Chef Malik decided to spend the grant money to package and deliver his meals to reach more community members. Each vegetarian meal now costs $2.25 to make and each meat meal now costs $2.75. Chef Malik wants to serve at least 400 meals and spend no more than $800.
Answers
A solution for the given system of linear inequalities is the shaded area below the solid line.
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the cost of vegetarian meal and cost of meat meal, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the cost of vegetarian meal.Let the variable y represent the cost of meat meal.Since each vegetarian meal cost $2.25 to make while each meat meal cost $2.75 and Chef Malik can spend no more than $800, a linear inequality which represents this situation is given by;
2.25x + 2.75y ≤ 800
Additionally, Chef Malik wants to serve at least 400 meals;
x + y ≥ 400
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities.
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Complete Question:
Chef Malik decided to spend the grant money to package and deliver his meals to reach more community members. Each vegetarian meal now costs $2.25 to make and each meat meal now costs $2.75. Chef Malik wants to serve at least 400 meals and spend no more than $800.
Write and solve the system of inequalities graphically.
Related Questions
Find two other points on the line passing through (1,5) and (3,-1)
Answers
Answer:
We can find two other points on the line passing through (1,5) and (3,-1) by using the slope-intercept form of a line: y = mx + b where m is the slope of the line, and b is the y-intercept.
To find the slope (m) of the line, we can use the formula: m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two given points: m = (-1 - 5) / (3 - 1) = -6 / 2 = -3
To find the y-intercept (b) of the line, we can use one of the given points and substitute the values of x, y and m into the equation y = mx + b.
Plugging in the coordinates of the point (1,5) and the value of m: 5 = -3(1) + b, b = 8
So the equation of the line is y = -3x + 8
We can use this equation and any x value to find two other points on the line. For example, if we choose x = -2, we get y = -3(-2) + 8 = 2
so the point (-2,2) is on the line.
If we choose x = 0, we get y = -3(0) + 8 = 8
so the point (0,8) is on the line.
So two other points on the line passing through (1,5) and (3,-1) are (-2,2) and (0,8)
If I helped you, could you please make my answer best?
Answer:
x + y = 4
m = -1
Step-by-step explanation:
(3 - 5) / (1 - (-1))
m = -2/2
(y - 5) = -1 × (x - (-1))
y - 5 = - x - 1 = 0
The length of Ms. Sheahan's office is
3x yards and the width is x + 4 yards.
Write a polynomial that represents the
area. Find the area if x = 1 yd.
Answers
Answer:
see explanation
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × width
= 3x(x + 4) ← distribute parenthesis by 3x
A = 3x² + 12x
when x = 1 , then
A = 3(1)² + 12(1) = 3 + 12 = 15 yd²
an online company sells and ships T-shirts. The company has to pay extra to ship a package that weighs over 13 oz. Before putting any T-shirts in the box, the package weighs 1.5 oz. Each shirt weighs 5 oz. Which number line best represents the possible number of shirts the company can ship in a package without playing extra for shipping?
Answers
The number line inequality that best represents the possible number of shirts the company can ship in a package without playing extra for shipping is given by the image presented at the end of the answer.
How to solve the inequality?Before putting any T-shirts in the box, the package weighs 1.5 oz. Each shirt weighs 5 oz, hence the total weight function for x shirts is given as follows:
y = 1.5 + 5x.
The maximum weight without needing to pay extra is of 13 ounces, hence the inequality is given as follows:
5x + 1.5 <= 13
x <= 11.5/5
x <= 2.3.
Which can be simplified as:
x <= 2.
(as the number of shirts is a countable amount).
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The solution to an inequality is graphed on the number
line.
-5-4-3 -2 -1 0 1 2 3 4 5
What is another way to represent this solution set?
Oxx<4.5}
O {x|x≤4.5}
Oxx>4.5)
Ox|x24.5}
Answers
The term "solution set" refers to the collection of all possible solutions to an equation thus {x|x≤4.5} holds it . The value is a solution because the equation holds true if both sides are equal.
Option B is correct.
What is set?The distinct items that make up a set are referred to as the set's members or elements. Set notation is a method for representing a set using a combination of symbols and numbers, and it can be used to define sets. "x | -5 x 4.5" is another way to show the solution set of the inequality -5 x 4.5 on a number line. Interval notation is the method by which all real numbers between two given values can be represented. The solution set can be read as "x such that -5 is less than x and x is less than or equal to 4.5" because "|" denotes "such that" and the vertical line denotes "and."
Why is the set of solutions infinite?When the lines coincide and have the same y-intercept, the number of solutions to an equation system is infinite. If the slope and y-intercept of the two lines are the same, they are in fact on the same exact line.
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A small town has two local high schools. High School A currently has 800 students
and is projected to grow by 35 students each year. High School B currently has 550
students and is projected to grow by 85 students each year. Let A represent the
number of students in High School A in t years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine the interval of years, t, for which High School A will have more
students than High School B.
Answers
Answer:
T < 5
Step-by-step explanation:
High School A: A(t) = 800 + 35t
High School B: B(t) = 550 + 85t
To find the interval of years in which High School A will have more students than High School B, we need to find the years in which A(t) > B(t).
So, we need to solve the inequality A(t) > B(t)
800 + 35t > 550 + 85t
250 > 50t
t < 5
Therefore, High School A will have more students than High School B for the first five years.
The interval of years, t, for which High School A will have more students than High School B is t < 5
(-xy)^2 * (2x^9y^5)^4
please show me the steps on how to get the answer
Answers
Answer: 16x^38y^22
Step-by-step explanation:
Re-order terms so constants are on the left
(−xy)2(2x9y5)4(−)2(295)4
Distribute exponent
(−xy)2(2x9y5)4(−)2(295)4
Evaluate the exponent
(−1)2(xy)2⋅(2x9y5)4(−1)2()2⋅(295)4
E is the encoding matrix.
Use E to decode the coded message matrix.
Answers
Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.
What is an encoding matrix?It should be noted that a type of code, that is extremely difficult to break, and one which makes use of a large matrix to encode a message is the encoding matrix.
Here, the receiver of the message decodes it by using the inverse of the matrix. In their case, the first matrix is the encoding matrix and the inverse is the decoding matrix.
To decode the message, we simony have to take the string of coded numbers and then multiply it by the inverse of the matrix in order to get the original string of numbers.
Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.
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Paul won a race with a time of 71. 3 seconds.
This time, t, is to the nearest tenth of a second.
Complete the error interval due to rounding.
____________________ ≤ t < ____________________
Answers
The error interval due to rounding:
71.25 ≤ t < 71.35
Now, According to the question:
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
"Information available from the question"
Paul won a race with a time of 71. 3 seconds.
The time, t, is to the nearest tenth of a second.
So, Rounding off to nearest tenth
Rounded to the nearest 0.1 or the Tenths Place will be
The error interval due to rounding:
So, 71.25 ≤ t < 71.35
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Brown's Tree Farm Company is going to plant pine trees and birch trees this planting season. On Farm A, the land type allows for them to plant 25 pine trees per acre and 75 birch trees per acre. On Farm B, the land type allows for them to plant 50 pine trees per acre and 75 birch trees per acre. There are a total of 200 pine trees and 450 birch trees available for planting.
1. Write and solve a system of equations to determine how many of each tree the company will plant on each farm.
Answers
Let x be the number of acres of Farm A planted with pine trees and birch trees, and let y be the number of acres of Farm B planted with pine trees and birch trees.
The system of equations would be as follows:
25x + 50y = 200 (the total number of pine trees planted)
75x + 75y = 450 (the total number of birch trees planted)
To solve this system of equations, we can use the method of substitution. Solving the first equation for x in terms of y:
x = (200 - 50y) / 25
We can substitute this expression for x into the second equation:
75((200 - 50y) / 25) + 75y = 450
Simplifying and solving for y:
(200 - 50y) + 75y = 450
25y = 250
y = 10
So 10 acres of Farm B are planted with pine and birch trees. To find the number of acres of Farm A that are planted with pine and birch trees, we can substitute this value of y back into the first equation:
25x + 50(10) = 200
25x = 50
x = 2
So 2 acres of Farm A are planted with pine and birch trees.
Therefore, the company will plant 25x = 50 pine trees and 75x = 225 birch trees on Farm A, and 50y = 500 pine trees and 75y = 750 birch trees on Farm B.
a cat's heart beats approximately 45 times and 15 seconds. at this rate how many times does the cat's heartbeat per second?
help.
Answers
Answer:
Step-by-step explanation:
For the cat's heart to beat 45 times in 15 seconds
for 1 second, we must divide 45 by 15
the answer will be 3 beats per second
Use Similar Polygons to Find x
Answers
Answer:
x = 8--------------------------
We know that corresponding sides of similar figures are proportional.
Thus we have equal ratios:
7x/9x = (8x - 1)/(10x + 1)Solve it for x:
7x/9x = (8x - 1)/(10x + 1) Cancel x on the left side as x ≠ 07/9 = (8x - 1)/(10x + 1) Cross- multiply7(10x + 1) = 9(8x - 1) Distribute70x + 7 = 72x - 9 Collect like terms72x - 70x = 7 + 9 Simplify2x = 16 Divide by 2x = 8 Answera basket holds at most 14 pounds of apple and oranges. there are atleast 3 pounds of apples in the basket
Answers
The point (4, 3) is a viable solution.
What are systems of inequalities?At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.
Given:
A basket holds at most 14 pounds of apples and oranges.
There are at least 3 pounds of apples in the basket.
This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges.
That means, we have the system of inequalities,
x + y ≤ 14,
x ≥ 3
Option B and C are discarded.
And y ≥ 0.
Option A is also discarded.
Substituting (4, 3),
x + y ≤ 14,
7 ≤ 14.
Therefore, (4, 3) is a solution.
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The complete question:
A basket holds at most 14 pounds of apples and oranges. There are at least 3 pounds of apples in the basket. This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges. Which point represents a viable solution?
The line passes through the points (3,5) and (6,11).
Algebraic rule (slope-intercept form or point-slope
form):
Answers
When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).
When should you use point-slope form?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.
One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.
The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.
The equation of a line can be represented in either slope-intercept form or point-slope form.
Slope-intercept form:
The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.
Point-slope form:
The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.
Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.
So, the equation of the line in slope-intercept form is:
y = 2x + b
We can use the point (3,5) to find the y-intercept:
5 = 2 * 3 + b
Solving for b, we get b = -1.
So the equation of the line in slope-intercept form is:
y = 2x - 1
In point-slope form, using the point (3,5), the equation of the line is:
y - 5 = 2(x - 3)
Both forms represent the same line, just in different ways.
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you go out to eat with your family. the subtotal on your bill is $45.50 you must pay a 8% sales tax. what is your bill INCLUDING sales tax? please help
Answers
45.50+ (0.08x45.50) = 49.14
$49.14 total
For the translation below, give the vertices of ABC
Answers
Answer:
see explanation
Step-by-step explanation:
A translation of [tex]T_{(5,2)}[/tex] means
add 5 to the original x- coordinate and add 2 to the original y- coordinate.
A (1, - 2 ) → A' (1 + 5, - 2 + 2 ) → A' (6, 0 )
B (- 3, - 3 ) → B' (- 3 + 5, - 3 + 2 ) → B' (2, - 1 )
C (3, 5 ) → C' (3 + 5, 5 + 2 ) → C' (8, 7 )
Substitute each variable to determine whether the inequality statement is true or false j/6 >3 if j =24
Answers
The inequality statement j/6 > 3 is true when j = 24.
How to Determine if an Inequality Statement is True?To substitute the value of j into the inequality statement, you will replace j with 24 and then simplify the expression.
j / 6 > 3
24 / 6 > 3
Simplifying, we get
4 > 3
Since 4 is greater than 3, the inequality statement is true.
You can also check by multiplying both sides of inequality by 6
j > 18
24 > 18
This is true because 24 is greater than 18. Therefore, the inequality statement j/6 >3 if j =24 is true.
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Question
True or False... (8, -7) is a solution to the inequality y<12x−9
Answers
The statement is true, the point (8, 7) is a solution to the inequality.
Is the statement true or false?Here we have the following statement:
"(8, -7) is a solution to the inequality y < 12x − 9"
To check if that is true, we just need to replace the values of the point on the inequality and check if the ienquaity becomes true.
We will get:
-7 < 12*8 - 9
-7 < 87
This is true, 87 is a number larger than -7, then the statement is true, (8, -7) is a solution of the inequality.
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Trey is having a party. He'll have 2 tables for every 10 guests.
Complete the table below showing the number of tables and the number of guests.
number of guests: (10) (15) (25) _ (50)
number of tables: (2)( _) (_) (7) (_)
Answers
The number of tables for 15 guests will be 3 tables.
The number of tables for 25 guests will be 5 guests
The number of tables for 50 guests will be 10.
How to calculate the number of tables and guest?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
In this case, Trey is having a party. He'll have 2 tables for every 10 guests. This means that 1 table will be for 10/2 = 5 guest
The number of tables for 15 guests will be:
= 15 / 5.
= 3 tables.
The number of tables for 25 guests will be:
= 25 / 5
= 5 guests
The number of tables for 50 guests will be:
= 50 / 5
= 10
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The statement, 81:135 = 36:60 is a proportion.
If a and b are non-zero numbers and c = 0, then a/c = b/c is a proportion.
State whether the following statements are proportions or not. If it is a proportion, then prove by the definition of proportion. If not, then solve the correct value of x. Be sure to show the complete steps in solving for x.
Answers
a) The value of x from the proportion is x = 2/5
b) The value of x from the proportion is x = 8
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
a)
3 / ( x + 2 ) = ( 5 / 4 ) be equation (1)
On simplifying the equation , we get
Multiply by ( x + 4 ) on both sides of the equation , we get
( 5/4 ) ( x + 2 ) = 3
Multiply by 4 on both sides of the equation , we get
5 ( x + 2 ) = 12
On further simplification , we get
5x + 10 = 12
Subtracting 10 on both sides of the equation , we get
5x = 2
Divide by 5 on both sides of the equation , we get
x = 2/5
Therefore , the value of x is 2/5
b)
( x + 2 ) / 5 = ( x - 2 ) / 3 be equation (2)
On simplifying the equation , we get
Multiply by 5 on both sides of the equation , we get
( x + 2 ) = 5( x - 2 ) / 3
Multiply by 3 on both sides of the equation , we get
3 ( x + 2 ) = 5 ( x - 2 )
On further simplification , we get
3x + 6 = 5x - 10
Subtracting 3x on both sides of the equation , we get
2x - 10 = 6
Adding 10 on both sides of the equation , we get
2x = 16
Divide by 2 on both sides of the equation , we get
x = 8
Therefore , the value of x is 8
Hence , the proportion is solved
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Javier is ordering a sandwich from a deli. There are 3 types of meat to choose from and 4 cheeses, and Javier must pick one of each. How many different sandwiches can Javier order?
Answers
The number of different sandwiches that Javier can order, given the number of types of meat and cheeses, is 12 sandwiches.
How to find the number of sandwiches ?Javier has 3 choices for the type of meat and 4 choices for the cheese, so the total number of different sandwiches he can order is the product of the number of choices for each ingredient.
To find the total number of different sandwiches, you can multiply the number of meat choices by 4 the number of cheese choices.
The number of sandwiches Javier can order are:
= 3 x 4
= 12 sandwiches
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Can someone help me find the missing angle measurements?
Answers
Subtract the given angle from 180° and the missing angle measurements is 42°.
What is meant by angle ?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.A+B+C=180°
57°+81°+C°=180°
138°+C=180°
C=138°-180°
C=42°.
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answers
[tex] \pmb{ \underline{\color{green} \huge{Αηςωεr : ∼}}}[/tex]
[tex] \large \frak{ \red{x } - 4 = 8}[/tex]
[tex] \: [/tex]
[tex] \large \frak{ \red{x } = 8 + 4}[/tex]
[tex] \: [/tex]
[tex] \underline{ \boxed{ \large \frak{ \red{x } = \green{12}}}}[/tex]
[tex] \: [/tex]
hope it helps!
Please help I need the answers ASAP.
Answers
Answer:
Refer to the step-by-step
Step-by-step explanation:
∠1 and ∠2 lie in the alternate interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal angles.
the difference between the squares of two positive integers is 2009. what is the maximum possible difference between these two integers?
Answers
Answer:
Step-by-step explanation:
i dont knpw
Formative REDO
1. Find the slope and y-intercept from the equation: y = -2x + 7
b=_
m=
2. Find the slope and y-intercept from the graph:
b=
m=
Answers
The equation in the problem is in slope intercept form. The slope-intercept form of a linear equation is: y = mx + b
What is meant by slope?
Slope is a numerical representation of how inclined a line is with respect to the horizontal. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment.A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.The foundation of differential calculus is the idea of a slope. The rate of change for non-linear functions varies along the curve.Both the slope and the y intercept can have a positive or negative value. Slope is defined as the y-axis divided by the x-axis.The slope-intercept form of a linear equation is: y = mx + b
Where m is the slope and b is the y-intercept value.
Therefore, for this equation y = -2x - 7
The Slope is: m = -2
The Y=Intercept is b = -7 (or)
slope and y-intercept from the graph: (0, -7)
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a square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. what is the smallest possible value of the length of the side of the original square?
Answers
Answer: I need help with this what is the answer
Step-by-step explanation:
Cody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days?
Answers
The correct explaination to calculate the total number of miles that Cody hiked in two days is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.
First of all, we must know the formula of average speed. The formula is as follows -
Average speed = distance ÷ time
Using this formula, we can calculate distance for Saturday and Sunday and subsequently add the distance to find the number of miles that Cody hiked in two days.
For Saturday -
Distance = 1 × 5
Performing multiplication
Distance = 5 miles
For Sunday -
Distance = 3 × 2
Performing multiplication
Distance = 6 miles
Total distance hiked = 5 + 6
Performing addition
Total distance hiked = 11 miles
Thus, the correct explaination is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.
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The complete question is -
Cody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days? Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Subtract the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products. Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Add the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Subtract the two products.
I need help in this problem
Answers
Answer:
b. 20°
Step-by-step explanation:
Find the missing angle in the top triangle:
180 - 40 - 20 = 120
because, the sum of interior angles of a triangle is 180.
The top angle of the bottom triangle = 120 because it is a vertical angle to the one you just found.
Now find the missing angle (x) on the bottom:
x = 180 - 120 - 40 = 20
4X+3 2x+9 linear pairs of angles
Answers
Answer:
x = 28°
Step-by-step explanation:
4x+3 and 2x+9 are on a straight line, so the sum is 180°, we solve with an equation
4x + 3 + 2x + 9 = 180°
6x + 12 = 180
6x = 180 - 12
6x = 168
x = 168 : 6
x = 28°
-------------------------------
check4 × 28 + 3 + 2 × 28 + 9 = 180 (remember PEMDAS)
112 + 3 + 56 + 9 = 180
180 = 180
Learning Task 1: Solve for n. Write your answer in your notebook.
1. 7. 26 x 0. 22 =n
2. 17. 92 x 0. 64 = n
3. 7. 65 x 0. 85 =n
4. 36. 20 x 0. 05 = n
5. 31. 85 x 0. 91 = n
Answers
The solutions of each expression for n are given as follows:
1. n = 1.5972.
2. n = 11.4688.
3. n = 6.5025.
4. n = 1.81.
5. n = 28.9835.
How to solve the expressions?
All the five expressions in this problem are multiplication operations involving two decimal numbers.
Hence, to obtain the solution for n of each expression, we must simply apply the multiplication operation of the two decimals, using a calculator.
The result of each expression is given at the beginning of the answer.
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