Answer: Order of operations
Step-by-step explanation:
Plug in 3 for x so...
y = -2(3)² + 12(3) - 15
Don't forget the order of operations, exponents go first
y = -2(9) + 12(3) - 15
Then multiply
y = -18 + 36 - 15
Simplify
y = 3
If of a number is 4 more than of the same number, what is the number?
12
20
24
28
Answer:
please your question is incomplete
Step-by-step explanation:
if....... of a number
Rewrite the Cartesian equation y = 3x^2 as a polar equation. r(θ) = 1/3 tan(θ) sec(θ)
Enter theta for θ if needed.
The Cartesian equation y = 3x^2 as a polar equation can be write as r(θ) = 3 sec(θ) / (1 + tan²(θ)).
To rewrite the Cartesian equation y = 3x² as a polar equation, we need to use the conversion formulas between Cartesian coordinates (x, y) and polar coordinates (r, θ):
x = r cos(θ)
y = r sin(θ)
Substituting these formulas into the Cartesian equation gives us:
r sin(θ) = 3(r cos(θ))²
Dividing both sides by r and rearranging terms gives us:
r = 3 cos²(θ) / sin(θ)
Using the identity 1 + tan²(θ) = sec²(θ), we can rewrite the equation in terms of tan(θ) and sec(θ):
r = 3 (1 / (1 + tan²(θ))) / (1 / sec(θ))
Simplifying gives us the final polar equation:
r(θ) = 3 sec(θ) / (1 + tan²(θ))
Therefore, the Cartesian equation y = 3x²can be rewritten as the polar equation r(θ) = 3 sec(θ) / (1 + tan²(θ)).
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Of the 650 juniors at Jefferson High School, 468 are enrolled in Algebra II, 292 are enrolled in
Physics, and 180 are taking both courses at the same time. If one of the 650 juniors was picked
at random, what is the probability they are taking Physics, if we know they are in Algebra II
(Physics given AII)? Round to the nearest hundredth.
Answer:
0.38
Step-by-step explanation:
I need help pls pls pls pls help quickly.
The length of the diagonal of this square is 11 and option 4 is the correct answer.
What is diagonal?A diagonal line is a line segment that joins two of a shape's vertices when there isn't already an edge between them. It doesn't go directly above, below, or across. The diagonals are always in the form of a straight line. In other terms, a diagonal is a line that passes through the vertex of a polygon or polyhedron and links its opposing corners.
Given that, x is the length of the diagonal of the square.
Also, x² = 132
The value of x is:
x = √132
x = 11.48
Hence, the length of the diagonal of this square is 11 and option 4 is the correct answer.
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At the grocery store Adrian spends $8 on food, plus $4 each for pumpkins. Which statements are true? Choose all that are correct. Responses If Adrian buys 3 pumpkins, his total cost is $12. If Adrian buys 3 pumpkins, his total cost is $12. If Adrian buys 5 pumpkins, his total cost is $44. If Adrian buys 5 pumpkins, his total cost is $44. If Adrian buys 4 pumpkins, his total cost is $24. If Adrian buys 4 pumpkins, his total cost is $24. Adrian’s total cost may be represented as 8+4x . Adrian’s total cost may be represented as 8 + 4 x . Adrian’s total cost may be represented as 4+8x . Adrian’s total cost may be represented as 4 + 8 x . Adrian’s total cost may be represented as 12x .
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
The expression can be expanded as a sum of three logarithms:
[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]
What is the logarithms?
Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.
Using the properties of logarithms, we can expand the expression as follows:
[tex]log4(xy^5 Z^4) = log4(x) + log4(y^5) + log4(Z^4)[/tex]
Now, we can simplify each logarithm using the property that log[tex](a^b[/tex]) = b log(a):
[tex]log4(x) + log4(y^5) + log4(Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]
Hence, the expression can be expanded as a sum of three logarithms:
[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]
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r each equation, determine whether its all symmetries that apply. (a) y^(2)-x+10=0
The equation y^(2)-x+10=0 has no symmetry.
Symmetry is when one part of an equation is the mirror image of another part. In this case, there is no symmetry because the equation cannot be mirrored on any axis.
To check for symmetry with respect to the y-axis, we can replace x with -x and see if the equation is still true. In this case, y^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the y-axis.
Similarly, to check for symmetry with respect to the x-axis, we can replace y with -y and see if the equation is still true. In this case, (-y)^(2)-x+10=0 is not the same as the original equation, so there is no symmetry with respect to the x-axis.
Finally, to check for symmetry with respect to the origin, we can replace x with -x and y with -y and see if the equation is still true. In this case, (-y)^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the origin.
Therefore, the equation y^(2)-x+10=0 has no symmetry.
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Given that tangent theta = negative 1, what is the value of secant theta, for StartFraction 3 pi Over 2 EndFraction less-than theta less-than 2 pi?
Negative StartRoot 2 EndRoot
StartRoot 2 EndRoot
0
1
Answer:
Step-by-step explanation:
Since tangent is negative and is equal to the ratio of opposite over adjacent, we can assume that the angle theta lies in either the third or the fourth quadrant, where the x and y coordinates have opposite signs.
In the third quadrant, sine is positive and cosine is negative. Therefore, we have:
tangent theta = opposite/adjacent = -1
sine theta = opposite/hypotenuse > 0
cosine theta = adjacent/hypotenuse < 0
Using the Pythagorean identity, we have:
sin² theta + cos² theta = 1
=> opposite²/hypotenuse² + adjacent²/hypotenuse² = 1
=> opposite² + adjacent² = hypotenuse²
Since we are given that 3π/2 < theta < 2π, we can place the triangle in the third quadrant with a reference angle of π/2. This means that the opposite side is equal to the absolute value of the adjacent side. Let's assume that the hypotenuse is equal to 1, then we have:
opposite/adjacent = -1
=> opposite = -adjacent
opposite² + adjacent² = hypotenuse²
=> adjacent² + (-adjacent)² = 1
=> 2adjacent² = 1
=> adjacent = ±1/√2
Since cosine is negative in the third quadrant, we have:
cosine theta = adjacent/hypotenuse = -1/√2
Finally, we can use the reciprocal identity to find secant:
secant theta = 1/cosine theta = -√2
Therefore, the answer is A. Negative StartRoot 2 EndRoot.
The value of tangent theta is equal to the negative 1. At this value the value of secant theta is [tex]\sqrt{2}[/tex].
What is tangent theta?The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]
Given information-
The value of tangent theta is equal to the negative 1.
[tex]tan\theta=-1[/tex]
The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]
The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,
[tex]-1=\dfrac{sin\theta}{cos\theta}[/tex]
Simplify it further as,
[tex]-cos\theta=sin\theta[/tex]
When the value of cosine and sine theta is equal, then the angle exist in
4th quadrant with the value of [tex]\dfrac{7\pi }{4}[/tex]. Which extent to the [tex]\sqrt{2}/2[/tex] for the cosine function.
In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,
[tex]\dfrac{1}{sec\theta} =\dfrac{\sqrt{2} }{}[/tex]
[tex]sec\theta=\sqrt{}\dfrac{2}{2}[/tex]
Thus the value of secant theta is [tex]\sqrt{2}[/tex]
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Fraction division Divide. Write your answer in simplest form. (13)/(15)-:(7)/(10)
The answer to 13)/(15)-:(7)/(10) in simplest form is (26)/(21).
To divide the fractions (13)/(15) and (7)/(10), we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of (7)/(10) is (10)/(7).
Now, we can multiply the two fractions as follows:
(13)/(15) * (10)/(7) = (13*10)/(15*7) = (130)/(105)
Next, we need to simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.The GCF of 130 and 105 is 5. So, we can divide both the numerator and denominator by 5 to get the simplest form of the fraction:
(130)/(105) = (130/5)/(105/5) = (26)/(21)
Therefore, the answer in simplest form is (26)/(21).
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120 rupees 5 paise = — ( 120. 50 / 120. 05) rupees
The expression of one hundred twenty rupees and five paise in rupees is equals to the rupees 120.05.
We have, 120 rupees and 5 paise and we will express as rupees using decimals.
We have been given 5 paise. As we see 120 rupees so it's remain as it but we have to change 5 paise in rupees. Using the conversation factor, as we know that 100 paise = rupee 1
=> 1 paisa = Rs. 1/100
so, here conversation factor is = 1/100
The required value is obtained by multiplying the observed values by conversion factor. Therefore,
5 paise = Rs. (5×1/100)
= 5/100
= Rs. 0.05
Therefore, in decimals 5 paise = Rs. 0.05. Now, 120 rupees 5 paise = Rs. 120 + Rs. 0.05 = Rs. 120.05
Hence, required value is Rs. 120.05.
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Complete question:
Express in form of rupees
120 rupees 5 paise = — rupees.
Ms. Volkerson bought 3 yards of
fabric. She used 1 yards to make an
apron. Which is the best estimate of
how many yards of fabric Ms. Volkerson
has now?
Alice drew a scale drawing of a swimming pool. She used the scale 1 centimeter : 4 meters. If the actual length of the pool is 32 meters, how long is the pool in the drawing?
The pool is 0.5 centimeters long in the drawing.
The ratio of 1 centimeter to 4 meters means that for every 4 meters in real life, Alice drew 1 centimeter in her drawing.
To find out how long the pool is in the drawing, we need to divide the actual length of the pool by the scale factor.
The scale factor is 4 meters : 1 centimeter, which is the same as 1 meter : 0.25 centimeters.
So to find the length of the pool in the drawing, we need to divide the actual length of the pool by 4 to get the length in meters, and then multiply by 0.25 to convert to centimeters:
Length in drawing = (32 meters / 4) x 0.25 = 2 x 0.25 = 0.5 centimeters
Therefore, the pool is 0.5 centimeters long in the drawing.
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During the summer, Olympic swimmer Adam Johnson swims every day. On sunny summer days, he goes to an outdoor pool, where he may swim for no charge. On rainy days, he must go to a domed pool. At the beginning of the summer, he has the option of purchasing a $15 season pass to the domed pool, which allows him use for the entire summer. If he doesn't buy the season pass, he must pay $1 each time he goes there. Past meteorological records indicate that there is a 60% chance that the summer will be sunny (in which case there is an average of 6 rainy days during the summer) and a 40% chance the summer will be rainy (an average of 30 rainy days during the summer).
Before the summer begins, Adam has the option of purchasing a long-range weather forecast for $1. The forecast predicts a sunny summer 80% of the time and a rainy summer 20% of the time. If the forecast predicts a sunny summer, there is a 70% chance that the summer will actually be sunny. If the forecast predicts a rainy summer, there is an 80% chance that the summer will actually be rainy. Assuming that Adam's goal is to minimize his total expected cost for the summer, what should he do? Also find EVSI and EVPI
Adam should purchase the long-range weather forecast for $1. By doing so, he will have the best chance of minimizing his total expected cost for the summer.
The expected value of the sample information (EVSI) is the expected cost if Adam does not purchase the forecast and goes with the meteorological records, which is $16.6 ($15 for the season pass plus an average of $1.6 per rainy day).
The expected value of perfect information (EVPI) is the expected cost if Adam purchases the forecast and uses it to make the decision, which is $15.6 ($15 for the season pass plus an average of $0.6 per rainy day).
Thus, purchasing the long-range weather forecast is the best decision for Adam, as it will save him $1 in expected costs and allow him to minimize his total expected cost for the summer.
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Find the value of x if the 8th term of the expansion of
(x^3+1)^12 is equal to 25952256
a. 2
b. 4
c. 6
d. 3
The value of x is if the 8th term of the expansion of given equation is equal to 25952256 = 2. The correct answer is option a.
In order to find the value of x, we first need to find the 8th term of the expansion of [tex](x^3 + 1)^12.[/tex] Using the binomial theorem, the general term in the expansion is given by: [tex]T(k) = C(n, k-1) * (x^3)^(n-k+1) * 1^(k-1).[/tex]where T(k) is the kth term, n is the power (in this case, 12), C(n, k-1) represents the binomial coefficient [tex](n! / [(k-1)! * (n-k+1)!]),[/tex] and x^3 is the term in the expansion.
Now, we plug in the values to find the 8th term: [tex]T(8) = C(12, 7) * (x^3)^(12-7+1) * 1^7, T(8) = 792 * (x^3)^6.[/tex] We are given that the 8th term of the expansion is equal to 25952256. So, 25952256 = 792 * (x^3)^6
Now, we need to solve for [tex]x: (25952256 / 792) = (x^3)^6, 32768 = (x^3)^6[/tex]
Taking the 6th root of both sides, we get:
[tex]x^3 = 2[/tex]
Now, taking the cube root of both sides, we find the value of x:
x = 2 (option a). The correct answer is option a.
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The graph and the table show the high temperatures in a city over a 10-day period.
a. What was the high temperature on Day 7?
b. On which days was the high temperature 61 degrees?
c. Is the high temperature a function of the day? Explain how you know.
d. Is the day a function of the high temperature? Explain how you know.
The graph and the table show the high temperatures in a city over a 10-day period. here are the right answer:
a. 60, b. 2, 4, and 6 days
c. Yes, the high temperature is a function of the day.
Reading the graph:The following group is shows a the high temperatures in a city for 10 -days. Where height temperature is on day 9, lowest temparature in day 7. Here the high temperature is a function of the day.
Here we have
The graph and the table show the high temperatures in a city for 10-days
From the table,
The high temperature on Day 7 = 60
The high temperature 61 degrees on 2, 4, and 6 days
Since the graph shows the change in temperature as well as the change in the number of days the high temperature is a function of the day
Therefore,
The answer are
a. 60, b. 2, 4, and 6 days
c. Yes, the high temperature is a function of the day.
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write a point slope form equation of the line that passes through the point (1, 7) with the slope 3/5
Answer:
y - 7 = 3/5 (x - 1)
Write the function in standard form and determine the end behavior. Be sure to use limit notation. 7. f(x)=-4 x^{3}-10 x^{12}+13 x) 8. ( f(x)=8 x^{21}-5 x^{2}+13 x ) 9. ( f(x)=x^{32}-10 x^{14}
The function in standard form of f(x)=-4 x³-10 x¹²+13 is f(x)=-10 x¹²-4 x³+13 x. The function in standard form of f(x)=8 x²¹-5 x²+13 x ) is f(x)=8 x²¹-5 x²+13 x. The function in standard form of ( f(x)=x^³²-10 x¹⁴ is f(x)=8 x²¹-5 x²+13 x
7. To determine the end behavior, we look at the highest degree term, which is -10 x^{12}. As x approaches positive infinity, -10 x^{12} will approach negative infinity. As x approaches negative infinity, -10 x^{12} will approach positive infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = -∞
lim_{x→-∞} f(x) = ∞
8. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is 8 x^{21}. As x approaches positive infinity, 8 x^{21} will approach positive infinity. As x approaches negative infinity, 8 x^{21} will approach negative infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = ∞
lim_{x→-∞} f(x) = -∞
9. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is x^{32}. As x approaches positive infinity, x^{32} will approach positive infinity. As x approaches negative infinity, x^{32} will approach positive infinity. Therefore, the end behavior is:
limx→∞ f(x) = ∞
limx→∞f(x) = +∞
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Pls answer need it ASAP
Answer:
a = 13.3
Step-by-step explanation:
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
c^2 = a^2 + b^2
15^2 = a^2 + b^2
a^2 = 15^2 - 7^2 = 225 - 49 = 176
a = √176 = 13.26 = 13.3
Express the following permutations as products of cyclic permutations S_(10)=([1,2,3,4,5,6,7,8,9,10],[4,6,9,5,10,2,8,3,7,1])
The given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).
The given permutations can be expressed as products of cyclic permutations as follows:
S10 = ([1,2,3,4,5,6,7,8,9,10],[4,6,9,5,10,2,8,3,7,1])
= (1 4 5 10)(2 6)(3 9 7 8)(7 8 3 9)
= (1 4)(4 5)(5 10)(2 6)(3 9)(9 7)(7 8)(8 3)
= (1 4 5 10)(2 6)(3 9 7 8)
Therefore, the given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).
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95/56 and 2 5/7 correct symbol
The correct symbol in the expression is 95/56 < 2 5/7
How to determine the correct symbolFrom the question, we have the following parameters that can be used in our computation:
95/56 and 2 5/7
Convert the improper number to a mixed number
So, we have the following representation
1 39/56 and 2 5/7
By comparison;
1 39/56 is less than 2 5/7
So, the inequality symbol is a less than inequality
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The original price of a polo shirt is $20. How much will Bert pay if he buys it during the sale?
Answer:
We would need to know the percentage of discount offered during the sale to determine the sale price of the polo shirt. Here's an example calculation for a 25% discount:
If the discount offered is 25%, Bert will only need to pay 75% of the original price. We can calculate this as:
Sale price = (100% - 25%) x $20
Sale price = 75% x $20
Sale price = 0.75 x $20
Sale price = $15
Therefore, if the discount offered during the sale is 25%, Bert will pay $15 for the polo shirt. However, if the discount is different, the sale price will be different.
Mr. Cortez is comparing the cost to join two different gyms. Gym A charges a $55 registration fee plus $24 per month . Gym B does not charge a registration fee but charges $35 per month. At what number of months will the cost be the same for both gyms?
Mr. Cortez is comparing the cost to join two different gyms. Gym A charges a $55 registration fee plus $24 per month. Gym B does not charge a registration fee but charges $35 per month. The cost will be the same for both gyms on the 5 months.
What is gym?
A gymnasium or gym is a place where people can exercise indoors. The word is a translation of "gymnasium," which is Greek. They are typically seen in athletic and fitness facilities, in addition to acting as activity and learning spaces in educational institutions. Gym is slang for "fitness centre," which is often a location for indoor entertainment.
Given,
Gym A charges a $55 registration fee and $24 per month
Total charges after 5 months with registration fee= (24*5+55)= $175
Gym B charges $35 per month
Total charges after 5 months= 35*5= $175
Hence the correct answer is the cost will be the same for both gyms on the 5 months.
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use the point-slope form to write the equation of a line that passes through the point (17,-12) with slope -3
The equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.
Explain about the point-slope form?Write the equation of a line with only a slope of 3 and then a y-intercept of 6 on a graph. Observe how Scenario A provides us with sufficient details straight away to formulate the equation in the form y=mx+b since we already understand the slope, m, and y-intercept, b. Here is how the equation can be expressed: y=3x+6equation of a line using point-slope form is-
y - y1 = m(x - x1)
Points: (17,-12) and slope -3.
Put the values:
y - (-12) = -3(x - 17)
y + 12 = -3x + 51
y = -3x + 51 - 12
y = -3x + 39
Thus, the equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.
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Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
Answer:
Step-by-step explanation:
it's -4.89279003
Solve the system of equation using the method of choice. Show work and steps.
10x+5y=-20
-4x+6y=-8
Answer:
Step-by-step explanation:
1
I need help im stuck (image attach)
Answer:
∠e = 32°
∠d = 69°
∠f = 79°
Step-by-step explanation:
Angle e and 32° are vertical angles, so this means that ∠e = 32° because vertical angles are congruent.
Next, a straight line is equal to 180°, and angle e is equal to 32°, so we can write the following equation to solve for angle f:
69° + e + f = 180° ➜ 69° + 32° + f = 180° ➜ 101° + f = 180° ➜ f = 79°
Lastly, angle d and 69° are also vertical angles, so this means that ∠d = 69° because vertical angles are congruent.
Andrew Albring purchases an inflatable shark for $12.99, 8 gallons of chlorine at $1.99 each, 2 gallons of
algaecide at $7.99 each, 1 thermometer for $12.99, and 2 sets of fins at $22.99 each. If the sales tax rate
is 7.5%, what is the total purchase price?
A)$63.37
B)$86.94
C)$111.13
D)$111.65
Option D is correct, the total purchase price is $111.65.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Lets find the price of each item
Inflatable shark: $12.99
8 gallons of chlorine at $1.99 each: 8 x $1.99 = $15.92
2 gallons of algaecide at $7.99 each: 2 x $7.99 = $15.98
1 thermometer for $12.99: $12.99
2 sets of fins at $22.99 each: 2 x $22.99 = $45.98
Now add the costs of all the items:
$12.99 + $15.92 + $15.98 + $12.99 + $45.98 = $103.86
we multiply the total cost by the tax rate to find the sales tax.
$103.86 x 0.075 = $7.79
Finally, we add the sales tax to the total cost to get the final purchase price:
$103.86 + $7.79 = $111.65
Therefore, the total purchase price is $111.65.Option D is correct.
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Mrs Shepard rode her bike 5. 25 miles in 0. 7 hours how fast was she going in miles per hour
Mrs Sheperd was going 7.5 miles per hour
Let us assume that d represents the distance covered by Mrs Shepard, 't' represents the time required and 's' represents the speed of her bike.
Here, d = 5.25 miles
t = 0.7 hours
We know that the formula of speed is speed = distance/time
Using this formula we calculate the speed (s) of Mrs Shepard's bike.
speed = distance/time
⇒ s = d/t
⇒ s = 5.25/0.7
⇒s = 7.5 miles per hour
This means that the speed (s) of Mrs Shepard's bike was 7.5 miles per hour
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Complete the square to find the standard form for this circle:
x²-10x + y²+14y-7=0
A. (x+5)²+(y-7)² = 81
B. (x+5)²+(y+7)² = 9
C. (x-5)²+(y-7)² = 9
D. (x-5)²+(y+7)² = 81
The standard form for the circle x² - 10x + y² + 14y - 7 = 0 is (x - 5)² + (y + 7)² = 81. The correct answer is D.
To find the standard form of the given circle, we must complete the square by rearranging the equation and adding constants to both sides of the equation to create perfect squares. Here are the steps:
1. Rearrange the equation so that the x and y terms are together:
x² - 10x + y² + 14y = 7
2. Complete the square for the x terms by adding (10/2)² = 25 to both sides of the equation:
x² - 10x + 25 + y² + 14y = 7 + 25
3. Complete the square for the y terms by adding (14/2)² = 49 to both sides of the equation:
x² - 10x + 25 + y² + 14y + 49 = 7 + 25 + 49
4. Simplify the equation by factoring the perfect squares:
(x² - 10x + 25) + (y² + 14y + 49) = 7 + 25 + 49
(x - 5)² + (y + 7)² = 81
So, the standard form for this circle is (x - 5)² + (y + 7)² = 81, which is option D.
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2. A package of paper is 2" high and 1.5" wide. If a warehouse shelf is 1' 5" high and 2 yards
long, how many packages of paper can be put on the shelf?
Therefore, approximately 408 packages of paper can be put on the shelf.
What is area?Area is a measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units such as square meters, square inches, or square feet. The area of a shape can be found by multiplying the length of the shape by its width. The concept of area is used in many areas of mathematics and in a wide range of real-world applications, including architecture, engineering, physics, and geography. The ability to calculate the area of a shape is an important skill in many fields and is a fundamental concept in geometry.
Here,
To solve this problem, we need to find the number of packages of paper that can fit on the warehouse shelf by dividing the total shelf area by the area of each package.
First, we need to convert the height of the shelf from feet and inches to inches:
1 foot = 12 inches
1' 5" = 1 * 12 + 5 = 17 inches
Next, we need to convert the length of the shelf from yards to inches:
1 yard = 36 inches
2 yards = 2 * 36 = 72 inches
Now we can find the area of the warehouse shelf:
Area = length * height
Area = 72 inches * 17 inches
Area = 1224 square inches
The area of each package of paper is:
Area = height * width
Area = 2 inches * 1.5 inches
Area = 3 square inches
Now we can find the number of packages of paper that can fit on the warehouse shelf:
Number of packages = Shelf area / Package area
Number of packages = 1224 square inches / 3 square inches
Number of packages ≈ 408
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