The simplified expression of 3 (-5 + 2x) is -15 + 4x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
3 (-5 + 2x)
The distributive property of multiplication over addition states that,
a x (b + c) = a x b + a x c
Now,
3 x (-5 + 2x)
3 x (-5) + 2 x (2x)
-15 + 4x
Thus,
The simplified expression is -15 + 4x.
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Graph the inequality on a number line:
x [tex]\geq[/tex] 11
The required graph has been attached below which represents the inequality x ≥ 11 on a number line.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question, as follows:
x ≥ 11
In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout.
A number line is typically shown horizontally and can be extended indefinitely in any direction.
Thus, the graph has been attached below which represents the inequality on a number line.
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Understand Only 93% of the airplane parts being examined pass inspection. What is the probability that the next 5 part examinedwill all pass inspection?
Answer:
0.67 or 67%
Step-by-step explanation:
The probability that a single part will pass inspection is 0.93, so the probability that all 5 parts will pass inspection is (0.93)^5 = 0.67 or 67%.
The solution is 0.67 or 67%, is the probability that the next 5 part examined will all pass inspection.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
Understand Only 93% of the airplane parts being examined pass inspection.
now, we have to find that the probability that the next 5 part examined will all pass inspection.
now, we have,
The probability that a single part will pass inspection is 0.93,
so the probability that all 5 parts will pass inspection is :
(0.93)^5
= 0.67
= 67%.
Hence, The solution is 0.67 or 67%, is the probability that the next 5 part examined will all pass inspection.
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How to find mirror image of point with respect to line in 3d?
To find the mirror image of a point with respect to a line in 3D, you can use the projection of the point on the line, multiply it with the normal vector of the line, and then subtract the obtained vector from the position vector of the point twice.
To find the mirror image of a point with respect to a line in 3D, you can use the following method:
Write the equation of the line in the form ax + by + cz + d = 0, where (a,b,c) is a normal vector to the line and d is a constant.Find the projection of the point on the line by taking the dot product of the position vector of the point and the normal vector of the line, and dividing by the square of the length of the normal vector.Multiply the projection obtained in step 2 with the normal vector of the line.Subtract the vector obtained in step 3 from the position vector of the point twice, this will give you the position vector of the mirror image point.Express the obtained coordinates as (x',y',z') which are the coordinates of the mirror image point.To learn more about 3D images at
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What is the coefficient of the term in the expression 5xyz2 3zy?
So on solving the provided question we can say that coefficient of expression 5xyz2 is 5 and 3zy is 3
what is expression ?It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.
Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression Numbers, variables, and functions make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.
here,
coefficient of 5xyz2 is 5
and 3zy is 3
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Felix built a ramp. If the height of Felix' ramp i 6 inche from the ground ,how long i the part of the ramp that i on the ground?
There is not sufficient data provided to answer the question. So it cannot be answered.
To find the length of the part of the ramp that is on the ground, we need to know the angle of the ramp and the height of the ramp. If the height of the ramp is 6 inches, and we know the angle of the ramp, we can use the Pythagorean theorem to find the length of the ramp.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the ramp in this case) is equal to the sum of the squares of the other two sides. If we call the length of the ramp "x", and the height of the ramp "h", we can write the equation as:
x^2 = h^2 + (6 inches)^2
We don't have the angle of the ramp, so we can't use the Pythagorean theorem. Therefore, we can't find the length of the part of the ramp that is on the ground with the information given. To find the length, we would need additional information, such as the angle of the ramp or the length of the ramp.
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The figure below is translated down 4 Units and then reflected over the x-axis.what are the coordinates of the images of point E after these transformations?
The coordinates of the image of point Y following these modifications are thus -2.
How do we find the Cartesian coordinate plane?There are no boundaries to the two dimensions of the Cartesian coordinate plane. Any two-dimensional figure can be drawn on an unending 2D plane. In a Cartesian plane, every point has a specific place.The provided number has been rotated 180 degrees anticlockwise and increased in scale by two units.
After these adjustments, the image of point Y has coordinates that are -2.
The coordinates of the image of point Y following these modifications are thus -2.
The x-axis and y-axis intersect to produce the two-dimensional coordinate plane known as the cartesian plane in mathematics. The origin is the point at where the x- and y-axes cross perpendicularly.The complete question is,
The figure below is translated up 2 units and then rotated 180° counterclockwise. What are the coordinates of the image of point Y after these transformations?
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What’s the factored answer of 27w^5-75w
Answer:
3w(3w²+5)(3w²-5)
A baseball is thrown upward in the air. The height of the baseball f seconds after it is released is approximated by the function.
h=-16t^2+64t+80
a. find the number of seconds that it takes for the baseball to reach the ground?
b. Find the number of seconds that it will take the baseball to be at its maximum height?
c. Find the maximum height of the baseball?
Show work!
The solution to the quadratic equations are
a) The number of seconds for the ball to reach the ground is t = 5 seconds
b) The number of seconds to reach the maximum height T = 2 seconds
c) The maximum height of the ball is h ( 2 ) = 144 feet
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as h ( t )
Now , the equation will be
h ( t ) = -16t² + 64t + 80 be equation (1)
a)
The number of seconds for the baseball to reach the ground be t
The height when the ball reaches the ground will be h = 0
Substituting the value of h ( t ) = 0 , we get
0 = -16t² + 64t + 80
On simplifying the equation , we get
16t² - 64t - 80 = 0
Divide by 16 on both sides of the equation , we get
t² - 4t - 5 = 0
On factorizing the equation , we get
t² + t -5t - 5 = 0
t ( t + 1 ) - 5 ( t + 1 ) = 0
( t - 5 ) ( t + 1 ) = 0
The value of t is time and it is not negative
So , when ( t - 5 ) = 0
Adding 5 on both sides of the equation , we get
t = 5 seconds
b)
The number of seconds the baseball to reach the maximum height be T
And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola
T = ( -b / 2a )
On simplifying the equation , we get
T = ( -64 / ( 2 ( 16 )
T = -64 / 32
T = 2 seconds
c)
The maximum height of the baseball is when T = 2
Substituting the value of t = 2 in the equation , we get
h ( t ) = -16t² + 64t + 80
h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80
On simplifying the equation , we get
h ( 2 ) = -64 + 128 + 80
h ( 2 ) = 64 + 80
h ( 2 ) = 144 feet
Hence , the equation is solved
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Express each question as a single power. Then state the Exponent law used.
A) 2^4 x 2^7
Exponent Law(s)
B) (-3)^9 divided (-3)^5
Exponent Law(s)
C) (5^2)^-3 x 5^0
Exponent Law(s)
Please answer this math problem asap. Thanks!
Answer:
A) 2^4 x 2^7 = 2^(4 + 7) = 2^11
Exponent Law(s): Product Law
B) (-3)^9 divided (-3)^5 = (-3)^(9 - 5) = (-3)^4
Exponent Law(s): Quotient Law
C) (5^2)^-3 x 5^0 = 5^(-6) × 1 = 5^(-6)
Exponent Law(s): Power of a power rule; zero exponent rule
Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 5(m∠Y) − 150°. Find m∠Y.
If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
Suppose you know that ∠S and ∠Y are complementary and that ∠S = 5(∠Y) − 150°.
Then the other equation is given as,
∠S + ∠Y = 90°
5(∠Y) − 150° + ∠Y = 90°
6 (∠Y) = 240°
∠Y = 40°
If the angle ∠S and ∠Y are complementary angles. Then the measure of the angle ∠Y will be 40°.
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Question content area top Part 1 a. Solve x+11=x+11 b. If you simplify an equation and get 0=0, what can you conclude about the solution(s) of the original equation? c. Write an equation for which every real number is a solution. Question content area bottom Part 1 a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=enter your response here (Simplify your answer.) Your answer is not correct.B. The solution is the set of all real numbers. This is the correct answer.C. There is no solution. Part 2 b. If you simplify an equation and get 0=0, what can you conclude about the solution(s) of the original equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is enter your response here. (Simplify your answer.) B. The solution is the set of all real numbers. Your answer is correct.C. There is no solution. Part 3 c. Write an equation for which every real number is a solution. Choose the correct answer below. A.3 left parenthesis x minus 2 right parenthesis equals 2 left parenthesis x minus 3 right parenthesis 3(x−2)=2(x−3) B.2 left parenthesis x minus 3 right parenthesis equals 2 left parenthesis x minus 3 right parenthesis 2(x−3)=2(x−3) C. x+2=x+3 VideoTextbook Get more help
Answer:
1a) x+11=x+11 becomes 0=0. What this means is that at all x values the y values are the same, in other words, they are the same line.
Please split up your questions as it is difficult to answer.
how can you use proportional and nonproportional linear relationships to solve problems? what does it mean to solve a system of equations?
Answer: Proportional and nonproportional linear relationships can be used to solve problems by creating equations and using them to find unknown values. A proportional linear relationship is a relationship in which the ratio of the dependent variable to the independent variable is constant. For example, y = kx is a proportional linear relationship, where k is the constant of proportionality. Nonproportional linear relationships, on the other hand, have a variable ratio between the dependent and independent variables. For example, y = mx + b is a nonproportional linear relationship, where m is the slope and b is the y-intercept.
To solve a system of equations is to find the values that make all the equations in the system true simultaneously. This can be done by using methods such as substitution, elimination, or graphing.
A system of equations is a set of two or more equations with the same variables, and solving such a system is finding the values of the variables that satisfy all the equations in the system.
For example, if we have a system of two equations,
y = 2x+1
y = -x+5
we can solve it by finding the values of x and y that make both equations true at the same time.
In summary, proportional and nonproportional linear relationships can be used to solve problems by creating equations and using them to find unknown values. Solving a system of equations is finding the values of the variables that satisfy all the equations in the system.
Step-by-step explanation:
Potatoes cost $3.64/lb. How much would 0.47 lb of potatoes cost?
Answer:
Step-by-step explanation:
1.7108 is the answer
O
-11-10-9-8
Select the values that make the inequality -s < 6 true.
Then write an equivalent inequality, in terms of s.
(Numbers written in order from least to greatest going across.)
0 -11
0-6
0 -1
05
6.1
0 -7
0 -5.9
D0
0.5-9
07
Equivalent Inequality: s
0-6.1
0-5
01
06
9 10 11
0 11
Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
9(x - y) = 30,
or (x-y) =30/9
To find :
a) 18(x - y) = ?
=> 2(9(x - y))
=> 2(30)
=> 60
b)6x - 6y = ?
=> 6(x-y) = 6(30/9)
=> 2*30/3
=> 20
c) 9(x-y)-9
=> 30 -9
=>21
Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.
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On solving the provided question, we can say that the inequality provided is -s < 6 he values that stratifies will be = 0-6
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
the inequality provided is
-s < 6
the values that stratifies will be = 0-6
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(question is in the image)
The pair of triangles are congruent. using the angle side angle (ASA) congruency theorem
What are congruent triangles?Two triangles are said to be congruent if all the three sides are equal to each other and all the three angles are equal to each other.
The angle side angle (ASA) congruency theorem states that two triangles are congruent if two angles and an included side of one triangle is equal to two angles and an included side of another triangle.
From the diagram, for both triangles, two angles and an included side is equal to that of the other triangle.
The pair of triangles are congruent.
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Why is the base of a exponential function not allowed to equal 1?
The base of a exponential function is not allowed to equal 1 because it would create a graph that would violate the properties of the exponential functions.
An exponential function cannot produce an increasing graph when base is taken as 1. This would lead to violation of its properties. However, an exponential function can have any positive number as its base, however some bases are more advantageous than others. The base 2 is useful, for instance, in computer science applications. The number represented by the letter e, however, is the most significant base. A function of the form is an exponential function, when:
f(x) = b^x
where x is any real value and b is a positive constant. B is frequently referred to as the base. Typically, the particular case b=1 is not considered because it would only produce the constant function f(x) = 1.
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The product of two numbers is 20⅚.If one of the number is 6⅔ Find the other number.
Answer:
X=3+1/8
Step-by-step explanation:
X * 40/6 = 125/6
(Multiply each side by 6 to get rid of the denominator)
X *40=125
Divide each side by 40
X = 125/40
X= 25/8
X=3+1/8
Which of the following is not a polynomial ? a: √3x^2-2√3x+3 , b: 3x^3/2-5x^2-1/√2x-1 , c: x+1/x , d: 5x^2-3x+ √2 please give full explanation of answer !!!
Answer: A polynomial is a mathematical expression that is composed of a sum of powers in one or more variables (indeterminates) with non-negative integer exponents, and coefficients that are real numbers.
Out of the options given, option "b" is not a polynomial.
Option "a" √3x^2-2√3x+3 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (√3, -2√3, 3)
Option "c" x+1/x is not a polynomial , it's called a rational function, it consists of one polynomial divided by another polynomial, it's not a polynomial because of the fraction 1/x
Option "d" 5x^2-3x+ √2 is a polynomial, it consists of terms with non-negative integer exponents (x^2, x^1) and the coefficients are real numbers (5, -3, √2)
So, option "b" 3x^3/2-5x^2-1/√2x-1 is not a polynomial, because of the fraction and the non-integer exponent (3/2)
Step-by-step explanation:
-1/3(12d+18) answer?
Answer:
-4d - 6
Step-by-step explanation:
-1/3(12d+18)
-4d - 6
That is the simplest we can simple the function
So, the answer is -4d - 6
23. Kumar wishes to cut the biggest possible squares
from a rectangular sheet of paper without any
leftover paper. The sheet of paper has a length of
65 cm and a breadth of 50 cm.
(1) What is the length of each square?
(ii) How many squares can he cut altogether!
The length of each square Kumar cuts is 10cm and 13cm, and altogether he cuts 130 squares.
What is the length of squares cuts?The perimeter of a square is really the total length of all of its sides. As a result, we can calculate the perimeter of a square by adding its four sides. A square's sides are all equal. As a result, the perimeter of a square is calculated by multiplying the side of a square by four.Given that,
Length of paper = 65 cm
Breadth of paper = 50 cm
The length of each square,
The greatest common factor of 65 and 50 is 5.
So,
50/5 = 10
65/5 = 13
Therefore the length of each square is 10cm and 13cm.
To find the number of squares cut altogether ,
10 x 13 = 130 squares.
Therefore altogether Kumar cuts 130 squares.
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On July 27, 2018, Mars will be about 57.6 million km from the earth. It will not be that close again until 2035. If a manned spacecraft could travel 40,000 km/hr, approximately how long would it take the spacecraft to reach Mars from Earth?
The time it would take the space craft to reach earth from Mars would be: 1440 hours
How to solve for the time it would take the space craft to reach earththe distance from Mars to Earth = 57.6 million km
= 57, 600,000 km
The time it takes the space craft to travel per km = 40000
We would use the formula t = d / v
where t is the unknown time we want to find
d is the distance = 57, 600,000 km
v is the velocity or speed = 40000
Hence we have
t = 57,600,000 / 40000
= 1,440 hours
It would take the space craft 1440 hours to reach mars from earth
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How many four-digit integers are even perfect squares and also perfect cubes?
The is 1 four-digit integers that is a perfect squares and perfect cube and it is 4096
What are perfect squares and perfect cubes?A perfect cube is the cube of a whole number, found by multiplying a whole number by itself three times. For example, the number 8 is a perfect cube because 2 × 2 × 2 = 8 .
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer. For example, 25 is a perfect square because it is the product of integer 5 by itself, 5 × 5 = 25.
The only four-digit integers that is a perfect square and a perfect cube is 4096
i.e 64² = 4096
16³ = 4096
Therefore the number of four-digit number that is a perfect square and a perfect cube is 1
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ITS COMPOUND INTERSET, ITS URGENT
a) The amount of money that Tony invested is; £1350
b) The rate of compound interest is; 4%
c) The graph that represents the growth in Toni's account is; Graph C
How to find the compound interest?The formula for the total value of her investment after t years is given by the formula; v = 1350 * 1.04^t
The general formula used to calculate the interest rate is given by,
a = p * (1 + r)^t
where;
a is amount
p is principal
r is rate of interest
t is time period
Comparing the given equation with standard equation, we have;
a = v
p = 1350
t = t
Now, 1 + r = 1.04
1 + r = 1 + 0.04
Thus;
r = 0.04 = 4%
Therefore, the money invested by tony P = £1350
The rate of compound interest is 4%
The graph that represents Toni's account is an exponential equation and since the initial amount is not zero, then the correct graph is graph C
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Help me with this worksheet please give me he answer!
I'm in a hurry!
The approximate annual cost of raising a child born in 2013 at age 17 is 15230.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
a) Plot (2, 12,940), (5, 12,970), (8, 12,800), (11, 13,600) 1nd (14, 14420) on graph.
b) (8, 12800) and (14, 14420)
Here, slope m=(14420-12800)/(14-8)
= 1,620/6
= 270
Substitute m=270 and (x, y)=(8, 12800) in y=mx+c, we get
12800=270(8)+c
12800=2160+c
c=10640
Substitute m=270 and c=10640 in y=mx+c, we get
y=270x+10640
c) Now, substitute x=17 in y=270x+10640, we get
y=270×17+10640
y=15230
Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is 15230.
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A wheelchair ramp is 10 feet long. The ramp sits up on a 2 foot platform.
How far is it from the end of the ramp to the bottom of the platform? (Round to the tenths place & include units!)
Answer: 9.8 feet!
Step-by-step explanation:
Is the midpoint method a stable?
Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.
what is order of rotation ?The maximum number of rotations that a geometry may accommodate is the order of rotational symmetry. The degree of rotational symmetry is denoted as 360°A°, where A° is the lowest angle that may be used to rotate a figure from its rotated shape back to its original shape. (170 degrees) How many times a perfect circle may be rotated while still preserving its appearance is a measure of a shape's rotational symmetry. The appearance of a full 360° revolution will be the same only when a triangle is placed back in its initial starting position.
given
Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.
A-stable time-stepping approach, is the recommended method for solving evolutive conservative systems of PDEs.
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Point B(4,-16) is dilated by a scale factor of 3/4 to create B'
Wrute a rule for the transformation
Give the locatiom of B'
The rule for the transformation, which is a dilation, is given as follows:
(x,y) -> (3x/4, 3y/4).
Hence the coordinates of B' are given as follows:
B'(3, -12).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The general rule is:
(x,y) -> (kx, ky).
In which k is the scale factor.
The scale factor for this problem is given as follows:
k = 3/4.
Hence the rule is:
(x,y) -> (3x/4, 3y/4).
The coordinates of B' are obtained multiplying each of the coordinates of B by the scale factor k = 3/4.
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Subtract (5x + 1/3) - (3x - 1/6)
[tex] \\ \\ \\ \\ \\ \\ [/tex]
ty:-;
The subtraction of the expression (5x + 1/3) - (3x - 1/6) is given by 2x + 1/2
How to subtract expressions?Subtraction refers to one of the mathematical operations which involves finding the difference between expressions or values.
(5x + 1/3) - (3x - 1/6)
Open parenthesis
= 5x + 1/3 - 3x + 1/6
Collect like terms
= 5x - 3x + 1/3 + 1/6
= 2x + (2+1) / 6
= 2x + 3/6
= 2x + 1/2
In conclusion, 2x + 1/2 is the result of the given expression (5x + 1/3) - (3x - 1/6)
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Answer:
2x + (1/2)
Step-by-step explanation:
Given expression,
→ (5x + (1/3)) - (3x - (1/6))
Let's simplify the expression,
→ (5x + (1/3)) - (3x - (1/6))
→ 5x + (1/3) - 3x + (1/6)
→ (5x - 3x) + ((1/3) + (1/6))
→ (2x) + ((2 + 1)/6)
→ 2x + (3/6)
→ 2x + (1/2)
Hence, answer is 2x + (1/2).
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
The graph of the Equation and Inequalities is attached below.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
1. 2y – 4x < 8
The region is shaded by red region.
and, the inequality intersect y axis at 4 and x axis at -2.
2. -4y > -x + 12
The region is shaded by red region.
and, the inequality intersect y axis at -3 and x axis at 12.
3. | x + 3 |= y
The vertex of the equation is (-3, 0)
4. |2x – 6| + 2 = y
The vertex of the equation is (3, 2)
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Mrs. James buys 5 hat and glove sets for charity. She has coupons for $1.50 off the regular price of each set. After using the coupons, the total cost is $48.75.
Item Cost ($)
Hat and glove set p
Scarf 9.99
Which equation can be used to determine the regular price, p, of a hat and glove set?
Multiple choice question.
cross out
A)
5p+9.99=48.75
cross out
B)
5(p−1.50)=48.75
cross out
C)
5(p+9.99)=48.75
cross out
D)
5(p+9.99−1.50)=48.75
Part B
Determine the regular price of a hat and glove set.
$__
The equation used to determine the regular price is :
5(p - 1.50) = 48.75
Regular price of a hat and glove set = $11.25
The correct option is (B).
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.
Given,
No. of hat and glove sets Mrs. James bought = 5
Discount with each coupon = $1.50
Total cost after using coupons = $48.75
Regular price of Hat and glove set = p
Cost of hat and glove set = p - $1.50
Cost of 5 sets of hat and glove = 5(p - 1.50)
By the question,
5(p - 1.50) = 48.75
p - 1.50 = 9.75
p = 9.75 + 1.50
p = 11.25
Regular price of a hat and glove set = $11.25
Hence, $11.25 is regular price of a hat and glove set,
5(p - 1.50) = 48.75
is the equation used to determine the regular price.
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