Solve the system using the substitution method. (If there is no solution, enter NO SOLUTION.)3x + 2y = 15x = y + 15(x, y) =
Answers
We hahve to solve the following system of equations:
\(\begin{gathered} 3x+2y=15 \\ x=y+15 \end{gathered}\)We can use the second equation to replace x in the first equation and solve for y as:
\(\begin{gathered} 3x+2y=15 \\ 3(y+15)+2y=15 \\ 3y+45+2y=15 \\ 5y=15-45 \\ 5y=-30 \\ y=\frac{-30}{5} \\ y=-6 \end{gathered}\)Knowing y we can calculate x as:
\(\begin{gathered} x=y+15 \\ x=-6+15 \\ x=9 \end{gathered}\)Answer: (x,y) = (9,-6)
Related Questions
Ana works 25 hours a week at the library. If she is paid $10 an hour, and her net salary each week is $212.50, what percent of her salary is withheld for taxes?
Answers
Approximately 17.65% of Ana's salary is withheld for taxes.
To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.
Number of hours worked per week (H) = 25 hours
Hourly wage (W) = $10
Net salary (S) = $212.50
Calculate the total earnings before taxes:
Total earnings = Hours worked * Hourly wage
Total earnings = 25 hours * $10/hour
Total earnings = $250
Determine the amount of tax withheld:
Tax withheld = Total earnings - Net salary
Tax withheld = $250 - $212.50
Tax withheld = $37.50
Calculate the percentage of salary withheld for taxes:
Percentage withheld = (Tax withheld / Net salary) * 100
Percentage withheld = ($37.50 / $212.50) * 100
Percentage withheld ≈ 17.65%
Therefore, approximately 17.65% of Ana's salary is withheld for taxes.
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Find the distance between two points (5,10) and (-4,6)
Answers
Answer:
Explanation:
The formula for calculating the distance between two points is:
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Substituting the values from the points in the problem gives:
d
=
√
(
−
6
−
−
3
)
2
+
(
−
4
−
−
5
)
2
d
=
√
(
−
6
+
3
)
2
+
(
−
4
+
5
)
2
d = √ ( − 3 ) 2+ 1 2
d = √ 9+ 1
d = √ 10
Or
d = 3.162
rounded to the nearest thousandth
NEED HELP NOW!!
Does this graph show a function? Explain how you know
A. No; there are y values that have more than one x value.
B. No, the graph fails the vertical line test.
C. Yes; there are no yvalues that have more than one x-value.
D. Yes; the graph passes the vertical line test.
Answers
Answer:
i am not sure to my answer
my answer is letter D
Answer:
yes answer is d.. this is clear
wesdfrgtygfyhujkilhiuh
Answers
Answer:
i do not know what are your talking about.
Step-by-step explanation:
what!. that's my answer.
How many different lines can be drawn if each line contains at least two of these points?
B
A
D
C
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B) unique line can be drawn through two given points.
Given the following, determine the set (B n C)'.
U= {x|x EN and x < 10}
B = {x|x EN and x is even and x< 10}
C = {x|x E N and x < 10}
Answers
Answer:
Step-by-step explanation:
U={x|x∈N and x<10}
or U={1,2,3,4,5,6,7,8,9}
B={x|x∈N and x is even and x<10}
or
B={2,4,6,8}
C={x|x∈N and x<10}
or
C={1,2,3,4,5,6,7,8,9}
(B∩C)={2,4,6,8}
(B∩C)'={1,3,5,7,9}
Write 1 1/6 as an improper fraction
Answers
Step-by-step explanation:
Improper fractions have a numerator that is larger than the denominator
1 = 6/6
so 1 1/6 = 7/6
simplify the expression by distributing combining like terns 2x + 3(2x+1)
Answers
Answer:
3
Step-by-step explanation:
23
Match the system of equations with the number of solutions.
y = 6z+8
y = 6x-4
y = 3x + 2
y + 3x = -7
4z - 2y = 10
2z-y = 5
4z + y = 8
y=-2z+8
No Solution
Answers
Answer:
Step-by-step explanation:
The system of equations with no solution is:
y + 3x = -7
4z - 2y = 10
The system of equations with exactly one solution is:
y = 6z+8
y = 6x-4
y = 3x + 2
2z-y = 5
y=-2z+8
The system of equations with infinitely many solutions is:
4z + y = 8
Number 6 I’m kinda having trouble on
Answers
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
Answers
The bus that is the most consistent, given the data collected on travel times to school from two groups of students is C Bus 18, with a range of 10
How to find the consistent bus ?To determine which bus is the most consistent, we should use the interquartile range (IQR) as the measure of variability. The IQR measures the spread of the middle 50% of the data, which makes it less sensitive to outliers compared to the range.
Bus 47:
Median (Q2): 16
Q1: 10
Q3: 22
IQR = Q3 - Q1 = 22 - 10 = 12
Bus 18:
Median (Q2): 12
Q1: 8
Q3: 18
IQR = Q3 - Q1 = 18 - 8 = 10
Bus 18 has a smaller IQR than Bus 47 (10 vs. 12), which means the travel times for Bus 18 are more consistent.
Note: Figures might be different due to options being for different variant but Bus 18 is the most consistent.
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just need help with a. please helppp
Answers
Answer:
Domain: \(-5\leq x\leq 4\)
Range: \(-5\leq y\leq 5\\\)
Function: yes
Step-by-step explanation:
Domain is all possible x values. In this function, domain would be: \(-5\leq x\leq 4\)
Range is all possible y values. In this function, range would be: \(-5\leq y\leq 5\)
This is a function because it passes the vertical line test.
Does the inequality 4x+84x-3 have a solution? Explain your reasoning.
Answers
Answer:
84 x^12
Step-by-step explanation:
(4x)(-3x^8)(-7x^3)
Multiply the numbers
4*-3 *-7 = 84
x* x^8 * x^3 = Add the exponents = x^(1+8+3) = x^12
84 x^12
Which method is best to use to solve the equation 4x^2– 29 = 0?
Answers
\(\huge\text{Hey there!}\)
\(\mathsf{4x^2 - 29 = 0}\\\\\large\textsf{ADD 29 to BOTH SIDES}\\\mathsf{4x^2 - 29 + 29 = 0 + 29}\\\\\textsf{CANCEL out: -29 + 29 because that gives you 0}\\\\\textsf{KEEP: 0 + 29 because that helps you solve for the x-value}\\\\\mathsf{0 + 29 = \bf 29}\\\\\textsf{NEW EQUATION: }\mathsf{4x^2 = 29}\\\\\large\textsf{DIVIDE 4 to BOTH SIDES}\mathsf{\dfrac{4x^2}{4}=\dfrac{29}{4}}\\\\\large\textsf{{CANCEL out:} }\mathsf{\dfrac{4}{4}}\textsf{ because that gives you 0}\)
\(\textsf{KEEP: }\mathsf{\dfrac{29}{9}}\large\textsf{ because that helps solve for the x-value}\)
\(\textsf{NEW EQUATION: }\mathsf{x^2=\dfrac{29}{4}}\)
\(\large\textsf{TAKE the SQUARE ROOT}\)
\(\mathsf{x = \pm \sqrt{\dfrac{29}{4}}}\)
\(\text{Random fact: if you see the symbol }\mathsf{\bf \pm}\text{ it usually means plus-or-minus.}\\\\\text{Okay, now lets answer the last step to your question!}\)
\(\mathsf{\sqrt{\dfrac{29}{4}}= \boxed{\bf 2.692582}}}\\\\\mathsf{OR}\\\mathsf{- \sqrt{\dfrac{29}{4}} =\boxed{ \bf -2.692582}}\)
\(\boxed{\boxed{\huge\textsf{Answer: \bf x = 2.692582 or x = -2.692582 }}}\\\huge\checkmark\)
\(\large\text{Good luck on your assignment and enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
Please help and show how you found the answer step by step.
Answers
According to the information, the perimeter of the triangle is ≈ 31.18
How to calculate the perimeter of the triangle?To find the distance between two points, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's label the coordinates as follows:
Point 1: (-2, 3)
Point 2: (3, -2)
Now we can substitute these values into the distance formula:
distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)
distance = sqrt((5)^2 + (-5)^2)
distance = sqrt(25 + 25)
distance = sqrt(50)
distance ≈ 7.07
Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.
To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.
Using the distance formula, we can find the length of the sides:
Side 1: (-2,3) to (3,-2)
d = √[(3 - (-2))^2 + (-2 - 3)^2]
= √[5^2 + (-5)^2]
= √50
= 5√2
Side 2: (3,-2) to (-7,-2)
d = √[(-7 - 3)^2 + (-2 - (-2))^2]
= √[(-10)^2 + 0^2]
= 10
Side 3: (-7,-2) to (-2,3)
d = √[(-2 - (-7))^2 + (3 - (-2))^2]
= √[5^2 + 5^2]
= 5√2
Therefore, the perimeter of the triangle is:
5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)
An two of the three sides are equal, so it is an isosceles triangle.
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A painter mixed 1/4 quart of red paint with 3/4 blue paint to make purple paint. How much purple paint did the painter make?
Answers
Answer:
1 quart
Step-by-step explanation:
1/4 + 3/4 = 1; add the numerators and make sure the denominators are the same
Answer: 1 whole cup: 3/4 +1/4
The measure of angle ABC is 36° ⇒ 1st answer
Step-by-step explanation:
Let us revise some important facts in the circle
The measure of the center angle is equal to the measure of its subtended arc
The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc
The vertex of a central angle is the center of the circle and its sides are radii in the circle
The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle
In circle D
∵ D is the center of the circle
∵ A and C lie on the circle
- DA and DC are radii
∴ ∠ADC is a central angle subtended by arc AC
∴ m∠ADC = m of arc AC
∵ m∠ADC = (7x + 2)°
∵ m of arc AC = (8x - 8)°
- Equate them to find x
∴ 8x - 8 = 7x + 2
- subtract 7x from both sides
∴ x - 8 = 2
- Add 8 to both sides
∴ x = 10
Substitute the value of x in the measure of ∠ADC
∵ m∠ADC = 7(10) + 2 = 70 + 2
∴ m∠ADC = 72°
∵ AB and BC are two chords in circle D
∴ ∠ABC is an inscribed angle subtended by arc AC
∵ ∠ADC is a central angle subtended by arc AC
- By using the 2nd fact above
∴ m∠ABC = m∠ADC
∴ m∠ABC = × 72
∴ m∠ABC = 36°
Answers
Answer:
What??????? Isn't that one of my answers to a question?
Step-by-step explanation:
During a single day at the radio station WMZH, the probability that a particular song is played is 1/6. What is the probability that this song will be played on exactly 6 days out of 7 days? Round your answer to the nearest thousandth.
Answers
Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.
Every day represents a trial in this binomial probability issue, and there are only two potential results:
either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.
The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.
We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:
P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹
where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:
(7 choose 6) = 7! / (6! * 1!) = 7
Plugging in the values, we get:
P(6 successes) = 7 * (1/6)⁶ * (5/6)¹
P(6 successes) ≈0.00012502
Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.
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What is the axis of symmetry?
Answers
Answer:
\( \frac{5x {}^{2} }{2} - 8x + 6\)
Step-by-step explanation:
That's your answer
What is the Y intercept of 10x+5y=30
Answers
Answer: (0,6)
The y-int is 6
If angle A is (2x) and angle B is (3x+11)° and the sum of angle A and angle B is 66°, find the measure of angle B.
11
22
44
25
Answers
The angle B is 66°
Given,
In the question:
If angle A is (2x) and angle B is (3x+11)°
and, the sum of angle A and angle B is 66°
To find the angle of B.
Now, According to the question:
Based on the given condition:
Angle A = 2x
Angle B = (3x + 11)°
The sum of angle A and B is 66°
2x + (3x + 11)° = 66°
5x + 11 = 66°
Calculate the sum or difference
5x = 66 - 11
3x = 55
x = 55/3
The angle B is = 3x + 11
Plug the value of x in angle B
3 × 55/3 + 11
= 66
Hence, The angle B is 66°
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The table below shows the cube roots of different numbers: Number (x) 8 27 64 125 Cube root (y) 2 3 4 5 Part A: Does the table represent y as a function of x? Justify your answer. (5 points) Part B: The total cost f(x), in dollars, for renting a bike for x hours is shown below: f(x) = 15 + 20x What is the value of f(80), and what does f(80) represent?
Answers
Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars. Select the equation that matches this situation. Choose 1 answer: Choose 1 answer: (Choice A) 5 = 15 \times w5=15×w5, equals, 15, times, w A 5 = 15 \times w5=15×w5, equals, 15, times, w (Choice B) w = 15 +5w=15+5w, equals, 15, plus, 5 B w = 15 +5w=15+5w, equals, 15, plus, 5 (Choice C) w = 5 \times 15w=5×15w, equals, 5, times, 15 C w = 5 \times 15w=5×15
Answers
The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.
Which equation correctly matches the given situation?It follows from the task content that the equation which correctly represents the Given situation is to be determined.
Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;
Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.
Consequently, answer choice C; w = 5 × 15 is correct.
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Please look at the photo! Thank you.
Answers
The output value of (g/f)(x) is 9x/(7x + 28).
The domain of g/f is (-∞, -4) U (-4, ∞)..
How to determine the corresponding composite function?In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;
(g/f)(x) = (9/(x + 4)) ÷ 7/x
By rearranging the mathematical expression using the multiplication operation, we have the following:
(g/f)(x) = (9/(x + 4)) × x/7
(g/f)(x) = 9x/(7x + 28)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
7x + 28 ≠ 0
7x ≠ -28
x ≠ -4
Domain = (-∞, -4) U (-4, ∞).
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(03.08A)
Rewrite 4 − 5 using the additive inverse and display the new expression on a number line.
4 + 5
An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9.
4 − (−5)
An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9.
5 − 4
An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 and ends at 5. Another arrow begins at 5 and ends at 1.
4 + (−5)
An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
I WILL MARK brainlessst HELP ME FASTTTTTT
Answers
Answer:
4 + (-5)
Step-by-step explanation:
4 - 5 = 4 + (-5) = -1
Additive inverse of 5 = (-5)
What is the slope of the line y = 7x + 3
-?
1
7
А
B
7
3
8
8
3
Answers
Answer:
7 :)
Step-by-step explanation:
SOMEONE PLEASE HELP ME RN!!! Ill mark brainliest
Answers
Answer:
B) y = -3/7x + 41/7
Step-by-step explanation:
Hope this helps! Pls give brainliest!
solve this to get brainiest
Answers
Answer:
1 a. commutative property of multiplication
b. distributive property of multiplication
2 x=23\12
-x = -23\12
-23\12+23\12=0
thus -(-x)+x
Answer:
See below ↓
Step-by-step explanation:
1.
a) commutative propertyb) commutative property2.
Given : x = 23/12To verify = -(-x) = x⇒ -(-(23/12)) ⇒ -1 x -1 x 23/12⇒ 1 x 23/12⇒ 23/12⇒ VerifiedEquatons Unit Test
Determine whether the units are commensurable or incommensurable with grams?
Answers
Yes kilometers and kilograms
A certain city prides itself on having sunny days. If it rains one day, there is a 95% chance that it will be sunny the next day. If it is sunny one day, there is a 28% chance that it will rain the following day. (Assume that there are only sunny or rainy days.)If today is sunny, what is the chance that it will be rain the day after tomorrow
Answers
Answer:
56% because the more sunny days the more likely it is to rain