Answer:
Step-by-step explanation:
To show that the points A(-1,-3), B(6, 1), and C(2,-5) form the vertices of a right angle triangle, we need to show that one of the angles of the triangle is a right angle, i.e., it measures 90 degrees.
We can use the Pythagorean theorem to check if the triangle is a right triangle. According to the Pythagorean theorem, the square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
First, let's calculate the lengths of the sides of the triangle:
AB = sqrt((6 - (-1))^2 + (1 - (-3))^2) = sqrt(49 + 16) = sqrt(65)
BC = sqrt((2 - 6)^2 + (-5 - 1)^2) = sqrt(16 + 36) = sqrt(52)
AC = sqrt((2 - (-1))^2 + (-5 - (-3))^2) = sqrt(9 + 4) = sqrt(13)
Next, let's check if the Pythagorean theorem holds true for this triangle:
If AB is the hypotenuse:
AB^2 = 65
BC^2 + AC^2 = 52 + 13 = 65
Since AB^2 = BC^2 + AC^2, we can conclude that angle BAC is a right angle.
Therefore, the points A(-1,-3), B(6, 1), and C(2,-5) form the vertices of a right angle triangle, with angle BAC measuring 90 degrees.
Which numbers are closest to 500
Answer:
the ans is below
Step-by-step explanation:
499 or 501
5) Write the equation for the function that results from each transformation applied to the base function
y = 7²
a) reflect in the x-axis (vertical reflection)
c) stretch horizontally by a factor of 2.4
b) stretch vertically by a factor of 3
d) reflect in the y-axis and stretch vertically by bafo 7
The equation that results from each transformation is given as follows:
a) reflect in the x-axis (vertical reflection): y = -7^x.
b) stretch vertically by a factor of 3: 3(7)^x.
c) stretch horizontally by a factor of 2.4: y = (7)^(x/2.4).
d) reflect in the y-axis and stretch vertically by a factor of 7: y = 7^(1 - x).
How to obtain the functions?The parent function in the context of this problem is given as follows:
y = 7^x.
The reflection over the x-axis means that the sign of the entire function is exchanged, hence:
y = -7^x.
The vertical stretch by a factor of 3 means that the entire function is multiplied by 3, thus:
y = 3(7)^x.
The horizontal stretch by a factor of 2.4 means that x -> x/2.4, hence:
y = (7)^(x/2.4).
The reflection over the y-axis means that x -> -x, while the vertical stretch by a factor of 7 means that the function is multiplied by 7, hence the function for item d is given as follows:
y = 7(7)^(-x)
y = 7^(1 - x).
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7. Nkaiseng who is 25 years wants to invest some money for her retirement when she is 65 years. If she invest at a compound interest rate of 11.5% per annum. How much money should she invested if she wants to retire R500 300? Round up your answer to the nearest rand (10 Points).
Answer:
The formula for calculating the future value of a present amount with compound interest is:
FV = PV * (1 + r)^n
where FV is the future value, PV is the present value, r is the annual interest rate (as a decimal), and n is the number of compounding periods.
In this case, Nkaiseng wants to invest some money now to retire with R500 300 in 40 years (from 25 to 65). The annual interest rate is 11.5%, which is equivalent to a monthly interest rate of 0.115/12 = 0.00958.
So we have:
FV = PV * (1 + 0.00958)^ (40*12)
500300 = PV * (1.00958)^480
Dividing both sides by (1.00958)^480, we get:
PV = 500300 / (1.00958)^480
PV = 500300 / 20.4524
PV = 24406.53
Therefore, Nkaiseng should invest R24406.53 (rounded up to the nearest rand) now to have R500 300 when she retires at 65 years with an interest rate of 11.5% per annum.
The volume of a right cone is 1824 � π units 3 3 . If its circumference measures 24 � π units, find its height.
The value of the height of the cone is 38 units
How to determine the height
The formula for calculating the circumference of a cone is represented as;
Circumference = 2πr
Now, substitute the value to determine the radius, we have;
24π = 2πr
Divide by the coefficient of r
r = 24π/2π
r = 12 units
The formula for the volume of a cone is;
Volume = πr²h/3
Substitute the values
1824 π = π × 144 ×h/3
Multiply the values
1824π = 144πh/3
Make h the subject
h = 38 units
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The dimensions of a rectangular prism are given in the net shown. Image shows a net of a rectangular prism. The net shows 6 faces which are all rectangular faces. The top rectangle is labeled 8 inches by 3 inches. The left rectangle is labeled 4 inches by 6 inches. The middle rectangle is labeled 8 inches by 6 inches. The other three faces are repeats of the three mentioned. What is the total surface area of this rectangular prism in square inches? Enter your answer in the box.
=The total surface area of the rectangular prism is 192 square inches.
You calculate the total surface area of the rectangular prism using the dimensions provided in the net. Since the net has 6 rectangular faces, we can find the area of each face and then sum them up to get the total surface area.
1. Top rectangle (8 inches by 3 inches): Area = length × width = 8 × 3 = 24 square inches.
Since the bottom rectangle is the same, its area is also 24 square inches.
2. Left rectangle (4 inches by 6 inches): Area = length × width = 4 × 6 = 24 square inches.
As the right rectangle is identical, its area is also 24 square inches.
3. Middle rectangle (8 inches by 6 inches): Area = length × width = 8 × 6 = 48 square inches.
The back rectangle is the same, so its area is 48 square inches as well.
Now, we'll sum up the areas of all 6 faces to get the total surface area:
Total Surface Area = (2 × 24) + (2 × 24) + (2 × 48) = 48 + 48 + 96 = 192 square inches.
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Use the 2021 marginal tax rates to compute the income tax owed by the following person.
Filing status: head of household
Gross income:
$72,000
Adjustments: none
Deductions:
$4500 state taxes
$2000 theft loss
Tax credit:
$6000
Using the tax credit we know that the net income of the person is $71,500.
What is a tax credit?Tax credits are financial incentives that let some taxpayers deduct their accumulated credits from the total amount they owe the state.
Additionally, it might be a "discount" offered by the state in some circumstances or a credit given in acknowledgment of prior tax payments.
A tax credit can also be compared to a rebate.
So, the income of the person would be:
Net income = 72,000 - 4500 - 2000 + 6000
Net income = 78,000 - 6,500
Net income = 71,500
Therefore, using the tax credit we know that the net income of the person is $71,500.
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Determine the area of the composite figure to the nearest whole number.
135cm²
117cm²
173cm²
74cm²
The area of the composite figure is A = 135 cm²
Given data ,
Let the figure consists of a rectangle and quarter circle
where the area of the rectangle is R and area of quarter circle is C
And , A = R + C
Area of rectangle A = 20 x 2 = 40 cm²
And , area of quarter circle C = ( 1/4 )π ( 11 )²
C = 95.033 cm²
So , A = 95 + 40
A = 135 cm²
Hence , the area of the figure is A = 135 cm²
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The complete question is attached below :
Determine the area of the composite figure to the nearest whole number.
135cm²
117cm²
173cm²
74cm²
An elevator has a placard stating that the maximum capacity is 1944 lb-12 passengers. So, 12 adult male
passengers can have a mean weight of up to 1944/12 = 162 pounds. If the elevator is loaded with 12 adult
male passengers, find the probability that it is overloaded because they have a mean weight greater than 162
Ib. (Assume that weights of males are normally distributed with a mean of 169 lb and a standard deviation of 29 lb.)
Does this elevator appear to be safe?
The probability the elevator is overloaded is
(Round to four decimal places as needed.)
The probability 0.7977 that the sample mean weight of 12 adult male passengers is greater than 162 lb.
There is a 79.77% chance that the elevator is overloaded
What is Central Limit Theorem?We can use the Central Limit Theorem here, which states that the sample mean of a sufficiently large sample size (n≥30) will be approximately normally distributed with mean μ and standard deviation σ/√n, where μ is the population mean and σ is the population standard deviation.
In this case, n=12, μ=169 lb, and σ=29 lb. Therefore, the sample mean weight of 12 adult male passengers will be approximately normally distributed with mean 169 lb and standard deviation 29/√12 ≈ 8.38 lb.
Now we can standardize this distribution to find the probability that the sample mean weight is greater than 162 lb:
z = (162 - 169) / 8.38 ≈ -0.83
We determine that the probability of z being less than or equal to -0.83 is approximately 0.2023, which can be calculated using a standard normal distribution table or calculator.
Therefore, there is a probability of 1 - 0.2023 ≈ 0.7977 that the sample mean weight of 12 adult male passengers is greater than 162 lb.
This indicates that if the elevator is filled with 12 adult male passengers, there is a 79.77 percent chance that it will be overloaded. The elevator does not appear to be safe for this many passengers, and this is a very high probability
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First show that x^3-1 is divisible by x - 1, then show that x^3- 8 is divisible by x - 2. One way to proceed is to think of what "divisible" means in terms of polynomials. Show that your results could be useful in finding the slope of a certain curve.
Since the remainders are zero x³ - 1 is divisible by x - 1 and x³ - 8 is divisible by x - 2. The results can be used to find the slopes.
Polynomial long division:Polynomial long division is a method used to divide one polynomial by another polynomial. It is similar to the long division of integers.
The process involves dividing the highest degree term of the dividend by the highest degree term of the divisor to obtain the first term of the quotient, and then multiplying the entire divisor by this term and subtracting it from the dividend.
Here we have
Show that x³ -1 is divisible by x - 1
Use polynomial long division to show that x³ - 1 is divisible by x - 1
x² + x + 1
x - 1 | x³ + 0x² + 0x - 1
x³ - x²
x² + 0x
x² - x
x - 1
x - 1
0
Since the remainder is zero x³ - 1 is divisible by x - 1
Use polynomial long division to show that x³ - 8 is divisible by x - 2
x² + 2x + 4
x - 2 | x³ + 0x² + 0x - 8
x³ - 2x²
2x² + 0x
2x² - 4x
4x - 8
4x - 8
0
Since the remainder is zero x³ - 8 is divisible by x - 2
These results can be useful in finding the slope of a certain curve.
Specifically, if we consider the curve y = x³, then we can use the fact that x³ - 1 is divisible by x - 1 and x³ - 8 is divisible by x - 2 to find the slope of the tangent line to the curve at the points (1,1) and (2,8), respectively.
Using the quotient rule of differentiation, find the derivative of y = x³ as:
=> dy/dx = 3x²
At x = 1, the slope of the tangent line is therefore 3.
At x = 2, the slope of the tangent line is also 3.
Therefore,
Since the remainders are zero x³ - 1 is divisible by x - 1 and x³ - 8 is divisible by x - 2. The results can be used to find the slopes.
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A recent research study reported that the mean daily internet usage among preparatory school students in Egypt is 70 minutes. Suppose that a random sample of 64 preparatory school students in UAE revealed a mean daily internet usage of 75 minutes with a standard deviation of 20 minutes. Is there sufficient evidence that preparatory school students in UAE spend more time on Internet compared to their peers in Egypt? Use 1% significance level.
State the hypothesis, calculate the statistical test (Round to three decimal places), find the p-value (Round to three decimal places) then write your conclusion in the context of the problem.
The hypothesis is an alternative hypothesis. And the p-value will be 0.25.
For the null hypothesis,
H0: μ = 70
For the alternative hypothesis,
Ha: μ > 70
The test statistic is calculated as:
t = (x - μ) / (s / √n)
t = (75 - 70) / (20 / √64)
t = 2.00
Using a significance level of 0.01 and a one-tailed test, the critical t-value is 2.390. Since the calculated t-value of 2.00 is less than the critical t-value of 2.390, we fail to reject the null hypothesis.
The p-value is calculated as,
p-value = (75 - 70)/20
p-value = 0.25
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sylvia watched a movie that was 1 whole 3/4 hours long. then she went to a baseball game that lasted for 3 wholes 1/3 hours. how much longer was the baseball game than the movie?
The calculated time of is that the baseball game was 1 7/12 hour longer than the movie
How much longer was the baseball game than the movie?The given parametes in the question are
Movie = 1 3/4 hours
Baseball = 3 1/3 hours
To calculate how much longer was the baseball game than the movie, we subtract
So, we have
Longer = 3 1/3 - 1 3/4
Evaluate
Longer = 19/12
This gives
Longer = 1 7/12
Hence, the baseball game was 1 7/12 hour longer than the movie
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A Collection of books consists of six Math books and four English books. A book is chosen at random from the collection. Finc the probability of choosing: a) a Maths book b) an English book c) either a maths or an English book d) neither a maths nor an English book.
Answer:
A. 60%
B. 40%
C. Math because Math has higher chance of being chosen.
D. 0%
Help me with this please
Answer:
Your answer will be B. A town's population grows at a rate of 7.2% every year.
Step-by-step explanation:
Pls give me brainliest thx
Help me with this please
Answer:
29°
Step-by-step explanation:
since a right angle in 90° just subtract 61 out of 90
90°-61°=29°
If a1 = 10 and an = an-1 + 4 then find the value of a5
We can use the given recursive formula to find the value of each term in the sequence.
Starting with a1 = 10, we can use the recursive formula to find a2:
a2 = a1 + 4 = 10 + 4 = 14
Similarly, we can find a3, a4, and a5:
a3 = a2 + 4 = 14 + 4 = 18
a4 = a3 + 4 = 18 + 4 = 22
a5 = a4 + 4 = 22 + 4 = 26
Therefore, the value of a5 is 26.
A recursive formula is what?
A formula which explains how to move from one word in a sequence to the next is known as a recursive rule for a sequence. The variable is typically used to represent the term "number."
What does a1 in the formula represent?
The first term of the formula, a1, and the nth term of the series, an, are both expressions containing the first term (the term preceding it), an-1.
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suface area of cuboid 9 5 4
The cuboid in question has a surface area of 202 square units.
We must sum together the areas of all six faces to determine a cuboid's surface area.
The dimensions of the given cuboid are:
length (l) = 9 units
width (w) = 5 units
height (h) = 4 units
The area of each face is given by:
Top and bottom faces:[tex]lw = 9 * 5 = 45[/tex] square units each
Front and back faces: [tex]lh = 9 *4 = 36[/tex] square units each
Left and right faces: [tex]wh = 5 * 4 = 20[/tex] square units each
Therefore, the total surface area of the cuboid is:
[tex]2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units[/tex]
Hence, the surface area of the given cuboid is 202 square units.
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Evaluate the expression
3(3a-1)+2, for a=2
Answer: 17
Step-by-step explanation:
Substitute the value of the variable into the equation and simplify.
3 ( 3 ( 2 ) - 1 ) + 2 = 17
Determine the rational zeros for the function f(x)= x² + 7x² +7x-15.
a. -5, -3, 1
C. -5,-3,-1
b.
-5, 3, 1
d. 5,-3, 1
Please select the best answer from the choices provided
A
B
C
D
Answer: C
Step-by-step explanation: -5,3,1 answer ;)
What is the median in this boxplot?
000
900
700
500
400
300
200
100
O 154
O 345
420
O 484
0000000000000
O924
22%3
04.0
Ma
(154,000)
The median of the boxplot is 420.
In a boxplot, the median is the line in the Centre of the box.
Given that;
The upper horizontal line of the box is at 490
The Lower horizontal line of the box is at 350
Therefore the median of boxplot
= (upper point + lower point)/2
= (490 + 350)/2
= 420
Hence middle point be at 420.
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Cane somebody help me with this??
The values of the variables x, y and a in the circles are calculated below
Calculating the values of the variablesCircle 1
The measure of the angle x is calculated as
28 = 1/2(x - 61)
So, we have
x - 61 = 56
This gives
x = 117
For y, we have
y² = 4 * 18
So, we have
y = 6√2
Circle 2
The measure of the angle x is calculated as
x + 48 = 180
So, we have
x = 132
The length y is calculated as
tan(24) = 7/y
So, we have
y = 7/tan(24)
Evaluate
y = 15.7
Circle 3
This is calculated as
9 * (9 + a) = 8 * 21
So, we have
81 + 9a = 168
So, we have
a = 9.67
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if ABCD is the square. Find the value of x if BE = 3x + 5 and CA= 8x+2.
Answer:
x = 4----------------------
The diagonals of a square bisect each other.
It makes all half-diagonals of equal length. Therefore:
CA = 2BESubstitute and solve for x:
8x + 2 = 2(3x + 5)8x + 2 = 6x + 108x - 6x = 10 - 22x = 8x = 4Hence the value of x is 4.
Given f(x) = X-4 and g(x) = 9x + 4, find (g of (x).
A)9x+32
B) x-1
C) X
D) x + 8
Answer:
To find (g of f)(x), we need to first find f(x) and then substitute it into g(x).
f(x) = x - 4
Now we can substitute f(x) into g(x):
g(f(x)) = 9f(x) + 4
g(f(x)) = 9(x - 4) + 4
g(f(x)) = 9x - 36 + 4
g(f(x)) = 9x - 32
Therefore, the answer is (A) 9x+32.
Answer:
the answer is d- (x-5)
Trigonometry. See attached image:
Show all work.
The expression sec θ / csc θ + 2sin θ / cos θ is equal to the expression 3tan θ is proven below.
Given that:
sec θ / csc θ + 2sin θ / cos θ = 3 tan θ
The properties are given as,
tan x = sin x / cos x
sec x = 1 / cos x
sin x = 1 / csc x
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Take the left-hand side, then
LHS = sec θ / csc θ + 2sin θ / cos θ
LHS = sin θ / cos θ + 2tan θ
LHS = tan θ + 2 tan θ
LHS = 3 tan θ
LHS = RHS
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Marty has 6 gallons of orange juice. How many pints of orange juice does Marty have?
Answer:
Marty has 768 pints of orange juice.
Step-by-step explanation:
To convert gallons to pints, we need to remember that 1 gallon is equal to 128 fluid ounces, and 1 fluid ounce is equal to 1/8 pint.
Given that Marty has 6 gallons of orange juice, we can calculate the total amount in pints as follows:
6 gallons x 128 fluid ounces/gallon x 1/8 pint/fluid ounce = 768 pints
So, Marty has 768 pints of orange juice.
vel K C.5 Solve proportions 2ZL
Solve for y in the proportion.
24 15
40
y
y=[
Submit
Learn with an example
F
or
Watch a video
Work it out
Answer:
[tex]y = 25[/tex]
Step-by-step explanation:
[tex]24y = 15 \times 40[/tex]
[tex]24y = 600[/tex]
[tex]y = \frac{600}{24} [/tex]
[tex]y = 25[/tex]
Solve please, see the picture
The area of the new shape is 74 squared cm
How to find the area of the new shape
The area of the new shape is solved by dividing the shape into three sections and then sum up all the areas
The area of the sections are as follows
Section 1: length x width
= 8 x 5
= 40 squared cm
Section 2: length x width
= 5 x 2
= 10 squared cm
Section 3: length x width
= 8 x 3
= 24 squared cm
Total area
= 24 + 10 + 40
= 74 squared cm
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The area of the new shape is 74cm²
What is area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
The shape is a combination of two rectangles. One of the rectangles cut out.
The area of the cut out is calculated as;
A = l × w
A = 3 × 2
A = 6cm²
The area of the cut out rectangle = area of the whole rectangle - area of cut out rectangle
= 8×5 -6
= 40-6
= 34cm²
The area of the second rectangle = l×w
= 8× 5
= 40cm²
Therefore area of the new shape = 40+34
= 74cm²
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The air in a kitchen has a mass of 60.0kg and a specific heat of 1505J/(kg°C).
What is the change in thermal energy of the air when it warms from 24°C to 31°C?
Question 10 options:
30,000J
100,835J
632,100J
90,300J
Answer: D
Step-by-step explanation:
So you have 60kg of air, and the specific heat per kilogram is 1505j/(kg°C), this means you need 1505j to increase 1°C to the temperature of a mass of 1kg of air.
So, if the change in temperature is from 24°C to 31°C, you are increasing 7°C to 60kg of air.
then, for each degree you need 60*1505 j= 90300j
and for 7°c you need 7*90300j = 632100j, wich is answer D.
If you are given odds of 4 to 5 in favor of winning a bet, what is the probability of winning the bet?
Answer:
the probability of winning the bet is 4/9 or approximately 0.444 or 44.44%.
Step-by-step explanation:
To calculate the probability of winning a bet given odds in favor, we can use the following formula:
Probability of winning = Odds in favor / (Odds in favor + Odds against)
In this case, the odds in favor are given as 4 to 5. This means that for every 4 favorable outcomes, there are 5 unfavorable outcomes.
Plugging these values into the formula:
Probability of winning = 4 / (4 + 5)
Probability of winning = 4 / 9
So, the probability of winning the bet is 4/9 or approximately 0.444 or 44.44%.
what is the factor form of the quadratic equation y=x^2-8x-9
Answer:
To factor the quadratic equation y = x^2 - 8x - 9, we need to find two numbers that multiply to give -9 and add to give -8 (the coefficient of the x term).
We can start by looking for two factors of -9 that add up to -8. The only pair of factors that works are -9 and 1. This is because (-9) + 1 = -8, and (-9) times 1 is -9.
Now we can use these factors to express the middle term of the quadratic in terms of two separate terms that can be factored by grouping. We can do this by splitting the -8x term into -9x + x:
y = x^2 - 9x + x - 9
Now we can group the first two terms together and the last two terms together:
y = (x^2 - 9x) + (x - 9)
We can factor out x from the first group, and factor out -9 from the second group:
y = x(x - 9) + (-9)(x - 9)
Finally, we can factor out the common factor of (x - 9):
y = (x - 9)(x - 1)
Therefore, the factor form of the quadratic equation y = x^2 - 8x - 9 is (x - 9)(x - 1).
A fitness expert was doing research on football teams. He randomly selected 10 players from a college team and 10 players from a professional team. The players were weighed and the statistics are shown below. First Quartile Second Quartile (Median) College Professional 190 205 235 255 232 Third Quartile 246 Based on these samples, what generalization can be made? O A. The median weight of the professional players is greater than the median weight of the college players. OB. Not enough information is provided to draw any of these conclusions. OC. The median weight of the college players is greater than the median weight of the professional players. OD. Out of the college and professional players, the professional players have the heaviest player. Reset Submit
Based on these samples, the generalization that can be made is The median weight of the professional players is greater than the median weight of the college players.
Therefore Option A is correct.
What is median weight?The median weight of the ordered data is found when the number that splits the data into two equal parts.
The median weight of the college players is
(215 + 232)/2 = 223.5 pounds.
The median weight of the professional players is
(235 + 255)/2 = 245 pounds.
In conclusion, the median weight of the professional players is greater than the median weight of the college players, so the generalization that can be made is The median weight of the professional players is greater than the median weight of the college players.
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