!!!!!!Please help ASAP!!!!!
AB and BC form a right angle at their point of intersection, B. If the coordinates of A and Bare (14, -1) and (2, 1), respectively, the y-intercept of AB is 4/3 and the equation of BC is y= 6 X + If the y-coordinate of point Cis 13, its x-coordinate is
Answers
Answer:
Step-by-step explanation:
Segments AB and BC intersect each other at 90° at B.
Let the equation of the segment AB → y = mx + b
Here, m = Slope of the line
b = y-intercept
Slope of the line AB passing through A(14, -1) and B(2, 1)
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{1+1}{2-14}[/tex]
= [tex]-\frac{2}{12}[/tex]
= [tex]-\frac{1}{6}[/tex]
Equation of the line will be,
[tex]y=-\frac{1}{6}(x)+b[/tex]
Since, AB passes through (2, 1)
[tex]1=-\frac{1}{6}(2)+b[/tex]
[tex]b=1+\frac{1}{3}[/tex]
[tex]b=\frac{4}{3}[/tex]
Therefore, y-intercept of AB = [tex]\frac{4}{3}[/tex]
Equation of AB → [tex]y=-\frac{1}{6}(x)+\frac{4}{3}[/tex]
Since, line BC is perpendicular to AB,
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
Here, [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of line AB and BC respectively.
By this property,
[tex]-\frac{1}{6}\times m_2=-1[/tex]
[tex]m_2=6[/tex]
Equation of a line passing through a point (h, k) and slope 'm' is,
(y - k) = m(x - h)
Therefore, equation of line BC passing through B(2, 1) and slope = 6,
y - 1 = 6(x - 2)
y = 6x - 11
Since, line BC passes through C(x, 13),
13 = 6x - 11
6x = 24
x = 4
Therefore, x-coordinate of point C will be, x = 4
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Answer:
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Step-by-step explanation:
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Your IPod has 3 hours of battery remalning. If it has 15 hours when fully charged, what percent charged is it right now?
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60%
Step-by-step explanation:
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1 hour - 100/5 = 20%
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Help solve the problem pls
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Answer:
x = 2
Step-by-step explanation:
Inverse variation between x and y can be represented as:
xy = k
Where k is the constant of proportionality.
If x = 1 when y = 11, the constant of proportionality, k, would be:
1*11 = k
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Consider the salt shaker shown.
5 cm
cm
What is the volume of the salt shaker, including the top? Round your answer to the nearest hundredth.
Volume of Salt Shaker =
Answers
Answer:
Volume of salt shaker = 42.4 cm³ (Approx.)
Step-by-step explanation:
Given:
Height of salt shaker = 5 cm
Diameter of salt shaker = 3 cm
Find:
Volume of salt shaker
Computation:
Radius of salt shaker = Diameter of salt shaker / 2
Radius of salt shaker = 3 / 2
Radius of salt shaker = 1.5 cm
Volume of salt shaker = Volume of cylinder + Volume of Hemisphere
Volume of salt shaker = πr²h + (2/3)πr³
Volume of salt shaker = (3.14)(1.5)²(5) + (2/3)(3.14)(1.5)³
Volume of salt shaker = (3.14)(2.25)(5) + (0.667)(3.14)(3.375)
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135°
Solve for <2.
62 = [?]
45°
&2
86°
Enter
Answers
Answer:
[tex] \displaystyle \angle2 = {49}^{ \circ} [/tex]
Step-by-step explanation:
remember that,
if a side of a triangle is extended then exterior angle so formed equal to the sum of the two opposite interior angles
thus our equation is
[tex] \displaystyle \angle2 + {86}^{ \circ} = {135}^{ \circ} [/tex]
cancel out 86° from both sides:
[tex] \displaystyle \angle2 = {49}^{ \circ} [/tex]
hence,
the measure of the missing angle is 49°
Answer:
Solution given'
<2+45+86=180°[sum of interior angle of a triangle]
<2=180-131
<2=49°
A bag contains 56 marbles: 7 red, green, 11 yellow, 17 brown, and 13 blue.
If a marble is chosen at random, what is the probability that the marble is green?
Answers
Answer:
8/56
Step-by-step explanation:
Add up all other marble colors then find the difference from the total.
Answer:
1/7
Step-by-step explanation:
there are 8 green marbles out of 56 so the probability would be 8/56 which simpliefies to 1/7 or 14.285714%
How many children would you need to invite to the party for the cost to be the same both places
Answers
Answer:
4 children
Step-by-step explanation:
Let the number of children = c.
The cost of the pizza place for c children (without the fee) = 8c
The cost of the pizza place for c children (with the fee) = 8c+30
The cost of the taco place for c children (without the fee) = 12c
The cost of the taco place for c children (with the fee) = 12c+14
To find c when the totals are equal, set 8c+30 equal to 12c+14 and solve:
8c+30=12c+14
8c-12c=14-30
-4c=-16
c=4
What is the perimeter of a square with a side length of 9 meters?
Answers
Answer:
36 meters
Step-by-step explanation:
A square has equal side lengths, and a total of 4 sides, so
9 times 4 is equal to 36.
Remember your units!
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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One pipe fills an empty tank in 3 hours. A second pipe fills the same tank in 6 hours. A third pipe can empty the full tank in 5 hours. If all three valves were left open, how long would it take to fill the empty tank?
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the amount of gas used by a household is shown in the table. what is the slope of the data from the table
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Step-by-step explanation:
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Answers
2) 40/4 = 10/1 = 10
3) 7/10
4) 48/3 = 16/1 = 16
5) 8/9
6) 32/5
if you have any questions, let me know!
what the the opposite of - 4.1 ?
Answers
Answer:
The opposite of -4.1 is 4.1.
opposites are the same number but either with a + sign or a - sign
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7, -7
5, -5
4, -4
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Answer:
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Step-by-step explanation:
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4. Solve the logarithmic equation for X:
log(x) -log(4) = 3
Answers
Answer:
X=7
Step-by-step explanation:
Suppose that there is a school bond referendum in Greensboro, and 73% of voters support it. You randomly ask 20 Greensboro voters whether they support the bond referendum. The standard error of the sample proportion is _____. The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is _____. Group of answer choices 0.0993; 0.6000 0.0993; 0.0951 0.1095; 0.1170 0.1095; 0.8830
Answers
Answer:
The standard error of the sample proportion is 0.0993.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
73% of voters support it.
This means that [tex]p = 0.73[/tex]
Sample of 20 voters
This means that [tex]n = 20[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.73[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.73*0.27}{20}} = 0.0993[/tex]
The standard error of the sample proportion is 0.0993.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is
12/20 = 0.6, so this is the p-value of Z when X = 0.6.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.6 - 0.73}{0.0993}[/tex]
[tex]Z = -1.31[/tex]
[tex]Z = -1.31[/tex] has a p-value of 0.0951.
So
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
The standard error of the sample proportion is 0.0098.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951
Given that,
Suppose that there is a school bond referendum in Greensboro, and 73% of voters support it.
You randomly ask 20 Greensboro voters whether they support the bond referendum.
We have to determine,
The standard error of the sample proportion is.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is .
According to the question,
There is a school bond referendum in Greensboro, and 73% of voters support it.
20 Greensboro voters whether they support the bond referendum.
To find standard deviation of sample proportion.
[tex]standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}[/tex]
Where, p = 73% = 0.73
And n = 20
Therefore,
[tex]Standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}\\\\ Standard \ deviation = \sqrt{\dfrac{0.73(1-0.73)}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.73\times 0.27}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.19}{20}}\\\\Standard \ deviation = 0.0098[/tex]
The standard error of the sample proportion is 0.0098.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is,[tex]\dfrac{12}{20 }= 0.6[/tex]
This is the p-value of Z when X = 0.6.
Therefore,
[tex]Z = \dfrac{X-\mu}{\sigma}\\\\Z = \dfrac{0.6-0.73}{0.993}\\\\Z = -1.31\\\\[/tex]
Z = -1.31 has a p-value of 0.0951.
Hence, The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
To know more about Probability click the link given below.
https://brainly.com/question/24248147
Complete the function table for each equation
Answers
Answer:
y=-32, 0, -16, -4, 16
Step-by-step explanation:
y=4(-6)-8= -32
y=4(2)-8 = 0
y=4(-2)-8 = -16
y=4(1) -8 = -4
y=4(6) -8= 16
For the given equation of the line, the complete table is attached below.
Use the concept of the equation of line defined as:
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
The given equation of a line is,
y = 4x - x
To complete the table:
Put x = -6 in this equation,
y = (-4)(-6) - 8
y = 16
Put x = 2 in the equation,
y = (-4)(2) - 8
y = -16
Put x = -2 in the equation,
y = (-4)(-2) - 8
y = 0
Put x = 1 in the equation,
y = (-4)(1) - 8
y = -12
Put x = 6 in the equation,
y = (-4)(6) - 8
y = -32
The complete table is attached below.
To learn more about the equation of line visit:
brainly.com/question/18831322
#SPJ6
The area of a rectangular shaped pool is 64 squared meters. The width is 9 meters. Write and solve an equation to determine the length of the pool. Show work.
Answers
Answer:
7.11
Step-by-step explanation: Area=lengthxwdth
64=lengthx9
64/9=length
7.11=length
Please Help. Lateena solved the equation below. Is her solution correct? Explain why or why not?
I've attached the picture for the problem.
Answers
Answer:
Not correct
Step-by-step explanation:
Given:
x² - 6x - 7 = 0
The following equation can be solved correctly by factoring Thus,
x² - x + 7x - 7 = 0
x(x - 1) +7(x - 1) = 0
(x - 1)(x + 7) = 0
(x - 1) = 0
x - 1 = 0
x - 1 + 1 = 0 + 1
x = 1
Or
(x + 7) = 0
x + 7 = 0
x + 7 - 7 = 0 - 7
x = -7
Therefore, the solution would be x = 1 or x = -7
Lateena solution is therefore NOT CORRECT because she used a wrong method.
Find the Area of the figure below, composed of a rectangle with a semicircle
removed from it. Round to the nearest tenths place.
Answers
Answer:
Area of the figure = 25.7 units²
Step-by-step explanation:
Area of the given figure = Area of rectangle ABCD - Area of the semicircle with diameter CD
Area of the rectangle ABCD = Length × Width
= BC × AB
= 8 × 4
= 32 units²
Area of the semicircle = [tex]\frac{1}{2}\pi r^{2}[/tex]
Here, r = radius of the semicircle
r = [tex]\frac{\text{Diameter}}{2}[/tex]
r = [tex]\frac{1}{2}(CD)[/tex]
r = [tex]\frac{4}{2}[/tex]
r = 2 units
Therefore, area of the semicircle = [tex]\frac{1}{2}\pi (2)^2[/tex]
= 2π
= 6.28 units²
Area of the given figure = 32 - 6.28
= 25.72 units²
≈ 25.7 units²
A. 19 units
B. 38 units
C. 12 units
D. 22 units
Answers
Answer:
I think 12 is 5he right answer
which set of side lengths can form a triangle?
А: 2 cm, 2cm. 6 cm
B:3 cm 6 cm, 9 cm
C:4 cm, 8 cm, 5 cm
D:8 cm, 3 cm, 4 cm
Answers
Answer:
C:4 cm, 8 cm, 5 cm
Step-by-step explanation:
sum of length of any two sides of a triangle will be larger than the third side.
72% of what number is 144? Answer please
Answers
Answer:
103.68
Step-by-step explanation:
Answer:
103.68
To solve you would convert the percent to decimal form .72.
Then divide by 144
.72/144=103.68
your answer is 103.68
Complete the square
to find the vertex
of this parabola.
2
x - 4y-12 x +68=0
Answers
Answer: (6,8)
Step-by-step explanation:
Answer:
(6, 8)
Step-by-step explanation:
Lauren went to a store to buy some clothes. The shirts were selling at a 20% discount. A pair of pants cost $5 less than 3 times the original cost of a shirt.
If she spent $36 in all, what was the original cost of a shirt?
Answers
Answer:
OMG
Step-by-step explanation:
I had the same question
Answer:
$10.79
Step-by-step explanation:
x = original cost of one t shirt
We can build this equation
x - (20/100) x + 3x- 5 = 36
-1/5x + 4x = 41
-x + 20x = 205
19x = 205
x = $10.79
Directions: identify weather the problem has a minimum or a maximum type an “X” in the box next to your answer
A) y= x^2+2x-1
Minimum or maximum
B) y=-x^2-8x-1
Minimum or maximum
C) y=2x^2+8x
Answers
Answer:
A) minimum
B) maximum
C) minimum
Step-by-step explanation:
A positive x² coefficent means the parabola opens up and the vertex is the minimum
A negative x² coefficent means the parabola opens up and the vertex is the maximum
---------------------------------
A) minimum
B) maximum
C) minimum
Suppose $3500 is invested at a rate of 5% per year compounded monthly.
Answers
A $146 tent was sold for 20% off. There was a sales tax of 4%. What was the discount
amount, sales tax and final cost of the tent?
Answers
The sales tax is $8.25
So the final cost of the tent is
146.00-35.00=$111.00
111+8.25= 119.25
Your answer is $119.25
the discount price was 29.2
step by step 146 minus 20% = 116.8 116.8 + 4% =121.472 the sales tax added 4.672$ to the total amount and the discount price removed 29.2 of the required pay