Solve the given system of equations utilizing either the substitution or addition method.
Answers
Answer:
Value of x=4 and y=-13/3
Step-by-step explanation:
We need to solve the systems of equations
[tex]5x+3y=7 \ and \ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}[/tex]
Solving using substitution method:
Let:
[tex]5x+3y=7---eq(1) \\ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}---eq(2)[/tex]
Find value of x from eq(1) and put in eq(2)
[tex]5x+3y=7\\5x=7-3y\\x=\frac{7-3y}{5}[/tex]
Put value of x in eq(2)
[tex]\frac{3}{2}(\frac{7-3y}{5}) -\frac{3}{4}y =\frac{37}{4}\\\frac{21-9y}{10} -\frac{3}{4}y =\frac{37}{4}\\Taking \ LCM\\\frac{21*2-9y*2-3y*5}{20} =\frac{37}{4}\\\frac{42-18y-15y}{20} =\frac{37}{4}\\42-33y=\frac{37}{4}*20\\42-33y=185\\-33y=185-42\\-33y=143\\y=\frac{143}{-33}\\y=-\frac{13}{3}[/tex]
Now, finding value of x by putting value of y in eq(1)
[tex]x=\frac{7-3y}{5}\\x= \frac{7-3(-\frac{13}{3}) }{5}\\x=\frac{7+13}{5}\\x=\frac{20}{5}\\x=4[/tex]
So, Value of x=4 and y=-13/3
Related Questions
I need serious help!
Answers
Answer:
a = 14 ; b = 10
Step-by-step explanation:
ΔJKL ≅ ΔXYZ
The order of letters in triangle's "names" is important, it indicates the corresponding angles and sides.
∠J ≅ ∠X, ∠K ≅ ∠Y, ∠L ≅ ∠Z
segment JK ≅ segment XY,
segment KL ≅ segment YZ,
segment JL ≅ segment XZ
m∠Z = m∠L = 180° - (60° + 55°) = 65°
(4a + 9)° = 65°
4a = 65 - 9 ⇒ a = 14
XY = JK = 24 units
3b - 6 = 24 ⇒ b = 10
The perimeter of the rectangle is 2,500 cm. Find the unknown side length. the other side is 750
Answers
Answer:
500 cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question we have
[tex]2500 = 2l + 2(750) \\ 2500 = 2l + 1500 \\ 2l = 2500 - 1500 \\ 2l = 1000 \\ \frac{2l}{2} = \frac{1000}{2} \\ l = \frac{1000}{2} \\ l = 500[/tex]
We have the final answer as
500 cmHope this helps you
5. You make $50 a week and you want to buy a car with an expected payment of $200 a month.
Answers
Answer:
what is the question
Step-by-step explanation:
you will not have enough money to pay your car bill though
$1.00 to 2/3 gallon
2
10 points
A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost $12. How much is the cost per
pound?
Answers
Answer:
$1.5/pound
Step-by-step explanation:
Number of pounds = 8pounds
Cost of pasta = $12
Now;
Unknown:
cost per pound of pasta
Solution:
To find the cost per pound of pasta;
Cost per pound of pasta = [tex]\frac{cost of pasta}{number of pasta}[/tex]
Cost per pound of pasta = [tex]\frac{12}{8}[/tex] = $1.5/pound
Which of the following could be the perimeters of the three squares below?
A 12ft, 16 ft and 20 ft
B 20 ft, 16 ft and 24 ft
C) 40 ft, 80 ft and 120 ft
D 16 ft, 24 ft and 28 ft
Answers
Answer:
Option (A)
Step-by-step explanation:
Option (A).
Since, perimeter of a square = 4×(side)
Perimeters of 3 squares = 12 ft, 16 ft and 20 ft
Side lengths of three squares will be = [tex]\frac{12}{4}, \frac{16}{4},\frac{20}{4}[/tex]
= 3 ft, 4 ft and 5 ft
If these sides are the measures of the sides of the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
5² = 4² + 3²
25 = 16 + 9
25 = 25
True.
Therefore, these are the sides of the given right triangle.
Option (B).
Perimeters of three squares are 20 ft, 16 ft and 24 ft.
Sides lengths of three squares = [tex]\frac{20}{4},\frac{16}{4}, \frac{24}{4}[/tex]
= 5 ft, 4 ft and 6 ft
By Pythagoras theorem,
6² = 4² + 5²
36 = 61
False.
Therefore, these sides are not of the given right triangle.
Option (C)
Perimeters of the squares = 40 ft, 80 ft and 120 ft
Side lengths of the squares = 10 ft, 20 ft and 30 ft
If these sides are the sides of the given right triangle, they will follow the Pythagoras theorem.
By Pythagoras theorem,
(30)² = (10)² + (20)²
900 = 500
False.
Option (D)
Perimeters of the given squares are 16 ft, 24 ft and 28 ft.
Side lengths of these squares will be 4 ft, 6 ft and 7 ft.
If these sides form a right triangle they will follow the Pythagoras theorem.
By Pythagoras theorem,
7² = 4² + 6²
49 = 16 + 36
49 = 52
False.
Therefore, these are not the sides of a right triangle.
Option (A) will be the answer.
Factor the expression 4x + 32. Explain each step you
take in the process.
I
Answers
Answer:
4(x+8)
Step-by-step explanation:
find the GCF (which is 4 in this case)
divide by 4 but don't forget to keep it.
4x/4=x
32/4=8
4(x+8)
And thats it!
Part D
You now have an equation to model the finances of the car wash. What is the value of the profit when the baseball team washes 0 cars? What point represents the value? What does the y-value of this point mean in terms of the problem?
Answers
Answer:
The equation for the profit made on the car wash is y = 5x – 75. Here, y is the profit made and x is the number of cars washed. So if the team washes 0 cars, x will be 0.
y = 5(0) – 75
y = -75
The point that represents this is (0, -75). Here, the value of the y-coordinate of the point is -75. Since it has a negative sign, it means that instead of making a profit, the team suffers a loss. So, if the baseball team washed no cars, it would lose $75.
Step-by-step explanation:
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
Answers
Answer:
man the answers are 40 10 30
Step-by-step explanation:
please help
what is the solution to the equation below?
34x + 95 = 3 (14x + 9)
Answers
Answer:
x=8+1/2
Step-by-step explanation:
Hope this helps, good luck!
Answer:
x=7/2=8.500
Step-by-step explanation:
(IM GIVING EXTRA POINTS AND BRAINLIEST TO WHO EVER HELPS ME! ;D)
Which of the following gives the most complete and accurate description of the
friction in the image?
A) The rough texture of the ground creates a small amount of friction.
B) The smooth texture of the ground creates a greater amount of friction.
C) The push of the suitcases causes friction between the wheels and the ground.
D) There is friction between the suitcases and the ground and between the feet and the ground.
(Here is the image) :
Answers
Answer:
I think D
Step-by-step explanation:
The ground looks pretty smooth to me, plus D has more info
Also, is that math?
Because it doesn't look like math.
Answer:
D
Step-by-step explanation:
all the others don't make sense
I'll take my brainlets
if R is the midpoint of QS, RS = 2x-4, ST = tx-1, and RT = 8x-43
Answers
The question is incomplete. Here is the complete question.
If R is the midpoint of QS, [tex]RS=2x-4[/tex], ST = [tex]4x-1[/tex] and RT = [tex]8x-43[/tex], find QS.
Answer: QS = 68 units
Step-by-step explanation: The figure below shows a line segment QT.
To determine QS, first, determine value of x:
RT = RS + ST
[tex]8x-43=2x-4+4x-1[/tex]
[tex]8x-43=6x-5[/tex]
2x = 38
x = 19
Now, we determine QS:
Midpoint is a point dividing a line segment in two equal parts.
Then, QR = RS.
QS = QR + RS
QS = 2RS
[tex]QS=2(2x-4)[/tex]
[tex]QS=4x-8[/tex]
Substituting x = 19:
[tex]QS=4.19-8[/tex]
QS = 68
The segment QS is 68 units.
Answer: x = 1
Step-by-step explanation:
I have no idea what the actual answer is, as you didn't ask a question. So i'm assuming that you want the value of x.
Step 1: Draw a line containing all the points
R is in between point Q and point S, while T is last, based on alphabetical order.
Illustration:
2x - 4 Tx - 1
Q R S T
8x - 43
Step 2: Find T's value
To find t, create the substitution equation RS + ST = RT
2x - 4 + tx - 1 = 8x - 43
-2x -2x
-4 + tx - 1 = 6x - 43
tx - 5 = 6x - 43
tx = 6x - 38
tx/x = 6x/x - 38
t = 6 - 38
t = -32
This is the value of t
By the way, there is no correlation between point T and the variable t.
Step 3: Find x's value
Now that we know what t is, we can solve for x
2x - 4 -32x - 1 = 8x - 43
-30x - 5 = 8x - 43
+30x +30x
-5 = 38x - 43
+43 +43
38 = 38x
38/38 = 38x/38
1 = x
This is the value of x
Which percent is modeled? 9% 19% 91% 99%
Answers
Answer:
9%
Step-by-step explanation:
Count the squares side which is 10
Then Count the bootom side of the square which is 10
10 x 10 =100
Now count how many squares are filled. 9
9/100=9%
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
Total value = b
Percentage = a/b x 100
The percent modeled is 9%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
Total value = b
Percentage = a/b x 100
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of cells in the box = 100
Number of shaded cells = 9
The percentage of the shaded cells.
= (Number of shaded cells / Total number of cells) x 100
= 9/100 x 100
= 9%
Thus,
The percentage of shaded cells is 9%
The percent modeled is 9%.
Learn more about percentages here:
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A star patterned quilt has a star with the angels shown. What is the value of x? Explain your answer.
Answers
Answer:
81°
Step-by-step explanation:
x° and 24° are interior angles of a triangle that are opposite to an exterior angle of measure 105°. According to the exterior angle theorem of a triangle, thus:
[tex] x + 24 = 105 [/tex]
Subtract 24 from both sides
[tex] x + 24 - 24 = 105 - 24 [/tex]
[tex] x = 81 [/tex]
Value of x = 81°
True or false: The mapping notation for reflecting point (x,y) about the x-axis is (−x,y).(1 point) This statement is true. This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (x,−y). This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (y,x). This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (−x,−y).
Answers
Answer:
This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (x,-y)
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
Write the letters of the expressions that are equivalent to the given expression.
5(2x + 3)
a. 10x + 15
b. 5x + 15x + 5x
c. 10x + 8
Answers
Answer: A.) 10x + 15
Step-by-step explanation:
You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.
Therefore, 10x + 15 is your answer.
Write 0.45 as a fraction.
Answers
Answer:
9/20
Step-by-step explanation:
0.45 = 45/100
45/100=9/20 (divide numerator and denominator by 5)
A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of Xis given (in units of months) byf(x) ={cxe -x/2 x>0 0 x<0 What is the probability that the system functions for at least 5 months?
Answers
Answer:
0.2397
Step-by-step explanation:
Given data:
fX(x) = Cxe^(−x/2) if x >0 0 otherwise, where C > 0 is some constant.
The probability that the system functions for at least 5 months
= 0.2397
attached below is a detailed solution
Irene makes 4⅔ cups of pancake batter. She splits the batter into 2 bowls.She mixes blueberries into 2¼ cups of batter and walnuts into the rest of the batter.
Answers
Answer:
You have to find the most simple estimation by finding the nearest whole number, but the actual answer in 2 5/12
Each Christmas elf makes x toys in an hour. n elves work for t hours to produce 1000 toys.
Write an equation that relates x, n, and t.
Answers
Answer:
e(X x T)=1000
Step-by-step explanation:
You do the number of toys they make(X) times the hours they work(T). Then multiply all of it by the number of elves(e). All of that equals the 1000 toys they make all together.
Equation relates x, n and t is n × x × t = 1000
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Each elf makes x toys in an hour
one elf will make x × t toys in t hours
n elf will make 1000 toys in t hours
So n elf will make 1000 toys in t hours
n × x × t = 1000
Hence, the equation relate x, n and t is n × x × t = 1000
Learn more about Equation here
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A city bus compny sold 35 one-way tickets and 20 round trip tickets from west elmwood to east elmwood. One way tickets cost $14. Round trip tickets cost $27. How much money did the bus company collect?
Answers
Answer:
$1,030
Step-by-step explanation:
Step 1- Multiply One way tickets by How much the tickets cost:
35 x 14= 490
Step 2- Multiply Round trip tickets by how much the tickets cost:
20 x 27= 540
Step 3- Add both sums together:
490 + 540= 1,030
Therefore, the answer is $1,030
A gardener makes a flower bed the bed is 14 in diameter calculate the circumference
Answers
Answer:
[tex]C=43.96[/tex]
Step-by-step explanation:
Circumference Formula:
C=2πr
The radius is half of the diameter...
[tex]14/2=7[/tex]
Pi is [tex]3.14[/tex]...
[tex]C=2*3.14*7[/tex]
[tex]C=43.96[/tex]
The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are six appetizers, two soups, four main courses, and six desserts. Your diet restricts you to choosing between a dessert and an appetizer. (You cannot have both.) Given this restriction, how many three-course meals are possible?
Answers
Answer: 96
Step-by-step explanation:
According to the fundamental principle of counting:
Total number of meals possible = (Choices for appetizers) x (Choices for soups) x (Choices for main courses) x (Choices for desserts)
If there is a restriction to choose between appetizer and dessert.
Then, Total number of meals possible = (Choices for appetizers) x (Choices for soups) x (Choices for main courses) + (Choices for soups) x (Choices for main courses) x (Choices for desserts)
= 6 x 2 x 4 + 2 x 4 X 6
= 48+48
= 96
Hence, the number of three-course meals are possible= 96
Answer:
96?
Step-by-step explanation:
cos 60 degrees=1/2 and sin 60 degrees = square root 3/2 true or false
Answers
Answer:
cos 60 degrees=1/2 and sin 60 degrees = square root 3/2
The answer it's true.
Just select yes and no for all three pls help
Answers
.....*+*Kill me*+*.....
*+*.......................*+*
*+*.......................*+*
Answer:
1. Yes 2. No 3. No
Step-by-step explanation:
What is the equation of the line that passes through the point (-1,7) and has a slope of -2?
Answers
Plug in the point
7 = -2(-1) + b
7 = 2 + b
b = 5
Final equation y = -2x + 5
the pic the pic this is it
Answers
Answer:
yes I agree with you
Step-by-step explanation:
thanks for the free question
Answer: mmmmmm Otae?
Step-by-step explanation:
Josie bikes 40 miles each month for five months she multiplies 40×5 what unit should she use for the product miles or months?
Answers
Answer:40x5 are the factors of every miles times each month so the units she should use is months
Step-by-step explanation: 40= (miles)
5=(months)
Which of the following shows only multiples of 12
Answers
Answer:
there is no following
Step-by-step explanation:
Answer: 12,24,36,48,60,72,84,96,108,120,132,144
Step-by-step explanation:
Hope this helps. Could not see the image attached.
Calleigh puts 5 nickels into an empty hat. She
wants to add enough pennies so that the probabil-
ity of drawing a nickel at random from the hat is 1/6
How many pennies should she put in?
Answers
A book company publishes 749 copies of
a novel and distributes them to 7 bookstores.
If each bookstore were to receive the same
number of copies, how many copies would
be sent to each store?
Answers
Answer:
107 copies to each books store
= 107
107 copies would be received from each bookstore