Answer:
slope: (11-1)/(-4+14)
m: 10/10
M: 1
11 = -4 + b
b = 15
y = x + 15
Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Use the distance formula and the Pythagorean theorem to determine if Steve is correct. Show your work and explain your reasoning.
(question 7)
Yes, the points are the vertices of a right triangle and we will prove that by using the Pythagorean theorem.
Are these the vertices of a right triangle?
Remember that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)² + (b - d)²)
The distance between (-4, 8) and (8, 8) is:
d₁ = √( (-4 - 8)² + (8- 8)²) = 12
The distance between (8, 8) and (-4, 3) is:
d₂ = √( (8 + 4)² + (8- 3)²) = 13
The distance between (-4, 8) and (-4, 3) is:
d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5
if the Pythagorean theorem is true, then the sum of the squares of the two shorter sides must be equal to the square of the larger side, then we must have that:
5² + 12² = 13²
Solving that we get:
25 + 144 = 169
169 = 169
This is true, so yes, the vertices are the vertices of a right triangle.
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Mickey simplified the expression below. He then checked his work by substituting 4 for x. He noticed his two values were not equal. What was Mickey’s error when simplifying?
Expression
Simplified Expression
2 x squared minus 4 x minus 9 minus x squared + 2 x + 3
x squared minus 6 x minus 6
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Mickey should have added 2 and 1 when combining the x squared terms.
Mickey should have added 9 and 3 when combining the constant terms.
Mickey should have added –4 and –1 when combining the x terms.
The correct option is, Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Given,
The expression; 2x² - 4x - 9 - x² + 2x + 3
We have to simplify the expression;
To group and arrange an expression in such a way that it is easier to understand and solve is to simplify the expression.
We first group and find like terms and then add and cancel out
2x²-x²- 4x+2x - 9+ 3
=x²-2x-6
Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients
Therefore the correct option is
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
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Find the lengths of PR and QS
The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.
What is the area of the right-angle triangle?The area of the right-angle triangle is given as
A = 1/2 x B x H
Where B is the base and H is the height of the right triangle.
The length of PT is 10 and the angle ∠TPS is 60°.
The length of PR is given as,
PR = PT + TR
PR = 10 + 10
PR = 20
And the length of QS is given as,
QS = QT + TS
QS = 10 + 10
QS = 20
The area of the rectangle is given as,
A = Area of triangle ΔPQR + Area of triangle ΔPSR
A = 2 [(1/2) x (20 cos 60°) x (20 sin 60°)
A = 173.21 square units
The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.
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find the volume of a sphere, if it has a radius of x-1
The volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex]. It can be obtained by using the formula of the volume of the sphere.
What is the formula of the volume of the sphere?
Volume of any object is the amount of 3 dimentional space occupied by that object. Volume of the sphere is given by the following expression:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Here, V is the volume of the sphere and r is the radius of the sphere.
Substitute x-1 for r in the above formula.
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (x-1)^3[/tex]
This is the simplest form.
In the above equation, you can apply the formula [tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex] but that will make the equation difficult and lenthy. Hence, there is no need to apply this formula.
Hence, the volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex].
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What is the solution to this system of linear equations 2x y 1 3x y 6 1 3?.
The solution to the linear equation is (-1, 3).
What is a linear equation ?
Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.
2x + y = 1 …… (1)
3x - y = -6 …… (2)
To solve the linear equations in two variables
By adding both the equations
5x = -5
x = -1
Substitute the value of x in equation (1)
2 (-1) + y = 1
-2 + y = 1
y = 1 + 2 = 3
y = 3
Therefore, the solution to the linear equation is (-1, 3).
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A machine costing $450,000 with a four-year life and an estimated $30,000 salvage value is installed by lux company on january 1. The factory estimates the machine will produce 1,050,000 units of product during its life. It actually produces the following units for the first 2 years: year 1, 260,000; year 2, 275,000. What is the depreciation amount for year 2 under the straight line method?.
Depreciation expense in year 2 = 2/4 x $225,000 = $112,500.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Depreciation expense using the double declining method = Depreciation factor x cost of the assetDepreciation factor = 2 x (1/useful life) Depreciation expense in year 1 = 2/4 x $450,000 = $225,000Book value at the beginning of year 2 = $450,000 - $225,000 = $225,000Depreciation expense in year 2 = 2/4 x $225,000 = $112,500hence,Depreciation expense in year 2 = $112,500.
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an inverted cone has a radius of 4 cm and a height of 16 cm. initially, the cone is full of water, and it flows from the bottom of the cone at a rate of 50 $\text{cm}^3$ per minute. find the rate at which the height of water is decreasing (in cm per minute) when the height of the water is 5 cm.
The flowrate of decreasing water is 3.98 cm/min after the water reaches 5cm of its height.
We need to know about the flowrate to solve this problem. The rate can be described as how much water flows in a unit of time. It can be represented by this equation
Q = V / t
where Q is flowrate, V is volume and t is time.
From the question above, the given parameters are
Inverted cone with
Q = 50 cm³/min
R = 4 cm
h = 5 cm
Hence, the rate of decreasing water is
Q = V / t
50 = A . h / t
50 = π . R² . h / t
50 = 22/7 . 4 . h / t
h/t = 3.98 cm/min
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A statistics student from a large high school takes a random sample of 200 students and finds that 123 are actively
involved in a political party. A 99% confidence interval for the proportion of students at this school who are actively
involved in a political party is (0.526, 0.704). Which statement correctly interprets the interval?
O The statistics student can be 99% confident that 62% of students from this school are actively involved in a
political party.
O There is a 99% probability that the proportion of students at this school who are actively involved in a political
party lies between 0.526 and 0.704.
If this procedure is repeated many, many times, the true proportion of students at this school who are actively
involved in a political party will be captured 99% of the time.
O The statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all
students at this school who are actively involved in a political party.
The last option is correct.
The statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all students at this school who are actively involved in a political party.
What is political party?
A political party is a group that arranges candidates to run in elections in a certain nation. It is typical for party members to share similar political viewpoints, and parties may support particular ideologies or policy objectives.
Given: A statistics student from a large high school takes a random sample of 200 students and finds that 123 are actively involved in a political party.
A 99% confidence interval for the proportion of students at this school who are actively involved in a political party is (0.526, 0.704).
Hence, the statistics student can be 99% confident that the interval from 0.526 to 0.704 captures the true proportion of all students at this school who are actively involved in a political party.
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Comparing Circles
Here are two circles. Their centers are A and F.
E
C
4 cm
A
B
H
F
8 cm
D
1. What is the same about the two circles? What is different?
G
This is an incomplete question and the complete question is in the image attached.
Both circles A and F have the same radius and diameter.
What is the center of the circle?
It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.
Given:
We have,
Two circles are named A and F.
The radius of circle A is 4cm
So, the diameter of Circle A is 4 x2 = 8 cm
The Diameter of Circle F is 8 cm
Hence, Both circles A and F have the same radius and diameter.
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if the probability that a particular event occurs is 7/10, what are the odds favoring the event not occurring? express your answer in the form a:b.
For the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to
7 : 3.
As given in the question,
Probability of any particular event occurring is equal to 7 /10
Probability of any particular event not occurring is = 1- (7/10)
= (10 -7) /10
= 3/10
Probability of the odds favoring the events which are not occurring
= (7 /10) / (3/10)
= ( 7 × 10) / (3 × 10)
= 7 /3
Odds favoring the events which are not occurring in the form a: b
= 7 : 3
Therefore, for the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to 7 : 3.
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a new pyramid has been found in south america. the pyramid has a rectangular base that measures by 180 yd, and has a height of 90 yd. the pyramid is not hollow like the egyptian pyramids and is composed of layer after layer of cut stone. the stone weighs 456 lb per cubic yard. how many pounds does the pyramid weigh?
Answer:
443,232,000 lb
Step-by-step explanation:
You want the weight in pounds of a pyramid 180 yd square and 90 yd high made of material weighing 456 lb/cubic yard.
VolumeThe volume of the pyramid is given by the formula ...
V = 1/3s²h . . . . . . . . where s is the side length and h is the height
V = 1/3(180 yd)²(90 yd) = 972000 yd³
WeightAt a weight of 456 pounds per cubic yard, the weight of the pyramid is estimated to be ...
(456 lb/yd³)×(972,000 yd³) = 443,232,000 lb
The pyramid weighs about 443,232,000 pounds.
__
Additional comment
At 456 lb per cubic yard, the stone is less dense than most wood and will float high in water.
A school is arranging a field trip to the zoo. the school spends 683.47 dollars on passes for 38 students and 3 teachers. the school also spends 334.78 dollars on lunch for just the students. how much money was spent on a pass and lunch for each student?
Answer:
1018.25
----------------------------------------------------------------------
hope you do well on the quiz/test/assignment!
Chin has $75.00 in a savings account that earns 5% interest,
compounded annually.
What will the balance be after 4 years?
Round to the nearest cent.
75÷100=0.75
0.75×5=3.75
3.75×4=15
75+15=90
Brayden is saving up to buy a new video game. He already has $25 and can save an additional $5 per week using money from his after school job. How much total money would Brayden have after 4 weeks of saving? Also, write an expression that represents the amount of money Brayden would have saved in ww weeks.
to can be driven before it would need to be junked is an exponential random variable with parameter smith has a used car that he claims has been driven only 10,000 miles. if jones purchases the car, what is the
Answer:
2334
Step-by-step explanation:
PLEASE HELP! best answer gets brainiest!!
ONLY QUESTIONS, 51 to 55
please answer in detail!
Answer:
[tex]x + ( - 43) = 102 \\ x - 43 = 102 \\ x = 102 + 43 \\ x = 145[/tex]
Step-by-step explanation:
Let the unknown number be represented by x
since sum means addition, we are adding the unknown to -43 and equating it to 102 which is said to be the final answer.
After equating, we find out that we have two symbols and + multiplied by - is always -, giving us an equation as in step 2
after collecting like terms , we get an easy linear equation.
A line that includes the point (5, 17) has a slope of 1. What is its equation in slope -intercept form?
Answer:
17 = 5 + b
b = 12
y = x + 12
Which of the following tables represents the proportional relationship for 6 cups of grape juice for every three fourths cup of rainbow sherbet?
Rainbow Sherbet (cups) 0.75 1.5 2.5
Grape Juice (cups) 6 8 10
Grape Juice (cups) 0.75 1.5 2.5
Rainbow Sherbet (cups) 6 8 10
Grape Juice (cups) 6 8 10
Rainbow Sherbet (cups) 0.75 1 1.25
Rainbow Sherbet (cups) 6 8 10
Grape Juice (cups) 0.75 1 1.25
Answer:
Step-by-step explanation:
D
6 3/4divided by 1 2/3
Answers-
7 divided by 2
6 divided by 1
8 divided by 3
3 divided by 2
If a mixed fraction, 6(3/4) is divided by another fraction 1(2/3), then the quotient will be 4.05.
As per the question statement, a mixed fraction, 6(3/4) is divided by another fraction 1(2/3),
And we are required to calculate the quotient of the above mentioned division.
To solve this question, we will first convert the mixed fractions, into improper fractions, and then use the reciprocal rule to obtain our desired answer, that is,
[{6(3/4)}/1(2/3)]
= [{(4 * 6) + 3}/4]/[{(3 * 1) + 2}/3]
= [{(24 + 3)/4}/{(3 + 2)/3}]
= [(27/4)/(5/3)]
= [(27/4) * (3/5)]
= [(27 * 3)/(4 * 5)]
= (81/20)
= 4.05
Hence, when a mixed fraction, 6(3/4) is divided by another fraction 1(2/3), then the quotient will be 4.05
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Write the equation of a line that passes through the points (4,6) and (−8,3)
Answer:
y= 1/4x+5
Step-by-step explanation:
y=mx+c
to calculate gradient: change in y/change in x
-3/-12 = 0.25
y = 1/4x+c
4 * 1/4 = 1
6-1 = 5
c= 5
Totally:
y= 1/4x+5
the median of the ordered set of observations 2,3, (4m-3), (3m + 1), 11 and 13 in asending order is 6. Find the value of m.
The value of [m] will be 2.
What is mean, median and mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.Given is the median of the ordered set of observations 2, 3, (4m-3), (3m + 1), 11 and 13 in ascending order is 6.
We have the following data as -
2, 3, (4m-3), (3m + 1), 11, 13
N = 6
So median will be -
{(4m - 3) + (3m + 1)}/2 = 6
(4m - 3) + (3m + 1) = 12
4m + 3m - 3 + 1 = 12
7m - 2 = 12
m = 2
Therefore, the value of [m] will be 2.
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A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 14 minutes?
Camel can drink 21 gallons of water in 14 minutes.
Given in question,
Gallons of water camel can drink in 10 minutes = 15
Gallons of water camel can drink in 1 minutes = 15/10
= 1.5
Gallons of water camel can drink in 14 minutes = 1.5 * 14
= 21
Hence, camel can drink 21 gallons of water in 14 minutes.
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NEED HELP ASAPPPPPPP
Answer:
76.93
Step-by-step explanation:
As the area of circle is πr^2
The area of semi-circle is
1÷2×πr^2
0.5×3.14×7×7
76.93
A specialty shop procures several refrigerators for $400 apiece and offers them to customers for $900 each. What is the mark-up, as a percentage?
The mark-up, as a percentage = 125%
What is Markup?
The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity.
A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.
Markup percentage=[(selling price - unit cost)/unit cost]*100
Markup percentage= [(900-400)/400]*100=1.25*100
= 125%
So, the mark-up, as a percentage = 125%
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THE VALUE OF JOHN'S
BASEBALL CARD
INCREASED BY $5. IT IS
NOW WORTH
$158.
(percent change)
The percent change of the worth is 3.26%.
Apples were for sale from a fruit vendor. He has 420 apples and sells 40% of them. How many apples did he have in total when he first started?
Solution: Assume a fruit vendor had x apples in stock.
According to the query,
(100 – 40%) of x = 420
60% of x = 420
60/100 x = 420
X = 700
The fruit vendor, therefore, had 700 apples in all.
Let , the worth is $x.
according to the question, $x + $5 =$158
∴ $x= $153
∴ percent change= (5/153)×100
=3.26%
The percent change of the worth is 3.26%.
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please solve this question
Answer 2
Step-by-step explanation and no not writing out how to do it.
Part-Time Job So far this week, you have worked 10 hours at your part-time job.
This is 80% of the number of hours you work each week. How many hours do you
work each week?
Answer:
12.5 hours a week
Step-by-step explanation:
So far this week, you have worked 10 hours at your part-time job. This is 80% of the number of hours you work each week. How many hours do you work each week?
10 hours = 80%
80% = 0.8
10/0.8 = 12.5 hours a week
Two angles are complementary to each other. one angle measures 18°, and the other angle measures (8x − 28)°. determine the value of x. 12.5 20 44.5 16
The value of x in complementary angle is 12.5⁰.
We need to know about complementary angles to solve this problem. The complementary angle is the angle that can make another angle has a value of 90⁰. It can be written as
A + B = 90⁰
where A and B are the complementary angles.
From the question above, the given parameters are
A = 18⁰
B = (8x - 28)⁰
By substituting the given parameters, we can calculate the x value
A + B = 90⁰
18⁰ + (8x - 28)⁰ = 90⁰
8x = 90 - 18 + 28
8x = 100
x = 12.5⁰
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Answer: 12.5
Step-by-step explanation:
18+8x-28=90
18-18
90-18
8x-28=72
28+28
72+28
8x=100
8x/8
100/8
x=12.5
The height of a triangle is 5 m longer than the base. If the area is 150 m2 , how long is the base?.
The base of the triangle is 15 meters.
Here, we are given that the height of a triangle is 5 m longer than the base.
Let the height of the triangle be h
Then, the base of the triangle will be = h - 5
Further, we are given that area of the triangle = 150 meter square
We know that area of a triangle = 1/2 × base × height
⇒ 150 = 1/2 × h × (h-5)
150 × 2 = h(h-5)
300 = [tex]h^{2}[/tex] - 5h
[tex]h^{2}[/tex] - 5h - 300 = 0
Now, we solve the above quadratic equation by splitting the middle term.
[tex]h^{2}[/tex] + 15h - 20h - 300 = 0
h( h + 15) - 20( h + 15) = 0
(h - 20) (h + 15) = 0
Thus, h = 20 or -15
But since height cannot be negative, h = 20
⇒ base = h - 5
= 20 - 5
= 15 meters
Thus, the base of the triangle is 15 meters.
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in a survey of 2480 golfers, 15% said they were left-handed. the survey's margin of error was 3%. construct a confidence interval for the proportion of left-handed golfers.
The confidence interval for the proportion of left-handed golfers is of:
(0.12, 0.18).
How to obtain a confidence interval?A confidence interval is calculated as the sample mean plus/minus the margin of error, hence the bounds of the confidence interval are given as follows:
Lower bound: sample mean - margin of error.Upper bound: sample mean + margin of error.In the context of this problem, these parameters are given as follows:
Sample mean: 15% as a percentage, 0.15 as a proportion.Margin of error: 3% as a percentage, 0.03 as a proportion.Hence the lower bound of the confidence interval for the proportion of left-handed golfers is:
0.15 - 0.03 = 0.12.
The upper bound of the confidence interval for the proportion of left-handed golfers is:
0.15 + 0.03 = 0.18.
Then the interval is:
(0.12, 0.18).
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