solve each system by eliminating one of the variables by addition or
subtraction.
Answers
Answer:
1) x- y = 8
x + y = 12
eliminate one variable by adding the equations
2x = 20
divided by 2 on both sides
x = 10
substitute the value of x in the equation 1
10 - y = 8
-y = 8- 10
y =2
[x , y]
[10 , 2]
2) 2x - y = 4
3x + y = 6
eliminate one variable by adding the equations
5x = 10
x = 2
substitute the value of x in the equation
2(2) - y = 4
4 - y = 4
y = 0
[x ; y]
[2; 0]
3) x + 2y = 10
x + 4y = 14
multiply equation 1 by - 1
-x -2y = -10
x + 4y = 14
eliminate one variable by adding the equations
2 y = 4
y = 2
substitute the value of y in the equation 1
x + 2(2) = 10
x + 4 = 10
x = 6
[x ; y]
[6 ; 2]
4 ) 3x + y = 9
y = 3x + 6
simplify the expression
3x + y = 9
- 3x + y = 6
eliminate one variable by adding the equations
2y = 15
y = 15/2
substitute the value of y in equation 1
3x + 15/ 2 = 9
3x = 3/2
x = 1/2
[x ; y]
[1/2 ; 15/ 2]
5) 4x + 5y = 15
6x - 5y = 18
eliminate one variable by adding the equations
10 x = 33
× = 33/10
substitute the value of x in equation I
4 (33/10) + 5y = 15
66/5 + 5y =15
5y = 9/5
y = 9/25
[x ; y]
[33/10 ; 9/25]
6) 5x = 7y
x + 7y = 21
in equation I move the variable to the left
5x - 7y = 0
x + 7 y = 21
eliminate one variable by adding the equations
6x = 21
x = 7/2
substitute the value of x in the equation
5(7/2) = 7y
35/2 = 7y
5/2 = y
[x ; y ]
[7/2 ; 5/2 ]
Related Questions
Krissi has $14 in the bank and earns $8 a day. John has 35$ and earns $5 a day when will krissi have more money?
Answers
Answer: 8 days
Step-by-step explanation:
K=14+8x
J=35+5x
when K=J they will have the same amount
14+8x=35+5x
8x=21+5x
3x=21
x=7 days until they have the same amount- 8 days until she has more
if sinθ =1/3 what are the values of cosθ and tanθ
Answers
solution in attachment
hope it helps
can you guys. guy's. Help me pls
Answers
Answer:
J) [tex]\frac{17}{24}[/tex]
Step-by-step explanation:
[tex]\frac{3}{8} +\frac{1}{3} \\\\\frac{9}{24} +\frac{8}{24} = \frac{17}{24}[/tex]
Find the common denominator ^^
Answer:
17/24
Step-by-step explanation:
3/8× 3/3=9/24
1/3×8/8=8/24
8/24 +9/24= 17/24
Surface Area Homework (Help)
Answers
sorry if it’s wrong
Maria is ordering comic books online. The equation y=8x + 4 represents the total cost in dollars, y, including shipping, for ordering x number of comic books. If the total cost including shipping is $60, how many comic books is Maria ordering? Use the graph to help you determine the answer.
Answers
Answer:
x will be equal to 7 comic books
The number of books Maria is ordering is 7 books
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of comic books Maria orders be = x
The cost of x books is = y
Now , the equation for the total cost be
y = 8x + 4 be equation (1)
Now , the total cost of all the books be = $ 60
So , substituting the value of y as 60 in equation (1) , we get
60 = 8x + 4
Subtracting 4 on both sides of the equation , we get
8x = 56
Divide by 8 on both sides of the equation , we get
x = 7 books
Therefore , the value of x is 7
Hence , The number of books Maria is ordering is 7 books
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ2
The question is down below.
AB=
Answers
Answer:
Step-by-step explanation:
Sin(35) = opposite / hypotenuse
Sin(35) = 4 / hypotenuse Multiply both sides by the hypotenuse
hypotenuse * sin(35) = 4 Divide by Sin(35)
hypotenuse = 4/Sin(35)
Sin(35) = 0.5736
hypotenuse = 4/0.5736
hypotenuse = 6.9737
Rounded answer 6.97
Chris works at a bookstore and earns $7.50 per h hour plus a $2 bonus for each book she sells. Chris sold 15 books. She
wants to earn a minimum of $300. Which inequality represents this situation, and what quantities are true for h?
A 2h + 30 > 300, where h > 135
B 7.50h + 30 > 300 where h > 36
7.50h + 30 < 300, where h <36
D2h + 30 < 300, where h < 135
Answers
Answer:
B
Step-by-step explanation:
Answer:
Step-by-step explanation:it is b because u multiply.
What is the probability of rolling a 2 or a 3 on a regular fair die
Answers
Answer:
The possibility of rolling a
3
on a fair die and getting tails on a coil is
1
12
. Based on this probability, there are
12
possible outcomes. As only 1 out of 12 possiblities would get this outcome, it is not a likely outcome.
Step-by-step explanation:
The probability of rolling a
3
on a fair die is
1
6
because there is only one
3
out of
6
numbers. The probability of getting tails on a coin is
1
2
because there are
2
possibilities and tails is one of them. To get the probability of rolling a
3
on a fair die and getting tails on a coil, we multiply their probabilities:
1
6
⋅
1
2
=
1
12
There are
12
possiblities because for each of the
6
possibilites for rolling a die, there are
2
possibilites for flipping a coin.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Camille is saving for a laptop that costs about $850. To model her savings plan and determine how many more months it will take her to reach her goal, she recently created this equation, where y represents the total amount saved and x represents the number of months. Which statement about her work is true?'
A. Camille used the associative property in step 3.
B. Camille used the multiplication property of equality in step 4.
C. Camille used the subtraction property of equality in step 5.
D. Camille used the substitution property in step 6.
Answers
What is the value of the digit 4 in 149,832?
Answers
Answer:
40,000
Step-by-step explanation:
Answer:
It would be 40,000
Explanation:
It is in the ten thousands digit.
When a new highway is formed, the smoothness of the surface must be verified. A contractor is making a bid for this job and has a truck with the relevant detector. This detector must meet minimum standards for detecting irregularities in the road surface. If there is a roadway irregularity, there is a probability of 0.99 the detector will detect it. If there is no irregularity, there is a 0.06 probability detector will identify it as irregular (a false positive). It is known through experience that 3 miles out of 100 miles actually contain irregularities.
a. What is the probability the detector will identify a random mile of roadway as irregular? Give your answer to four decimal places.
b. Given a randomly selected miles has been identified as irregular by the detector, what is the probability it actually is irregular? Give your answer to four decimal places.
Answers
Answer:
a) 0.0879 = 8.79% probability the detector will identify a random mile of roadway as irregular.
b) 0.3379 = 33.79% probability it actually is irregular
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. What is the probability the detector will identify a random mile of roadway as irregular?
99% of 3%(it is irregular).
6% of 97%(false positive). So
[tex]p = 0.99*0.03 + 0.06*0.97 = 0.0879[/tex]
0.0879 = 8.79% probability the detector will identify a random mile of roadway as irregular.
b. Given a randomly selected miles has been identified as irregular by the detector, what is the probability it actually is irregular? Give your answer to four decimal places.
Conditional probability:
Event A: Identified as irregular
Event B: It is irregular.
0.0879 = 8.79% probability the detector will identify a random mile of roadway as irregular, which means that [tex]P(A) = 0.0879[/tex]
99% of 3% arre irregulars identified as, which means that [tex]P(A \cap B) = 0.03*0.99 = 0.0297[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0297}{0.0879} = 0.3379[/tex]
0.3379 = 33.79% probability it actually is irregular
Baseball statisticians studied how often triples (a certain event in a baseball game) occurred in professional games played between 1947 and 2017. A 98 percent confidence interval to estimate the slope of the linear regression line relating the year, x, and the mean number of triples per game, y, yielded (−0.006,−0.002). A check shows that the conditions necessary for inference for the slope of the regression line are met.
Based on the confidence interval, which of the following claims is supported?
A. The mean number of triples per game is between 0.002 and 0.006.
B. The number of triples per game has increased, on average, per year.
C. There is no linear relationship between the mean number of triples per game and year.
D. There is a negative linear relationship between the mean number of triples per game and year.
E. A conclusion cannot be made about the relationship between year and mean number of triples per game because the values are close to 0.
Answers
Answer: D. There is a negative linear relationship between the mean number of triples per game and year.
Step-by-step explanation: This claim is supported by the interval. The interval contains plausible values for the slope of the linear regression line relating year and mean number of triples per game. Since all the values in the interval are negative, the interval supports the claim that increases in the year are associated with decreases in the mean number of triples per game.
I need help!! thnaks
Answers
Answer:
7a + 2b
Step-by-step explanation:
Given
4a + 3b + 3a - b ← collect like terms
4a + 3a + 3b - b
= 7a + 2b
Express -36/78 as a rational number with numerator 6:
Answers
Answer:
6/9
Step-by-step explanation:
Answer:
6/9 I think that's the answer
What is 3 + 4 1/3
Plz help I really would appreciate it :D
Answers
Answer:
7 1/3
Step-by-step explanation:
Add the whole numbers in the equation:
3+4=7
This will get you 7 1/3
Look at this triangle.
B
8 cm
A А
22 cm
С
Work out length AB.
Answers
Answer:
AB=23.40cm
Step-by-step explanation:
(AB)²=(AB)²+(BC)²
(AB)²=22×22+8×8
=484+64
(AB)²=548
AB=23.40 cm
hope it helps...
have a great day!!
You have
A square piece of confetti has a perimeter of 24 millimeters. How long is each side of the
piece of confetti?
Please no links and please explain!!!
Answers
Answer:
6 millimeters
Step-by-step explanation:
All the sides on a square are equal and a square has four sides. For perimeter you add up all the sides which in this case have to add up to 24.
So, 6 + 6 + 6 + 6 = 24
The sample mean tip amount for the 20 parties to which the waitress gave her name was $5.44, with a standard deviation of $1.75. These statistics were $3.49 and $1.13, respectively, for the 20 parties to which the waitress did not give her name. The data were not strongly skewed in either group.
Required:
Use appropriate symbols for the six numbers reported in this paragraph.
Answers
Answer:
First sample size, [tex]n_{x}[/tex] = 20
Second sample size, [tex]n_{y}[/tex] = 20
Sample mean of first sample, [tex]\bar{x}[/tex] = 5.44
Sample mean of second sample, [tex]\bar{y}[/tex] = 3.49
Sample Standard deviation of first sample, [tex]\sigma_{x}[/tex] = 1.75
Sample Standard deviation of second sample, [tex]\sigma_{y}[/tex] = 1.13
Step-by-step explanation:
Given - The sample mean tip amount for the 20 parties to which the waitress gave her name was $5.44, with a standard deviation of $1.75. These statistics were $3.49 and $1.13, respectively, for the 20 parties to which the waitress did not give her name. The data were not strongly skewed in either group.
To find - Use appropriate symbols for the six numbers reported in this paragraph.
Proof -
First sample size, [tex]n_{x}[/tex] = 20
Second sample size, [tex]n_{y}[/tex] = 20
Sample mean of first sample, [tex]\bar{x}[/tex] = 5.44
Sample mean of second sample, [tex]\bar{y}[/tex] = 3.49
Sample Standard deviation of first sample, [tex]\sigma_{x}[/tex] = 1.75
Sample Standard deviation of second sample, [tex]\sigma_{y}[/tex] = 1.13
On Friday,
1
6
of band practice was spent trying on uniforms. The band spent
1
8
of practice on marching. The remaining practice time was spent playing music.
What fraction of practice time was spent playing music?
Answers
Answer:
[tex]\frac{17}{24}[/tex]
Step-by-step explanation:
First, you have to make all of the fractions have a common denominator. You can find the LCM (least common multiple) of 6 and 8.
6, 12, 18, 24 . . .
8, 16, 24 . . .
Their LCM is 24.
So now, change the fractions:
1 4
---- = -----
6 24
Remember, whatever you multiply the bottom by to get to 24 is what you multiply the top number by. You have the make sure the fractions are equivalent.
1 3
---- = -----
8 24
Remember, whatever you multiply the bottom by to get to 24 is what you multiply the top number by. You have the make sure the fractions are equivalent.
So if we have 1 band practice, we know that
24 1
---- = ---- = 1
24 1
So the fraction of practice time spent playing music is:
[tex]\frac{24}{24}-\frac{3}{24} -\frac{4}{24}=\frac{17}{24}[/tex]
Y = 5x + 2
6y = 18x + 12
What is the value of X?
Answers
Step-by-step explanation:
x= 0, y = 2
have a great day
PLS ILL GIVE 40 POINTS
Use the stem and leaf below to answer the questions.
What is the minimum:
What is the maximum:
What is the range:
How many data are displayed in the table?
Answers
Answer:
What is the minimum:
The first stem and the first leaf0 and 4 = 4What is the maximum:
The last stem and the last leaf5 and 7 = 57What is the range:
Difference between minimum and maximum57 - 4 = 53How many data are displayed in the table?
Count the number of leaves1 + 3 + 5 + 7 + 5 + 2 = 23Find the exact value of the expression cos-1(1/2)
Answers
Answer:
60
Step-by-step explanation:
Plug it into the calculator
PLEASE HELP ILL MARK BRAINLIST The drama club is going on a trip to Brenau University's theatre. The trip costs each member $65. Included in that price is $10 for the cost of renting a charter bus and the cost of 2 plays. Each play costs the same price.
Write an equation representing the cost of the trip for each member. Let x represent the cost of each play.
Determine the price of one play. Solve your equation by showing your work and steps. (10 points)
Answers
9514 404 393
Answer:
65 = 10 + 2x . . . equation for trip costx = 27.50 . . . cost of playStep-by-step explanation:
We are told that the costs add up this way:
trip cost = bus rental + 2 × (cost of play)
Given that ...
trip cost = $65bus rental = $10cost of play = xThe above equation can be rewritten as ...
65 = 10 + 2x . . . . . . the desired equation
__
Solving for x, we have ...
55 = 2x . . . . subtract 10
27.50 = x . . . . divide by 2
The cost of one play is $27.50.
Suppose the sample space for a probability experiment has 8 elements. If elements from the sample are selected
without replacement, how many different ways can you select all of them?
55
Drive
Remember that "without replacement" means that the items are not returned to the sample space after they are chosen.
Recording
Write your answer in factorial notation.
Answers
Answer:
You can select all of them is 40320 ways.
Step-by-step explanation:
Number of arrangements of n elements:
The number of arrangements of n elements, that is, the number of ways in which n elements can be chosen without replacement, is given by:
[tex]A_{n} = n![/tex]
In this question:
8 elements, so:
[tex]A_{8} = 8! = 40320[/tex]
You can select all of them is 40320 ways.
Katie worked 40.5 hours this week. She makes $8 per hour. How much money did she earn this week?
Answers
Answer:
$324
Step-by-step explanation:
if
=> 1hr = $8
then,
=> 40.5 x 8 = 324
=> 40.5 hr = $324
She earned $324 this week.
hope this helps and is right :)
Answer:
$324
Step-by-step explanation:
So, First we have to establish what we are solving for, in this equation we are solving for how much money Katie made this week after working 40.5 hours at a salary of $8 per hour.
To find how much Katie made we have to multiply 40.5 and 8!
Let's make it easier by splitting 40.5 into 40 and 0.5
40 × 8 = 320
0.5 × 8 = 4
320 + 4 = 324
Katie made $324 this week!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Find the value of x in the triangle shown below.
a.164
b.2
c.6
d.80
Answers
Answer:
[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex]
by using Pythagoras law:
h²=p²+b²
10²=z²+8²
z²=100-64
z=√36=6
z=6 units.
If a family has four children, determine the probability that exactly two of the
children are girls
Answers
Answer:
the porbality is 50%, since if we make a diagram a circle and we split it in two the possibility is 50% since the circle is 100%
Step-by-step explanation:
Carlos worked at a farmer's market on 4 summer weekends. He worked 5 hours on Saturdays and 4 hours on Sundays. How many hours did Carlos work in all at the farmer's market?
Answers
Answer:
36
Step-by-step explanation:
5x4=20
4×4=16
16+20=36
HELP ASAP oooooooooooooooooooooooooo
Answers
Answer:
The answer is b Maria will run 1.75 miles more than her goal.
Step-by-step explanation:
For this you take the total number of miles divided by miles per day. 17.5 divided by 2.75 is approximately six slightly over. That remaining time is less than 1 day so she can’t do 2.75 over her goal and the other options talk about going under so that leaves us with option two.
Hope this helps.
someone please help me with this please
Answers
Hi there!
[tex]\large\boxed{P = 22 cm}[/tex]
To find the perimeter, we must find the length of the rectangle.
We know the area is 24, thus:
A = l × w
24 = l × 3
24/3 = l = 8 cm
Find the perimeter using the formula:
P = 2l + 2w
Plug in the solved length and width:
P = 2(8) + 2(3) = 16 + 6 = 22 cm.