Answer:
the correct options are:
(–1, 3), (–2, 2) and (–5, –1)
Step-by-step explanation:
Given that a line passes through two points
A(-2, -4) and B(4, 2)
Another point P(0, 4)
To find:
Which points lie on the line that passes through P and is parallel to line AB ?
Solution:
First of all, let us the find the equation of the line which is parallel to AB and passes through point P.
Parallel lines have the same slope.
Slope of a line is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{2-(-4)}{4-(-2)} = 1[/tex]
Now, using slope intercept form ([tex]y = mx+c[/tex]) of a line, we can write the equation of line parallel to AB:
[tex]y =(1)x+c \Rightarrow y = x+c[/tex]
Now, putting the point P(0,4) to find c:
[tex]4 = 0 +c \Rightarrow c = 4[/tex]
So, the equation is [tex]\bold{y=x+4}[/tex]
So, the coordinates given in the options which have value of y coordinate equal to 4 greater than x coordinate will be true.
So, the correct options are:
(–1, 3), (–2, 2) and (–5, –1)
Answer:
b,c,e
Step-by-step explanation:
I got it right on edge
Recall the formula V = four-thirds pi r cubed.
Answer:
1308.33
Step-by-step explanation:
In the pic
Identify the vertex of the graph. Tell whether it is a minimum or maximum.
(-2,-2); maximum
(-2,-2); minimum
(-2, -1); minimum
(-2, -1); maximum
Answer:
(-2,-2); minimum
Step-by-step explanation:
From the graph, the vertex is (-2, -2) and since there are no y values that go less than the y value of the vertex, it is a minimum.
7 less than the quotient of a number and 3 is 5. Find the number.
Answer:
The answer is 36
Step-by-step explanation:
Let the number be x
7 less than the quotient of a number and 3 is written as
[tex] \frac{x}{3} - 7[/tex]The result is 5
So we have
[tex] \frac{x}{3} - 7 = 5[/tex]Move - 7 to the right side of the equation
That's
[tex] \frac{x}{3} = 7 + 5[/tex][tex] \frac{x}{3} = 12[/tex]Multiply both sides by 3 to make x stand alone
We have
[tex]3 \times \frac{x}{3} = 12 \times 3[/tex]We have the final answer as
x = 36Hope this helps you
How many solutions does 2−9x=−6x+5−3x have?
Answer:
There are no values of x that make the equation true.
No solution
Step-by-step
hope it help
Hi
2-9x = -6x+5-3x
-9x+6x+3x = 5-2
0x = 3
as 0 ≠ 3 , there is no answer possible to your equation.
the difference of two complementary angles is 17 degrees. find the measures of the angles
Answer:
The angle measures are 53.5° and 36.5°.
Step-by-step explanation:
We can create a systems of equations, assuming x and y are the angle measures.
Since the two angles are complementary, their angle measures will add up to 90.
x + y = 90
x - y = 17
We can now use the process of elimination, and end up with:
2x = 107
Dividing both sides by two gets us
x = 53.5
Substituting this value into an equation will get us y
53.5 + y = 90
y = 36.5
Hope this helped!
Find x. A. 44√3 B. 33 C. 33√2 D. 11√3
Answer:
B
Step-by-step explanation:
Sin 45 = y/(11√6)
1/√2 = y/(11√6)
y= (11√6)/√2
y= 11√3
tan 60 = x/y
√3 = x/y
x = y√3
= (11√3)√3
= 11(3)
= 33
Find the vector and parametric equations for the line through the point P(0, 0, 5) and orthogonal to the plane −1x+3y−3z=1. Vector Form: r
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
Ashton needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Ashton only has $50 to spend on the car rental, what is the maximum number of miles she can drive?
Answer:
166.9 miles or 166 miles
Step-by-step explanation:
We can form an equation like this:
19.95 + .18x = 50
In this equation, "x" is the number of miles.
=> 19.95 - 19.95 +.18x = 50 -19.95
=> .18x = 30.05
=> .18x/.18 = 30.05/.18
=> x = 166.9
Ashton can drive 166.9 miles.
**Note: We cannot round the answer to 167, as she would not have enough money to drive the extra 0.1 mile.
A circle has center (3, -5) and the point (-1, -8) lies on the circumference of the circle. What is the equation of the circle in Standard Form?
Answer:
[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]
Step-by-step explanation:
First find the radius
Which is the distance between the 2 points.
Radius =5
The answer in the standad form is above.
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
The standard equation of a circle is given as:
(x - a)² + (y - b)² = r²
where (a, b) is the center of the circle and r is the radius of the circle.
Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:
[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]
hence:
(x - 3)² + (y - (-5))² = 5²
(x - 3)² + (y + 5)² = 25
The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25
Find out more at: https://brainly.com/question/13658927
Choose the correct simplification of 9x^2(4x + 2x^2 − 1)
━━━━━━━☆☆━━━━━━━
▹ Answer
18x⁴ + 36x³ - 9x²
▹ Step-by-Step Explanation
9x²(4x + 2x² - 1)
36x³ + 18x⁴ - 9x²
18x⁴ + 36x³ - 9x²
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Do phone surveys provide adequate coverage of households with respect to one particular parameter? The parameter is the proportion of households without children. If telephone surveys provide adequate coverage of households, then p , the proportion of households without children in the set of all future samples reached by phone, must be equal to the proportion of households without children in the population of all households. Suppose that Thomas, a market analyst, contacts a simple random sample of 300 households as part of a national telephone survey. Of the households contacted, 129 households, or 43 %, have no children and 57 % have at least one child. The most recent census indicates that 48 % of all households have no children and 52 % have at least one child.
Complete Question
The complete question is shown on the first uploaded image
Answer:
Based on the result of his test , Thomas should fail to reject null hypothesis at a significance level of 0.01. Thomas sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
Step-by-step explanation:
From the question we see that the p-value is greater than the level of significance (0.01 )so we fail to reject the null hypothesis.
This means that Thomas has sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
Please help with this
The shape has 11 sides.
Using the angle formula for polygons:
The sum of all the interior angles is:
11-2 x 180 = 9 x 180 = 1,620 degrees.
For one angle divide the total by number of sides:
1620 / 11 = 147.27 which rounds to 147.2
The answer is D.
Suppose that it rains in Spain an average of once every 9 days, and when it does, hurricanes have a 2% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 1% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford? (Round your answer to four decimal places.)
Answer:
I found the answer on Yahoo
Step-by-step explanation:
P[rains in spain] = 1/9
P[hurricane in hartford & rain in spain] = 0.03*1/9 = A
P[hurricane in hartford & no rain in spain] = 0.02*8/9
P[hurricane in hartford] = 0.03*1/9 + 0.02*8/9 = 0.19/9 = B
P[rain in spain | hurricane in hartford] = A/B = 3/19 <---------
Help please!!!!!!!!!!!!
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Explanation:
When we reflect any point (x,y) over the line y = x, the x and y coordinates swap. So for instance, we have K = (5, -9) turn into K ' = (-9, 5).
Consider a point like (1,2). We can move it down 1 unit to have it land on the line y = x, then we can move it one unit to the right to move it to (2,1). These two translations effectively move the original point to its reflected location. The distance from (1,2) to y = x, is the same as the distance from (2,1) to y = x. Furthermore, the line connecting (1,2) to (2,1) is perpendicular to y = x.
If 2x + 5 = 8x, then 12x = ?
A 5
B
10
C
15
D 20
Answer:
10
Step-by-step explanation:
2x + 5 = 8x
Subtract 2x from each side
2x-2x + 5 = 8x-2x
5 = 6x
We want 12x so multiply each side by 2
2*5 = 6x*2
10 = 12x
Answer:
B. 10
Step-by-step explanation:
To find 12x, you first need to find the value of x using the first equation:
[tex]2x+5=8x[/tex]
You need to get the variables (x) on the same side of the equation in order to simplify them. To do this, use reverse operations. Subtract 2x from both sides to keep the equation balanced:
[tex]2x-2x+5=8x-2x\\\\5=6x[/tex]
Now isolate the variable (x) by dividing both sides of the equation by 6 (using reverse operations):
[tex]\frac{5}{6}=\frac{6x}{6} \\\\\frac{5}{6}=x[/tex]
Now insert the given value of x into 12x:
[tex]12(\frac{5}{6})[/tex]
Simplify:
[tex]12*\frac{5}{6} \\\\\frac{12}{1}*\frac{5}{6}\\\\\frac{60}{6}=10[/tex]
12x equals 10.
:Done
WILL MARK BRAINIEST!!! Segment AC has two endpoints; (-2,5) and (2,-5). What are the coordinates of point B on segment AC such that the ratio of AB to BC is 5:1? Any help would be appreciated; first correct answer get brainiest and a 5 star review!
Answer:
[tex](\frac{4}{3},-\frac{10}{3})[/tex]
Step-by-step explanation:
If the extreme ends of a line segment AC are A[tex](x_1,y_1)[/tex] and C[tex](x_2,y_2)[/tex].
If a point B(x, y) divides the segment in the ratio of m : n
Then the coordinates of the point B are,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
If the ends of AC are A(-2, 5) and C(2, -5) and a point B divides it in the ratio of m : n = 5 : 1
Therefore, coordinates of this point will be,
x = [tex]\frac{5\times (2)+1(-2)}{5+1}[/tex]
= [tex]\frac{10-2}{5+1}[/tex]
= [tex]\frac{8}{6}[/tex]
= [tex]\frac{4}{3}[/tex]
y = [tex]\frac{5\times (-5)+1(5)}{5+1}[/tex]
= [tex]\frac{-25+5}{6}[/tex]
= [tex]-\frac{20}{6}[/tex]
= [tex]-\frac{10}{3}[/tex]
Therefore, coordinates of the point B are [tex](\frac{4}{3},-\frac{10}{3})[/tex].
Could anyone help me with this question please? Thank you.
Answer:
C) 549 km²
Step-by-step explanation:
The area of the regular pentagon is given by ...
A = (1/2)Pa
where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.
The lateral area is the product of the perimeter and the height:
LA = Ph
Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...
total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)
= (45 km)(6 km +6.2 km) = 549 km^2
Ava started her hw at 7:20pm she finished it at 8:05 pm how long did she take to her hw?
Answer:
45 mins
Step-by-step explanation:
Money is invested into an account earning 4.25% interest compounded annually. If the accumulated value after 18 years
will be $25,000, approximately how much money is presently in the account?
a $5,875
b. $11,820
c. $19,125
d. $23,960
Answer:
b. $11,820
Step-by-step explanation:
The 'rule of 72' tells you the doubling time of this account is about ...
(72 years)/(4.25) = 16.9 years
So, in 18 years, the amount will be slightly more than double the present value. That is, the present value is slightly less than half the future amount.
$25,000/2 = $12,500
The closest answer choice is ...
$11,820
__
The present value of that future amount is ...
PV = FV×(1 +r)^-t = $25,000×1.0425^-18 ≈ $11,818.73
The present value is about $11,820.
Answer:
B
Step-by-step explanation:
Match the ones on the left to the right
Answer/Step-by-step explanation:
[tex] (4 + 5) + 2 = 4 + (5 + 2) [/tex] => any combination of numbers were formed or grouped when adding. The associative property of addition was applied.
[tex] 2(2x + 4) = 4x + 8 [/tex] => the sum of two terms (addend) are multiplied by by a number separately (I.e., a(b + c) = a(b) + a(c) = ab + ac). The property applied is distributive property.
[tex] (7x * x) * 3 = 7 * (x * 3) [/tex] => the numbers were grouped in any combination to arrive at same result when multiplying. Associative property of multiplication was applied.
[tex] (8 * x * 2) = (x * 8 * 2) [/tex] => the numbers where ordered in any manner to arrive at same result when multiplying. Cummutative property of multiplication was applied.
[tex] (7 + 3) + 1 = (1 + (7 + 3) [/tex] => the order in which the nnumbers in the were arranged doesn't matter, as same result is arrive at. This is Cummutative property of addition.
Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
a. (4,2,−4)
b. (0,8,15)
c. (√2,1,1)
d. (−2√3,−2,3)
Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:
[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]
[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]
For angle θ:
If x > 0 and y > 0: [tex]\theta = tan^{-1}\frac{y}{x}[/tex];If x < 0: [tex]\theta = \pi + tan^{-1}\frac{y}{x}[/tex];If x > 0 and y < 0: [tex]\theta = 2\pi + tan^{-1}\frac{y}{x}[/tex];Calculating:
a) (4,2,-4)
[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6
[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]
[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]
For θ, choose 1st option:
[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]
[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]
b) (0,8,15)
[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17
[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]
[tex]\theta = tan^{-1}\frac{y}{x}[/tex]
The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]
c) (√2,1,1)
[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2
[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]
[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]
[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]
d) (−2√3,−2,3)
[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5
[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]
Since x < 0, use 2nd option:
[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]
[tex]\theta = \pi + \frac{\pi}{6}[/tex]
[tex]\theta = \frac{7\pi}{6}[/tex]
Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:
[tex]r=\sqrt{x^{2}+y^{2}}[/tex]
Angle θ is the same as spherical coordinate;
z = z
Calculating:
a) (4,2,-4)
[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]
[tex]\theta = tan^{-1}\frac{1}{2}[/tex]
z = -4
b) (0, 8, 15)
[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8
[tex]\theta = \frac{\pi}{2}[/tex]
z = 15
c) (√2,1,1)
[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]
[tex]\theta = \frac{\pi}{3}[/tex]
z = 1
d) (−2√3,−2,3)
[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4
[tex]\theta = \frac{7\pi}{6}[/tex]
z = 3
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Playing the game of roulette, where the wheel consists of slots numbered 00, 0, 1, 2, ..., To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.a. The sample space is (00, 0}. b. The sample space is (00, 0, 1,2,., 33). c. The sample space is (00). d. The sample space is (1, 2,..., 33).
Answer:
The correct option is (B).
Step-by-step explanation:
It is provided that, in a game of roulette the wheel consists of slots numbered 00, 0, 1, 2, ..., 33.
The sample space of an experiment, is the set of all the possible outcomes of the random trials.
There are a total of 35 slots on the roulette wheel where the ball can land.
So, there are a total of 35 outcomes for one rotation of the wheel.
Then the sample space consists of all the 35 outcomes, i.e.
S = {00, 0, 1, 2, 3, ..., 33}
Thus, the correct option is (B).
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees.
Answer:
6.5
Step-by-step explanation:
The sum of all angles in a triangle are 180 degrees.
=> 10x -10 + 8x + 10x + 8 = 180
=> 28x -2 = 180
=> 28x = 182
=> x = 6.5
So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees
Angle B = 8 x 6.5 = 52 degrees
Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.
55 + 52 + 73 = 55 + 125 = 180 degrees
[tex](y - 1) log_{10}(4?) = log_{10}(16?) [/tex]
find the value of y
Answer:
3Step-by-step explanation:
Given the log function [tex](y-1)log_{10}(4) = log_{10} 16\\ \\[/tex] to get the value of y, the following steps must be carried out;
[tex](y-1)log_{10}(4) = log_{10} 16\\\\(y-1)log_{10}(2^2) = log_{10} 2^4\\\\ (y-1)2log_{10}(2) = 4log_{10} 2\\ \\DIvide\ both\ sides\ by \ log_{10}2\\\\\frac{2(y-1)log_{10}2 }{log_{10}2} = \frac{4log_{10}2}{log_{10}2} \\\\2(y-1) = 4\\\\[/tex]
Open the bracket
[tex]2y-2(1) = 4\\\\2y -2 = 4\\\\add \ 2 \ to \ both \ sides\\\\2y-2+2 = 4+2\\\\2y = 6\\\\Divide \ both \ sides\ by \ 2\\\\2y/2 = 6/2\\\\y = 3[/tex]
Hence the value of y is 3
A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale? a.3.8 grams b.120.01 grams c.800.0 grams d.54 milligrams
Answer:
Step-by-step explanation:
The answer is b
120.01 grams
how would you write six times the square of a number
Answer:
[tex]\huge \boxed{6x^2 }[/tex]
Step-by-step explanation:
6 times a number squared.
Let the number be [tex]x[/tex].
6 is multiplied to [tex]x[/tex] squared.
[tex]6 \times x^2[/tex]
The probability density function for random variable W is given as follows: Let x be the 100pth percentile of W and y be the 100(1 – p)th percentile of W, where 0
Answer:
Step-by-step explanation:
A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).
X = 100pth percentile of W
Y = 100(1-p)th percentile of W
Expressing Y as a function of X;
Y = 100(1-p)th = 100th - 100pth
Recall that 100pth is same as X, so substitute;
Y = 100th - X
where 100th = hundredth percentile of W and X = 100pth percentile of W
find the dimension of the swimming pool if the sum must be 50 feet and the length must be 3 times the depth.
Answer:
depth 5 8.3 ft, length 5 24.9 ft, width 5 16.8 ft
illustrate the distributive property to solve 144/8
Answer:
8 (19) or 8 (18 +1)
Step-by-step explanation:
Distributive property means to distribute.
HCF of 144 and 8.
=> 8 is the HCF of 144 and 8
8 (18 + 1)
=> 8 (19)
The Centers for Disease Control and Prevention (CDC) report that gastroenteritis, or stomach flu, is the most frequently reported type of recreational water illness. Gastroenteritis is a viral or bacterial infection that spreads through contaminated food and water. Suppose that inspectors wish to determine if the proportion of public swimming pools nationwide that fail to meet disinfectant standards is different from 10.7%, which was the proportion of pools that failed the last time a comprehensive study was done, 2008.
A simple random sample of 30 public swimming pools was obtained nationwide. Tests conducted on these pools revealed that 26 of the 30 pools had the required pool disinfectant levels.
Does this sample meet the requirements for conducting a one-sample z ‑test for a proportion?
a. No, the requirements are not met because the population standard deviation is not known.
b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.
c. No, the requirements are not met because the sample is not random, even though the number of successes and the number of failures are both at least 10, ensuring that the distribution is approximately normal.
d. Yes, the requirements are met because the sample size is more than 30, ensuring that the distribution is approximately normal.
e. Yes, the requirements are met because the number of successes and the number of failures of this random sample are both at least 10, ensuring that the distribution is approximately normal.
b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.
Step-by-step explanation:
from the question, the number of successes is equal to 30
and it is more than the number of failures
for us to conduct this test such as the z test the data we are using should be a random sample from the population that we are interested in. the population should be at least as big as the sample by 10 times. first of all We need to check if the mean of the sample is normally distributed.
if 26 are successes out of a sample of 30, then failures would be 4. therefore option b is correct.
