The solution to the system of equation are as follows:
1. x = 3, y = 0
2. x = -3 , y = 3
3. x= -9, y = -9
1.
y = x - 3
y = -2x + 6
multiply equation(i) by 2
Combined equation2y = 2x - 6
y = -2x + 6
3y = 0
y = 0
x = 0 + 3
x = 3
2.
-x + 5y = 18
x + 4y = 9
9y = 27
y = 27 / 9
y = 3
x + 4(3) = 9
x = -3
3.
3x + 5y = -72
2x + 3y = -45
multiply equation(i) by 2 and equation(ii) by 3
Combined equation6x + 10y = -144
6x + 9y = -135
y = -9
2x + 3(-9) = -45
2x = -45 + 27
2x = -18
x = -18 / 2
x = -9
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Question 17 of 25
how many solutions does the following system of equations have?
y=5/2x+2
2y=5x+4
a. zero
b. one
c.infinitely many
d. two
Answer:
c
Step-by-step explanation:
y = \(\frac{5}{2}\) x + 2 → (1)
2y = 5x + 4 ( divide through by 2 )
y = \(\frac{5}{2}\) x + 2 → (2)
the 2 equations are the same and will have infinitely many solutions
The chain and gears of bicycles or motorcycles or belt around two pulleys are some-real
illustrations of tangents and circles. Using these real-life objects or similar ones, formulate
problems involving tangents, then solve.
The distance between the point where the stick touches the rim and the ground is √(dL - L^2) inches.
A bicycle wheel has a diameter of d inches. A stick of length L inches is placed along the rim of the wheel such that it is tangent to the rim and also touches the ground. What is the distance between the point where the stick touches the rim and the ground?
Let O be the center of the wheel, A be the point where the stick touches the rim, and B be the point where the stick touches the ground. Then, OA is the radius of the wheel, which is d/2 inches, and AB is the distance we want to find.
Since OA is perpendicular to AB, we can use the Pythagorean theorem to find AB:
AB^2 = OA^2 - OB^2
OB is the length of the part of the stick that touches the ground, which is L - OA inches. Substituting the values we know, we get:
AB^2 = (d/2)^2 - (L - d/2)^2
Simplifying, we get:
AB^2 = dL - L^2
Taking the square root of both sides, we get:
AB = √(dL - L^2) inches
Therefore, the distance between the point where the stick touches the rim and the ground is √(dL - L^2) inches.
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What is the slope of the line?
A: 2/5
B: -2/5
C: 1/3
D: 5/2
There are two similar triangles in the diagram. Find the unknown measurement.
Answer: x=180
Step-by-step explanation:
360/120=x/60
3=x/60
x=180
By the similarity of triangles the length of the side RS is 180 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know in similar triangles the ratio of their corresponding sides are equal.
Given, Are two triangles OPQ and ORS.
Therefore,
OP/PR = PQ/RS.
120/360 = 60/x.
120x = 21600.
12x = 2160.
x = 2160/12.
x = 180.
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Please help me!! Please explain and I’m pretty sure the answer needs to have < and > signs or >_ and <_ with “_” under < and >.
(For other ppl who search this)
4. Jim makes 8.50 an hour. Each week, 26% of his total pay is deducted for taxes. How many hours does Jim have to work if he wants his take-home pay to be AT LEAST $300 per week? Write and solve an inequality for this situation.
Answer:
Jim has to work 48 hours to earn at least $300 per week.
Step-by-step explanation:
Jim makes 8.50 per hour
so in x hours he makes 8.5x
26% is deducted for taxes
so his take home pay is 8.5x(1 - .26) = 8.5x(.74) = 6.29x
To make > = $300 Jim must work enough hours so that
6.29x >= 300
x >= 17.49
The um of Joy' age and her brother' age i $24. Her brother' age i $3 year older than twice Joy' age. What i the difference, in year, between Joy' age and her brother' age?
To determine their ages, the substitution approach is used.
Joy's age and her brother's age are differed by 10 years.
What is linear system?
It is an system of equation where the maximum power of the variable is consistently 1. a single-dimensional object with no breadth. It consists of an endless number of dots placed side by side.
Given
The combined ages of Joy and her brother total 24.
Joy's older brother is three years older than twice his age she is.
To locate
Joy's age as compared to that of her brother.
Assume that Joy is x years old and her brother is y.
then in line with the first circumstance.
x + y = 24 ...(1)
And according to the second condition.
2x + 3 = y ...(2)
On solving equations 1 and 2. We get
x + 2x + 3 = 24
x = 7
Then
y = 2x + 3
y = 17
Then, the difference between Joy's age and her brother's age.
y - x = 17 - 7 = 10
Thus, the difference between Joy's age and her brother's age is 10.
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A contractor is preparing a bid to install swimming pools at a new housing addition. The estimated time to build the first pool is 30 hours. The contractor estimates an 85 percent learning rate. Using POM for Windows or OM Explorer, how long do you estimate the time required to install the fifth pool? The time required to install the fifth pool is __ hours. (Enter your response rounded to two decimal places.) What is your estimate of the total time for all five pools? The total time for all five pools is __ hours. (Enter your response rounded to two decimal places.)
Previous question
The estimated total time for all five pools is approximately 13.85 hours.
To estimate the time required to install the fifth pool using the learning curve, we can use the formula:
Time for nth unit = Time for first unit * (n^b)
Where:
Time for nth unit is the estimated time to install the nth pool
Time for first unit is the estimated time to build the first pool (30 hours)
n is the number of units (in this case, n = 5 for the fifth pool)
b is the learning curve exponent (85% learning rate corresponds to b = log(0.85) / log(2))
Let's calculate the estimated time for the fifth pool:
b = log(0.85) / log(2) ≈ -0.157
Time for fifth pool = Time for first pool * (5^b)
Time for fifth pool = 30 * (5^(-0.157))
Calculating this, we find:
Time for fifth pool ≈ 30 * 0.6764 ≈ 20.29 hours
Therefore, the estimated time required to install the fifth pool is approximately 20.29 hours.
To calculate the total time for all five pools, we need to sum the time required for each pool from the first to the fifth. Since the learning curve assumes decreasing time with increasing units, we can use a summation formula:
Total time for all units = Time for first unit * ((1 - (n^b)) / (1 - b))
Using this formula, let's calculate the total time for all five pools:
Total time for all five pools = Time for first pool * ((1 - (5^b)) / (1 - b))
Total time for all five pools = 30 * ((1 - (5^(-0.157))) / (1 - (-0.157)))
Calculating this, we find:
Total time for all five pools ≈ 30 * 0.4615 ≈ 13.85 hours
Therefore, the estimated total time for all five pools is approximately 13.85 hours.
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f(x,y)=x³-12x+y³ +3y²-9y Ans: Max (-2,-3); Saddle point (2,-3) and (-2,1); Min (2,1)
The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).
To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.
Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:
∂F/∂x = 3x² - 12
∂F/∂y = 3y² + 6y - 9
To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:
3x² - 12 = 0 --> x² = 4 --> x = ±2
3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1
Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).
To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:
∂²F/∂x² = 6x
∂²F/∂y² = 6y + 6
Now, let's evaluate the second partial derivatives at each critical point:
At (-2, -3):
∂²F/∂x² = 6(-2) = -12 (negative)
∂²F/∂y² = 6(-3) + 6 = -12 (negative)
Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.
At (2, -3):
∂²F/∂x² = 6(2) = 12 (positive)
∂²F/∂y² = 6(-3) + 6 = -12 (negative)
Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.
At (-2, 1):
∂²F/∂x² = 6(-2) = -12 (negative)
∂²F/∂y² = 6(1) + 6 = 12 (positive)
Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.
Therefore, the critical points are classified as follows:
Local maximum: (-2, -3)
Saddle points: (2, -3) and (-2, 1)
Local minimum: (2, 1)
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Twice the difference of a number and 3.
Answer:
5
Step-by-step explanation:
Suppose a survey of 580 women in the United States found that more than 64% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey.64% of women in the sample are the primary investor in their household.
There is an association between U.S. women and being the primary investor in their household.
The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.
What will the inference be?This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.
According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.
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help pleaseee due tomorrow!?!!
1 simplify.
3/4x × 12/11 ÷ 3x/22
Answer:
6 just 6 Your welcome !!
Step-by-step explanation:
Select the correct answer. Four lines of X axis from Negative 3 to plus 3. A. A point marked at Negative 2.5, B. A point marked at plus 1.5, C. A point marked at Negative 0.5, and D. A point marked at plus 2.5. Which image shows the correct position of − 2 1 2 on the number line? A. A B. B C. C D. D
A point marked at Negative 2.5, is the correct image that shows the position of -2.5 on the number line.
The correct answer is A, a point marked at Negative 2.5.
To locate -2.5 on the X-axis, we need to find the position that corresponds to a point 2.5 units to the left of the origin (0,0) on the X-axis.
Since each line segment on the X-axis represents one unit, we can count 2.5 units to the left of the origin to find the position of -2.5.
Therefore, A, which shows a point marked at Negative 2.5, is the correct image that shows the position of -2.5 on the number line.
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PLSSS HELP ANSWER THESE QUESTIONS! WORTH 35 POINTS WILL GIVE BRIANLIEST IF ANWRS ARE CORRECT!
For which value of x do following expressions make sense?
THE FOLLOWING QUESTION HAVE TO BE ANWERED AS X IS LE THAN OR GREATER THAN WHATEVER THE ANWER IS
43a) √x+5 40a) ∛a 44b) √(-5x)^3 47e) √13-(13-2x)
THE NEXT COUPLE OF QUETION HAVE TO ANWERED AS X = WHATEVER THE ANSWER IS.
43b) √|x| + 1 44a) √(-2x)^2
45a) √x-5 = 3 The root is only over x-5
45b) √2x+4 = 2 the root is only over 2x+ 4
45c) √x(x+1) = 0 root is only over x(x+1)
45d) √x+5 = -1 the root is only over x+5
45e) √x + x^2 = 0 the root is only over x
42d) root 5 over x+3 = 17 1
9e) root 4 over x = 1 THE ANSWER IS NOT 1
19f) ∛x - 2 = 0 the root is only over x
THE FOLLOWING QUESTIONS HAVE NUMERICAL ANSWERS
9a) root 0.6 over 36 9h) root (4-10) over 0.01
The values of the variables and numbers in radical form are presented as follows;
43a) x > -5
40a) a > 0
44b) x < 0
47e) x > 0
43b) x = The set of all real numbers
44a) The set of all numbers
45 a) x = 14
45 b) x = 0
45 c) x = -1
45 d) x = -4
45 e) x = 1
42 d)x = 5/196
9 e) x = 4
9 f) x = 8
9 a) √(0.6/36) ≈ 0.13
9 h) √((4 - 10)/(0.01)) = i·10·√6
What is a radical expression in mathematics?A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.
43 a) \(\sqrt{x + 5}\)
x + 5 > 0
Therefore, x > -5
40a) ∛a
a > 0
44b) √(-5·x)³
-5·x < 0
x < 0
47e) √(13 - (13 - 2·x))
(13 - (13 - 2·x)) > 0
13 > (13 - 2·x)
0 > -2·x
x > 0
43b) √|x| + 1
x = All real numbers
44 a) √(-2·x)²
√(-2·x)² = -2·x
x = Set of all numbers
45 a) √(x - 5) = 3
(x - 5) = 3² = 9
x = 9 + 5 = 14
45b) √(2·x + 4) = 2
2·x + 4 = 2²
2·x = 2² - 4 = 0
x = 0/2 = 0
45c) √(x·(x + 1)) = 0
(x·(x + 1)) = 0
(x + 1) = 0
x = -1
45 d) √(x + 5) = -1
(x + 5) = (-1)²
x + 5 = 1
x + 5 = 1
x = 1 - 5 = -4
x = -4
45e) √x + x² = 0
√x = -x²
(√x)² = (-x²)² = x⁴
x = x⁴
1 = x⁴ ÷ x = x³
x = ∛1 = 1
x = 1
42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)
\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)
\(\dfrac{5}{x} }=14^2=196\)
\(x = \dfrac{5}{196}\)
9e) \(\sqrt{\dfrac{4}{x} } = 1\)
\(\dfrac{4}{x} } = 1^2\)
x × 1² = 4
x = 4
19f) ∛x - 2 = 0
∛x = 2
x = 2³ = 8
9a) \(\sqrt{\dfrac{0.6}{36} }\)
\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)
9h) \(\sqrt{\dfrac{4-10}{0.01} }\)
\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6
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which transformation maps the pre-image to the image?
A. dilation
B. translation
C. reflection
D. rotation
Answer:
A. dilation
Step-by-step explanation:
The triangle are the same but different sizes so it would be a dilation
*plssss give me brainlistttt*
what theorem can be used to find segment lengths in a triangle with a segment drawn parallel to a side of the triangle?
The midsegment linking the cartesian coordinates of two of a triangle's sides is parallel to the fourth aspect of the triangle, and its length is half that of the third side, according to the midsegment theorem.
Whence came the triangle?The assertions that the Greek mathematician Pythagoras discovered the properties of right-angled triangles in the fifth century BC just did not match up, according to many. Some people think following commentary shows it was a joint effort among his disciples, the Pythagoreans.
Which four primary triangles are there?Equilateral: equal angles and all three sides. Acute isosceles: two identical sides and angles, both of which are only about 90 degrees. Acute scalene has irregular sides and angles, all of which are under 90 degrees. Obtuse isosceles: two identical sides and angles, one of which is more than 90 degrees.
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Professor Goodheart has two exams, exam 1 and exam 2. The exam 1 weights 40% and the exam 2 weights 60% of the final grades. Put the grades on the exam 1 on the horizontal axis and the grade on the exam w on the vertical axis. What kind of preference a student should have for these two grades
Answer:
Imperfect substitutes
explanation:
The choices above are not perfect substitutes, meaning they can not be perfectly or directly replace the other. Imperfect substitutes are close substitutes but not perfect substitutes. Unlike perfect substitutes, imperfect substitutes satisfies same utility but has different characteristics and therefore not entirely substitutable. For example, while one may want to have the 40 marks too, he'd rather have 60 marks even if the criteria for a 60 mark score was increasingly hard.
8% of the High School students have their license. If there are 1000 high school students in your neighborhood, how many have their license internet Enter your answer in the sface below. ??? teachers
Answer:
80.
............................
triangle duh is rotated and then dilated by a scale factor of n
When triangle DUH is rotated and then dilated by a scale factor of n, it means that the triangle is first turned around a fixed point, and then all of its sides are enlarged or reduced by a factor of n.
The rotation changes the position and orientation of the triangle in the plane, while the dilation changes its size. The resulting triangle will have different angles and side lengths than the original triangle, but it will be similar to it because the shape remains the same. The scale factor n determines how much bigger or smaller the triangle becomes after the dilation.
If triangle DUH is rotated and then dilated by a scale factor of n, it means the triangle has undergone two transformations. First, the triangle is rotated around a point, changing its orientation but keeping its shape and size. Second, the triangle is dilated by a scale factor of n, which enlarges or shrinks the triangle proportionally while maintaining its overall shape. The final result is a triangle with the same shape as the original DUH but with a different size and orientation.
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Answer each question and round your answer to the nearest whole number
Please help-
And please explain if you know how to-
Answer:
1 is 2/44=40/88
2 is 24/50=48/25
3 is 50/30=100/60
4 is 41/20.5=19/2
Step-by-step explanation:
your just multiplying or dividing by 2
pls mark braliest
Answer:
1: 880, 2: 24, 3: 30, 4: 82
Step-by-step explanation:
1: If we divide by 2 we get 20. Then multiply 44 x 2 = 880
2: 25 is half of 50. So then, we divide 48 by 2 = 24
3: 50 x 2 = 100. Then, we divide 60 by 2 becasue it is reverse; 60÷2 = 30
4: 38 divided by 19 = 2. Then we multiply 41 by 2 becasueit is reversed. 41 x 2=82
Whats the remainder when 14952 divide by 41
Use complete sentences to state who is correct and why.
Answer:
I dont think you gave the entire question but
bridget is saying x > 3
dana is saying x < 3
a goat is six times as heavy as its kid if their total mass is 70 kg find each of their masses in kg
plzz help i need it fast
Answer:
10kg and 60 kg.
Step-by-step explanation:
Let the kid's mass be x kg, then the goat's mass is 6x.
x + 6x = 70
7x = 70
x = 10.
can somene explain this to me please?
Answer:
10/3
Step-by-step explanation:
rate of change = gradient
(17-7)/(6-3) = 10/3
basically difference of y values / difference of x values
hi, can you help me answer this question, please, thank you:)
Notice that the total probability is distributed in 8 minutes. Furthermore, the total probability has to be equal to 1, then:
\(\begin{gathered} h\cdot8=1 \\ \Rightarrow h=\frac{1}{8}=0.125 \end{gathered}\)Where h is the height of the distribution. The first answer is 0.125.
b) Notice that 16-13=3 min. Therefore, the probability we are looking for is:
\(P(13The second answer is 0.375c) Notice that the probability for the bus to arrive before 15 minutes is:
\(P(X\le15)=\frac{15-9}{8}=\frac{6}{8}=0.75\)Thus, the probability that will we wait more than 15 minutes is:
\(P(X>15)=1-0.75=0.25\)The third answer is 0.25
d) The probability that one will wait at most 15 minutes was found in the previous step:
\(P(X\le15)=\frac{15-9}{8}=\frac{6}{8}=0.75\)The fourth answer is 0.75
can you guys help me please as much as you can ^^
Answer:
Step-by-step explanation:
m<1 = 50
m<2 = 22
m<3 = 108
m<4 = 50
m<5 = 65
m<6 = 50
m<7 = 43
m<8 = 65
m<9 = 75
m<10 = 18
m<11 = 25
m<12 = 40
m<13 = 115
m<14 = 65
m15 = 115
Simplify 4 over quantity 2 plus 7 i
Answer:
(8-28i)/53
hope it helps!
Step-by-step explanation:
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
~inequality
3(8 - 4x) < 6(x - 5)
= 24 - 12x < 6x - 30
= -12x - 6x < - 30 - 24
= -18x < - 54
= x > 3 ✔️
~ nice to help you ^^
What does the point (7,84) represent in this situation?
The point (7,84) represents a precise location on a graph or coordinate plane.
A coordinate is a set of values that specifies the position or location of a point in a geometric space.
The point (7,84) represents a specific location on a graph or coordinate plane. The first number, 7, represents the point's position on the x-axis, which is a horizontal line that runs left to right. The second number, 84, represents the point's position on the y-axis, which is a vertical line that runs up and down. Together, the two numbers give us a precise location for the point.
In this situation, we don't have enough context to know what the point (7,84) represents. It could be the location of a city on a map, the amount of rainfall in inches on a specific day, or the price of a stock at a particular time. However, regardless of the situation, the point (7,84) is simply a specific location in a two-dimensional space that has been identified using coordinates.
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Complete Question:
What does the point (7,84) represent in the graph? And define the explanation for each value.