Solve the system of linear equations by substitution. Check your solution.
2x = 18
x-5y = 29
Answer:
x = 4, y = –5
Step-by-step explanation:
2x = 18 --------(1)
x-5y = 29. -------(2)
x = 5y + 29 -----(3)
just substitute for x in equation 1
2( 5y + 29) = 18
10y + 58 = 18
10y = 18 – 58
10y = –50
y = –5
since y = –5 we will just substitute for y in equation (2)
x = 5(–5) + 29
x = –25 + 29
x = + 4
Let's check if our answer is correct
x – 5y = 29
4 – 5(–5) = 29
4 + 25 = 29
29 = 29
LHS = RHS
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4. The Smith and Jones families each have six family members. They wanted to compare the
differences in ages between the two families. The ages of the members of Smith family are
45, 43, 13. 11, 5, and 2, while the Jones family members are 45, 39, 17, 16, 4, and 1. Find
the mean absolute deviation and range in ages for each family.
Jones Family MAD
Jones Family Range -
Smith Family MAD =
Smith Family Range -
Which family has the greatest difference in ages?
Smith Family MAD = 16.1 Jones Family MAD = 14.4
Smith Family Range = 43 Jones Family Range = 44
What are MAD and Range?The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is.
The mean absolute deviation can be calculated as shown below.
First, determine the mean.
Step 2: Determine the positive distances between each data point and the mean. Absolute deviations are those.
Step 3: Combine those deviations.
Step 4. Divide the sum by the quantity of data points.
MAD=∑([tex]\frac{mod(xi-x)}{n}[/tex])
Range is the difference of top most element and least element of the data set
Calculation:Smiths Family:
Mean=[tex]\frac{45+43+13+11+5}{5}[/tex]=23.4
MAD=[tex]\frac{(45-23.4)+(43-23.4)+(13-23.4)+(11-23.4)+(5-23.4)+(2-23.4)}{5}[/tex]=16.1
Range=45-2=43
Jones Family:
Mean=[tex]\frac{45+39+17+16+4}{5}[/tex]=24.2
MAD=[tex]\frac{(45-24.2)+(39-24.2)+(17-24.2)+(16-24.2)+(4-24.2)}{5}[/tex]=14.4
Range=45-4=41
Smith Family MAD = 16.1 Jones Family MAD = 14.4
Smith Family Range = 43 Jones Family Range = 44
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Determine which set of side measurements could be used to form a right triangle. 17, 6, 20 10, 15, 13 5, 12, 13 9, 3, 11
Option C is correct, the set of side measurements that could be used to form a right-angle triangle is 5,12, and 13.
The side length of the triangle is shown in the option:
As we know,
Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
Using Pythagoras' theorem:
From option(C):
5, 12 and 13
= (5) ² + (12) ² = (13) ²
= 25 + 144 = 169 (True)
Thus, the set of side measurements that could be used to form a right triangle is 5, 12, and 13 option (C) is correct.
An imperative theorem is a Pythagorean theorem, which states in any right triangle, the rectangle of the duration of the hypotenuse equals the sum of the squares of the lengths of the two different facets. If the hypotenuse has period c, and the legs have lengths a and b, then the theorem states that a² + b² =c²
The converse is real: if the lengths of the sides of a triangle satisfy the above equation, then the triangle has a right angle opposite side c.
some other facts about right triangles:
the acute angles of a right triangle are complementary.
= a + b+ 90°=180°
= a + b=90°
= a = 90° - b.
If the legs of a right triangle have the identical period, then the angles opposite those legs have the identical measure. considering those angles are complementary, it follows that every measure has 45 stages. via the Pythagorean theorem, the duration of the hypotenuse is the length of a leg times √2.
In a right triangle with acute angles measuring 30 and 60 degrees, the hypotenuse is two times the length of the shorter facet, and the longer side is the same as the length of the shorter side times √3:
= c = 2a
= b = a x √3.
All triangles, angles, and facets are related with the aid of the regulation of cosines and regulation of sines (additionally called the cosine rule and sine rule).
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jason is trying to remember the five digit combination to his safe. he knows that he only used digits $1$ through $5$ (possibly repeated), that every even digit was followed by an odd digit, and every odd digit was followed by an even digit. how many possible combinations does jason need to try?
180 possible combinations does jason need to try
What is Permutation?
In mathematics, permutation relates to the act of arranging all the members of a set into some sequence or order. In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting. Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered.
What is a Combination?
The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.
If the combination begins with an odd digit
We have 3 * 2 * 3 * 2 * 3 = 108 possible combinations
If the combination starts with an even digit
We have 2 * 3 * 2 * 3 * 2 = 72 possible combinations
So 108 + 72 = 180 possible combinations
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plesae i am struguling with this problem: 2+2
Answer: 4
Step-by-step explanation:
2+2=4
Answer:
2 + 2 = 4
Step-by-step explanation:
If u just started to learn how to sum, you can use sticks
II + II = IIII
pls help me with this question
Answer: 11
Step-by-step explanation: I think it is 11 if you look and the 20 it goes down to 15 this is minus 5 so if you look at 16 I would think you just subtract 5
Leila spent a total of $45 at the grocery store. Of this amount, she spent $27 on fruit. What percentage of the total did she spend on fruit?
Answer:
She spend on fruit:
60%
Step-by-step explanation:
27/45 = 0.6
0.6 * 100 = 60%
write 36 as a product of its prime factors, write the factors in order from smallest to biggest
Answer:
1, 2, 3, 4, 6, 9, 12, 18, 36
Step-by-step explanation:
From smallest to biggest, the necessary variables are 1, 2, 3, 4, 6, 9, 12, 18, and 36. By expressing 36 as the product of the components, we may get the factors.
Find the slope of the line that passes through (8,3) and (1,7)
Answer:
Slope = -4/7
Step-by-step explanation:
The slope of a line is determined by the formula m = (y2 - y1) / (x2 - x1), where m is the slope of the line, (x1, y1) and (x2, y2) are two points on the line. Plugging in the values from the given points, we get:
m = (7 - 3) / (1 - 8) = 4 / -7 = -4/7
Therefore, the slope of the line that passes through (8,3) and (1,7) is -4/7.
An entry-level civil engineer earns an average bi-weekly net pay of $2,104.95. The engineer has created a monthly budget using the following percentages for expenses:
Percent
Housing 30%
Food/Household 20%
Savings 5%
Transportation 10%
Debt 10%
Entertainment 5%
Medical/Personal Care 3%
Giving 5%
Clothing 2%
Miscellaneous 10%
Which balance sheet correctly represents the engineer's income, expenses, and balance?
Income
Amount
Bi-weekly income $2,104.95
Total Monthly Income $4,560.73
Expenses
Percent Amount
Housing 30% $1,368.22
Food/Household 20% $912.15
Savings 5% $228.04
Transportation 10% $456.07
Debt 10% $456.07
Entertainment 5% $228.04
Medical/Personal Care 3% $136.82
Giving 5% $228.04
Clothing 2% $91.21
Miscellaneous 10% $456.07
$4,560.73
Balance
Income $4,560.73
Expenses $4,560.73
Balance $0
Income
Amount
Bi-weekly income $2,104.95
Total Monthly Income $4,209.90
Expenses
Percent Amount
Housing 30% $1,262.97
Food/Household 20% $841.98
Savings 5% $210.50
Transportation 10% $420.99
Debt 10% $420.99
Entertainment 5% $210.50
Medical/Personal Care 3% $126.30
Giving 5% $210.50
Clothing 2% $84.20
Miscellaneous 10% $420.99
$4,209.90
Balance
Income $4,209.90
Expenses $4,209.90
Balance $0
Income
Amount
Bi-weekly income $2,104.95
Total Monthly Income $2,104.95
Expenses
Percent Amount
Housing 30% $631.49
Food/Household 20% $420.99
Savings 5% $105.25
Transportation 10% $210.50
Debt 10% $210.50
Entertainment 5% $105.25
Medical/Personal Care 3% $63.15
Giving 5% $105.25
Clothing 2% $42.10
Miscellaneous 10% $210.50
$2,104.95
Balance
Income $2,104.95
Expenses $2,104.95
Balance $0
Income
Amount
Bi-weekly income $2,104.95
Total Monthly Income $3,157.43
Expenses
Percent Amount
Housing 30% $947.23
Food/Household 20% $631.49
Savings 5% $157.87
Transportation 10% $315.74
Debt 10% $315.74
Entertainment 5% $157.87
Medical/Personal Care 3% $94.72
Giving 5% $157.87
Clothing 2% $63.15
Miscellaneous 10% $315.74
$3,157.43
Balance
Income $3,157.43
Expenses $3,157.43
Balance $0
The balance sheet that correctly represents the engineer's income, expenses, and balance is balance number 4.
How to determine percentages of income?We should know that a balance sheet is a summary of assets and liabilities and income and expenses of a legal person. This implies that a month has two bi-weeks. therefore every income and expense is multiplied by 2 to get the following figures.
Income Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $0
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How would you describe the graph for the equation |x|=2?
Answer:
Below
Step-by-step explanation:
It will be just two vertical lines one at x = -2 the other at x = 2
( There are no 'circles' ) ....here is a graph:
Which point is the solution set of the given system of inequalities?
After solving, the solution set of the give inequality is (-1, 3)
In the given question, we have to find the solution set of the given system of inequalities.
The given inequalities are
x+y≥2...................(1)
4x+y≥-1.................(2)
To solve the given inequality we use the elimination method.
Multiply equation 1 by 4 on both side, we get;
4x+4y≥8...................(3)
Subtract equation 3 and 2, we get;
3y≥9
Divide by 3 on both side we get;
y≥3
Put the value of y in equation 1
x+3≥2
Subtract 3 on both side, we get;
x≥-1
Hence, the solution set of the give inequality is (-1, 3).
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The write question is;
Which point is the solution set of the given system of inequalities?
x+y≥2
4x+y≥-1
Which sentence from the article would be MOST important to include in a summary of the article?
Tomika uses 619 6 1 9 inches of wire to make a necklace and 313 3 1 3 inches of wire to make a bracelet. How many necklace and bracelet sets can she make if she uses 2813 28 1 3 inches of wire in all? enter your answer in the box.
About 3 necklace and bracelet sets can be made by Tomika using the given wire length.
A division is an action of dividing a sum into equal pieces. In division, a number being divided is referred to as the dividend, and the number being divided by it is referred to as the divisor. The quotient is the result of the division.
In mixed fractions, this is written as [tex]\text{quotient}\frac{\text{remainder}}{\text{divisor}}=Q\frac{R}{D}[/tex].
Given the inch of wire required to make a necklace is [tex]6\frac{1}{9}[/tex].
The inch of wire required to make a bracelet is [tex]3\frac{1}{3}[/tex].
The total inch of wire available is [tex]28\frac{1}{3}=\frac{85}{3}[/tex].
Then, the total inch of wire required to make a set of necklaces and bracelets is
[tex]\begin{aligned}6\frac{1}{9}+3\frac{1}{3}&=\frac{55}{9}+\frac{10}{3}\\&=\frac{55+30}{9}\\&=\frac{85}{9}\end{aligned}[/tex]
To find the number of sets made from the given wire is,
[tex]\begin{aligned}\text{number of sets}&=\frac{\text{total wire length available}}{\text{required length of wire}}\\&=\frac{\frac{85}{3}}{\frac{85}{9}}\\&=3\end{aligned}[/tex]
The answer is 3 sets.
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What is a function calculator?
A Function Calculator is a free online tool that displays the graph of the given function.
Function Calculator
The calculator will try to find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical (stationary) points, extrema (minimum and maximum, local, relative, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single-variable function. The interval can be specified. Parity will also be determined.
It's able to do simple arithmetic, which includes addition, subtraction, multiplication, and division.
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How do you find the slope intercept form with one point and parallel lines?
Parallel lines have equal slopes, so the slope of the line is then put in slope-intercept form.
First, put the equation of the line given into slope-intercept form by solving for y. You get [tex]y=-2x+5[/tex], so the slope is –2. Parallel lines have equal slopes, so the slope of the line we want to find is [tex]-2[/tex]. Plugging in the point given into the equation [tex]y=-2x+b[/tex] and solving for b, we get [tex]b=5[/tex].
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how do i write a composition of transformations that maps a polygon onto another polygon that are congruent
Answer:A conductor is mapping a trip and records the distance the train travels over certain time intervals. time (hours) Distance (miles) 0.5 22.5 1 45 1.5 67.545 The train travels at a constant speed. What is its speed in miles per hour?
Step-by-step explanation:
do not uses this site i got all my answers wrong going here
3(2x-5)-4x=33 solve for x
Answer: x =24
Step-by-step explanation:
3(2x-5)-4x=33
6x - 15 -4x = 33
2x - 15 = 33
2x = 48
x = 24
Answer:
x = 24
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(2x−5)−4x=33
(3)(2x)+(3)(−5)+−4x=33(Distribute)
6x+−15+−4x=33
(6x+−4x)+(−15)=33(Combine Like Terms)
2x+−15=33
2x−15=33
Step 2: Add 15 to both sides.
2x−15+15=33+15
2x=48
Step 3: Divide both sides by 2.
2x/2 = 48/2
x = 24
What is a percentage of 1 2?
There is no percentage of 1 2, as percentages are a fraction of 100 and 1 2 is not a fraction.
A percentage is a fraction of 100, while 1 2 is not a fraction. Therefore, there is no percentage of 1 2.A percentage is a way to express a number as a fraction of 100. For example, 25% is equivalent to the fraction 25/100. However, 1 2 is not a fraction, and therefore cannot be expressed as a percentage.1 2 can be expanded to 100 by multiplying both numerator and denominator by 50. 1 2 would then be equal to 50/100, or 50%.
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Quadrilateral LMNP has diagonals LN and MP. The two diagonals intersect at Point D. If D is the midpoint of LN and MP, which of the following relationships must
be true?
The correct relationship is Δ PDN ≅ Δ MDL
What is a quadrilateral?The quadrilateral is a type of 2D geometrical shape with four sides, the sum of its interior angles is 360°.
Given that, Quadrilateral LMNP has diagonals LN and MP. The two diagonals intersect at Point D. If D is the midpoint of LN and MP.
Considering the triangles, Δ PDN and Δ MDL
According to definition of midpoints,
LO ≅ ON
MO ≅ OP
∠ MDL ≅ ∠ PDN (vertically opposite angles)
Therefore, Δ PDN ≅ Δ MDL by SAS rule.
Hence, option a) Δ PDN ≅ Δ MDL, is correct.
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Explain the differences between a positive association and a negative association of bivariate data
Answer:
A positive association between two variables means that as the values of one variable increase, so do the values of the other variable. This is often represented by a line or curve that slopes upward to the right on a scatterplot. On the other hand, a negative association between two variables means that as the values of one variable increase, the values of the other variable decrease. This is often represented by a line or curve that slopes downward to the right on a scatterplot.
The last time Caralina visited the post office, she spent $4.49 to mail letters and packages. Each letter cost $0.37 to mail, while each package cost $0.88 to mail. if she sent two more letters than packages, how many letters did she mail?
Answer:
5 letters
Step-by-step explanation:
let x = # of packages
x+2 = # of letters
$0.37(x+2) + $0.88x = $4.49
.37x + .74 + .88x = 4.493
1.25x + .74 = 4.49
1.25x = 3.75
x = 3.75/1.25 = 3 = # of packages
# of letters = x+2 = 3+2 = 5
what is 3 3/4 + 2 5/7 pls tell me and whoever answers thank you
Answer:
1 13/28
Step-by-step explanation:
Hopefully you can see the picture, that picture shows how I solved it bc it's hard to type it and also bc u might have to show your work in order for you to solve it and get credit.
the pessimistic approach assumes that the worst possible outcome for each alternative will occur and selects the best of these. is it true or false ?
True. The pessimistic approach assumes that the worst-case scenario for each alternative will occur and chooses the best of these.
An optimistic approach indicates that the decision-makers believe the outcomes will benefit the organisation. A pessimistic approach, on the other hand, indicates that the decision-makers are convinced that the outcomes will be detrimental to them. The pessimistic approach allows decision-makers to plan for the worst-case scenario. In the optimistic approach, decision-makers believe that the alternatives chosen will produce the best results. In other words, the decision-makers are confident that their options are the best for the circumstances. The pessimistic approach is characterised by decision-makers assuming that the choices they make will have the most negative outcomes.
Thus, the pessimistic approach is the approach which is used to assume the worst possible outcomes for each alternative will occur.
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A farmer has 63 cows and 81 sheep. Write the ratio of cows to sheep in its lowest terms.
Answer:
7:9
Step-by-step explanation:
The basic ratio is 63:81 but to simplify this ratio you can simplify each number as a multiplication of its factors.
63=3*3*7
81=3*3*3*3
Now find the factors they have in common and get rid of them.
63=3*3*7
81=3*3*3*3
The numbers in bold are all the factors that they have in common.
You can cancel these numbers out.
Now the remaining numbers you can put into a ratio in the same order
7:3*3
7:9
one commercially available ten-button lock may be opened by depressing -- in any order -- the correct five buttons. the sample shown below has \{1, 2, 3, 6, 9\}{1,2,3,6,9} as its combination. suppose that these locks are redesigned so that sets of as many as nine buttons or as few as one button could serve as combinations. how many additional combinations would this allow?
The required additional combinations would this allow is 770.
What is combination?Mathematical technique that decides the quantity of potential game plans in an assortment of things where the request for the choice doesn't make any difference. In mixes, you can choose the things in any request. Combinations can be mistaken for changes.
According to question:Right now there are ¹⁰C₅ possible combinations. With any number x from 1 to 9, the quantity of ways of picking a bunch of x buttons is ∑₁⁹ ¹⁰Cₐ
Using identity,
∑ⁿₐ ⁿCₐ = 2ⁿ
So the quantity of extra combinations is simply,
2¹⁰ - ¹⁰C₀ - ¹⁰C₁₀ - ¹⁰C₅
1024 - 1 - 1 - 252 = 770
Thus, possible combinations are 770.
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What is 1 squares in square Metres?
Answer:
Squares are the most common unit of measurement referenced when it comes to overall house size, and one square is equivalent to 9.290304 square metres (confusing, huh
What is slope formula in 7th grade?
The slope formula generally used in the 7th grade is as follows -
1. The Point slope form -
Suppose you are given two points (x1,y1) and (x2,y2) or a graph consisting of two points whose slope is asked, then you use this method.
These points are often intercepts of the x and/or y axes.
Here you can use the formula for the equation of the slope which is -
m= (y2−y1) / (x2−x1).
2. The Slope-intercept Form-
Here, you are given the linear equation that is in the form y=mx+b.
If not you can manipulate it into that form.
Now, the slope here is m which is the coefficient of x.
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Which one of the following is NOT equivalent to 3/4
a 16/24
b 15/20
c 6/8
d 24/32
Which of the following is NOT equivalent to 3/4?
Simplest form:
a. [tex]\dfrac{16}{24}[/tex]
[tex]\dfrac{16\div8}{24\div8} =\dfrac{2}{3}[/tex]
Option A is not equivalent to 3/4
b. [tex]\dfrac{15}{20}[/tex]
[tex]\dfrac{15\div5}{20\div5} =\dfrac{3}{4}[/tex]
Option B is equivalent to 3/4
c. [tex]\dfrac{6}{8}[/tex]
[tex]\dfrac{6\div2}{8\div2} =\dfrac{3}{4}[/tex]
Option C is equivalent to 3/4
d. [tex]\dfrac{24}{32}[/tex]
[tex]\dfrac{24\div8}{32\div8} =\dfrac{3}{4}[/tex]
Option D is equivalent to 3/4.
Option A would be your answer since it is the only option that isn't equivalent to 3/4.
Solve
3(2x + 9) = 24
Answer:
-0.5
Step-by-step explanation:
3(2x+9)=24
Distribute the 3
3(2x)+3(9)=24
6x+27=24
Subtract both sides by 27
6x= -3
Divide both sides by 6
x= -0.5
Hopes this helps
Answer:
x = -1/2
Step-by-step explanation:
Given equation,
→ 3(2x + 9) = 24
Now the value of x will be,
→ 3(2x + 9) = 24
→ 6x + 27 = 24
→ 6x = 24 - 27
→ 6x = -3
→ x = -3/6
→ [ x = -1/2 ]
Hence, the value of x is -1/2.