I need to use substitution to solve each system of equations then use ordered pairs
Answers
From the given question
There are given that the equation
[tex]\begin{gathered} 2x+5y=38\ldots(1) \\ x-3y=-3\ldots(2) \end{gathered}[/tex]Now,
From the equation (1)
[tex]\begin{gathered} 2x+5y=38 \\ 2x=38-5y \\ x=\frac{38}{2}-\frac{5}{2}y \\ x=19-\frac{5}{2}y\ldots(3) \end{gathered}[/tex]Then,
Put the equation (3) into the equation (2)
So,
[tex]\begin{gathered} x-3y=-3 \\ 19-\frac{5}{2}y-3y=-3 \\ 38-5y-6y=-6 \\ 38-11y=-6 \\ -11y=-6-38 \\ -11y=-44 \\ y=4 \end{gathered}[/tex]Then,
Put the value of y into the equation (3)
So,
[tex]\begin{gathered} x=19-\frac{5}{2}y \\ x=19-\frac{5}{2}(4) \\ x=19-\frac{20}{2} \\ x=19-10 \\ x=9 \end{gathered}[/tex]Hence, the value of x is 9 and y is 4.
Related Questions
Find the equation of the line passing through point (3,5) and with a slope ⅓
Answers
hello
we are given 1 point with x and y co-ordinate and a slope, we can easily write down the equation of the line
standard equation of a straight line is
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]to solve this problem, we need to find the intercept first
substitute the x and y co-ordinates in the equation
[tex]\begin{gathered} y=mx+c \\ m=\frac{1}{3} \\ y=5 \\ x=3 \\ 5=\frac{1}{3}(3)+c \\ 5=1+c \\ c=4 \end{gathered}[/tex]we know our intercept is equal to 4 and we can proceed to write out our equation
[tex]y=\frac{1}{3}x+4[/tex]we can leave it this way or multiply through by 3
[tex]3y=x+12[/tex]Which expressions simplify to a rational answer.
Question is attached below
Answers
The expression that simplify to rational number are as follows:
1 / 4 + 1 / 2 2.√9 3.7.(1 / 3) 7. √81 How to find rational numbers?A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0.
In a simpler terms, If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.
Rational numbers can also be expressed in decimal form.
Rational numbers have terminating decimals.
Therefore, let's find the rational simplification in the options.
1 / 4 + 1 / 2 = 3 / 4 2.√9 = 2 × 3 = 93.7.(1 / 3) = 21 × 1 / 3 = 77. √81 = 7 × 9 = 72learn more on rational numbers here:https://brainly.com/question/7129080
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May I please help with this. I have tried to find the correct answers but still couldn’t get them right
Answers
Solution
[tex]1cm\text{ to 7in}[/tex]We can use ratio to solve the problem
Part A
5cm to x in
[tex]\begin{gathered} 1cm\colon7in \\ 5cm\colon x\text{ in} \end{gathered}[/tex]Now
[tex]\begin{gathered} 1\colon7 \\ 5\colon x \\ \therefore\frac{1}{7}=\frac{5}{x} \\ \\ \text{cross multiply} \\ 1\times x=5\times7 \\ x=35 \end{gathered}[/tex]The final answer
[tex]5cm\text{ to 35inches}[/tex]Part B
Similar step as part a
[tex]\begin{gathered} 1\colon7 \\ y\colon63 \\ \frac{1}{7}=\frac{y}{63} \\ \\ \text{cross multiply} \\ 7y=63 \\ \text{divide both sides by 7} \\ \frac{7y}{7}=\frac{63}{7} \\ y=9 \end{gathered}[/tex]The final answer
[tex]9cm\text{ to 63inches}[/tex]Summary
WILL GIVE BRIANLYEST 100 POINTS ACULLY 200 BC IM GIVING EXTRA POINTS
Answers
Answer:
the mean would increase to a value to about 24.6
Q2: median is 7.
Step-by-step explanation:
Answer:
Q1) the mean would increase in value to about 24.6
Q2) 7
Solve for u.u + 8 = 16
Answers
In this case the answer is very simple. .
We must apply algebraic rules to find the solution.
u + 8 = 16
u = 16 - 8
u = 8
The answer is:
u = 8
if a fraction product always l esser than the lesser factor
Answers
We have that whenever you multiply two positive fractions, the product will be smaller than both factors. For example, if we have the following:
[tex]\frac{1}{2}\cdot\frac{3}{4}=\frac{3}{8}[/tex]notice that both factors are fractions and the product is less than both factors.
REDUCE 48/96 TO THE LOWEST TERMS
Answers
Which mapping diagram is NOT a function?
Answers
Answer:
D is not a function--an x-value cannot correspond to more than one y-value.
Convert the numeral in base ten. (Explanation please)
Answers
Converting the given expression which is [tex]43_{8}[/tex] to base ten gives 35 in base ten.
How to convert a number in base eight to base tenConversion of bases is achieved based on how the conversion to be done are are basically of two methods which are
conversion from other bases to base tenconversion from base ten to other basesThe question is about converting other bases (base eight) to base ten. The steps required are as follows:
For other bases, the number 8 as used is replaced by the number required to be convertedThe exponents starts from zero and increases from left to right as seen belowThe given data is a number in base eight
[tex]43_{eight}[/tex]
[tex]43_{eight}=4*8^{1}+3*8^0[/tex]
[tex]43_{eight}=4*8+3*1[/tex]
[tex]43_{eight}=32+3[/tex]
[tex]43_{eight}=35[/tex]
The number 35 is now in base ten and can be written as [tex]35_{10}[/tex]
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pls help fast I have to submit this soon!! :)
Answers
Since the rectangles are similar, that means their sides are proportional.
Since the bigger rectangle has a base of 24cm and the smaller one's base is 20cm, the proportion the sides hold is
[tex]\frac{24}{20}=1.2[/tex]This means the sides of the larger rectangle are 1.2 times larger than those of the smaller one.
The area of the small rectangle is 80cm². Since
[tex]A=b\mathrm{}h[/tex]where b is the lenght of the base and h is the lenght of the height, then
[tex]80=20\cdot h_1[/tex][tex]\frac{80}{20}=h_1=4[/tex]So the height of the small rectangle will be 4cm. But as we previously deduced, the height of the larger rectangle will be 1.2 times larger than that of the smaller one, so it's height will be
[tex]h_2=4\cdot1.2=4.8[/tex]And so, its are is
[tex]A_2=24\cdot4.8=115.2[/tex]We can confirm this because
[tex]\frac{115.2}{80}=1.44=1.2^2[/tex]which is the proportion the areas of the rectangles hold.
Lesson 4-2: Relations VA Name the ordered pair for each point. C С 1.A 2.B DI 3.C 4.D e е )
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Assign the pair of coordinates for each point (use the graph)
A. (1,4)
B. (-2,-4)
C. (-2,2)
D. (4,-2)
What is theUpper Quartile (the median of 35, 38, 39, 61)?
Answers
Solution:
Given the following data below
[tex]35,38,39,61[/tex]The upper quartile, Q₂, (median) will be
[tex]\begin{gathered} Q_2=\frac{38+39}{2}=\frac{77}{2}=38.5 \\ Q_2=38.5 \end{gathered}[/tex]Hence, the answer is 38.5
1. Jessica finishes her book in 2 1/3
hours. Eric takes 1 1/2
times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1/3
. The model is 2 1/3 out of 3
Answers
Proportionately, the number of hours it takes Eric to finish the book as Jessica is 3¹/₂ hours.
What is proportion?Proportion refers to the ratio of the quantity contained in a number or value concerning another value's ratio.
Proportions, like ratios, are fractional values, represented using decimals, fractions, or percentages.
In ratio terms, Eric's reading time is 3¹/₂ hours to Jessica's 2¹/₃ hours, giving an absolute ratio of 3: 2 with a constant proportionality of 1.5 hours.
For instance, the product of Eric's reading time, compared to Jessica's reading time, shows that Jessica does a faster reading than Eric.
The total number of hours it takes Jessica to finish her book = 2¹/₃ hours
The total hours it takes Eric to finish the book = 2¹/₃ hours x 1¹/₂
= 3¹/₂ hours (2¹/₃ x 1¹/₂).
Thus, whereas Jessica takes 2¹/₃ hours to finish the book, in proportion, Eric consumes 3¹/₂ hours reading the same book.
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Complete Question:Jessica finishes her book in 2¹/₃ hours. Eric takes 1¹/₂ times longer than Jessica to finish his book. How long did Eric take to finish the book?
What is the area of the blue shape?
Pls help :(
Answers
Answer:
38.5 sq units
Step-by-step explanation:
Hello!
We can split the shape into two rectangles.
The small rectangle at the top has an area of 14 sq units (2 * 7).
The middle rectangle has an area of 49 sq units ( 7*7).
Since the blue part in the middle rectangle is half of the whole rectangle, the area of the blue part there is 24.5 sq units.
Adding that to 14 sq units will give us 38.5 sq units.
6. The graph shows how much money Priya has in her savings account weeksafter she started saving on a regular basis.
Answers
Given:
Graph is given.
6a.
[tex]\text{Money in the account after 10 weeks= \$320}[/tex]6b.
[tex]\text{Number of weeks take to save \$200= 5 weeks}[/tex]6c.
[tex]\text{Priya have \$80 in her account when she started the savings regularly}[/tex]mark wrote this description of a quadrilateral he drew it has one pair of parallel lines and two congruent lines but the lines that are congruent are not parallel
Answers
First, draw two parallel lines:
Next, draw to additional lines of the same length that connect both parallel lines:
Notice that this can be done in two different ways. In the case in red, both lines are not parallel. In the case shown in blue, they are. Since the problem asks for the case when they are not parallel, keep in mind the figure with the lines in red. That figure is a trapezoid.
Hello, I need some assistance with this precalculus question, please?HW Q8
Answers
STEP - BY - STEP EXPLANATION
What to find?
• The system of equation of the argumented matrix.
,• The resultant after the given row operations.
Given:
The system of equation is:
7x - 7y + z = -5
3x - 3y + 8z = -5
-6x + y + 3z = 7
Hence, the correct option is D
The following row operations are to be performed;
[tex]\begin{gathered} R_1=-2r_2+r_1 \\ \\ R_3=2r_2+r_3 \end{gathered}[/tex]The first row operation implies that you will multiply row 2 by -2 and then add to row. The resultant gives a new row 1.
This means that the elements in row 1 becomes:
Row 1 : 1 -1 - 15 | 5
Row 2: 3 -3 8 | -5
As for row 3, we will multiply row 2 by 2 and then add to row 3 to get a new row 3.
That is;
Row 3 : 0 -5 19 | -3
ANSWER
Option D
Part B
[tex]\begin{bmatrix}{1} & {-1} & {-15\text{\mid}} & {5} \\ {3} & {-3} & {8\text{ }}| & {-5} \\ 0{} & -5{} & {19\text{ }|} & {-3} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}[/tex]1 -1 - 15 | 5
3 -3 8 | -5
0 -5 19 | -3
A study done by researchers at a university concluded that 60% of all student athletes in the country have been subjected to 74 repeating the study is based on responses from 1600 athlete what is the margin of error and the 95% confidence interval of the study 
Answers
The marginal error is 0.0240
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
Given,
The percentage of students surveyed = 60%
Number of athletes = 1600
Confidence interval = 95%
We have to find the marginal error and 95% confidence interval of the study;
The following results are obtained from a sample of n people that were surveyed, with a probability of success of π and a level of confidence of 1 - ∝
π ± z [tex]\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
Where,
z is the z score with a p value of 1 - ∝/2
Here we have,
n = 1600 and π = 0.6
95% confidence level
So ∝ = 0.05 , z is the value of Z that has a pvalue of 1 - 0.05/2 , so Z = 1.96.
Then, the margin of error is;
M = [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
M = [tex]1.96\sqrt{\frac{0.6.0.4}{1600} }[/tex]
M = 0.0240
M = 2.40 percentage points.
Lower limit of the interval;
π - M = 0.6 - 0.0240 = 0.576
Upper limit of the interval;
π + M = 0.6 + 0.0240 = 0.624
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
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Original amount: 25End amount: 18
Answers
The formula to calculate the percentage change is given as
[tex]\text{Percentage Change = }\frac{Original\text{ Amount}-\text{Final Amount}}{Original\text{ Amount}}\times100[/tex]The question gives us:
Original amount: 25
End amount: 18
Substituting, we have
[tex]\begin{gathered} C=\frac{25-18}{25}\times100 \\ =\frac{7}{25}\times100 \\ =28 \end{gathered}[/tex]The percentage change is a 28% decrease.
Maria is planting a row of flowers in a bed 77 feet long. The instructions say to space the plants 1 foot apart, allowing room for 77 flowers. The flowers come in flats containing 6 plants per flat.
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She will need 12 flats and there will be 5 leftovers
The number of flats she will needFrom the question, we have
Length = 77 feetDistance apart = 1 footNumber of flowers = 77Rate = 6 plants per flatThe number of flats is calculated as
So, we have the following equation
Number of flats = (Length)/Rate
So, we have
Number of flats = (77)/6
Evaluate
Number of flats = 12
The number of plants leftoverThis is calculated as
Leftover = Length - Number of flats * Rate
So, we have
Leftover = 77 - 12 * 6
Evaluate
Leftover = 5
Hence, the left over is 5
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Missing information in the question
How many flats will she need?How many plants will she have left over?Owners of a recreation area are adding water to a pond. The graph below shows the amount of water in the pond (in liters) versus the amount of time that water is added (in hours).Use the graph to answer the questions.(a)How much does the amount of water increase for each hour that water is added?liters=(b)What is the slope of the line?
Answers
GIVEN:
We are given a graph showing the increase in the amount of water pumped into a pond for every passing hour.
Required;
To determine the amount of increase in the water level for each hour that water is added.
Also, to determine the slope of the line as shown in the graph.
Step-by-step solution;
(a) Notice that the graph shows an increase in the water level for every passing hour. Notice also the following relationship;
[tex]\begin{gathered} (hours,liter) \\ \\ (0,100) \\ \\ (1,400) \\ \\ (2,700) \\ \\ (3,1000) \end{gathered}[/tex]We can see that the rate of change for every hour is 300 liters increment.
Therefore, for each hour that water is added, there is an increase of 300 liters.
(b) To calculate the slope of the line shown in the graph, we shall take the change in liters and divide by the corresponding change in the hours.
We now have the following;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(0,100) \\ \\ (x_2,y_2)=(1,400) \end{gathered}[/tex]We now have the slope as follows;
[tex]\begin{gathered} m=\frac{400-100}{1-0} \\ \\ m=\frac{300}{1}=300 \end{gathered}[/tex]The slope therefore is 300.
ANSWER:
[tex]\begin{gathered} (a)\text{ }Liters=300 \\ \\ (b)\text{ }slope=300 \end{gathered}[/tex]Drag and drop the correct value next to its equivalent expression number maybe use ones are not at all.
Answers
Solution:
Expression:
[tex]\begin{gathered} \frac{2}{3}\times42=2\times14 \\ \frac{2}{3}\times42=28 \end{gathered}[/tex]Expression:
[tex]\begin{gathered} \frac{5}{12}\times26=\frac{5}{6}\times13 \\ \\ \frac{5}{12}\times26=\frac{65}{6} \\ \\ \frac{5}{12}\times26=10\frac{5}{6} \end{gathered}[/tex]ANSWER:
[tex]\frac{5}{12}\times26=10\frac{5}{6}[/tex]Expression:
[tex]\begin{gathered} \frac{11}{15}\times20=\frac{11}{3}\times4 \\ \\ \frac{11}{15}\times20=\frac{44}{3} \\ \\ \frac{11}{15}\times20=14\frac{2}{3} \end{gathered}[/tex]ANSWER:
[tex]\frac{11}{15}\times20=14\frac{2}{3}[/tex]Expresion:
[tex]\begin{gathered} \frac{3}{8}\times54=\frac{3}{4}\times27 \\ \\ \frac{3}{8}\times54=\frac{81}{4} \\ \\ \frac{3}{8}\times54=20\frac{1}{4} \end{gathered}[/tex]ANSWER:
[tex]\frac{3}{8}\times54=20\frac{1}{4}[/tex]A) Write an expression for the given number trick B) Simplify the expression you came up with
Answers
a)
Since we need an Expression, we also need a variablel for the "number".
Let's use "n".
We will translate each of the lines:
Pick a number : n
Mutiply that number by 12, so it becomes: n x 12
Add 15 to that, so we put parenthesis around that expression and add "15" to it:
(n x 12) + 15
Divide by 3, then we simply divide whole thing by 3, so we have:
[tex]\frac{(n\times12)+15}{3}[/tex]b)
To simplify, let's re-write:
[tex]\begin{gathered} \frac{(n\times12)+15}{3} \\ =\frac{12n+15}{3} \\ =\frac{12n}{3}+\frac{15}{3} \\ =4n+5 \end{gathered}[/tex]This is the simplified form.
Given the exponential decay function below:Determine the intervals of increase and decrease.
Answers
Given the equation of exponential decay function:
[tex]y=(\frac{1}{3})^x-3[/tex]The given function always decreases overall the domain
so, the answer will be the intervals of decrease is:
[tex](-\infty,\infty)[/tex]Alision has an interest in entomology, the study of insects. Her collection of insects from around the world includes the four specimens shown in the table below.
Answers
we know that
the mass of Alison's Emperor Scorpio is
[tex]2^{-5}=(\frac{1}{2})^5=\frac{1}{2^5}=\frac{1}{32}\text{ kg}[/tex]The answer is the second optionI don’t really need explanation just give answer honestly I will rate you a 5star regardless I thankyou so much for the help!
Answers
Explanation
The information given directly by the picture is that:
[tex]\begin{gathered} CG\cong CH \\ \angle G\cong\angle H \end{gathered}[/tex]This means we have a pair of congruent sides and a pair of congruent angles.
We need one more information to prove congruency. There is no way of getting side information, by if we see the vertex C, the angles make a pair of vertical angles. Vertical angles are congruent, so:
[tex]\angle FCG\cong\angle JCH[/tex]This means now that we have 2 pairs of congruent angles and one pair of congruent sides, so we will use either AAS or ASA.
To determine which is the case, we can visualize the order in which the angles and side appear going around the triangle.
We can see that we have an Angle then the side then the other Angle, so the order is Angle-Side -Angle, so the rule we need to use is ASA.
Answer
Angle-Side-Anlge, that is ASA.
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 4 boys and 5 girls are competing, how many different ways could the six medals possibly be given out?
Answers
ANSWER
1,440
EXPLANATION
We have that 4 boys are competing and also 5 girls are competing. 3 medals are given to the boys and 3 medals are given to the girls.
For the boys, the gold medal can be awarded to one of 4 boys, then the silver medal can be awarded to 3 boys because 1 of them already got the gold medal. Finally, the bronze medal can be awarded to one of 2 boys, since the gold and silver medals are already taken. The number of ways the medals can be given to the boys is,
[tex]permutations_{boys}=4\cdot3\cdot2=24[/tex]This situation is similar for the girls, but in this case, there are 5 girls in total,
[tex]permutations_{girls}=5\times4\times3=60[/tex]The total ways the six medals can be given is,
[tex]permutations_{boys}\times permutations_{girls}=24\times60=1,440[/tex]Hence, there are 1,440 ways to give the six medals to the 4 boys and 5 girls.
1 x(x-2) how I do this
Answers
x(x-2)
Apply the distributive property:
x(x)+x(-2)
x^2-2x
A savings account has $2000 in it, earns no interest, andreceives a deposit of $150 per month.What type of growth characterizes the account's change invalue?
Answers
SOLUTION
The question can be written in equation form as:
Select the postulate that is illustrated for the real numbers.
2(x + 3) = 2x + 6
A. The multiplication inverse
B. The addition inverse postulate
C. The commutative postulate for multiplication
D. Multiplication identity
E. The distributive postulate
F. The addition of zero postulate
G. Commutative postulate for addition
Answers
The postulate that is illustrated for the real numbers 2(x + 3) = 2x + 6 is The Distributive postulate , the correct option is (E) The Distributive postulate .
The Distributive Postulate states that for any three numbers a,b and c ,
a(b+c) = a*b + a*c
For Example : 5(6+1) = 5*6 + 5*1
5*7 = 30+5
35=35
In the question ,
it is given that
2(x + 3) = 2x + 6
On applying Distributive postulate in 2(x + 3)
we get
= 2*x + 2*3
= 2x + 6
hence Distributive postulate is applied in 2(x + 3) = 2x + 6 .
Therefore , the postulate that is illustrated for the real numbers 2(x + 3) = 2x + 6 is The Distributive postulate , the correct option is (E) The Distributive postulate .
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