One plane can be drawn, so it contains all three points.
What is spherical coordinates?
The coordinate system that is most frequently employed in three-dimensional systems is called spherical coordinates of the system, represented as (r,Ф,∅ ). The surface area in three dimensions is calculated using the spherical coordinate system. Radial distance, polar angles, and azimuthal angle are the three numbers that these coordinates indicate. Additionally known as spherical polar coordinates.
Consider points R, S, and T. Point S is in the middle. Point R is below and to the left of point S.
Suppose that the S coordinate is at the origin, that is (0, 0)
The coordinates of R and T with respect to S will then be (-x, -y) and (x, -y).
Hence One plane can be drawn, so it contains all three points.
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Prove: The square of a number that is two more than a multiple of 3 is one more than a multiple of 3.
Step-by-step explanation:
x is the number
x = 3y + 2
the square
x² = (3y + 2)² = 9y² + 12y + 4
9y² is a multiple of 3 (because of the factor 9)
12y is a multiple of 3 (because of the factor 12)
4 is 1 more than a multiple of 3 (1×3).
so, the sum of all 3 terms is 1 more than a multiple of 3.
Consider the equation 4x^4 - 38x^3 = 17x^2 + 30x. One of the real solutions to the equation is 10. What are the other solutions, both real and nonreal
Answer: Option (1)
Step-by-step explanation:
[tex]4x^4 -38x^3 -17x^2 -30x=0[/tex]
Dividing both sides by [tex]x-10[/tex] (10 is a root, so x-10 is a factor), yields
[tex]4x^3 +2x^2 +3x=0\\\\x(4x^2 +2x+3)=0\\\\x=0, 4x^2 +2x+3=0[/tex]
Solving the second case by the quadratic formula yields [tex]x=\frac{-1 \pm i\sqrt{11}}{4}[/tex].
So, the answer is Option (1).
ANSWER ONLY THANK YOU
A. (1,4)
EXPALINATION :
IF WE WRITE THE VALUE x = -1 AND y = 4
THEN, y= -8x - 4
4= -8×-1-4
4= 8-4
AND SECOND EQUATION IS : y = x+5
y = -1 +5
y = 4
hence, solved and explained
thank you And mark me brainlist if you understand And hopes so
Which is the graph of the function f(x)=√x?
The graph is shown in the attached image.
Evan collected data about the amount of time each student in his math class spends studying. If the range of these data is 2, what does this reveal about the data?
All the students in his math class spend exactly 2 hours studying.
All the students in his math class spend an average of 2 hours studying.
The smallest and largest data values are 2 units away from each other.
The middle data value for time spent studying by all students in his class is 2 hours.
A range of 2 reveals that the smallest and largest data values are 2 units away from each other.
What does the range reveal?Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.
Range = highest value - lowest value
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The scatterplot to the left shows the cost, CCC, in thousands of dollars, and living space, xxx, in square feet (\text{ft}^2)(ft
2
)left parenthesis, start text, f, t, end text, squared, right parenthesis for several houses in a certain neighborhood. According to the data, which of the following best approximates the cost for an additional square foot of living space for homes in this neighborhood?
Choose 1 answer:
\$80$80dollar sign, 80
\$300$300dollar sign, 300
\$1{,}000$1,000dollar sign, 1, comma, 000
\$13{,}000$13,000dollar sign, 13, comma, 000
According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.
How to determine the cost for an additional square foot?By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.
Next, we would approximate two points on the line of best fit and then find the slope as follows:
Slope, m = ΔC/Δx
Slope, m = (C₂ - C₁)/(x₂ - x₁)
Slope, m = (400 - 200)/(4000 - 1500)
Slope, m = 0.08.
Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.
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Three times the age of Abel is four more than the age of Asare.In three years,the sum of their ages will be 30 years.Find their present ages
Answer:
Abel is 7 and Asare is 17 years old
Step-by-step explanation:
Let the age of Abel is x and age of Asare is y.
Three times the age of Abel is four more than the age of Asare:
3x = y + 4And
In three years, the sum of their ages will be 30 years:
x + 3 + y + 3 = 30We got two equations.
Simplify and solve by substitution:
y = 3x - 4x + y = 243x - 4 + x = 24 Substitute y4x - 4 = 244x = 28x = 7Find y:
17 + y = 24y = 7here is a table of values for y= f(x)
mark the statements that are true.
Answer:
B. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6}
D. f(-1) = 6
Step-by-step explanation:
The question gives a table marking the different coordinate pairs for a function, where f(x) is y. The top row represents the x-values and the bottom row represents the y-values.
Domain
The domain of a function is the set of x-values that the graph covers. In this case, the x-values are all integers between -2 and 6. We can see this in the top row of the table. Answer choice B best represents this domain.
Solving for F(x)
F(x) represents a specific y-value, for example, f(-1) represents the y-value when x = -1. So, to test choice D, we need to find what y-value matches -1 on the table. The table shows that when x = -1, f(x) = 6. This means that answer choice D must be correct.
The estimated population of Los Angeles in 2019 was 3,979,576. Its area is 469 square miles. What is the population density of Los Angeles, in people per square mile?
Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its area is 469 square miles, the population density of Los Angeles is 8486 people per square miles.
What is the population density of Los Angeles, in people per square mile?Population density simply the measurement of population per unit area.
It is expressed as;
Population density = Number of people / Area
Given the data in question;
Number of people in Los Angeles N = 3,979,576 peopleArea of Los Angeles A = 469 square milesPopulation density = ?We substitute the given values into the above equation.
Population density = Number of people / Area
Population density = 3,979,576 people / 469 square miles
Population density = 8485.23667 ≈ 8486 people per square miles
Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its area is 469 square miles, the population density of Los Angeles is 8486 people per square miles.
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Find the dimensions of the rectangle
Answer:
length: 12 mwidth: 4.5 mStep-by-step explanation:
The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.
SetupLet w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.
A = LW
54 = (2w +3)(w)
SolutionRewriting this equation to standard form gives ...
2w² +3w -54 = 0
(2w -9)(w +6) = 0 . . . . factored
w = 9/2, -6 . . . . . . . . . values that make the equation true
Only the positive width makes sense in a geometry problem, so we have ...
w = 9/2
length = 2w +3 = 12
The length of the rectangle is 12 meters; its width is 4.5 meters.
The difference of the square of a number and 8 is equal to 8 times that number. Find the positive solution.
Answer:
[tex]2\sqrt{6} +4[/tex]
Step-by-step explanation:
Let x be that unknown number.
From the information given from the question, we can deduce:
[tex]x^{2} -8=8x[/tex]
From here, we can solve for x to find what is the number.
[tex]x^{2} -8=8x\\x^{2} -8x-8=0[/tex] (Quadratic Equation)
From here we can use the Quadratic Formula to solve for x.
[tex]x=\frac{-b+/-\sqrt{b^{2} -4ac} }{2a}[/tex]
In this case,
a = 1, b = -8 , c = -8
We substitute a, b and c to find x.
[tex]x=\frac{-(-8)+/-\sqrt{(-8)^{2}-4(1)(-8) } }{2(1)} \\= 2\sqrt{6} +4[/tex]
(Reject the negative solution)
find each lettered angel measure
Answer:
a = 64°
b = 138.7°
Step-by-step explanation:
First, Let's find the measure a,
180° = 116° + a180 - 116 = aa = 64°______
Now,
90° + a + 82° + x + x + x = 360°90+ 64 + 82 + 3x = 360° 236 + 3x = 360 3x = 124/ 3x = 41.3°______
Now that we found out what x equals, let's find 'b'-
b + x = 180°b + 41.3 = 180b = 180 - 41.3b = 138.7°The quantities xxx and yyy are proportional. xxx yyy 777 353535 121212 606060 202020 100100100 Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x. r =r=r, equals
The constant of proportionality of our given tables is; 5.
How to find the constant of Proportionality?We are given that x and y are proportional, and this means that:
y = r*x
where;
r is the constant of proportionality.
We are given the table;
x y
7 35
12 60
20 100
Now, we can replace those values in our equation and get, for the first pair: 35 = r*7
r = 35/7 = 5
For the second pair:
60 = r*12
60/12 = r
r = 5
Thus, we can conclude that the constant of proportionality is 5.
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Answer: 3
Step-by-step explanation:
what’s 5x times 2-7 min
Answer:33
Step-by-step explanation: The expressions have equivalent values when x + 6
The expressions have equivalent values for any value of x.
When x=10 , both expressions have a value of 33.
Children learn to duplicate patterns when they can identify the rule, that is, when the unit repeats and the pattern becomes predictable.
a. True
b. False
Children learning to duplicate patterns when they can identify the rule, that is, when the unit repeats and the pattern becomes predictable is a true statement.
What are Patterns?
This involves the regularity or repeated way in which something is done or arranged.
Children are very inquisitive and tend to make logical connections when dealing with patterns due to their reasoning skills thereby aiding their learning process.
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The company stock you are monitoring for your Economics class increases five-eighths point the first week and then it increases one- half point the second week and one-quarter point the third week. What is the total increase during the three weeks?
Based on the change in the company stock over the three weeks, the total increase in those three weeks is 1.38%.
how much did the stock increase by?assuming the stock has a value of $1, the value in the third week would be:
= 1 x (1 + 5/8%) x (1 + 1/2%) x (1 + 1/4%)
= $1.013809453125
the total increase is:
= (1.013809453125 - 1) / 1
= 1.38%
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Divide. (7x − 6x^2 + x^3 − 1) ÷ (x − 1)
Hope that helps...........................
10. What is the product of 6% and 14%
The prep club and honor society are joining forces
Given that the inequalities and that
x ⇒ pep club donations
y ⇒ represent donations raised by the honor society
The inequality is represented by x + y≥ 500
The solution for this is the shaded area above the solid line.
Given x ≥ 100, this is also indicated by the shaded region to the right
What does point (300, 100) represent? is it a viable Solution? why?The point (300,100) indicates that the contributions made for the pep club were $300 and the donations raised by the honor society were $100.
The point (300,100) is NOT a feasible solution since it does not conform to the gray area of the system of inequalities solution.
To proof the above,
Let x = 300; and y = 100
Plugin in both values in the inequalities we have:
300 + 100 [tex]\ngeq[/tex] 500
400 [tex]\ngeq[/tex] 500 ; Hence it is NOT true; also
300 [tex]\ngeq[/tex] 500.
What does (500, 200) represent? Is it a viable Solution? why?The point (500,200) indicates that the contributions raised for the pep club were $500 and the donations raised by the honor society were $200.
The point (500,200) IS A possible solution since it falls inside the darkened area of the system of inequalities solution.
To proof the above,
Let x = 500; and y = 200
Plugin in both values in the inequalities we have:
500 + 200 ≥ 500
700 ≥ 500; hence, this is true and it is safe to indicate that the ordered pair satisfies the inequality A.
Conclusion:
The point (500, 200) is a viable solution.
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kindly solve these questions for me.
The perimeter of the rectangle based on the factors given is 46.
How to calculate the perimeter?The area of the rectangle is given as (x² + 13x - 90). This will be:
= (x² + 13x - 90)
= x² + 18x - 5x - 90
= x(x + 18) - 5(x + 18)
= (x - 5)(x + 18)
The sides of the rectangle are 5 and 18. The perimeter will be:
= 2(l + w)
= 2(5 + 18)
= 46
The area of the rectangle is given as (x² + 24x - 81.
= (x² + 24x - 81)
= x² + 27x - 3x - 81
= x(x + 27) - 3(x + 27)
= (x - 3)(x + 27)
The sides are 3 and 27. The perimeter will be:
= 2(l + w)
= 2(27 + 3)
= 60
= (x + 1)² + 3(x + 1) + 2
= (x + 1)(x + 1) + 3x + 3 + 2
= x² + x + x + 1 + 3x + 5
= x² + 5x + 6
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A baseball player had 4 hits in 8 games. At this rate, how many hits will the baseball player have in the next 28 games?
O 14
O24
28
O 56
Answer:
14
Step-by-step explanation:
If a baseball player records 4 hits in 8 games, then the player records 1 hit every 2 games. Therefore, the player will have 14 more hits in the next 28 games.
In a given year, residents of a country spent approximately $54.6 billion on their pets. Of this amount, $17.1 billion was for veterinarian bills. What percent of the total was spent on veterinary care
Percent of the total was spent on veterinary care is 31.3186% .
Applying simple percentage formula,
let x be the percentage
x=[tex]\frac{17.1}{54.6} \ 100[/tex]
x=31.3186 %
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A researcher uses a random number generator to simulate the results of an experiment. Which of the following assignments of
random digits is appropriate for its experimental design?
A. let 0,2,4,6,8 represent selecting a face card (King, Queen, Jack) and 1,3,5,7,9 represent a non-face card in the selection of one card from a well-
shuffled 52-card deck of cards
B. let 0,1,2,3,4,5 represent flipping a heads on a fair coin and 6,7,8,9 represent flipping a tails with a fair coin
C. let 4 represent rolling a 4 on a fair 6-sided die and 0,1,2,3,5,6,7,8,9 represent not rolling a 4 on a fair 6-sided die
D. let 1,3,5,7, and 9 represent flipping a heads with a fair coin, and 0,2,4,6, and 8 represent flipping a tails with a fair coin.
The correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.
In the question, we are given that a researcher uses a random number generator to simulate the results of an experiment and are asked for the appropriate assignment of random digits for its experimental design.
For the assignment to be correct, the probability of the random numbers must be equal to the probability of the experiment.
We analyze each option:
A. let 0,2,4,6,8 represent selecting a face card (King, Queen, Jack) and 1,3,5,7,9 represent a non-face card in the selection of one card from a well-shuffled 52-card deck of cards. The probability of a face card is 3/13, whereas the probability of an assigned digit is 5/10 = 1/2, which implies improper assignment.B. let 0,1,2,3,4,5 represent flipping heads on a fair coin and 6,7,8,9 represent flipping tails with a fair coin. The probability of getting heads is 1/2, whereas the probability of an assigned digit is 6/10 = 3/5, which implies improper assignment.C. let 4 represent rolling a 4 on a fair 6-sided die and 0,1,2,3,5,6,7,8,9 represent not rolling a 4 on a fair 6-sided die. The probability of rolling a 4 on a fair 6-sided die is 1/6, whereas the probability of assigned digits is 1/10, which implies improper assignment.D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin. The probability of heads and tails is 1/2, and that of the assigned digits is 1/2, which implies proper assignment.Thus, the correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.
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I need help with this geometry question asap!
Answer: True
Explanation: Parallel lines are two lines that lie on the same plane and they never intersect.
Find the area of the regular polygon. Round to the nearest tenth
Answer:
1/2×base×height
1/2×8×8
32cm²
Rate:
168 ounces
14 boxes
How much does the spaghetti in each box weigh? Find the unit rate.
Answer:
12 ounces
Step-by-step explanation:
168 divided by 14 = 12
(-4, 7), (-6,-4)
find the slope of the line through each pair of points
Answer:
slope = 11/2
Step-by-step explanation:
If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.
Point 1: (-4, 7) Point 2: (-6, -4)
x₁ = -4 x₂ = -6
y₁ = 7 y₂ = -4
y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form
7 - (-4) = m(-4 - (-6)) <----- Insert values
11 = m(2) <----- Simplify
11/2 = m <----- Divide both sides by 2
[tex]\huge\boxed{\frac{11}{2}}[/tex]
The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".
Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values and simplify to find the answer.
[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]
[tex]\dfrac{-4-7}{-6+4}[/tex]
[tex]\dfrac{-11}{-2}[/tex]
[tex]\boxed{\frac{11}{2}}[/tex]
Here is this question im stuck on.
The polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0
Dividing polynomialsFrom the question, we are to divide the given polynomial P(x) by the divisor d(x)
From the given information,
P(x) = x³ + 8
d(x) = x + 2
The division operation is shown in the attachment below.
The quotient, Q(x) = x² -2x + 4
and the remainder, R(x) = 0
We area to express P(x) in the form
P(x) = d(x).Q(x) + R(x)
Thus, we get
x³ + 8 = (x+2)(x² -2x + 4) + 0
Hence, the polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0
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Is this figure a polygon? Explain.
please fill in the blanks of the question i sent a pic of
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
What is the center and the radius of the circle?
In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:
(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)
(h, k) = (4, 8)
And the radius is found by Pythagorean theorem:
[tex]d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}[/tex]
d = 5
r = 0.5 · 5
r = 2.5
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
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