0.225 can be expressed as the fraction 1/200.
To convert 0.225 to a fraction, we need to understand the place value of each digit. In this case, the digit 2 is in the hundredths place (2/100), the digit 2 is in the thousandths place (2/1000), and the digit 5 is in the ten-thousandths place (5/10000).
Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 2, 100, 1000, and 10000 is 2.
Now, we divide both the numerator and denominator by 2 to simplify the fraction. The numerator becomes 1 (2 divided by 2) and the denominator becomes 5000 (10000 divided by 2).
Further simplification is possible by dividing both the numerator and denominator by 5. The numerator becomes 1 (1 divided by 1) and the denominator becomes 1000 (5000 divided by 5).
Again, we can divide both the numerator and denominator by 5. The numerator remains 1 and the denominator becomes 200 (1000 divided by 5).
Therefore, 0.225 can be expressed as the fraction 1/200.
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Determine the equation of the ellipse with foci... 100points
The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is[tex](x^2/289) + (y^2/225) = 1.[/tex]
To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.
In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.
Now we have the values of a and b, so we can substitute them into the standard form equation:
[tex](x^2/17^2) + (y^2/15^2) = 1[/tex]
Simplifying further, we have:
[tex](x^2/289) + (y^2/225) = 1[/tex]
Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:
[tex](x^2/289) + (y^2/225) = 1.[/tex]
This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.
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Answer:
The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is
To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:
where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.
In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.
Now we have the values of a and b, so we can substitute them into the standard form equation:
Simplifying further, we have:
Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:
This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.
What is the average rate of change in f(x) on the interval [5,9]?
A)-1.5
B)6/4
C)4
D)-6
Answer:
A) -1.5
Step-by-step explanation:
We can find the average rate of change of a function over an interval using the formula:
(f(x2) - f(x1)) / (x2 - x1), where
(x2, f(x2)) is the rightmost part of the interval. In this problem, 9 is our x2 and f(x2) is 3 since 3 is the y-coordinate when you plug in 9 for f(x))(x1, f(x1)) is the leftmost part of the interval of the interval.In this case, 5 is our x1 and f(x1) is 9 since 9 is the y-coordinate when you plug in 5 for f(x).Thus, we can plug in (9, 3) for (x2, f(x2)) and (5, 9) for (x1, f(x1)) to find the average rate of change in f(x) on the interval [5,9].
(3 - 9) / (9 - 5)
(-6) / (4)
-3/2
is -3/2.
If we convert -3/2 into a normal number, we get -1.5
Thus, the average rate of change in f(x) on the interval [5,9] is -1.5
Answer:
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
In this case, we need to find the average rate of change on the interval [5, 9], so a = 5 and b = 9.
From inspection of the given graph:
f(5) = 9f(9) = 3Substitute the values into the formula:
[tex]\textsf{Average rate of change}=\dfrac{f(9)-f(5)}{9-5}=\dfrac{3-9}{9-5}=\dfrac{-6}{4}=-1.5[/tex]
Therefore, the average rate of change of f(x) over the interval [5, 9] is -1.5.
An English teacher counted the number of misspelled words in a 1000-word essay he assigned to his students. From a group of 49 students, the mean number of misspelled words was 9.1. The distribution of the student population is normal with a variance of 12.25. What is a confidence interval for the mean number of misspelled words in the student population, considering a confidence level of 99.7%? (Use 3 for the Z value in the formula below)
Answer:
C. [7.6, 10.6]
Step-by-step explanation:
To calculate the confidence interval for the mean number of misspelled words in the student population, we can use the confidence interval formula:
[tex]\boxed{CI=\overline{x}\pm z\left(\dfrac{s}{\sqrt{n}}\right)}[/tex]
where:
[tex]\overline{x}[/tex] is the sample mean.z is the confidence level value.s is the sample standard deviation.n is the sample size.Given values:
[tex]\text{Mean}\;\overline{x} = 9.1[/tex][tex]\text{Variance}\;s^2=12.25[/tex][tex]\text{Sample size}\;n=49[/tex]The standard deviation is the square root of the variance:
[tex]s=\sqrt{s^2}=\sqrt{12.25}=3.5[/tex]
The empirical rule states that approximately 99.7% of the data points will fall within three standard deviations of the mean.
Therefore, z-value for a 99.7% confidence level is z = 3.
Substituting these values into the formula, we get:
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{\sqrt{49}}\right)[/tex]
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{7}\right)[/tex]
[tex]CI=9.1\pm 3\left(0.5\right)[/tex]
[tex]CI=9.1\pm 1.5[/tex]
Therefore, the 99.7% confidence limits are:
[tex]CI=9.1-1.5=7.6[/tex]
[tex]CI=9.1+1.5=10.6[/tex]
Therefore, the confidence interval for the mean number of misspelled words in the student population is [7.6, 10.6].
A dime is flipped, and a single die is rolled. Find the odds against obtaining a head.
Answer:
11 : 1
Step-by-step explanation:
The probability of obtaining a head when a dime is flipped is 1/2, since there are two possible outcomes (heads or tails) and each is equally likely.
The probability of rolling any particular number on a fair six-sided die is 1/6, since there are six equally likely outcomes (the numbers 1 through 6).
To find the odds against obtaining a head and rolling any number on the die, we need to multiply the probabilities of the two events. This gives us
(1/2) x (1/6) = 1/12
So the probability of obtaining a head and rolling any number on the die is 1/12.
To find the odds against this event, we need to compare the probability of the event happening to the probability of it not happening. The probability of the event not happening is 1 - 1/12 = 11/12.
Therefore, the odds against obtaining a head and rolling any number on the die are:
11 : 1
. Calculez P(5) sachant que P(x) = x3 − 5x2 − 2x + 7.
Answer:
P(5) = - 3
Step-by-step explanation:
to evaluate P(5) substitute x = 5 into P(x)
P(5) = (5)³ - 5(5)² - 2(5) + 7
= 125 - 5(25) - 10 + 7
= 125 - 125 - 3
= 0 - 3
= - 3
Given the sequence 9/8, 3/4, 1/2,...,8/81 is the geometric sequence. Find the common ratio and the number of all terms of this sequence.
Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
As we know that,
Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.
So, r= (n+1)th term / nth term
where r ⇒ common ratio
(n+1)th term⇒ succeeding term
nth term⇒ preceding term
According to the given question, r = (9/8) / (3/4)
r = (2/3)
We also know,
Any term of a G.P. [nth term] can be obtained by the formula:
Tₙ= a[tex]r^{n-1}[/tex]
where, Tₙ= nth term
a= first term of G.P.
r=common ratio
Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.
Tₙ= a[tex]r^{n-1}[/tex]
⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])
⇒ (64/729)= ([tex]2/3^{n-1}[/tex])
⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])
⇒ n-1 = 6
⇒ n = 7
∴ The total number of terms in G.P. is 7.
Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.
Explanation:The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.
So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.
To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.
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Given that P(A)=0.450 and P(B)=0.680 and P( A U B)=0.824. Find the probability
The probability of the union of events A and B, P(A U B), is 0.824.
To find the probability, we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Given that P(A) = 0.450, P(B) = 0.680, and P(A U B) = 0.824, we can substitute these values into the formula:
0.824 = 0.450 + 0.680 - P(A ∩ B)
To find the probability of the intersection of events A and B (P(A ∩ B)), we rearrange the equation:
P(A ∩ B) = 0.450 + 0.680 - 0.824
P(A ∩ B) = 1.130 - 0.824
P(A ∩ B) = 0.306
Therefore, the probability of the intersection of events A and B, P(A ∩ B), is 0.306.
We can also calculate the probability of the union of events A and B, P(A U B), by substituting the given values into the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A U B) = 0.450 + 0.680 - 0.306
P(A U B) = 0.824
Therefore, the probability of the union of events A and B, P(A U B), is 0.824.
In summary, we have found that the probability of the intersection of events A and B, P(A ∩ B), is 0.306, and the probability of the union of events A and B, P(A U B), is 0.824, based on the given probabilities.
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The better definition of Intersection is:
OA system that has at least one solution.
O Where lines cross over each other. The lines have a common point.
OA value we can put in place of a variable (such as x) that makes the equation true.
OA system that has no solutions.
Answer:
Where lines cross over each other. The lines have a common point.
Find the perimeter of the following square and the area of the shaded part if the radius of the
circle is 12 cm.
The perimeter of the square and the area of the shaded part are 48cm and 454.16cm² respectively²
How to determine the valueThe formula for calculating the area of a circle is expressed as;
Area = πr²
Now, substitute the value, we have;
Area = 3.14 × 12²
Find the square and multiply the values, we have;
Area = 3.14(144)
Multiply the values
Area = 452. 16 cm²
Perimeter of a square take the formula;
Perimeter = 4a
Substitute the value
Perimeter = 4(12) = 48 cm
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So i'm doing this Equation and it told me to use the values below, bit I'm so confused on how to do it can some of y'all help me out?
Part A: solve the equation---
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
Part B: use the values
x= -0.5, 0, 1
Answer:
when substituting x = -0.5, 0, and 1 into the equation, we get the results -8, -7, and -5, respectively.
Step-by-step explanation:
Part A:
To solve the equation 5 + x - 12 = 2x - 7, follow these steps:
Combine like terms on each side of the equation:
-7 + 5 + x - 12 = 2x - 7
-14 + x = 2x - 7
Simplify the equation by moving all terms containing x to one side:
x - 2x = -7 + 14
-x = 7
To isolate x, multiply both sides of the equation by -1:
(-1)(-x) = (-1)(7)
x = -7
Therefore, the solution to the equation is x = -7.
Part B:
Now let's substitute the given values of x and evaluate the equation:
For x = -0.5:
5 + (-0.5) - 12 = 2(-0.5) - 7
4.5 = -1 - 7
4.5 = -8
For x = 0:
5 + 0 - 12 = 2(0) - 7
-7 = -7
For x = 1:
5 + 1 - 12 = 2(1) - 7
-6 = -5
1. The difference of two supplementary angles is 70° which is the larger angle?
A/ 135° B/145 C/55 D/125°
1. The difference of two supplementary angles is 70° which is the larger angle?
A/ 135°
B/145
C/55
D/125° ✓Let the numbers be x and x-70 we know that,sum of two supplimentary angles = 180°x+x-70=180°2x-70=180°2x=180°+70°2x=250°x=125°and x-70°= 125°-70° = 55° hence,the larger angle is 125°Consider the equation: 0=x^(2)+4x+1 Rewrite the equation by completing the square. Your equation should look like (x+c)^(2)=d or (x-c)^(2)=d.
The equation after completing the square is (x+2)²=3. Consider the equation: 0=x²+4x+1. To rewrite the equation by completing the square, we need to complete the square by adding and subtracting the square of half of the coefficient of the x.
Let's see how to complete the square: 0 = x² + 4x + 1(1)
We'll take the constant term (1) to the right-hand side of the equation, so it becomes negative. 0 = x² + 4x - 1(2)
To complete the square, we add and subtract the square of half of the coefficient of x. (a) Half of the coefficient of x is 4/2 = 2.
(b) We'll add and subtract 2² = 4. 0 = x² + 4x + 4 - 4 - 1(3)
The first three terms can be expressed as the square of the quantity x+2: (x+2)² = 0 + 4 - 1(4)This simplifies to: (x+2)² = 3
Thus, the equation after completing the square is (x+2)²=3.
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GEOMETRY 100POINTSSS
Find x
Answer:
5.9
Step-by-step explanation:
sin Θ = opp/hyp
sin 36° = x/10
x = 10 × sin 36°
x = 5.88
Answer: 5.9
Cual es la velocidad de un auto que recorre 10800m en 560s?
Which set of ordered pairs represents a function?
O {(6,-8), (2,-2), (6, -1), (8, -7)}
O {(-7,-8), (-3,9), (7,4), (-1,4)}
O {(1, -2), (-6, 2), (5,0), (1,6)}
{(3,8), (3, 6), (8,-6), (1, -7)}
Submit Answer
Answer:
{(-7, -8), (-3, 9), (7, 4), (-1, 4)} represents a function.
seven more than a certain number is nin nine less than twice the number. find the number.
Answer:
number is 16
Step-by-step explanation:
let n be the number , then 7 more than the number is n + 7 and 9 less than twice the number is 2n - 9
equating the 2 expressions
2n - 9 = n + 7 ( subtract n from both sides )
n - 9 = 7 ( add 9 to both sides )
n = 16
the required number is 16
The answer is:
n = 16Work/explanation:
Let's call the number n.
Seven more than n = n + 7
Nine less than twice n = 2n - 9
Put the expressions together : n + 7 = 2n - 9
Now, we have an equation that we can solve for n.
First, flop the equation
2n - 9 = n + 7
Subtract n from each side
n - 9 = 7
Add 9 to each side
n = 16
Therefore, n = 16.The graph of a function h (x) is shown.
What is the average rate of change of h(x) over the interval [4, 8]?
A)-6
B)-2
C)-32
D)-23
Answer:
[tex]\textsf{C)} \quad -\dfrac{3}{2}[/tex]
Step-by-step explanation:
To find the average rate of change of a function over an interval, we can use the formula:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]
In this case, the interval is [4, 8], so:
a = 4b = 8From inspection of the given graph:
h(a) = h(4) = 9h(b) = h(8) = 3Substitute the values into the formula to calculate the average rate of change:
[tex]\begin{aligned}\text{Average rate of change}&=\dfrac{h(8)-h(4)}{8-4}\\\\&=\dfrac{3-9}{8-4}\\\\&=\dfrac{-6}{4}\\\\&=-\dfrac{3}{2}\end{aligned}[/tex]
Therefore, the average rate of change of h(x) over the interval [4, 8] is -3/2.
Which scatter diagram fits the given paired data
Systolic Blood Pressure
Diastolic Blood Pressure
119 125
76
84
131 130 123 118 142
91
84
89
76
91
138 125 131 128 140 123
93 78 88 75 94 76
the correct scatter diagram that fits the given paired data is option A, as shown in the attached image.
The scatter plot that fits the given paired data is as follows:
Firstly, the data needs to be paired correctly: Systolic Blood Pressure | Diastolic Blood Pressure119 125131 130123 118118 142138 125131 128140 123Then the data pairs are plotted on a graph to create a scatter plot. It is a graph that shows the relationship between two sets of data. In this case, the Systolic blood pressure is on the horizontal axis (X-axis) and the Diastolic blood pressure is on the vertical axis (Y-axis).
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HELP I WILL MARK BRAINLIEST AND GIVE 30 POINTS
The points A, B and C have position vectors a, b, c, referred to an origin O. i. Given that the point X lies on AB produced so that AB : BX = 2 : 1, find x, the position vector of X, in terms of a and b. ii. If Y lies on BC, between B and C so that BY : Y C = 1 : 3, find y, the position vector of Y, in terms of a and b iii. Given that Z is the midpoint of AC, Calculate the ratio XY : Y Z.
i. The position vector of X is 2b - a.
ii. The position vector of Y is (3b + c)/4.
iii. The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.
i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.
ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.
iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].
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amar is a unmarried newly secondary class joint secretary of minister of finance. his monthly salary with dearness allowance is Rs 58,786. he gets one month salary for expense of festival at once. 10% of his monthly salary deposited in employee's provident fund (EPF) and Rs 3,300 in life insurance in each month.the government deposits the same EPF amount in the fund
1) find his yearly income assessable income
2) find taxable income of amar
3) how much income tax does he pay in total? find it
The correct answer is Yearly income assessable income: Rs 7,75,974
Taxable income of Amar: Rs 7,66,796
To find Amar's yearly income, we'll consider his monthly salary and additional benefits:
Yearly Income:
Monthly salary = Rs 58,786
Yearly salary = Monthly salary * 12 = Rs 58,786 * 12 = Rs 7,05,432
Additional benefits:
One month salary for festival expense = Rs 58,786
EPF contribution per month (deducted from salary) = 10% of monthly salary = 0.10 * Rs 58,786 = Rs 5,878
Government's EPF contribution = Rs 5,878
Total additional benefits per year = One month salary + EPF contribution + Government's EPF contribution = Rs 58,786 + Rs 5,878 + Rs 5,878 = Rs 70,542
Yearly income assessable income = Yearly salary + Total additional benefits = Rs 7,05,432 + Rs 70,542 = Rs 7,75,974
Taxable Income:
To calculate the taxable income, we deduct certain deductions from the assessable income.
Deductions:
EPF contribution per month (deducted from salary) = Rs 5,878
Life insurance per month = Rs 3,300
Total deductions per year = EPF contribution + Life insurance = Rs 5,878 + Rs 3,300 = Rs 9,178
Taxable income = Assessable income - Total deductions = Rs 7,75,974 - Rs 9,178 = Rs 7,66,796
Income Tax:
To determine the income tax paid, we need to apply the applicable tax rate to the taxable income. Since tax rates can vary based on the country and specific rules, I am unable to provide the exact income tax amount without additional information.
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how to find surfes area
Remember to use the appropriate units for measurements when calculating surface area.
To find the surface area of an object, you need to calculate the total area of all its exposed surfaces. The method for finding the surface area will vary depending on the shape of the object. Here are some common shapes and their respective formulas:
1. Cube: The surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 since a cube has six equal faces. The formula is: SA = 6s^2, where s is the length of a side.
2. Rectangular Prism: A rectangular prism has six faces, each of which is a rectangle. To find the surface area, calculate the area of each face and add them up. The formula is: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.
3. Cylinder: The surface area of a cylinder includes the area of two circular bases and the area of the curved side. The formula is: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.
4. Sphere: The surface area of a sphere can be found using the formula: SA = 4πr^2, where r is the radius.
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Can someone help me, please???
Given: AB || DC and m22=m24
Prove: AD || BC
D
4
2
1. AB||DC
2. m22-m24
B
Statements
3
3. 21 and 24 are supplements
4. ?
5. m21+m22-180°
6. 21 and 22 are supplements
7. AD BC
Reasons
1. given
2. given
3. same side interior angles thm.
4. def. of supplementary angles
5. substitution
def. of supplementary angles
converse same side interior angles thm
6.
7.
The missing statement 4 of the two column proof of AD ║ BC is:
Statement 4: m∠1 + m∠4 = 180°
How to complete the two column proof?The complete two column proof to show that AD || BC is as follows:
Statement 1: AD ║ DC
Reason 1: Given
Statement 2: m∠2 = m∠4
Reason 2: Given
Statement 3: ∠1 and ∠3 are supplements
Reason 3: Same side interior angles theorem
Statement 4: m∠1 + m∠4 = 180°
Reason 4: Def. of Supplementary angles
Statement 5: m∠1 + m∠2 = 180°
Reason 5: Substitution
Statement 6: ∠1 and ∠2 are supplements
Reason 6: Def. of Supplementary angles
Statement 7: AD ║ BC
Reason 7: Converse same side interior angles thm
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Question 8 of 10
How does the graph of f (x) = 3 (4)2-5 + 3 relate to its parent function?
A. The parent function has been 'stretched.
B. The parent function has been translated to the right.
C. The parent function has been translated up.
D. The parent function has been compressed.
Answer:
The correct answer is D. The graph of f(x) = 3(4)² - 5 + 3 is a transformation of the parent function. The parent function is y = x², which is a simple quadratic function.
In the given equation, the number 4 inside the parentheses represents a horizontal compression or shrink of the graph. The factor of 3 outside the parentheses represents a vertical stretch or expansion. The constant term -5 represents a vertical translation down by 5 units, and the constant term 3 represents a vertical translation up by 3 units.
Therefore, the graph of f(x) = 3(4)² - 5 + 3 is a compressed version of the parent function y = x², shifted down by 5 units and then shifted up by 3 units.
the peterson family and the stewart family each used their sprinklers last summer. the water output rate for the peterson family’s sprinkler was 35 L per hour. the water output rate for the stewart family’s sprinkler was 40 L per hour. the families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1,650 L. how long was each sprinkler used?
The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.
The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.
Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).
According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:
35x + 40(45 - x) = 1,650.
Simplifying the equation, we get:
35x + 1,800 - 40x = 1,650,
-5x = 1,650 - 1,800,
-5x = -150.
Dividing both sides of the equation by -5, we find:
x = -150 / -5 = 30.
So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.
Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
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pleasee help so disssicult
When going from left to right, the item goes up, it increases, and when it goes down, it decreases
The height h(x), of an object is given by the function h(x) = -16x + 176x + 65
where x is time in seconds and h(x) is height in feet. When does the object reach its maximum height? Round your answer to two decimal places.
To find an object's maximum height, we need to find the vertex of this quadratic equation.
Answer: 5.50 seconds
Terms to know:
Quadratic function: A quadratic function is a polynomial function of degree 2, which means the highest power of the variable in the equation is 2.
Vertex: The vertex of a quadratic function is the point on the graph where the function reaches its highest or lowest point. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex is given by the coordinates (x, f(x)).
Step-by-step explanation:
The vertex of a quadratic equation can be represented as [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]
Since we only are looking at the time it takes to reach maximum height we will only look at the x value.
[tex]x= \frac{-176}{2(-16)}[/tex]
[tex]x= 5.50[/tex]
Evaluate leaving your answer in a standard form 0.0048*0.81 /0.027*0.04
Step-by-step explanation:
When we simplify the expression, we get:
0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)
Using a calculator to evaluate the two fractions separately, we get:
0.0048 / 0.027 ≈ 0.1778
0.81 / 0.04 = 20.25
Substituting these values back into the original expression, we get:
(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25
Multiplying these two values together, we get:
0.1778 * 20.25 ≈ 3.59715
To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:
3.59715 ≈ 3.59715 × 10^(-3)
Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).
f(x)=-4x+7 and g(x)=x^3 choose the expression for (fog)(x)
Answer:
(fog)(x) = -4x^3 + 7.
Step-by-step explanation:
We can think of (f o g)(x) as f(g(x)). This shows that we plug in the entire g(x) function for x in f(x) and simplify:
f(x^3) = -4(x^3) + 7
f(x^3) = -4x^3 + 7
Thus, (f o g)(x) = -4x^3 + 7
