Riley bought 2 boxes of thank you cards and 3 boxes of get well cards.
What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let Riley have bought x boxes of thank you cards and y boxes of get well cards.
Therefore according to the question,
x + y = 5.......(1)
9x + 4y = 30........(2)
Multiplying equation 1 with 4 we get.
4x + 4y = 20.......(a)
Subtracting (a) form (2) we get:
5x = 10
=> x = 2
Putting the value of in (1) we get y= 3
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Find the difference: 11/21 - 3/7
We will operate as follows:
[tex]\frac{11}{21}-\frac{3}{7}=\frac{2}{21}[/tex]convert 0.43 to a percent
Answer:
43%
Step-by-step explanation:
To convert a decimal to a percent, you have to move the decimal over 2 times to the right.
using the path method for multivariable limits, demonstrate that the limit doesn't exist:
[tex]lim_{(x,y) \to (1,1)} \frac{x y - x - y + 1}{x^2 + y^2 - 2 x - 2 y + 2}[/tex]
Demonstrating that the limit doesn't exist
What is Limits?
The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are used to define continuity, derivatives, and integrals.
The limit exists only if the value of the limit along every direction that leads to (1,1) is same.
So by calculating,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line x = 1
Similarly,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line y = 1
And the last limit you calculated is along line y=x.
To answer your question, the calculation of the limit along y=1 would not have been necessary. It is sufficient to demonstrate the absence of a limit by giving just two cases in which it appears to vary along several directions.
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In a standard normal distribution, the range of values of z is from _____.
In a standard normal distribution, the range of values of z is from: D. d. -∞ to ∞.
What is a z-score?A z-score is also known as a standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than the data that are far from the mean.
In conclusion, the range of values of z in a standard normal distribution are all real numbers which typically ranges from negative infinity (-∞) to positive infinity (∞).
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Complete Question:
In a standard normal distribution, the range of values of z is from ______.
a. -3.09 to 3.09
b. -1 to 1
c. 0 to 1
d. -∞ to ∞
Determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data.
An elementary school has 92 first graders. Because the first graders are all about the same age, they have heights that are pretty similar to one another.
Would it be best to use the mean, median, or mode to describe the height of the first-graders?
Group of answer choices
Mean
Median
Mo
First graders in an elementary school number 92. We use mode.
Given that,
Determine which statistic would be most appropriate to characterize the middle of the next set of data: the mean, median, or mode.
First graders in an elementary school number 92. The first graders' heights are fairly similar to one another because they are all roughly the same age.
We have to find which statistic—the mean, median, or mode—does the first-graders' height best represent.
First graders in an elementary school number 92.
Depending on which their birthday walls, the first graders might be six, seven and eight on the last day of the second year.
Therefore, We use mode.
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Shauna calculated the net sales for her company using the following figures: Gross sales = $72,900 Sales discounts = $2,450 Purchase returns and allowances = $3,750 Sales returns and allowances = $2,550 The net sales of Shauna's company are __________.
The net sales of Shauna's company when she calculated the sales for her company using the figures is $66700.
What are net sales?The total of a company's net sales is its gross sales less any returns, allowances, and discounts. Externally, net sales calculations are not always obvious. They can frequently be taken into account when calculating top-line revenues that are shown on the income statement.
The total number of units sold is multiplied by the price per unit for the purpose of calculating gross sales. The term "returns" or "sales returns" refers to products that customers have sent back in exchange for reimbursement.
The nets sales based on the information given will be:
Gross sales = $72900
Less: Retuned sales = $3750
Less Discount = $2450
Net sales = $66700
Therefore, the net sale is $66700.
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Perform the given operations on the functions
21) f(x)=x² + 3x, g(x) = 2x + 2,
A. (f+g)(x)
B. (f- g)(x)
Answer:
see explanation
Step-by-step explanation:
A
(f + g)(x)
= f(x) + g(x)
= x² + 3x + 2x + 2 ← collect like terms
= x² + 5x + 2
B
(f - g)(x)
= x² + 3x - (2x + 2)
= x² + 3x - 2x - 2 ← collect like terms
= x² + x - 2
Which of the following ordered pairs is either the
x- or y-intercept of the function 3x + 2y = -6?
A. (-3,0)
B.(-2,0)
C.(0,2)
D.(0,3)
List the first 6 common multiples of 8
List the first 6 common multiples of 12
The first six common multiples of 6 and 8 are :
24,48,72, 96, 120 and 144.
The first six common multiples of 12 and 18 are :
24, 36, 72, 108, 144, 216.
In order to resolve this, we shall use the multiples idea.
(A) The two numbers given are 6 and 8.
Six is the first multiple of which there are the following: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, and 144.
multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, and 144.
Therefore, common multiples are: 24, 48, 72, 96, 120 and 144.
(B) The two numbers given are 18 and 12.
The first few multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, and 240.
Similarly, the multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, and 270.
Therefore, common multiples are: 24, 36, 72, 108, 144, 216.
Hence we get the required common multiples.
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Please help me with this question
Notice from the graph that data are mostly to the right.
Answer: Option C The distribution is tailed.
someone help please, dk what to do
Step-by-step explanation:
equation format: y = mx + b where m is slope and b is the y intercept.
From the points given we find that it is a horizontal line, which means slope or m = 0. So we know so far:
y = 0x + b or y = b
The y-intercept occurs where x = 0. This occurs at y = -7. So the equation for these two points:
EQUATION: y = -7
(Plotted graph attached)
18 is 50% of what????????
Let the unknown value be x.
18 is 50% of ________n can also be written as;
18 = 50% of x
of means multiplication;
18 = 50% * x
18 = 50/100 * x
18 = 50x/100
cross multiply
18 * 100 = 50x
1800 = 50x
Divide both sides by 50
1800/50 = 50x/50
180/5 = x
x = 180/5
x = 36
Hence 18 is 50% of 36
Volume is 10x3 + 67x2 + 30x − 72, length is 5x − 4, width is 2x + 3
Answer:
height = x + 6
Step-by-step explanation:
Volume = length x width x height
V = 10x³ + 67x² + 30x − 72
length = 5x - 4 and width = 2x + 3
So length x width = (5x - 4 ) x (2x + 3)
Using the FOIL method:
= (5x)(2x) + (5x)(3) + (-4)(2x) + (-4)(3)
= 10x² + 15x - 8x - 12
= 10x² + 7x -12
So to find height, divide Volume by (length x width)
10x³ + 67x² + 30x − 72 ÷ 10x² + 7x -12
Use polynomial long division. See image ( I did the best I could to capture the process)
The answer is x + 6
To verify
Multiply (5x-4) (2x + 3) (x + 6) = 10x³ + 67x² + 30x − 72
|||
=
O DECIMALS, PROPORTIONS, PERCENTS
Simplifying a ratio of whole numbers: Problem type 1
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
40 L: 72 L
Answer:
5/9
Step-by-step explanation:
You want the reduced fraction equivalent to the ratio 40L : 72L.
Reduced ratioA ratio is reduced by removing the greatest common factor from all parts of the ratio. Here, that factor is 8L.
40L : 72L = (8L)(5) : (8L)(9) = 5 : 9 = 5/9
The ratio is 5/9.
__
Additional comment
The greatest common factor can be found several ways. The easiest is for you to make use of your knowledge of multiplication tables:
40 = 5·8
72 = 9·8
8 is a common factor. Since 5 and 9 have no common factors, 8 is the greatest common factor of 40 and 72.
3.5 divided by 85
answers:
at least 500/ at least 50/ at least 20/ at least 200
Ive looked up answers to this question in iready but everyone says the answer is 24?
The value of 3.5 divided by 85 will be 0.4118.
What is division?Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.
Division's opposite is multiplication. Dividend Divisor = Quotient + Remainder is a formula for calculating the division of two numbers.
The dividend in this situation refers to the number that is being divided. The divisor is the number that divides the number (dividend) into equal parts.
In this case, 3.5 ÷ 85 = 0.4118. This can be computed through the use of a calculator.
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please show all work
The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])
What is coordinate plane ?Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.The following is a definition of a coordinate plane: The intersection of the Y-axis, a vertical line, and the X-axis, a horizontal line, creates a coordinate plane, also referred to as a rectangular coordinate plane grid.
The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])
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Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function
The definition of the functions implies that the value of x if f(x) = g(x) is 3
The solution for the value of xThe equations of the functions are given as
f(x) = -2x + 4
g(x) = 2x - 8
This means that, we have the following equation
f(x) = g(x)
Substitute the known values in the above equation
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms in the above equation
So, we have
2x + 2x = 8 + 4
Evaluate the like terms in the above equation
So, we have
4x = 12
Divide both sides by 4
x = 3
Hence, the value of x such that the equations are equal is 3
The graph of the functionsThe graph of the functions can be plotted using a graphing tool
See attachment for the graph of the functions
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Write an equation in standard form for the line that passes through the given points.
(5,0) and (0,3)
The equation of the line in standard form is
(Type your answer in standard form.)
3x + 5y = 15 is the equation of the line in standard form that passes through the point (5,0) and (0,3).
What is the equation of line that passes through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is the slope and b is the y-intercept.
Given the data in the question;
Point 1 ( 5,0 )
x₁ = 5y₁ = 0Point 2 ( 0,3 )
x₂ = 0y₂ = 3First, we determine the slope of the line.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 3 - 0 )/( 0 - 5 )
Slope m = ( 3 )/( -5 )
Slope m = -3/5
Now, we plug the slope and coordinates of one the point into the equation of line to determine the y-intercept b.
y = mx + b
0 = (-3/5)5 + b
Solve for b
0 = -15/5 + b
0 = -3 + b
b = 3
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-3/5)x + 3
Convert to standard form; Ax + Bx = C
Multiply each term by 5
y = (-3/5)x + 3
5y = 5(-3/5)x + 5(3)
5y = -3x + 15
Reorder the equation
3x + 5y = 15
Therefore, the equation of the line is in standard form is 3x + 5y = 15.
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A zookeeper is 6 14 feet tall. A young giraffe in his care is 93/8 feet tall. How many times as tall as the zookeeper is the giraffe?
Estimate 5.209 + 2.667 by rounding to the nearest whole number.
Answer:
I'm pretty sure it would be 8 though forgive me if I'm wrong
A contractor bought 8.2 ft2 of sheet metal. He has used 3.7 ft² so far and has $90 worth of sheet metal remaining. The equation 8.2x-3.7x = 90 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
By solving the equation, we get the cost of sheet metal =$20 per sq. feet
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.
Given equation 8.2x-3.7x = 90
or, 4.5x = 90
or, x = 90/4.5 = 20
Hence, the cost of sheet metal is $20 per sq. feet
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7. Jill was 80th in a class of 200, whereas Nathan, who is in the same class, has a percentile rank of 80. Which student has the higher standing in the class?
The student that has the higher standing in the class is Jill
How to determine the student that has the higher standing in the class?The given parameters are:
Number of students = 200
Jill's position =80th
Nathan's position = Percentile rank of 80
The above means that
Nathan's position = 80 percentage of the number of students in the class
Substitute the known values in the above equation
So, we have the following equation
Nathan's position = 80 percentage of 200
Rewrite as
Nathan's position = 80 percentage * 200
Express as percentage
Nathan's position = 80% * 200
Express 80% as decimal
Nathan's position = 0.80 * 200
Evaluate the product
Nathan's position = 160
So, we have
Jill's position =80th
Nathan's position = 160th
By comparing the positions, 80th is greater than 160th
Hence, Jill has the higher standing in the class
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Use the square root property to solve the equation.(x + 8)² = 2Select one:O A. (-8+√√2)OB. √2-√√8O C. (√2+8,-√2+8}O D. (-8± √2)
Answer: D
What are the coordinates of a point 4/5 of the way B to A
A(3,-4)
B(13,11)
[tex]\textit{internal division of a segment using a fraction}\\\\ B(\stackrel{x_1}{13}~,~\stackrel{y_1}{11})\qquad A(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{4}{5}\textit{ of the way from B to A} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_2}{3}-\stackrel{x_1}{13}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{11})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment BA}}}{\left( -10 ~~,~~ -15 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{13}~~+~~\frac{4}{5}(-10)~~,~~\stackrel{y_1}{11}~~+~~\frac{4}{5}(-15) \right) \\\\\\ (13~~ - ~~8~~,~~11~~ - ~~12)\implies {\Large \begin{array}{llll} (5~~,~~-1) \end{array}}[/tex]
The length of a ruler is 12 inches. There are approximately 25.4 millimeters in 1 inch.
The length of the ruler is approximately 304.8 millimeters .
Length is used to measure distance.
According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the metre.The longest dimension of an object is typically understood to be what is meant by length.However, this isn't always the case depending on the object's position.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.Given that there are approximately 25.4 millimeters in 1 inch.
Therefore the length of the ruler = 25.4 × 12 = 304.8 mm
Hence the length of the ruler is approximately 304.8 millimeters .
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Answer:
304.8
Step-by-step explanation:
12*25.4 = 304.8
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
It should be noted that when the graph of a relationship is a line that passes through the origin, then it is proportional.
How to illustrate the information?A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
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I need the answer ASAP
In order to rationalize the denominator of the fraction, we need to multiply the fraction by the conjugate of the expression in the denominator.
The conjugate is the same expression but with the signal between the numbers changed.
So we have:
[tex]\frac{4}{3+\sqrt[]{7}}=\frac{4}{3+\sqrt[]{7}}\cdot\frac{3-\sqrt[]{7}}{3-\sqrt[]{7}}=\frac{4(3-\sqrt[]{7})}{3^2-(\sqrt[]{7})^2}=\frac{12-4\sqrt[]{7}}{9-7}=\frac{12-4\sqrt[]{7}}{2}[/tex]So the new denominator of the fraction is 2, therefore the correct option is D.
Simplify the fraction 112 144 as much as possible.
Answer:
7/9
Step-by-step explanation:
Answer:
7/9
Step-by-step explanation:
I took the quiz
The ratio of the area between a small square of land and a large squareof land is 3: 7. Given that the total area of the two squares of land is4,000 m2, find the area of each square of land.
Given:
The ratio of the area between a small square of land and a large square
of land is 3: 7.
Total area of the two squares of land (in sq. meter) is 4000.
Required:
The area of each square of land.
Answer:
We have the ratio of the area between a small square of land and a large square of land is 3: 7.
Let
[tex]x^[/tex]be the area of the square of land.
Then their ratio is given by,
[tex]3x^:7x^[/tex]Also given that the total area of the two squares of land (in sq.meter) is
4,000.
The area of
Therefore,
[tex]\begin{gathered} 3x^+7x^=4000 \\ \Rightarrow10x^=4000 \\ \Rightarrow x^=400 \\ \end{gathered}[/tex]Therefore,the area of small square (in sq. meter) is,
[tex]3x=3(400)=1200[/tex]and the area of large square (in sq. meter) is,
[tex]7x=7(400)=2800[/tex]Final Answer:
The area of small and large square respectively (in sq. meter) is,1200 and 2800.
solve for x. 7/13=x/48
Answer:
25.7
Step-by-step explanation:
7/13=x/48. By cross multiplication 13 x=326 = 25.7