The solution to the set of equations are:
x = 17/7
y = 20/7
We have,
The two equations are:
x + y = 7 ______(1)
x² - y² = 15 _______(2)
We can use the method of substitution.
From the first equation.
y = 7 - x
We can substitute this expression for y into the second equation.
x² - (7 - x)² = 15
Expanding the square in the second term gives:
x² - (49 - 14x + x²) = 15
Simplifying this equation.
-14x + 34 = 0
Solving for x gives:
x = 17/7
Substituting this value of x into the first equation.
y = 7 - x = 20/7
Therefore,
The solution to the set of equations are:
x = 17/7
y = 20/7
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The complete question:
Solve the set of algebraic equations.
x + y = 7
x² - y² = 15
Justin makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
what is the probability that a random point on AK will be on BE? pls help me
The probability that a random point on the AK line will be on the BE line is 0.5 or 50%, since the length of the BE line is 10 units and the length of the AK line is 20 units.
To find the probability that a random point on the AK line will be on the BE line, we need to determine the length of the BE line and the length of the AK line.
The BE line extends from point -5 to point 5, a distance of 5 - (-5) = 10 units.
The AK line extends from point -10 to point 10, a distance of 10 - (-10) = 20 units.
Therefore, the probability that a random point on the AK line will be on the BE line is
Length of BE line / Length of AK line = 10 / 20 = 0.5
So, the probability that a random point on the AK line will be on the BE line is 0.5 or 50%.
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What is 1 1/4miles+1 3/8 miles = how far does Fred run in total?
Answer:
Fred doesn't run
Step-by-step explanation:
Fred doesn't run, Fred likes to walk, you obviously don't know Fred enough to answer this question, so tell your teacher how you can get in touch with Fred for a better relationship
let's firstly convert the mixed fractions to improper fractions, then sum them up.
[tex]\stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{3}{8}} \implies \cfrac{1\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{11}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}+\cfrac{11}{8}\implies \cfrac{(2)5~~ + ~~(1)11}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{10+11}{8}\implies \cfrac{21}{8}\implies 2\frac{5}{8}~miles[/tex]
HELP ITS DUE TODAY IM GIVING OUT 15 POINTS IM SORRY I ONLY HAVE 75
The values of the variables x and y are;
1, x = -y and y = 5. Option D
2. x= 1 and y = -1. Option A
How to determine the valueUsing the substitution method of solving simultaneous equations, we have;
4x + 7y = 19
y - x = 9
Now, make 'y' the subject from equation 2
y = 9 + x
Substitute the equation into equation 1
4x + 7(9 + x)= 19
expand the bracket, we have;
4x + 63 + 7x = 19
collect the like terms
11x = -44
x = -4
then,
y = 9 - 4 = 5
-3x + y = -4
4x + 3y = 1
make y' the subject from equation 1
y =-4 + 3x
Substitute the value
4x + 3(-4 + 3x) = 1
expand the bracket
4x - 12 + 9x = 1
13x = 13
x = 1
Substitute the value
y = -4 + 3
y = -1
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A car and a plane are racing each other. Both start at the same position, with the plane being 500m above the car. The car has a maximum speed of 200km/h and the plane has a maximum speed of 300km/h. What is the rate of change of the distance between the plane and the car when both are maximum speed and the plane is ahead by 70m?
-63.63 m/s is the rate of change of the distance between the plane and the car when both are maximum speed and the plane is ahead by 70m?
Let's use the Pythagorean theorem to relate the distance between the car and the plane to their individual distances traveled. Let d be the distance traveled by the car, then the distance traveled by the plane is d + 70 (since the plane is ahead by 70m). Then, the distance between them is given by:
distance = [tex]\sqrt{d^{2}+500^{2} }[/tex] (using Pythagorean theorem)
Now, let's differentiate both sides with respect to time (t) to find the rate of change of the distance between the car and the plane:
d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex] * (2d/dd)(dd/dt)
where the first term on the right side is the derivative of the square root expression and the second term is the derivative of d with respect to time.
Now we need to find d in terms of t, given the maximum speeds of the car and the plane. Let's assume that they both start at time t = 0 and are racing for a time of T. Then, we can write:
d = 200T (distance traveled by the car)
d + 70 = 300T (distance traveled by the plane)
Solving for T, we get:
T = 70/100 = 0.7 hours = 42 minutes
Substituting T back into the expressions for d, we get:
d = 200(0.7) = 140 km
d + 70 = 300(0.7) = 210 km
Now we can substitute these values into the expression for the rate of change of the distance between the car and the plane:
d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex] * (2d/dd)(dd/dt)
d(distance)/dt = (1/2)[tex](140^{2} +500^{2} )^{(-1/2)}[/tex] * (2*140/60)(300 - 200)
d(distance)/dt = -63.63 m/s
Therefore, the rate of change of the distance between the car and the plane when both are at maximum speed and the plane is ahead by 70m is approximately -63.63 m/s. Note that the negative sign indicates that the distance between them is decreasing, since the plane is ahead of the car.
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I don't know how to do.
The diameter of a circle is 9cm. Find its area to the nearest whole number
I need help? I’m not sure what to do in this equation?
The measure of angle C is given as follows:
m < C = 44º.
How to obtain the measure of angle C?To obtain the measures of the angles in this problem, we must consider that the sum of the measures of the internal angles of a triangle is of 180º.
Considering that the sum of the measures of the internal angles of a triangle is of 180º, and angles C, D and E, the value of x is obtained as follows:
4x - 16 + 6x - 1 + 4x - 13 = 180
14x - 30 = 180
14x = 210
x = 210/14
x = 15.
Hence the measure of angle C is obtained as follows:
m < C = 4 x 15 - 16 = 44º.
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Solve for x.
x+6= √2x+29 +9
The solution to the equation is x = 10 or x = -2.
What is an equation?An equation refers to a mathematical expression showing that two expressions are equal.
It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).
To solve for x, we shall start with the given equation:
x + 6 = √(2x + 29) + 9
Subtract 9 from both sides:
x - 3 = √(2x + 29)
Square both sides:
[tex](x - 3)^2[/tex] = 2x + 29
Expand the left side:
[tex]x^2[/tex] - 6x + 9 = 2x + 29
We then subtract 2x and 9 from both sides:
[tex]x^2[/tex] - 8x - 20 = 0
Next, actor the quadratic equation:
(x - 10)(x + 2) = 0
Therefore, the equation x = 10 or x = -2
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6. find the open intervals where the function is concave up and concave down.
Show steps
Answer:
Concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).
Step-by-step explanation:
To find the intervals where the function y = -cot(x) is concave up and concave down, we need to find the second derivative of the function and then determine its sign for different intervals.
First, we find the first derivative of y = -cot(x):
dy/dx = csc^2(x)
Then, we find the second derivative by differentiating the first derivative:
d^2y/dx^2 = -2csc^2(x) * cot(x)
We know that the function is concave up when the second derivative is positive, and concave down when the second derivative is negative.
Now, we need to determine the intervals where the second derivative is positive and negative.
d^2y/dx^2 > 0 when:
-2csc^2(x) * cot(x) > 0
csc^2(x) < 0 and cot(x) < 0 or csc^2(x) > 0 and cot(x) > 0
Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is positive when cot(x) > 0.
d^2y/dx^2 < 0 when:
-2csc^2(x) * cot(x) < 0
csc^2(x) > 0 and cot(x) < 0 or csc^2(x) < 0 and cot(x) > 0
Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is negative when cot(x) < 0.
Recall that cot(x) = cos(x)/sin(x), which changes signs at x = kπ, where k is an integer.
So, we can now use this information to determine the intervals of concavity:
For x in (-π/2,0) and (0,π/2), cot(x) is positive and therefore, the function is concave up.
For x in (-π,-π/2) and (π/2,π), cot(x) is negative and therefore, the function is concave down.
Therefore, the function y = -cot(x) is concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).
Find the union of each of the following pairs of sets A={2,4,6,8} and B={1,2,3}
Answer:
The union of sets A and B is:
A U B = {1, 2, 3, 4, 6, 8}
Ming is paid an hourly rate. One week he earned $157.50 by working 30 hours per week. If he works 35 hours the next week, how much will he earn?
Simplify sqrt(27) \cdot sqrt(12) \cdot sqrt(147)
Answer:
Step-by-step explanation:
A square pyramid has a base measuring 10 inches on each side. The height of the pyramid is 5 inches.
A similar square pyramid has a base measuring 2 inches on each side.
How do the surface areas of these pyramids compare?
The surface area of the larger pyramid is Response area times the surface area of the smaller pyramid.
The surface area of the larger pyramid in discuss would be 25 times the surface area of the smaller pyramid.
How did the surface areas of the pyramids compare?It follows from the task content that the surface area of the larger pyramid and the smaller pyramid are to be compared.
By observation; the differing dimensions are such that the ratio of the larger pyramid to the smaller pyramid is; 10 / 2 = 5.
On this note, the ratio of the area of the pyramids are such that the larger pyramid is 5² = 25 times larger than that of the smaller pyramid.
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You want to determine what percentage of working adults in your neighborhood regularly ride the bus to work. Which sampling method and survey question ar
best?
OA. Wait at the bus stop one morning and ask all working adults, "How many times per week do you ride the bus to work?"
O B. Go to every fifth house and ask the working adults, "How many times per week do you ride the bus to work?"
O C. Leave a note at each house asking working adults to call and answer the question, "Do you ever ride the bus to work?"
OD. Enter the names of all adults in your neighborhood into a computer program to randomly select a sample and ask, "Do you ever ride the bus to work?"
To determine what percentage of working adults in your neighborhood regularly ride the bus to work, the best sampling method and survey question are D. Enter the names of all adults in your neighborhood into a computer program to randomly select a sample and ask, "Do you ever ride the bus to work?"
What is the best sampling method?The best sampling method involves random sampling of the population.
A random sample gives each member of the population an equal chance of being selected as a participant in the survey.
It is also described as a probability sampling method.
Thus, in this instance, the correct option is D.
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Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
m²
14 m
2 m
The lateral surface area of the cylinder is approximately 175.84 square meters.
We have,
The lateral surface area of a cylinder.
= 2πrh
where r is the radius of the base, h is the height of the cylinder, and π is approximately 3.14.
Now,
r = 2 m, h = 14 m
Substituting these values in the formula, we get:
Lateral surface area = 2πrh
= 2 x 3.14 x 2 x 14
= 175.84 m² (rounded to the nearest tenth)
Therefore,
The lateral surface area of the cylinder is approximately 175.84 square meters.
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The product of two negative integers is a negative integer.
Answer:
False. The product of two negative integers is a positive integer.
Find x and y in terms of a and b.
Sax + by = 0
x + y = 2
(x, y) =
(a + b)
help i will have more questions
Answer:
3/23 or 0.1304 or 13%
Step-by-step explanation:
Given 3 students have a brother and sister, and 20 students have only a brother, you want the probability that a student who has a brother also has a sister.
Conditional probabilityThe conditional probability formula is ...
P(A | B) = P(A&B)/P(B)
Here, this means ...
P(has a sister | has a brother) = P(has both)/P(has a brother)
= 3/(3 +20)
= 3/23 ≈ 0.1304 ≈ 13% . . . . . probability of a sister if has a brother
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Question 10 (10 points)
You have this great idea for a business, but need to write at
least a 50 page business proposal to hand out to potential
investors. As of today, you have 15 pages done. How many
pages do you have left to write?
Inequality:
+p>
Solution: p>
Blank 1:
Blank 2:
Blank 3:
Answer:
p≥35
Step-by-step explanation:
because you have done 15 so you subtract 15 from 50 giving you 35 and then you would say p is greater than or equal to 35 cause 50 pages is your minimum
Triangle ABC is given with coordinates A(-8, -8), B(-8, -2), C(-4, -2).
The ordered pair (2,y) is on line AC. Enter the value of y for this ordered pair.
The value of y for this ordered pair is 7.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of line AC;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 8)/(-4 + 8)
Slope (m) = 6/4
Slope (m) = 3/2
At data point (-4, -2) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 2 = 3/2(x + 4)
y = 3x/2 + 4
When x = 2, the y-value is given by;
y = 3(2)/2 + 4
y = 7.
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Which system of equations has a solution of (1, 2, 3)?
A. -2 - 2z = -8
Y+3z = 7
x + y m - -3x= -3
B. x + y + 2z = 9
2x + 2y + 3z = 15
x - z = -2
C. -3x + 2y + z = 4
X + y + 2z
X - y - z = -2
D. X + Y = 3
Y - z = 1
X + y - z = 0
Please I really need this class to graduate and I have no idea how to do this
Convert the given Cartesian equation into a polar equation.
x2+y2=2y
Answer: r=2sinθ.
Step-by-step explanation:To convert to polar coordinates, we use the relationships
xy=rcosθ=rsinθ.
Substituting these into the given equation, we find
x2+y2(rcosθ)2+(rsinθ)2r2cos2θ+r2sin2θ=2y=2(rsinθ)=2rsinθ
Factoring and applying the Pythagorean identity, we obtain
r2(cos2θ+sin2θ)r2(1)r2=2rsinθ=2rsinθ=2rsinθ
Dividing both sides by r yields
r2rr=2rsinθr=2sinθ
Thus, a polar equation representing the given function is r=2sinθ.
Solve the logarithmic equation by writing in exponential form or by graphing. Round to the nearest thousandth if necessary. log (x − 2) = 1
The solution in the equation is x = 12.
We have,
To solve the logarithmic equation log (x − 2) = 1,
We can use the definition of logarithm which states that log base b of x equals y if and only if b to the power of y equals x, where b is the base of the logarithm.
In this case, the base is not specified, so we assume it is 10, which is the common base used in most calculators and mathematical applications
Using the exponential form, we have:
log (x - 2) = 1
10^1 = x - 2
10 = x - 2
x = 12
Therefore,
The solution is x = 12.
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John is taking a true/false quiz. There are 4 questions. How many outcomes?
Answer:
16
Step-by-step explanation:
2×2×2×2=16
So, the answer is 16.
Zayn and Attia are thinking of a number each. What is Attia's number? My number is greater than 2. 12 and 20 are multiples of my number. My number is the 11th multiple of Zayn's number.
Answer:
Me: 60
Zayn and Attia: 6
Step-by-step explanation:
12 = 2 × 2 × 3
20 = 2 × 2 × 5
LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60
My number is 60.
Zayn's and Attia's numbers are 6.
Which of the points below correctly plots the point (5,−2π/3)?
Answer: the answer is E
Step-by-step explanation:
Remember that the coordinates (5,−2π3) tell us the radius r=5 and the angle θ=−2π3. So the point should be on the circle labeled 5 and form an angle of −2π3 with the positive x-axis. Point E is the correct point.
Answer:
Step-by-step explanation:
Remember that the coordinates (5,−2π/3) tell us the radius r=5 and the angle θ=−2π/3. So the point should be on the circle labeled 5 and form an angle of −2π/3 with the positive x-axis. Point E is the correct point.
What is the next number in the following series: 101, 001, 66, ______?
The next number in the series would be 31 so the complete series is 101, 001, 66, 31.
How to find the next number ?The first thing we observe is that 101 equals 100 plus one. The second term, 001, equals 0 plus 1. Now consider the distinctions between consecutive terms:
101 - 001 = 100
001 - 66 = -65
When we look at the disparities (100, -65), we can see a pattern. The difference between 100 and 65 is a factor of 35. We can now apply this distinction to the final term in the series:
66 - 35 = 31
So the next number in the series is 31, completing the sequence: 101, 001, 66, 31.
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4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z
Step-by-step explanation:
a) 11*5=55
15*5=75
8*5+5=45
b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°
In the picture below, find the length of JK
The length of the secant line JK is 32.
What is the length of JK?The secant-tangent power theorem states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.
It is expressed as:
( tangent segment )² = External part of the secant segment × Secant segment.
From the diagram:
Tangent line JI = 24
External part of the secant segment LJ = 18
Secant segment JK = x + 18
Plug these values into the above formula and solve for b.
( tangent segment )² = External part of the secant segment × Secant segment.
24² = 18 × ( x + 18 )
576 = 18x + 324
18x = 576 - 324
18x = 252
x = 252/18
x = 14
Hence, secant line JK will be:
x + 18 = 14 + 18 = 32
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