False. Using the unit rate of cost per pound, 5 pounds of apples cost $6.00.
Cost per pound = $12.00 / 8 pounds = $1.50
5 pounds of apples cost = 5 pounds x $1.50 = $7.50
The unit rate of cost per pound can be calculated by dividing the total cost of 8 pounds of apples by the total number of pounds. In this case, the unit rate of cost per pound is $1.50. This means that for every pound of apples, the cost is $1.50. To calculate the cost of 5 pounds of apples, we need to multiply the unit rate of cost per pound by the number of pounds. In this case, 5 pounds of apples cost $7.50, which is calculated by multiplying $1.50 by 5. Therefore, the statement that using the unit rate of cost per pound, 5 pounds of apples cost $7.50 is false.
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The quotient of 18 and the number is three what is the number
Answer:
Step-by-step explanation:
Divide: 18 ÷3=?
The answer is 6
You're working late one night and notice that the hard drive on your new computer is very active even though you aren't doing anything on the computer and it isn't connected to the Internet. What is the most likely suspect?
Answer:
The most likely suspect for the hard drive being very active even though the computer is not being used and is not connected to the Internet is malware. Malware is a type of software that is designed to cause harm to a computer system, and it can often run in the background without the user's knowledge.
What does an inverse function look like?
Inverse functions are indicated by the symbol [tex]f^{-1}[/tex] and are functions whose inverse is the function itself (x).
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The inverse function, which also returns the beginning value, returns the result of a function.
The relationship that results from swapping out an independent variable for a variable that depends on a given equation, and which may or may not be a function. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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Does anyone know how to do this
The experimental probability of spinning a number less than 3.
7/25.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The total number of spuns.
= 8 + 6 + 9 + 11 + 9 + 7
= 50
Total number of spuns of the spinner less than 3.
= 8 + 6
= 14
The probability of spinning a number less than 3.
= 14/50
= 7/25
Thus,
The probability is 7/25.
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Use the quadratic formula to find both solutions to the quadratic equation
given below.
4x² + 5x+1=0
A. X=-
-3-√√-7
8
□ B. x=-3-√7
8
C. x=
E. x=
-3+√√-7
8
D. x=-¹
+3+√7
8
F. x= -1
Answer: x=-1/4 and x=-1
Step-by-step explanation:
The answer choices you give are extremely hard to figure out, so I hope my explanations and answers help.
The quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]. Once we figure out a, b, c, we can plug them into the formula and solve for x.
The standard form equation is ax²+bx+c=0. The equation given matches this so we know that:
a=4
b=5
c=1
Plug them into the formula. There is a [tex]\pm[/tex] symbol, which stands for "plus or minus". This means we solve the formula with addition and subtractions separately. We should have 2 solutions at the end. Let's do them separately to show work.
Solution 1: addition
[tex]x_1=\frac{-5+\sqrt{5^2-4(4)(1)} }{2(4)}[/tex] [exponents]
[tex]x_1=\frac{-5+\sqrt{25-4(4)(1)} }{2(4)}[/tex] [multiply]
[tex]x_1=\frac{-5+\sqrt{25-16} }{8}[/tex] [inside square root]
[tex]x_1=\frac{-5+\sqrt{9} }{8}[/tex] [square root]
[tex]x_1=\frac{-5+3}{8}[/tex] [add]
[tex]x_1=\frac{-2}{8}[/tex] [divide top and bottom by 2]
[tex]x_1=-\frac{1}{4}[/tex]
Solution 2: subtraction
[tex]x_2=\frac{-5-\sqrt{5^2-4(4)(1)} }{2(4)}[/tex] [exponents]
[tex]x_2=\frac{-5-\sqrt{25-4(4)(1)} }{2(4)}[/tex] [multiply]
[tex]x_2=\frac{-5-\sqrt{25-16} }{8}[/tex] [inside square root]
[tex]x_2=\frac{-5-\sqrt{9} }{8}[/tex] [square root]
[tex]x_2=\frac{-5-3}{8}[/tex] [subtract]
[tex]x_2=\frac{-8}{8}[/tex] [divide]
[tex]x_2=-1[/tex]
I am not able to find the answer choices, but we know that x=-1/4 and x=-1.
Simplify the expression. Explain each step. 7(9w) 7(9w) = 11 Associative Property of Multiplication Multiply 7 and 9.
Answer:
Step-by-step explanation:
7(9w)7(9w) = 11
(7 ×7)(9×9)(w×w) = 11
49 ×81 w² = 11
3969w² = 11
[tex]\frac{3969w^{2} }{3969}[/tex] = [tex]\frac{11}{3969}[/tex]
w² = [tex]\frac{11}{3969}[/tex]
[tex]\sqrt{w^{2} }[/tex] = [tex]\sqrt{11/3969}[/tex]
w = ± [tex]\frac{\sqrt{11} }{63}[/tex]
Because the solution contains a square root the answer contains both a negative and a positive solution.
The circular region of the sign (below, left) has an area of 154 square inches. Vanessa would like to place a tiny ribbon (shaded) around the circle's edge. To be sure she has enough ribbon, she decides to buy 2 inches more of the ribbon than the original circle's circumference. How many inches of ribbon will Vanessa need to buy if she estimates $\pi = 22/7 ?
Vanessa needs to buy 2*(22/7)sqrt(1547/22) + 2 inches of ribbon.
What is the area of circle?
The area of a circle is given by the formula: A = πr^2, where A is the area of the circle, π is a constant (approximately equal to 3.14) and r is the radius of the circle.
Given the area of the circular region is 154 square inches. We can use the formula to find the radius: 154 = πr^2
By substituting π = 22/7 we get:
154 = (22/7)r^2
Solving for r, we get:
r = sqrt(154*7/22)
The circumference of the circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
By substituting the value of r we got before, we get:
C = 2πr = 2*(22/7)sqrt(1547/22)
To be sure she has enough ribbon, Vanessa decides to buy 2 inches more of the ribbon than the original circle's circumference. So she needs to buy:
C + 2 = 2*(22/7)sqrt(1547/22) + 2 inches
Hence, Vanessa needs to buy 2*(22/7)sqrt(1547/22) + 2 inches of ribbon.
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What is the slope of a line that pass through the points (3,-2) and (5,-2)?
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{-2 +2}{2} \implies \cfrac{ 0 }{ 2 } \implies \text{\LARGE 0}[/tex]
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, - 2 ) and (x₂, y₂ ) = (5, - 2 )
m = [tex]\frac{-2-(-2)}{5-3}[/tex] = [tex]\frac{-2+2}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
Cherri brought $2,100 computer on an installment plan. She made a $400 down payment, and she has to make a monthly payment for $79. 50 for the next two years. How much interst will she pay
If Cherri brought $2100 computer on an installment plan and made $400 down payment and monthly payment for $79. 50 for the next two years, then the interest amount is $208 .
the cost of the computer is = $2100 ;
the amount paid as down payment is = $400 ;
the amount that will be paid in monthly installment is = $79.50 ;
the time for the loan is = 24 months ;
So , the amount paid as installment is 24 months is = [tex]24 \times79.50[/tex]
= $1908 .
So , the total amount paid by Cherri with installment plan is = [tex]\$1908+\$400[/tex]
= $2308 .
So , the interest amount paid is = [tex]\$2308-\$2100[/tex]
= $208 .
Therefore , Cherri will pay $208 as interest .
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How do you tell if a graph is a function and inverse is a function?
If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).
What is a function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The function f has an inverse if and only if the result of reflecting a function's graph about the line y = x is the function's graph (passes the vertical line test).
Therefore, if and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).
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What is associative property example?
The example of an associative property is a+(b+c) = (a+b) + c for additional operation and a × (b × c) = (a × b) × c for the multiplication operation. The associative property is used to solve an equation or expression of real numbers.
What are the properties of real numbers?
In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.
The four primary characteristics of real numbers are as follows:
Commutative property
Associative property
Distributive property
Identity property.
Associative property: The associative property is applicable on two arithmetic operations. They are multiplication and addition.
For multiplication operations: a × (b × c) = (a × b) × c
For additional operation: a+(b+c) = (a+b) +
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How do you make a graph compare two sets of data?
There are several ways to make a graph to compare two sets of data, but one common method is to use a line graph.
The steps to create a line graph to compare two sets of data:
Organize the data: Arrange the data into two columns, one for each set of data. Each column should have a label at the top to indicate what the data represents.
Choose a scale: Decide on an appropriate scale for the x- and y-axes that will allow you to clearly display the data. The x-axis should represent the categories being compared, and the y-axis should represent the values of the data.
Plot the data: Using the chosen scale, plot the data points for each set of data on the graph. Use different colors or symbols for each set of data to make it easy to distinguish between the two.
Add a title: Give the graph a title that describes what the graph is showing.
Add a legend: Add a legend to the graph to indicate what each set of data represents.
Add labels: Label the x- and y-axes to indicate what they represent.
By following these steps, you can create a clear and informative line graph that allows you to easily compare two sets of data.
Other types of graph that can be used to compare two sets of data are bar charts, scatter plots, and stacked bar charts. The choice of graph depends on the type of data you have, and what you want to compare or highlight.
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How do you make an XY graph in Excel?
Select the data for which you want to create a chart slope . Click INSERT > Recommended Charts. On the Recommended Charts tab, scroll through the list of charts that Excel recommends for your data
When you find the chart you like, click it > OK.
The formula for a horizontal line at y=4 is as follows: There is no slope. 4.0 is the y-intercept.
What are the Slope and intercepts ?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.
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Dobra has 20 birr to Spenclon juice boxes for her son's preschool picnic. Each pack of juice boxes Corts 2.50- what is the maxiumum a numbers of packs she can buy
Using simple unitary method and with the total and per unit value provided, The answer is 8 boxes maximum can be bought.
What is unitary method?The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.
Why is unitary method important?The unitary method is a useful tool for solving problems involving units of measurement, it simplifies the problem and improves understanding of conversions. It also helps to develop critical thinking skills and is a useful tool for problem-solving in a variety of subjects.
each box costs = 2.5
total money =20
maximum that can be bought = 20/2.5 =8
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Each league plays 80 games in a month.
Based on the mean from the sample, how many more goals will be scored in the English League than in the French League in a month?
Answer:
Step-by-step explanation:
the answer is 152
What is the x-coordinate of the solution to the system shown?
3x - y = 6
3x + y = 34
Answer:
6[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
In this equation I will do the elimination method.
3x-y=6
3x+y=34
6x=40
Simplify
x=6[tex]\frac{2}{3}[/tex].
Check:
3(6.666...)-y=6
20-y=6
-20 from 6
-y=-14
y=14
20-14=6
6=6
3x(6.666...)+y=34
20+14=34
34=34
The circumference of a circle B is 80% of the circumference of circle A.
a) Find the ratio of the area of circle A to the area of circle B, giving your
answer in the form 100:n
100 :
(2)
Square E has sides of length e cm.
Square F has sides of length fcm.
The area of square E is 69% greater than the area of square F.
b) Work out the ratio of e:f
Your final line should say, Ratio of e:f is
(2)
The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.
The area of the circle is equal to the multiplication of the square of the circle's radius and π.
A = πr²
where 'r' is the radius
Circumference of circle A × 0.8 = circumference of circle B
So, taking r as the radius of A,
2πr = circumference of circle A
2πr × 0.8 = circumference of circle B
So the radius of B is r × 0.8.
Now we can substitute that in the area equations :
Area of A = π×r²
Area of B = π × (r × 0.8)² = π × r² × 0.64
The circumferences of the A to B ratio is
Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)
= 1: 0.8 = 100: 80,
The areas of circle A to circle B ratio is
Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64
e² = f² × 1.69
69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.
We have this equation:
e² = f² × 1.69
Apply the square root on both sides.
e = f × √(1.69) = f × 1.3
e/f = 1.3 = 1.3/1 = 13/10
the ratio e:f = 13: 10
Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.
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Find the value of x.
x+16
9
Answer:
x = - 7
Step-by-step explanation:
given that the 3 angles in the triangle are congruent, then the triangle is equilateral with the 3 sides congruent , then
x + 16 = 9 ( subtract 16 from both sides )
x = - 7
Answer:
x=-7
Step-by-step explanation:
The triangles sides are all the same in length, therefore, you need all the sides to be equal to 9.
-12+16=4 This addition problem does not equal to 9 so it is not correct.
-7+16=9 This is correct because -7+16 or 16-7 = 9.
-9+16=7 This addition problem does not equal to 9 so it is not correct.
-11+16=5 This addition problem does not equal to 9 so it is not correct.
So, x = -7.
PROBLEM SOLVING Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two spades
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
We will start by calculating the probability of drawing a spade from one deck, and then square it since we need to get the chance of getting two spades. We know there are 13 spades in a deck, out of 52 cards, giving us:
[tex]\frac{13}{52}[/tex]
Which can be simplified to :
[tex]\frac{1}{4}[/tex]
Then, we will square this fraction since we need two spades in a row:
[tex]\frac{1}{4} * \frac{1}{4} = \frac{1}{16}[/tex]
So the probability is [tex]\frac{1}{16}[/tex].
Hope this helped!
Hey I need help with this problem here in the picture, would rlly appreciate some quick help
Using the Pythagoras Theorem the value of c=11.40 and the number that goes beneath the radical is 130.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The rectangle is divided into two triangles which have exactly same sides.
So take any one triangle.
Apply the Pythagoras theorem since it is a right-angled triangle with base = 9 and perpendicular = 7.
So, according to Pythagoras theorem -
(Hypotenuse)^2=(Base)^2+(Perpendicular)^2
Plugging in the values in the equation -
c^2=(9)^2+(7)^2
c^2=81+49
c^2=130
c=[tex]\sqrt{130}[/tex]
c=11.40
Therefore, the value of c is obtained as 11.40.
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A hotel is offering two weekend specials. The first special is 3 nights and 4 meals for $233. The second
special is 3 nights and 3 meals for $226.50.
Part A: Write a system of equations to represent cost per night x and cost per meal y.
Part B: What is the cost per night and the cost per meal?
Answer: Part A:
To represent the cost per night x and cost per meal y in a system of equations, we can use the information provided in the question:
First Special:
3x + 4y = 233
Second Special:
3x + 3y = 226.50
Where x is the cost per night and y is the cost per meal.
Part B:
To find the cost per night and the cost per meal, we can use the information provided in the question and system of equations.
We can solve this system of equations using several methods: substitution or elimination method.
One common method to find the solution is by substitution method, where we find the value of x in terms of y from one of the equations and then substitute it into the other equation to solve for y.
x = (233 - 4y)/3
then substitute it into the other equation:
3(233 - 4y) + 3y = 226.50
now solve for y:
699 - 12y + 3y = 226.50
-9y = -472.50
y = 52.50
and we can substitute it back into the first equation:
3x + 4(52.50) = 233
3x = 80.50
x = 26.83
So the cost per night is $26.83 and the cost per meal is $52.50
Step-by-step explanation:
What is the number of terms in the expansion of 2x 3y 2 )( 2x 3y 2 2?
The number of terms in the expansion of [tex](2x^3y^2)(2x^2y^3)[/tex] is 12.
When expanding the product of two polynomials, the number of terms in the expansion is equal to the product of the number of terms in each polynomial. In this case, the first polynomial has 1 term (2x^3y^2) and the second polynomial has 1 term (2x^2y^3), so the number of terms in the expansion will be 1*1=1.
A polynomial function is one in which the variable's non-negative integer powers or positive integer exponents are the only parts of the equation. Examples of polynomial functions include quadratic, cubic, and other equations. An example of a polynomial with an exponent of 1 is 2x+5.
However, the expression provided is not a polynomial, it is a number.
[tex]2x^3y^2 * 2x^2y^3 = 4x^5y^5[/tex]
It is just one term.
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200 Litres of a punch that contains 35% fruit juice is mixed with 300 L of another punch. The resulting fruit
punch is 20% fruit juice. Find the percent of fruit juice in the 300L of punch.
Please help me, (with show of math)
Yes, because as x increases, y increases and because all of the pairs represent the same ratio.
What does it mean when a ratio is proportional?When two sets of provided numbers change in proportion, the ratios are said to be directly proportional if they do so in the same direction.
If two ratios or fractions are equivalent, it may be shown using the proportion formula. By dividing the supplied numbers, we may determine the value that is missing. You may write the percentage formula as a: A and d are the extreme terms, and b and c are the middle terms, according to the formula b::c: d = a/b = c/d.
Yes, because as x increases, y increases.
Yes, because all of the pairs represent the same ratio.
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Help please,I’ll give 20points (if I can)
On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
y = 2x +1
y = 3x - 1
x- 1 = 0
x = 1, y = 2
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Anyone pls? I'll give brainliest
Answer:The answer to your question is 5
What is the value of DX for solving simultaneous equations 3x 2y =- 11 and 7x 4y 9 by Cramer's rule?
The value of DX for solving simultaneous equations 3x 2y =- 11 and 7x 4y 9 by Cramer's rule is -13/5.
The general formula for Cramer's rule is
DX = detX/detA
Where detX is the determinant of the matrix formed by replacing the x-column of the original matrix with the constant column vector, and detA is the determinant of the original matrix.
For the given equations,
A = [3, 2; 7, 4]
X = [-11; -9]
Therefore,
detA = 3*4 - 2*7 = -10
detX = 3*(-9) - 2*(-11) = 13
Hence, DX = detX/detA = 13/-10 = -13/5
The value of DX for solving simultaneous
3x 2y =- 11 and 7x 4y 9 by Cramer's rule equation is -13/5.
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Please help as soon as possible!
22. x=?
23. y=?
The unknown angles in the parallel lines are as follows;
x = 28
y = 23
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal line, angle relationships are formed such as linear angles, vertically opposite angles, interior angles, corresponding angles, alternate interior angles, alternate exterior angles etc.
using vertical angles and same side interior angles,
5y - 4 + 3y = 180 (same side interior angles are supplementary)
8y - 4 = 180
8y = 180 + 4
8y = 184
divide both sides by 8
y = 184 / 8
y = 23
Hence,
3y = 2x + 13(corresponding angles)
corresponding angles are congruent.
Hence,
3(23) = 2x + 13
69 - 13 = 2x
2x = 56
x = 56 / 2
x = 28
Therefore,
x = 28
y = 23
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HELP ASAP
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes. What does the number 3 represent in this equation?
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 3 times of the time, increased.
Given,
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes.
The number '3' is constant term, which basically represents the the distance covered by the snail, in terms of time or, the rate of increment of distance is terms of time.
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 1/3 of the time, increased.
For example if the snail is moving for 1 unit time, the t will be considered as 1. so, the d will be 3*1 = 3, i.e. 3 unit distance will be covered by the snail in 1 unit time.
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What is the quotient (3x2 4x − 15) ÷ (x 3)? 3x 5 3x − 5 3x 1 3x − 1, r = 1
By solving the expression (3x2 +4x − 15) ÷ (x +3) the quotient is 3x-5 and r=0
What do you meant by quotient?When solving a division problem, the quotient is obtained by dividing the dividend by the divisor.
Mathematically, we denote the outcome of this division by separating the quotient and remainder with a capital R. (see below). The entire number that results from simplifying a fraction is known as the quotient.
We can do it by long division method the required quotient is 3x-5 and r=0
not 3x-1 , r=1
multiply the divisor with 3x we will get 3x²+9x to cancel out the first term of dividend.
Now after solving we will get -5x -15
Now, multiply the divisor by -5 we will get -5x-15 which will cancel the entire dividend.
So that the quotient is 3x-5 and r=0
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Find the length and width of the actual room, shown in the scale drawing. Then find the area of the actual room. Round the final answer, if necessary, to the nearest tenth.
The actual dimensions are 9.75 feet and 7.5 feet. The area will be 73.125 square feet.
What is the scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). The scale factor is defined as the proportion of the new image's size to that of the previous image.
Here the scale factor for the given image is 2 inch = 3 ft.
The measure of the actual dimensions will be calculated as,
2 in = 3 ft
1 in = 3/2 ft
6.5 in = 6.5 x 3 / 2 = 9.75 ft
5 in = 5 x 3 / 2 = 7.5 ft
The actual area will be calculated as,
Area = 9.75 x 7.5
Area = 73.125 square feet
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