if the equations 2x +y =7 and x-y=2are solved simultaneously, then y=_________
Answers
Answer:
y = -2x + 7 and y = x - 2
Step-by-step explanation:
2x + y = 7
y = -2x +7
x - y = 2
-y = -x +2
y = x - 2
Related Questions
how large must a group of people be in order to guarantee that there are at least two people in the group whose birthdays fall in the same month?
Answers
Answer: A group of 12 or more people is needed to guarantee that there are at least two people in the group whose birthdays fall in the same month.
Step-by-step explanation:
We can solve this problem using the Pigeonhole Principle. There are 12 possible months that a birthday can fall in. If we have 12 or more people in a group, then it is guaranteed that at least two people have birthdays in the same month.
This is because if there are 12 or more people, then there are not enough months to go around, so at least one month must have two or more people with birthdays in it.
Therefore, a group of 12 or more people is needed to guarantee that there are at least two people in the group whose birthdays fall in the same month.
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Estimate the instantaneous rate of change at x=1
Answers
The instantaneous rate of change at x=1.
What is function?In mathematics, a function is a relation between sets that assigns to each element of a given set, exactly one element of a related set. This relationship between two sets is called a mapping, and it is commonly represented using a function notation. Functions are used to describe mathematical relationships and are studied extensively in mathematics, computer science, and other related fields.
The instantaneous rate of change at x=1 can be estimated using the concept of derivatives. A derivative is a mathematical operation that measures the rate at which a function changes with respect to its input. In this case, the derivative of the given function will measure the rate at which the function changes with respect to the input x=1.
The derivative of a function can be calculated using the formula:
f′(x)=limh→0[f(x+h)-f(x)]/h
Where f′(x) is the derivative of the function, f(x) is the function, and h is a small number close to zero.
To calculate the derivative of the function at x=1, we can plug in x=1 into the formula:
f′(1)=limh→0[f(1+h)-f(1)]/h
By calculating this limit, we can estimate the instantaneous rate of change at x=1.
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21 The graph of an exponential function is shown on the grid.
Based on the graph, which statement about the function is true?
A The range is the set of all real numbers less than 0.
B The domain is the set of all real numbers greater than-4.
C The range is the set of all real numbers greater than 0.
D The domain is the set of all real numbers less than-4.
Answers
Answer:
C The range is the set of all real numbers greater than 0.Step-by-step explanation:
We see that the function has positive range and no restriction of domain.
A The range is the set of all real numbers less than 0.
Incorrect, positive values onlyB The domain is the set of all real numbers greater than-4.
Incorrect, the domain can get any valueC The range is the set of all real numbers greater than 0.
Correct, the range is restricted to positive valuesD The domain is the set of all real numbers less than-4.
Incorrect, no restrictionsAnswer:
C is the correct answer!!
Step-by-step explanation:
hope this helped!!
find the value of x. ANSWER IS NOT 31.9. NO LINKS OR SPAMS. THANKS FOR THE HELP!!!!
Answers
Answer:
x = 7.0588235294
Step-by-step explanation:
similar triangles have the same proportion for corresponding sides
long leg / hypotenuse ratio
small triangle to big triangle
x/8 = 15/17
Multiply both sides by 8
x = 15/17 * 8
x = 7.0588235294
A college president is interested in student satisfaction with recreational facilities on campus. A questionnaire is sent to all students and asks them to rate their satisfaction on a scale of 1 to 5 (with 5 being the best). The instrument of measurement is - the rating on the scale - satisfaction - a student.
- the questionnaire
Answers
A college president is interested in student satisfaction with recreational facilities on campus. A questionnaire is sent to all students and asks them to rate their satisfaction on a scale of 1 to 5.
The instrument of measurement is:
=> the questionnaire
The common types of measuring tools include speedometers, measuring tape, thermometers, compasses, digital angle gauges, levels, laser levels, macrometer, measuring squares, odometers, pressure gauges, protractors, rulers, angle locators, bubble inclinometers, and calipers.
The measuring instruments in mechanical engineering are dimensional control instruments used to measure the exact size of object. These are adjustable devices and can measure with an accuracy of 0.00 l mm or better. The gauges are fixed dimension instruments and are not graduated.
The correct option is (d).
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suppose a batch of steel rods produced at a steel plant have a mean length of 164 millimeters, and a variance of 121. if 287 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.56 millimeters? round your answer to four decimal places.
Answers
The probability that the mean length of the sample rods differs from the population mean by less than 0.56 millimeters is approximately 0.8051.
To solve this problem, we need to calculate the probability that the mean length of the sample rods differs from the population mean by less than 0.56 millimeters.
Given:
Population mean (μ) = 164 millimeters
Variance (σ²) = 121
Sample size (n) = 287
Standard deviation of the sample mean (σₘ) = σ / √n
First, let's calculate the standard deviation of the sample mean:
σₘ = √(σ² / n)
= √(121 / 287)
= √(0.4216)
= 0.6495 (rounded to four decimal places)
Next, we need to calculate the Z-score for the given difference of 0.56 millimeters:
Z = (difference from population mean) / σₘ
= 0.56 / 0.6495
= 0.8624
Using a standard normal distribution table or calculator, we can find the probability corresponding to this Z-score. The probability will be the area under the curve to the left of the Z-score.
Looking up the Z-score of 0.8624 in the standard normal distribution table, we find that the corresponding probability is approximately 0.8051.
Therefore, the probability that the mean length of the sample rods differs from the population mean by less than 0.56 millimeters is approximately 0.8051.
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Tim uses 9 liters of water (w) to water 24 flower pots (f). If this relationship is proportional, what equation represents this relationship? *
Answers
The relationship between the amount of water (w) and the number of flower pots (f) is proportional.
In a proportional relationship, the ratio between the two quantities remains constant. In this case, the amount of water used (w) is directly proportional to the number of flower pots (f) that need to be watered. To find the equation that represents this relationship, we can set up a proportion using the given information.
Let's assume that x represents the constant ratio between the amount of water used and the number of flower pots. The equation can be written as:
w/f = x
Substituting the given values, we have:
9/24 = x
Simplifying the equation, we find:
x = 9/24
To find the final equation, we can multiply both sides of the equation by 24:
24x = 9
Therefore, the equation that represents the proportional relationship between the amount of water (w) and the number of flower pots (f) is 24x = 9. This equation shows that for every 24 flower pots, 9 liters of water are required.
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How do confidence intervals tell you whether your results are statistically significant?.
Answers
It can be inferred that there is a statistically significant result if the confidence interval excludes the value of zero effect.
Confidence Interval;
In statistics, confidence is another word for probability. For instance, if you create a confidence interval with a 95% confidence level, you can be sure that 95 times out of 100 the estimate will fall between the upper and lower values indicated by the confidence interval.
Therefore,
The confidence level is 95% if your significance level is 0.05. The hypothesis test is statistically significant if the P value is lower than your significance (alpha) level. The findings are statistically significant if the confidence interval excludes the null hypothesis value. 0
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A rectangular prism has a length of 10in, a height of 15in, and a width of 8in. What is its volume, in cubic in?
Answers
Answer:
Volume of rectangular prism = 1200 cubic inches
Step-by-step explanation:
Given that:
Length of rectangular prism = 10 inches
Width of rectangular prism = 8 inches
Height of rectangular prism = 15 inches
Volume of rectangular prism = Length * Width * Height
Volume = 10 * 8 * 15
Volume = 1200 cubic inches
Hence,
Volume of rectangular prism = 1200 cubic inches
What is the value of x in the solution to this system of equations?
3 x-5 y= 22
y=-5 x + 32
Answers
Answer:
6.4
Step-by-step explanation:
The intersection point of 3x-5y=22 and y=-5x+32 is (6.4,0) on a graph, therefore, "x"=6.4
How much money will Adriano’s online business earn this month
Answers
Fill in the missing numbers in the sequence: 0.1, 0.25, 0.4, __, 0.7 ?
Answers
0.55
Step-by-step explanation:
0.25-0.1=0.15
0.7-0.4=0.3
0.4+0.15=0.55
0.55+1.5=0.7
In right triangle PQR, m∠Q = 90° and sin R=5/13
What is the value of cos R?
a) 5/13 b)5/12 c) 12/13 d) 12/5
Answers
Answer:
C
Step-by-step explanation:
Given
sinR = \(\frac{5}{13}\) = \(\frac{opposite}{hypotenuse}\)
This is a 5- 12- 13 triangle with legs PQ = 5, QR = 12, hypotenuse PR = 13
cosR = \(\frac{adjacent}{hypotenuse}\) = \(\frac{QR}{PR}\) = \(\frac{12}{13}\)
For the function below, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or a
minimum value and find that value; and (d) graph the function.
f(x) = -x2 - 6x-4
Answers
Answer:
Step-by-step explanation:
f(x) = ax² + bx + c
"x" coordinate of vertex is ( - \(\frac{b}{2a}\) )
axis of symmetry is x = - \(\frac{b}{2a}\)
If a > 0 the function opens upward and has minimum value.
If a < 0 the function opens downward and has maximum value.
f(x) = - x² - 6x - 4
(a). x = - \(\frac{-6}{-2}\) = - 3 ; y = - (- 3)² - 6( - 3) - 4 = 5
Coordinates of vertex are (- 3, 5)
(b). The axis of symmetry is x = - 3
(c). The given function opens downward
y = 5 is a maximum of a given function.
Find the arc length of the semicircle
Answers
Answer:
Arc length of the semicircle is 12.57 cm.
Step-by-step explanation:
From the given picture,
Measure of diameter = 8 units
Radius of the semicircle = \(\frac{\text{Diameter}}{2}\)
= \(\frac{8}{2}\)
= 4 units
Since, circumference of a semicircle is given by the expression,
C = πr
Here, r = radius of the semicircle
Circumference of the given semicircle = π(4)
= 4π
= 12.57 cm
Therefore, arc length of the semicircle is 12.57 cm.
Answer:
Its 16 pi
Step-by-step explanation:
helpp!!!! i will mark as brainliest!!
solve i and ii ....
Answers
Answer: The value of x is 60 and two prime numbers are 2 and 3
Step-by-step explanation:
This is because 2 multiplied by 30 is 60 and 2 and 3 are prime numbers because their only factors are one and themselves.
Answer:
I) the value of X is 60
60=1×_
2×30
3×20
4×15
5×12
6×12
6×10 = 60
ii) 2 and 3 you also can put 5
Hope this helps
Roy received math test scores of 05, 90, 90, and 85.
7. What is Roy's median test score?
8. What score would Roy need to get on
his next test to have a mean of 92
Answers
Median = 87.5 Sorry about the other one
8. I maybe the other p help
The midpoint of \overline{\text{AB}} AB is M(0, -3)M(0,−3). If the coordinates of AA are (2, -5)(2,−5), what are the coordinates of BB?
The formating kinda screwed up
Answers
Using the mid-point concept, it is found that the coordinates of B are (-2, -1).
The mid-point of two points is the mean of the coordinates of each point.In this problem:
The points are: A(2, -5) and B(x,y).The mid-point is (0, -3).Applying the concept for both the x and y-coordinates, we have that:
\(\frac{x + 2}{2} = 0\)
\(x + 2 = 0\)
\(x = -2\)
\(\frac{-5 + y}{2} = -3\)
\(-5 + y = -6\)
\(y = -1\)
The coordinates of B are (-2, -1).
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A company has a multi-tier investment. They have $40 million in operating expenses each year and a cost of capital of 12%. They can invest $12 million in new technology for their plant. There is a 40% chance that the new equipment reduces expenses by 15%, a 30% chance it reduces expenses by 10%, and a 30% chance it reduces expenses by 5%. Shareholders will view the results after 3 years and vote on continuing or abandoning the project. Abandoning costs the company $5 million. If expenses drop 15%, there is a 95% chance the vote is yes, to continue for another 3 years, If they drop 10%, the vote has a 75% chance to be yes. If expenses only drop 5%, there is a 40% change the shareholders vote to continue the project. Draw out the timeline, decision tree, and calculate the probabilities for all six possible scenarios.
Answers
The probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.
To analyze the given scenario and calculate the probabilities for all six possible scenarios, let's create a decision tree and timeline to visualize the information provided.
Timeline:
Year 1: Initial investment of $12 million in new technology.
Year 2: Results evaluated by shareholders.
Year 3: Final decision made by shareholders.
Decision Tree:
``` ┌─── Continue (95%)
│
15% ─────┼─── Continue (75%)
│
$12 million ─────┼─── Continue (40%)
investment │
│
10% ─────┼─── Abandon ($5 million cost)
│
│
5% ─────┼─── Abandon ($5 million cost)
│
└─── Abandon ($5 million cost)
```
Now, let's calculate the probabilities for each scenario:
1. New equipment reduces expenses by 15% (40% probability):
Probability = 40% * 95% = 0.4 * 0.95 = 0.38 (38%)
Outcome: The shareholders vote to continue for another 3 years.
2. New equipment reduces expenses by 10% (30% probability):
Probability = 30% * 75% = 0.3 * 0.75 = 0.225 (22.5%)
Outcome: The shareholders vote to continue for another 3 years.
3. New equipment reduces expenses by 5% (30% probability):
Probability = 30% * 40% = 0.3 * 0.4 = 0.12 (12%)
Outcome: The shareholders vote to continue for another 3 years.
4. New equipment does not reduce expenses (10% probability):
Probability = 10%
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
5. New equipment reduces expenses by 15%, but shareholders vote to abandon (5% probability):
Probability = 15% * (1 - 95%) = 0.15 * 0.05 = 0.0075 (0.75%)
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
6. New equipment reduces expenses by 10%, but shareholders vote to abandon (5% probability):
Probability = 10% * (1 - 75%) = 0.1 * 0.25 = 0.025 (2.5%)
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
To summarize, we have calculated the probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.
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La rueda de una bicicleta de aro 26 tiene alrededor de 0,6 m de diámetro. Aproximadamente, ¿cuántos metros recorre una bicicleta de aro 26 cuando sus ruedas dan 200 vueltas?
Answers
Answer:
Una bicicleta de aro 26 recorre 377 metros cuando sus ruedas dan 200 vueltas.
Step-by-step explanation:
Para encontrar la respuesta, primero tienes que calcular la longitud de la circunferencia utilizando la siguiente formula:
Longitud=π*diámetro
El diámetro es 0,6m y el valor de π es 3,1416 y puedes reemplazar estos valores en la fórmula:
Longitud=3,1416*0,6
Longitud=1,885
Ahora que tienes la longitud que recorre la rueda en cada vuelta, puedes multiplicar este valor por el número de vueltas para encontrar los metros que recorre una bicicleta de aro 26:
200*1,885=377
De acuerdo a esto, la respuesta es que una bicicleta de aro 26 recorre 377 metros cuando sus ruedas dan 200 vueltas.
Usando la circunferencia de la rueda, se encuentra que la bicicleta recorre 377 metros.
Qual es la cincunferencia de un círculo?
La cincunferencia de un círculo de diametro d es dada por:
\(C = \pi d\)
En este problema, en cada vuelta, la distancia es la circunferencia de la rueda, o sea:
\(C = \pi(0.6) = 0.6\pi\)
Considerando 200 vueltas:
\(d = 200(0.6\pi) = 120\pi = 377\)
La bicicleta recorre 377 metros.
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can someone help me with this problem?
Answers
Answer:
B) f^-1(x)=3-5x
Step-by-step explanation:
y=3-x/5
rearrange the equation so you have x variable on the left side
5y=3-x
+x +x
5y+x=3
-5y -5y
x=3-5y
so answer is b)
f^-1(x)=3-5x
990*500/600+51-100+10
What is the answer
Answers
Answer:786?
Step-by-step explanation:
Answer: if that is supposed to be a multiplication sign its 786
Step-by-step explanation:
7x + 2 = -19 (b) 3x - 1/3 = 5 (c) 5x - 4 = 21 (d) -7x = 21 (e) 18 - 7x = -3 (f) 3(x + 4) = 21 (g) 3x - 9 = 5x - 3 (h) 4x + 6 - 7x + 9 = 18 (i) - 4/9 x = - 36 (j) -7/8x - 6 = 8 can any please elp me find the variables in the question
Answers
Answer:
Step-by-step explanation:
a)7x + 2 = -19 {subtract 2 from both sides}
7x + 2 - 2 = -19 - 2
7x = -21 {Divide both sides by 7}
7x/7 = -21/7
x = -3
b) 3x - 1/3 = 5
3x - 1/3 +1/3 = 5 + 1/3 {Add 1/3 to both sides}
3x =15/3 + 1/3
3x =16/3
3x/3 = 16/3*3 {Divide both sides by 3}
x =16/9
x =1 7/9
c) 5x - 4 = 21
5x -4 + 4 = 21 +4 {Add 4 to both sides}
5x = 25
5x/5 = 25/5 {Divide both sides by 5}
x = 5
d) -7x = 21 {Divide both sides by -7}
-7x/-7 = 21/-7
x = -3
e) 18 - 7x = -3
18 - 7x - 18 = -3 - 18 {Subtract 18 from both sides}
-7x = -21 {Divide both sides by -7}
-7x/-7 = -21/-7
x = 3
f) 3(x+4) = 21 {use distributive property}
3x + 3*4 = 21
3x + 12 = 21
3x + 12 - 12 = 21 - 12 {Subtract 12 from both sides}
3x = 9 {Divide both sides by 3}
3x/3 = 9/3
x = 3
g) 3x - 9 = 5x - 3 {add 9 to both sides}
3x - 9 + 9 = 5x - 3 + 9
3x = 5x + 6
3x - 5x = 5x + 6 - 5x { subtract 5x form both sides}
-2x = 6 {Divide both sides by -2}
-2x/-2 = 6/-2
x = -3
h) 4x + 6 - 7x + 9 = 18 {Add the like terms}
-3x + 15 = 18 {Subtract 15 from both sides}
-3x + 15 -15 = 18 - 15
-3x = 3 {Divide both sides by -3}
-3x/-3 = 3/-3
x = -1
\(i) \frac{-4}{9}x = -36\)
Multiply both sides by 9
\(9*\frac{-4}{9}x =9*-36\)
-4x = -324 {Divide both sides by -4}
-4x/-4 = -324/-4
x = -81
\(j)\frac{-7}{8}x - 6 = 8\) {Add 6 to both sides}
\(\frac{-7}{8}x-6+6=8+6\\\\\frac{-7}{8}x=14\\\) {Multiply both sides by 8}
\(\frac{-7}{8}x*8=14*8\\\\-7x=14*8\\\) {Divide both sides by -7}
\(\frac{-7}{-7}x=\frac{14*8}{-7}\)
x =-2*8
x = -16
Evaluate if x = -4.
- 3x +7
Answers
Replace x with -4:
-3(-4) + 7 =
12 + 7 = 19
Answer: 19
Answer:
19Basic fact:
two negatives make a positive
Step-by-step explanation:
x=-4
so replace 3x with x being -4
so it is
-3(-4)+7
-3 x-4+7
-3 x -4 = 12
12+7=19
I work hard on my answers so a brainliest would be appreciated
2) Write the equation of a line that passes through the point (-4,-5) and is perpendicular to a line that passes through the points (-6, 8) and (10,0).
Answers
Answer:
y= - 1/4x
Step-by-step explanation:
The equation of the line passing through that point with the required slope is y=2x+3.
What is slope?The slope of a line is the change in the y-coordinate relative to the change in the x-coordinate. The net change in the y-coordinate is indicated by Δy and the net change in the x-coordinate by Δx. Thus, the change in y-coordinate with respect to change in x-coordinate is given by: m = change in y/change in x = Δy/Δx Where "m" is the slope of the line. The slope of a straight line can also be represented by the formula tan θ = Δy/Δx So, tan θ is the slope of a straight line. In general, the slope of a line indicates its steepness and direction.
Given:
The angle of slope of a line between two points (x1,y1) and (x2,y2) can be easily determined by finding the difference in the coordinates of the points. The slope is usually indicated by the letter "m".
The slope of a line passing through points (x1,y1)and(x2,y2) is given by
m=(y2−y1)/(x2−x1)
The slope (\(m^p)\) of a line perpendicular to a line with slope (\(m^p)\) is =−1/m because the product of the slopes of two perpendicular lines is -1, except in the pathological case where the lines are parallel to the x and y axis.
slope m of a line, and the coordinates of a known point (x1,y1) it is simple to plug them into the point-slope formula for a line to determine the equation for that line.
y=mx +b
y1=mx1+b
solve for b
Going through those steps:
(x1,y1)=(-6, 8)
(x2,y2)=(10,0)
m=(0-8)(10-(-6))=-0.5
\(m^p\)=−1/-0.5= 2
our known point is (−4,−5)
−5=2(−4)+b
-5 = -8+b
b = 3
Therefore, the equation of the line passing through that point with the required slope is y=2x+3.
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How to do the nth term test?
Answers
The nth term test is a mathematical method used to determine if a sequence converges or diverges. It helps to find the behavior of the sequence as n approaches infinity.
Here's how to do the nth term test:
Find the nth term formula for the given sequence.
Calculate the limit of the nth term as n approaches infinity.
Based on the value of the limit, determine if the sequence converges or diverges:
If the limit is finite and non-zero, the sequence diverges.
If the limit is finite and zero, the sequence converges to zero.
If the limit is infinite or does not exist, the sequence diverges.
The nth term test is important because it provides a quick and easy way to determine the behavior of a sequence, without having to calculate all the terms.
It's important to understand the nth term test and how to apply it, so that you can analyze the behavior of sequences in mathematics and other related fields.
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Explain how you solve the question
Answers
Answer:
Perimeter = 72 feet (24 yards) Cost = $144
Step-by-step explanation:
A hexagon has 6 sides, and each side is 12 feet long
6 x 12 = 72
So she needs 72 feet of brick
But the brick is sold in yards, so convert feet to yards
1 yard = 3 feet
72 / 3 = 24
So the perimeter of the garden is 72 feet or 24 yards
If the brick costs $6 per yard then multiply 24 x 6 to find the cost
24 x 6 = 144
So the total cost is $144
Answer:
Perimeter: 24 yards
Cost: $144
Step-by-step explanation:
There are 3 feet in a yard. In the picture, it's given that the length of a side in the hexagon is 12 feet.
12 / 3 = 4 yards
Each side in the hexagon is equal, so the length of every side is 4 yards.
There are 6 sides in a hexagon, meaning the perimeter is 4 * 6 = 24 yards.
The cost per yard is $6.
$6 * 24 yards = $144 to edge the garden with brick.
Priya, Han, and Elena, are members of the running club at school.
Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week. How many miles did Priya run last week?
Answers
Which of the following is the difference of two squares

4g-16h
16a^2-4y^2
2x^2-4y^2
25m^3+100n^2
Answers
Answer:
2nd option
Step-by-step explanation:
A difference of squares has the general form
a² - b²
where the terms on either side of the subtraction ( the difference ) are both perfect squares.
The only one fitting this description is
16a² - 4y²
= (4a)² - (2y)² ← difference of squares
solve for x
Help please
Answers
Answer:
Step-by-step explanation:
The volume of a prism is V = Bh, where B is the area of the base shape and h is the height of the prism. Find the area of the parallelogram that is the base, length x width, then multiply this by the height of the prism. l x w x h.