is the same as asking, "What is 16.00 rounded to one decimal point?" or "How to round 16.00 to one decimal place."
The main point (pun intended), is that you want to round 16.00 to one digit or place after the decimal point. Thus, we want to eliminate the last digit in 16.00. To eliminate the last digit, we use the following One Decimal Place rules to get the answer:
One Decimal Place Rule #1: If the last digit in 16.00 is less than 5, then remove the last digit.
One Decimal Place Rule #2: If the last digit in 16.00 is 5 or more and the second to the last digit in 16.00 is less than 9, then remove the last digit and add 1 to the second to the last digit.
One Decimal Place Rule #3: If the last digit in 16.00 is 5 or more and the second to the last digit in 16.00 is 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the left of the decimal place.
When rounding 16.00 to one decimal place we use One Decimal Place Rule #1. Therefore, the answer to "What is 16.00 rounded to 1 decimal place?" is:
The area of the wheel of a car is 1.54m^2, what is the circumference of the wheel?
Answer:
4.4 m
Step-by-step explanation:
Area of the wheel of a car= 1.54 m²
Area of a circle= [tex]\pi r^{2}[/tex]
1.54= 3.14 x r²
r²= [tex]\frac{1.54}{3.14}[/tex]
r²= 0.49
r= 0.7 m
Circumference of the wheel= [tex]2\pi r[/tex]
= 2 x 3.14 x 0.7
= 4.4 m
∴ the circumference of the wheel is 4.4 m
Broonzy is on her schools battle of the books team. She still has 40 pages to read in her final book before the competition if she reads five times number of pages tonight as she read last night and then the last 10 pages tomorrow night she will be finished with her book right and solve an equation to determine how many pages Brinsey has to read tonight
Answer: 25
Step-by-step explanation:
Let x represent the number of pages Broonzy read last night. Then, 5x represents the number of pages she will read tonight. According to her plan, after reading 5x pages tonight and 10 pages tomorrow night, she will complete the remaining 40 pages. The equation can be expressed as:
x (last night) + 5x (tonight) + 10 (tomorrow night) = 40 (total remaining pages)
Combining the terms, we get:
6x + 10 = 40
Now, let's solve for x:
6x = 30
x = 5
So, Broonzy read 5 pages last night. To determine the number of pages she needs to read tonight, we multiply x by 5:
5x = 5 * 5 = 25
Therefore, Broonzy has to read 25 pages tonight to finish her book according to her plan.
The temperature, T (in degrees Kelvin), of an enclosed gas varies
jointly with the product of the volume, V (in cubic centimeters), and
the pressure, P (in kilograms per square centimeter). The temperature
of a gas is 294 degrees K when the volume is 8000 cubic centimeters and the
pressure is 0.75 kilogram per square centimeter. What is the
temperature when the volume is 7000 cubic centimeters and the
pressure is 0.87 kilogram per square centimeter?
Answer: 298.41 K
Step-by-step explanation:
given from the problem: T=VPC
where C is a constant
plug in knowns to get C
294= (8000)(0.75)C
C=0.049
T=VP(0.049)
T = (7000)(0.87)(0.049)
T = 298.41 K
Determine which expressions can be simplified further.
Answer:
[tex]{ \colorbox{lightgreen}{can \: be \: simplified}} \\ \dashrightarrow \: { \sf{ \blue{9x + 6x}}} \: \: \: \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \: \: \: \\ { \sf{ = (9 + 6)x}} \\ { \underline{ \sf{ \: = 15x \: \: \: \: \: \: \: \: \: \: }}} \\ \\ \dashrightarrow \: { \sf{ \blue{4x + x}}} \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (4 + 1)x}} \\ { \underline{ \sf{ \: = 5x \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \\\dashrightarrow \: { \sf{ \blue{y + 2y}}} \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (1 + 2)y}} \\ { \underline{ \sf{ \: = 3y \: \: \: \: \: \: \: \: \: \: \: \: }}}[/tex]
[tex]{ \colorbox{lightgreen}{cannot \: be \: simplified}} \\ \dashrightarrow \: { \sf{2x + 3y}} \\ \dashrightarrow \: { \sf{7y + 1 \: \: }} \\ \dashrightarrow \: { \sf{4y + 4x}}[/tex]
Type the missing number in this sequence -3, -6, -12, , -48
Answer:
-24
Step-by-step explanation:
Hey there!
First we need to find the ratio
ratio = -6/-3 = 2
r = 2
-3, -6, -12, ? , -48
T1 = a
T2 = ar
T3 = ar²
T4 = ar³
T5 = ar⁴
And so on...
T1 means first term, T2 means second term
We're finding the fourth term which is T4
Remember T1 = a = -3
So, T4 = ar³
= -3 × 2³
= -3× 8
= -24
Therefore, the fourth unknown term is -24
You're welcome y'all
use property of rational numbers to simplify the expression
(23 - 12.3) - (166.4 + 2)
Answer:
-157.7
Step-by-step explanation:
Subtract 12.3 from 23 to get 10.7
10.7 - (166.4 + 2), next add 166.4 and 2 to get 168.4
10.7 - 168.4, finally subtract 168.4 from 10.7 to get -157.7
What polygon is this?
Answer:
Step-by-step explanation:
irregular quadrilateral
Answer:
The name of this shape is (Irregular Pentagon)
Really need help with this test is tomorrow
1 centimeter on the scale drawing of rectangular park represents 15 feet of the actual parking lot.
What is rectangle?
A rectangle is a four-sided flat shape with four right angles. It is a type of quadrilateral. Rectangles have opposite sides that are parallel and equal in length, and all four interior angles are right angles (90 degrees).
We know that the width of the actual parking lot is 48 feet. We also know that on the scale drawing, the width is represented by 3.2 cm. Therefore, we can set up a proportion to find out how many feet are represented by 1 centimeter on the scale drawing:
[tex]$\frac{48 \text{ feet}}{3.2 \text{ cm}} = \frac{x \text{ feet}}{1 \text{ cm}}$[/tex]
where x is the number of feet represented by 1 centimeter on the scale drawing.
We can solve for x by cross-multiplying:
[tex]$48 \text{ feet} \times 1 \text{ cm} = 3.2 \text{ cm} \times x \text{ feet}$[/tex]
Simplifying, we get:
[tex]$x = \frac{48 \text{ feet} \times 1 \text{ cm}}{3.2 \text{ cm}} = 15 \text{ feet}$[/tex]
Therefore, 1 centimeter on the scale drawing represents 15 feet of the actual parking lot.
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In ma persons class 75% of the students are boys. There are 18 boys in the class . What is the total number of students in Ms persons class
The total number of students in Ms. Persons class is 24.
What is an Equation?An equation is simply a mathematical formula that expresses the equality of two expressions.
Given the data in the question:
75% of the students are boys.number of boys in the class is 18 boys.Total number of students in the class y = ?Lets y be the number of students in the class
Hence:
[tex]75\% \ \text{of y = 18}[/tex]
[tex]\text{Lets find y}[/tex]
[tex](\dfrac{75}{100} ) \times y = 18[/tex]
[tex]75 \times y = 18 \times 100[/tex]
[tex]75 \times y = 1800[/tex]
[tex]y = 1800 \div 75[/tex]
[tex]y = 24[/tex]
Therefore, the total number of students in Ms. Persons class is 24.
Please help me!!!!!!!
The range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.
Describe Function?In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.
A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.
To find the range of the function f(x) = x + 3, we need to apply the function to each value in the given domain and collect the resulting outputs.
When the domain is {-1, 3, 5, 7}, we have:
f(-1) = -1 + 3 = 2
f(3) = 3 + 3 = 6
f(5) = 5 + 3 = 8
f(7) = 7 + 3 = 10
Therefore, the range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.
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Find the equation of a line perpendicular to y= 4/3x−1 that passes through the point (−4,−8)
Answer: y=-3/4x-11
Step-by-step explanation: slope= -3/4
y+8=-3/4x+4
y+8=-3/4x-3
y=-3/4x-11
Explain how to find the cost for 2 pounds of candy and state that cost.
Answer these questions using CER. According to the Claim, Evidence, and Reasoning, an explanation consists of a claim that answers the question. Evidence from students' data. Reasoning that involves a rule or scientific principle that describes why the evidence supports the claim.

After answering the provided question, we can conclude that As a result, equation the cost of 2 pounds of candy is $7.00.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9"[/tex] asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.
Claim: To calculate the cost of 2 pounds of candy, multiply the cost per pound of candy by 2.
According to the data provided, the cost per pound of candy is $3.50.
Reasoning: In order to determine the cost of 2 pounds of candy, we must first determine the total cost of 2 pounds of candy. Because the price per pound of candy is $3.50, we can calculate the total cost by multiplying the price per pound by the number of pounds. In this case, we want to know how much it costs for two pounds, so we multiply $3.50 by two to get:
2 pounds of candy = $3.50 per pound x 2 pounds = $7.00
As a result, the cost of 2 pounds of candy is $7.00.
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helpp!! solve the system of equations using substitution
3x + 2y = 7
x = 3y + 6
1. ( 0, -2 )
2. ( 1, 2 )
3. ( 3, -1 )
4. ( 6, 0 )
Answer:
3. ( 3, -1 )
Step-by-step explanation: