Solve this system of equations byusing the elimination method.6x » 5y = 33x – 8y = –15=72
Answers
Given: The system of equations below
[tex]\begin{gathered} equation1:6x-5y=3 \\ equation2:3x-8y=-15 \end{gathered}[/tex]To Determine: The solution of the equations
Solution
Step 1: Eliminate x by multiplying equation 1 by 1 and equation 2 by 2
[tex]\begin{gathered} 1\times(6x-5y=3)\rightarrow6x-5y=3 \\ 2\times(3x-8y=-15)\rightarrow6x-16y=-30 \end{gathered}[/tex]Step 2: Subtract derived equation from equation 2 from the derived equation from equation 1
[tex]\begin{gathered} (6x-5y=3)-(6x-16y=-30) \\ 6x-6x-5y--16y=3--30 \\ -5y+16y=3+30 \\ 11y=33 \\ y=\frac{33}{11} \\ y=3 \end{gathered}[/tex]Step 3: Substitute the value of y into equation 1
[tex]\begin{gathered} 6x-5y=3 \\ 6x-5(3)=3 \\ 6x-15=3 \\ 6x=3+15 \\ 6x=18 \\ x=\frac{18}{6} \\ x=3 \end{gathered}[/tex]Hence, x = 3, y = 3
(3,3)
Related Questions
You consume 48 pounds of beef annually At a discount store , the price of beef is $ 1.19 less per pound than at a supermarket . How much would you save annually in dollars , if you bought all of your beef at the discount store ?
Answers
Solution
Given that 48 pounds of beef is consumed annually,
Since the discount rate is $ 1.19 per pounds less than the price at the supermarket,
=> $ 1.19 × 48 = $ 57.12 would you save annually in dollars
(a) The perimeter of a rectangular garden is 356 m. If the length of the garden is 95 m, what is its width?(b) The area of a rectangular window is 8514 cm2. If the width of the window is 86 cm, what is its length?
Answers
The perimeter of a rectangle is given by:
[tex]P=2w+2l[/tex]we know that P=356 m and l=95 m, plugging this values into the expression above and solvinf for w we have:
[tex]\begin{gathered} 356=2w+2(95) \\ 2w=356-2(95) \\ 2w=356-190 \\ 2w=166 \\ w=\frac{166}{2} \\ w=83 \end{gathered}[/tex]Therefore the width of the rectangle is 83 m.
Can you tell me what the distance is please I would really appreciate it.
Answers
To answer this question, we need to apply the formula for the distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Then, we have:
x1 = -6, y1 = 2
x2 = 6, y2 = -3
Thus, we have:
[tex]d=\sqrt[]{(6-(-6))^2+(-3-2)^2}\Rightarrow d=\sqrt[]{(6+6)^2+(-5)^2}\Rightarrow d=\sqrt[]{12^2+(-5)^2}[/tex]Then, we have:
[tex]d=\sqrt[]{144+25}\Rightarrow d=\sqrt[]{169}\Rightarrow d=13[/tex]Hence, the distance between these two points is d = 13 units.
which logarithmic equation correctly rewrites this exponential equation? 8^x=64
Answers
which logarithmic equation correctly rewrites this exponential equation? 8^x=64
we have that
64=2^6
so
substitute
8^x=2^6
8=2^3
so
(2^3)^x=2^6
2^(3x)=2^6
therefore
3x=6
x=2with logapply log both sideslog(8^x)=log(64)apply property of logx*log(8)=log(64)x=log(64)/log(8)simplifyx=log(2^6)/log(2^3)x={6log(2)}/{3log(2)}x=6/3x=2Answer:
log8 64=x
Step-by-step explanation:
Find the length of each side of an equilateral triangle with a perimeter of 147kilometers.
Answers
Given:
Perimeter (P) of an equilateral triangle = 147 km.
Required:
To find the length of each side (s) of an equilateral triangle.
Explanation:
The perimeter of an equilateral triangle is given by,
[tex]P=3\times s[/tex]Substituting values, we get the length of each side (s) of an equilateral triangle (in km) as follows:
[tex]\begin{gathered} P=3\times s \\ \Rightarrow147=3\times s \\ \Rightarrow s=\frac{147}{3} \\ \Rightarrow s=49 \end{gathered}[/tex]Final Answer:
The length of each side (s) of an equilateral triangle (in km) is,
[tex]s=49[/tex]the vault shown is in the shape of a cube if each side is 4y to the 4th power find the volume
Answers
Take into account that the volume of a cube is given by:
V = a³
where a is the side of the cube. In this case a = 4y⁴ feet. Replace this value of a into the previous expression for V:
V = (4y⁴ ft)³ = 4³y¹² ft³ = 64y¹² ft³
where you have used properties of exponents.
ence, the volume of the box with a shape of a cube is 64y¹² ft³
what is the constant of variation k of the direct variation y=kk, through (5,8)
Answers
SOLUTION:
We are to find the constant of variation k, of the direct variation, y = k x through (5, 8).
x = 5
y = 8
y = k x
8 = k (5)
8 = 5k
or
5k = 8
Dividing both sides by 5
k = 8/5 (option D)
Find the inverse of the function then sketch the graph.
Answers
The given function is
f(x) = x^3 - 1
We want to find the inverse of the function, f^-1(x). The first step is th replace f(x) with y. It becomes
y = x^3 - 1
The next step is to interchange x and y and solve for y. We have
x = y^3 - 1
Adding 1 to both sides of the equation, we have
x + 1 = y^3 - 1 + 1
y^3 = x + 1
Taking the cube root of both sides of the equation, we have
[tex]\begin{gathered} y\text{ = }\sqrt[3]{x\text{ + }1} \\ \text{Put y = f}^{-1}(x),\text{ we have} \\ f^{-1}(x)\text{ = }\sqrt[3]{x\text{ + }1} \end{gathered}[/tex]To plot the graph of the the inverse of the function, we would substitute values of x into the function and find corresponding values of y. These x and y values would be plotted on the graph. We have
[tex]\begin{gathered} \text{if x = 0, y = }\sqrt[3]{0\text{ + 1}}\text{ = }\sqrt[3]{1}\text{ = 1} \\ \text{If x = 7, y = }\sqrt[3]{7\text{ + 1}}\text{ = }\sqrt[3]{8}\text{ = 2} \\ \text{if }x\text{ = 26, y = }\sqrt[3]{26\text{ + 1}}\text{ = }\sqrt[3]{27}\text{ = 3} \end{gathered}[/tex]The graph is shown below
what is equivalent to 6.038+100603.8/1060.38/1,0000.6038+10
Answers
Answer:
Matching the given expressions with their equivalent ones
[tex]\begin{gathered} a\rangle6.038\times100\rightarrow603.8 \\ b\rangle\frac{603.8}{10}\rightarrow60.38 \\ c\rangle\frac{60.38}{1000}\rightarrow0.06038 \\ d\rangle0.6038\times10\rightarrow6.038 \end{gathered}[/tex]Explanation:
Given the expressions;
[tex]\begin{gathered} 6.038\times100 \\ \frac{603.8}{10} \\ \frac{60.38}{1000} \\ 0.6038\times10 \end{gathered}[/tex]Simplifying the expressions;
[tex]\begin{gathered} a\rangle6.038\times100=603.8 \\ b\rangle\frac{603.8}{10}=60.38 \\ c\rangle\frac{60.38}{1000}=0.06038 \\ d\rangle0.6038\times10=6.038 \end{gathered}[/tex]Therefore, matching the given expressions with their equivalent ones
[tex]\begin{gathered} a\rangle6.038\times100\rightarrow603.8 \\ b\rangle\frac{603.8}{10}\rightarrow60.38 \\ c\rangle\frac{60.38}{1000}\rightarrow0.06038 \\ d\rangle0.6038\times10\rightarrow6.038 \end{gathered}[/tex]Joey recorded the monthly change in his saving account balance, in dollars, for 5 months. His balance change each month was: -10,5, 55, -15, -20 What is the average monthly change in Joey's saving account balance?
Answers
His balance change each month are
-10, 5, 55, -15, -20
we need to re arrange in the ascending order
-20, -15, -10, 5, 55
Average = sum of all the numbers / total numbers
total numbers = 5
sum = -20 + (-15) + (-10) + 5 + 55
sum = -20 - 15 - 10 + 5 + 55
sum = -45 + 5 + 55
sum = 15
Average = 15 / 5
Average = 3
The answer is 3
my question is which fraction correctly represents one whole and the answer are 7/7, 7/1, 1/7, 3/7
Answers
7/7
Explanation:The given fractions are 7/7, 7/1, 1/7, and 3/7
The number at the top of the fraction is the numerator
The number at the bottom of the fraction is the denominator
For the fraction to give a whole number, the numerator has to be the same as the denominator
Out of the given options, only 7/7 has the same numerator and denominator. Therefore, it will give a whole number
Consider the following graph. Determine the domain and range of the graph.
Answers
Answer:
• Domain: (-∞, ∞)
,• Range: (-∞, ∞)
Explanation:
The arrows at the endpoints indicate that the graph continues infinitely.
The domain is the set of all values of x that the graph satisfies. The domain of the graph is:
[tex](-\infty,\infty)[/tex]The range is the set of all values of y that the graph satisfies. The range of the graph is:
[tex](-\infty,\infty)[/tex]Elizabeth owns a small business selling bagels. She knows that in the last week 16 customers paid cash, 78 customers used a debit card, and 15 customers used a credit card. Based on these results, express the probability that the next customer with something other than cash as a percent to the nearest whole number. pay
Answers
P= probability
[tex]P=\frac{numberof\text{ customer used cash}}{total\text{ number of customers }}[/tex][tex]p=100\times\frac{93}{16+78+15}[/tex][tex]p=100\times\frac{93}{109}[/tex][tex]p=85\text{ percent}[/tex]Evaluate and simplify the expression when A=4 and b=- 1
Answers
Since the given expression is
[tex]\frac{5-2(a+3b)}{2}[/tex]Since a = 4 and b = -1
Substitute them in the expression above
[tex]\begin{gathered} \frac{5-2(a+3b)}{2}=\frac{5-2(4+3\lbrack-1\rbrack)}{2} \\ =\frac{5-2(4+\lbrack-3\rbrack)}{2} \end{gathered}[/tex]Simplify the bracket
[tex]\begin{gathered} \frac{5-2(4-3)}{2}=\frac{5-2(1)}{2} \\ =\frac{5-2}{2} \end{gathered}[/tex]Simplify the numerator
[tex]\frac{5-2}{2}=\frac{3}{2}[/tex]The missing is 3
I need an explanation of:There are 75 pennies, quarters, and dimes in a box.There are 4 times as many pennies as quarters.There are 3 more dimes than quarters.How many pennies are there in the box?
Answers
Let:
p = number of pennies (one cent)
q = number of quarters (25 cents)
d = number of dimes (10 cents)
The total number of coins in the box is 75, thus:
p + q + d = 75
This gives us the first equation.
We also know there are 4 times as many pennies as quarters, thus:
q = 4p
We also know there are 3 more dimes than quarters, thus:
d = q + 3
Since q = 4p:
d = 4p + 3
It's required to find the number of pennies in the box (p).
Substituting the last two equations in the first one:
p + 4p + 4p + 3 = 75
Simplifying:
9p = 72
Dividing by 9:
p = 8
There are 8 pennies in the box
To complete the answer, we find:
q = 4*8 = 32
d = 32 + 3 = 35
There are also 32 quarters and 35 dimes in the box
Convert the following to meters.55 yards=meters.(Enter you answer as a decimal number. Round to two decimal places)
Answers
Answer:
50.29 meters
Step-by-step explanation:
55 yards = x meters
1 yard = 0.9144 meters
55 yards = 50.292 meters
55 yards = 50.29 meters
27,9,3,1,1/3,1/9......Find the sum of the infinite series. ________________
Answers
Given the following series:
[tex]27,9,3,1,\frac{1}{3},\frac{1}{9},.....[/tex]The given series is a geometeric sequence
the first term = 27
And the common differnce = 1/3
we will use the following formula to find sum of the series as the number of terms tends to infinite:
[tex]S_{\infty}=\frac{a}{1-r}[/tex]substitute a = 27, and r = 1/3
[tex]S_{\infty}=\frac{27}{1-\frac{1}{3}}=\frac{27}{\frac{2}{3}}=40\frac{1}{2}=40.5[/tex]So, the answer will be, the sum of the infinite series = 40.5
8. A bowling alley costs $6 for shoes and charges $12.50 per game. If you pay $68.50, how many games did you play?
Answers
The total cost is 68.50 dollars, and out of this you paid 6 dollars for shoes, and then paid 12.50 dollars per game. That means the total cost is given as;
[tex]\begin{gathered} \text{Cost}=6+12.5x \\ 68.50=6+12.5x \\ \text{Subtract 6 from both sides} \\ 62.5=12.5x \\ \text{Divide both sides by 12.5} \\ x=5 \end{gathered}[/tex]That means you played just 5 games
Point Ais at (-3, 4) and point C is at (2,-6). Find the coordinates of point Bon AC such that the ratio of AB to dC is 4:5. B = (
Answers
If point B lies on the line joining points A (-3, 4) and C (2, -6) in such a manner that, the ratio of AB to BC is (4 : 5), then the coordinates of point B are [(7/9), (-4/9)].
As per the question statement, two points, A (-3, 4) and C (2, -6) are joined by a straight line AC, and point B lies on the line in such a manner that, the ratio of AB to BC is (4 : 5).
We are required to calculate the coordinates of point B.
To solve this question, we need to know the formula to calculate the coordinates of a point B (x₃, y₃) that lies on the line joining two other points A (x₁, y₁) and C (x₂, y₂) in such a manner that, the ratio of AB to BC is (m : n), which goes as,
[x₃ = {(mx₂ + nx₁)/(m + n)}] and [y₃ = {(my₂ + ny₁)/(m + n)}]
Here, comparing with the data provided in the question statement, we get, A [(x₁, y₁) = (-3, 4)], C [(x₂, y₂) = (2, -6)] and [(m : n) = (4 : 5)], and using these values in the above mentioned formula, we further get,
x₃ = [(4 * 2) + {5 * (-3)}]/(4 + 5) and y₃ = [{4 * (-6)} + (5 * 4)/(4 + 5)]
Or, [x₃ = {8 + (-15)}/9] and [y₃ = {(-24) + 20}/9]
Or, [x₃ = {(15 - 8)/9}] and [y₃ = {(20 - 24)/9}]
Or, [x₃ = (7/9)] and [y₃ = (-4/9)]
Therefore, the coordinates of point B are [(7/9), (-4/9)].
Ratio: In Mathematics, Ratio is a term that is used to compare two or more numbers, typically used to indicate how big or small a quantity is when compared to another.To learn more about Ratios and Straight Lines, click on the link below.
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I need to answer in a rush ABC or D or
Answers
Given:
a data is given as below
Find:
we have to find the percentage of high schools in orange country which have more than 130 band members
Explanation:
Since the maximum value is given as 130.
So, there is no school which have more than 130 band members.
Therefore, percentage is
Solving Equations Reminder need to show ALL work **Number 1
Answers
1.I WILL USE CROSS MULTIPLICATION
[tex] \frac{ - n}{4} = 13 \\ - n = 13(4) \\ - n = 52 \\ \frac{ - n}{ - 1} = \frac{52}{ - 1} \\ n = - 52[/tex]
2.
[tex] \frac{3x}{4} - 5 = 4 \\ \frac{3x}{4} (4) - 5(4) = 4(4) \\ 3x - 20 = 16 \\ 3x = 16 + 20 \\ 3x = 36 \\ \frac{3x}{3} = \frac{36}{3} \\ x = 12[/tex]
ATTACHED IS THE SOLUTION.
please tell me how to do percent proportions! c/o AND p/w! please explain thoroughly. all i really need to know is how to write the equation!
Answers
we know that
total animals--------> 500
25% ----> reptiles
30% fish
rest are mammals
Find out the percentage of the rest
we have taht
100%-(25%+30%)=100%-55%=45%
so
45% -----> mammals
applying proportion
REmember that
100% -------> 500 animals
so
500/100%=x/45%
solve for x
x=(500/100)*45
x=225
therefore
the answer is 225 mammalswhat id the last step when solving the equation below for x7x-6=218
Answers
We are given the following equation to solve for x.
[tex]7x-6=218[/tex]The goal is to separate out the variable x.
Step 1:
Add 6 to both sides of the equation
[tex]\begin{gathered} 7x-6+6=218+6 \\ 7x=224 \end{gathered}[/tex]Step 2: (last step)
Divide each side of the equation by 7
[tex]\begin{gathered} \frac{7x}{7}=\frac{224}{7} \\ x=32 \end{gathered}[/tex]Therefore, the last step would be to "Divide each side of the equation by 7"
Kareem is on his way home in his car he is driven 24 miles so farWhich is 2/3 of the way homeWhat is the total length of his drive
Answers
36 miles
Explanation
Step 1
to solve this we can use a rule of three
let x represents the total distance of his drive
hence
[tex]\begin{gathered} \text{if} \\ 24\text{ miles }\Rightarrow\frac{2}{3}\text{of th total } \\ x\text{ miles }\Rightarrow1\text{ total } \end{gathered}[/tex]therefore, the proportion would be.
[tex]\begin{gathered} \frac{24\text{ miles }}{\frac{2}{3}\text{ of total }}=\frac{x\text{ miles}}{1\text{ total }} \\ \frac{24}{\frac{2}{3}}=x \\ \frac{24\cdot3}{2}=x \\ \frac{72}{2}=x \\ 36=x \end{gathered}[/tex]so, we can conclude that
the total length is
36 miles
I hope this helps you
Convert. Express your answer as a mixed number, ifpossible.5 in= Ft
Answers
First we need to know
1 in = 0.0833 ft
5 in = x ft
In order to find x we need to multiply 5 by 0.0833
[tex]x=5\times0.0833=0.4165[/tex]5 in = 0.4165ft
OLA group consists of six men and seven women. Four people are selected to attend a conference.a. In how many ways can four people be selected from this group of thirteen?b. In how many ways can four women be selected from the seven women?c. Find the probability that the selected group will consist of all women.a. The number of ways to select four people from the group of thirteen isb. The number of ways to select four women from the group of seven women isc. The probability is(Type an integer or a simplified fraction.)
Answers
Hello!
This is an exercise about combinations. To solve it, we must remember the formula below:
[tex]C_{n,p}=\frac{n!}{p!(n-p)!}[/tex]• n,: total of elements
,• p,: number of elements of the group that we need
Knowing it, let's solve your exercise:a. In how many ways can four people be selected from this group of thirteen?[tex]\begin{gathered} C_{13,4}=\frac{13!}{4!(13-4)!}=\frac{13!}{4\times3\times2\times1\times(9!)} \\ \\ =\frac{13\times12\times11\times10\times\cancel{9!}}{4\times3\times2\times1\times(\cancel{9!})}=\frac{17160}{24}=715 \end{gathered}[/tex]b. In how many ways can four women be selected from the seven women?[tex]C_{7,4}=\frac{7!}{4!(7-4)!}=\frac{7!}{4!\times(3!)}=\frac{7\times6\times5\times\cancel{4!}}{\cancel{4!}\times3\times2\times1}=\frac{210}{6}=35[/tex] c. Find the probability that the selected group will consist of all women.4 women, from a total of 7: 35 combinations
(we calculated it in b.)
Total of Combinations: 4 people, from a total of 13: 715 combinations
(we calculated it in a.)
So, we have to write it as a fraction:
[tex]\frac{35}{715}=\frac{7}{143}[/tex]Find the number of distinguishable permutations of the letters in the wordTALLAHASSEEYour answer is : Find the number of distinguishable permutations of the letters in the wordMISSISSAUGAYour answer is :
Answers
Here are the steps in determining the distinguishable permutation of a given word.
1. Count the total numbers in a word. For the word TALLAHASSEE, there are a total of 11 letters.
2. List down the unique letters and their frequencies or how many times they occurred.
T - 1 time only
A - 3 times
L - 2 times
H - 1 time
S - 2 times
E - 2 times
3. Get the product of the factorial of each frequency per letter.
[tex]1!\times3!\times2!\times1!\times2!\times2![/tex][tex]1\times6\times2\times1\times2\times2=48[/tex]4. Divide the factorial of the total number of letters by the result in step 3.
[tex]11!\div48=831,600[/tex]Hence, there are a total of 831, 600 distinguishable permutations for the word TALLAHASSEE.
For the word MISSISSAUGA, there are a total of 11 letters too. These are:
1 Letter M
2 Letter I
4 Letter S
2 Letter A
1 Letter U
1 Letter G
So, similar to the previous word, we multiply the product of the factorial of each frequency per letter.
[tex]1!\times2!\times4!\times2!\times1!\times1![/tex][tex]1\times2\times24\times2\times1=96[/tex]Then, divide the factorial of the total number of letters which is 11! by 96.
[tex]11!\div96[/tex][tex]39,916,800\div96=415,800[/tex]Hence, there are 415,800 distinguishable permutations of the word MISSISSAUGA.
Which of the following lengths represent the sides of a right triangle? Select all that apply. 9 cm, 12 cm, 16 cm 8 cm, 15 cm, 17 cm 10 cm, 24 cm, 28 cm 6 cm, 8 cm, 10 cm
Answers
Given data:
The given sides of the right angle triangle.
9, 12 and 16 are not the pythagorean triplets, so it can never form right angle triangle.
8, 15 and 17 are the pythagorean triplets as,
(8)^2 +(15)^2 =(17)^2
64+225=289
289=289
10, 24 and 28 are also not the pythagorean triplets.
6, 8 and 10 are the pythagorean triplets as,
6^2 +8^2 =10^2
36+64=100
100=100
Thus, the second and fourth option are correct.
are labelas Lesson 10: Changing Scales in Scale Drawings Let's explore different scale drawings of the same actual thing. 10.1: Appropriate Measurements 1. If a student uses a ruler like this to measure the length of their foot, which choices would be appropriate measurements? Select all that apply. Be prepared to explain Inches Centimeters 2 Specials your reasoning 1 2 3 3 4 5 8 9 (X 10 Monday a 9-inches b.9 inches c. 23.47659 centimeters Tuesday d. 23.5 centimeters e. 23.48 centimeters
Answers
Given:
a student uses a ruler like this to measure the length of their foot as shown in the figure
The appropriate measurements are:
a) 9 1/4 inches
d) 23.5 Centimeters
So, the answer will be the options (a) and (d)
Because as shown: the small distance that can be measured by the rule is
0.1 cm or 1/8 inches
So, it will be appropriate to measure 9 1/4 inches or 23.5 cm
need help pls I'm failing
Answers
Let:
x = Quarts of paint
y = # of square feet that can be painted
the function which represents the situation is given by:
[tex]y(x)=200x[/tex]Therefore, for 4qt:
[tex]y(4)=200\times4[/tex]We can conclude that:
Four quarts of paint covers 4x200 square feet of fencing
