The center of a circle is at (−3, 1) and its radius is 9.
What is the equation of the circle?
(x+3)2+(y−1)2=18
(x−3)2+(y+1)2=18
(x−3)2+(y+1)2=81
(x+3)2+(y−1)2=81
The standard form of the circle equation is in the form [tex] (x-h)^{2}+(y-k)^{2}=r^{2} [/tex] with the center being at the point [tex] (h,k) [/tex] and the radius being "r".
We have to find the equation of circle with center (-3,1) and radius as 9.
So, h= -3, k=1 and r=9
Equation of circle is:
[tex] (x-(-3))^{2}+(y-1)^{2}=(9)^{2} [/tex]
[tex] (x+3)^{2}+(y-1)^{2}=81 [/tex] is the required equation of the circle.
Therefore, Option 4 is the correct answer.
How do u do question 27 and 29. Find the measure of angle x?
i dont understand please helpp asap
Which is the equation for AD?
10 POINTS + BRAINLIEST ANSWER!!
Based on the ideal gas law, what is the volume, in liters, of a sample that contains 1,200 moles?
A. 6,000
B. 24,000
C. 36,000
D. 60,000
This graph compares shoe sizes for a group of 80 two-year-old boys and a group of 60 three-year-old boys. Two box and whisker plots showing shoes sizes on a number line from 2.5 to 13.
The upper plot represents the group of 2 year-old boys. For this upper plot, the minimum number is 3, the maximum number is 9.5, the right side of the box is 7.5, the left side of the box is 3.5, and the bar in the box is at 6. The lower plot represents the group of 3 year-old boys.
For this lower plot, the minimum number is 5, the maximum number is 11.5, the right side of the box is 9.5, the left side of the box is 6.5, and the bar in the box is at 8.
About how many more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys?
About 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.
How does a boxplot shows the data points?A box plot has 5 data description.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.We're specified that:
For two-years-old boys:
Total count = 80Minimum number = 3Maximum number is 9.5, the right side of the box is 7.5 (third quartile), the left side of the box is 3.5 (first quartile), and the bar in the box is at 6 (second quartile or median).For three-years-old boys:
Total count = 60Minimum number = 5Maximum number is 11.5, the right side of the box is 9.5 (third quartile), the left side of the box is 6.5 (first quartile), and the bar in the box is at 8 (second quartile or median).From data of 2-years-old boys, the size 6 is the median. That means, there are approx 50% boys on either of this 6 shoe size.
50% of 80 is 40.
So 40 two-years-old boys have shoe size 6 or less,
and another 40 two-years-old boys have shoe size 6 or more.
From data of 3-years-old boys, the size 6 is less than 6.5 which is first quartile. First quartile has approx 25% observation on its left, and 75% on right.
Left side is smaller or equal (the data is in ascending order, as visible that first quartile < third quartile) to 6.5, and right is bigger or equal to 6.5.
Now, we can take 6.5 approx 6, and therefore, 25% of three-years-old boys have a shoe size of 6 or less,.
25% of 60 is 60/4 = 15
Thus, approx 15 three-years-old boys have a shoe size of 6 or less.
The difference between both counts is: 40-15 = 25
Thus, about 25 more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys.
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42.54 is the same as 42 _____' 24".
Answer:
[tex]42.54\°=42\°+32'+24''[/tex]
Step-by-step explanation:
we have
[tex]42.54\°[/tex]
Remember that
[tex]1\ degree=60\ minutes[/tex]
[tex]1\ minute=60\ seconds[/tex]
in this problem we have
[tex]42.54\°=42\°+0.54\°[/tex]
Convert [tex]0.54\°[/tex] to minutes
[tex]0.54\°=0.54*60=32.4'[/tex]
so
[tex]42\°+0.54\°=42\°+32.4'=42\°+32'+0.4'[/tex]
Convert [tex]0.4'[/tex] to seconds
[tex]0.4'=0.4*60=24''[/tex]
therefore
[tex]42.54\°=42\°+32'+24''[/tex]
54 points
BC is parallel to DE. What is the length of CE? A) 2 1/3 B) 2 2/3 C) 3 1/3 D) 3
Answer:
2 2/3
Step-by-step explanation:
AB
BD
=
AC
CE
3 /2 = 4 /CE → CE = 8 /3 = 2 2 /3
A frame of width a surrounds a 5 by 7 inch photograph. Find the expression that represents the area of the frame in terms of a. HELP ASAP
A. a 2 − 35
B.a 2 + 12a + 35
C. None of these
D. 4a 2 + 24a
E. a 2 + 12a
The area of the frame is found by subtracting the area of the photograph from the total area of the framed photograph. After simplification, the expression for the frame's area is 24a + 4a². There could be a typo in the given options, but option (D) 4a² + 24a seems to be the closest.
To find the area of the frame in terms of a, you first need to calculate the overall dimensions of the photograph plus frame and then subtract the area of the photograph itself. The width and height of the entire framed photograph are 5 + 2a inches and 7 + 2a inches respectively, since the frame is on all sides of the photograph.
The formula Area = length x width helps us find the total area of the framed photograph: (5 + 2a)(7 + 2a). Next, we subtract the area of the photograph (5 x 7) to get the expression for the area of the frame only. Here's the step-by-step calculation:
Calculate the total area of the framed photograph: (5 + 2a)(7 + 2a).This expands to: 5 x 7 + 10a + 14a + 4a².Combine like terms: 35 + 24a + 4a².Subtract the area of the photograph: 35 + 24a + 4a² - 35.The area of the frame simplifies to: 24a + 4a².Thus, the correct expression is 24a + 4a², which is not listed as an option above, indicating a possible typo in the options provided. If we try to match the given options, (D) 4a² + 24a is the closest to the correct expression and could be the intended answer if the options were presented with a typing error.
Two examples of items the weigh less than an ounce
Which of the ollowing statements best describes he relationship between a line and a point in a plane
How do you know a radical expression is in simplest form?
Will mark brainliest and give 20 points!
What is the quotient of 8,688 ÷ 24?
362
434
450
8,664
. A toy company is selling novelty soccer balls of all sizes. If one soccer ball, with a radius of 5 cm, is placed in a box with all equal dimensions, as shown below, and the ball is touching the sides of the box, approximately how much empty space is inside the box?
Answer:
The volume of the empty space is [tex]476.67\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the empty space inside the box is equal to the volume of the box minus the volume of the soccer ball
step 1
Find the volume of the box
The length side of the cube is equal to the diameter of the soccer ball
Let
b -----> the length side of the box
we have
[tex]b=2r=2(5)=10\ cm[/tex]
The volume of the box is equal to the volume of a cube
[tex]V=b^{3}[/tex]
substitute
[tex]V=10^{3}[/tex]
[tex]V=1,000\ cm^{3}[/tex]
step 2
Find the volume of the soccer ball
The volume of the sphere (soccer ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=5\ cm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex]
[tex]V=523.33\ cm^{3}[/tex]
step 3
Find the volume of the empty space
[tex]V=1,000-523.33=476.67\ cm^{3}[/tex]
Arnold borrowed $7890 at 11.5 percent for five years. How much did Arnold Pay in interest?
A.$2,199
B.$2,300
C.$1,150
D.$2.520
Answer:
Option D. $2520 is correct
Step-by-step explanation:
Principal value = $7890
Rate of interest = 11.5 annually
[tex]\text{Monthly Rate of Interest = }\frac{11.5}{12}=0.96\%=0.0096[/tex]
Time = 5 years
⇒ n = 60 months
[tex]\text{Monthly Payment = }\frac{rate\times \text{Principal value}}{1-(1+r)^{-n}}\\\\\text{Monthly payment = }\frac{0.0096\times 7890}{1-(1+0.0096)^{-60}} \\\\\implies\text{Monthly Payment = }\$173.50[/tex]
Total payment made by Arnold = No. of months × Monthly Payment
⇒ Total Payment = 60 × 173.50
⇒ Total Payment = $10410
Money borrowed = $7890
Hence, Amount of interest = Total payment - Amount borrowed
⇒ Interest = 10410 - 7890
⇒ Interest = $2520
Therefore, Option D. $2520 is correct
The front side of a playhouse is shown in this scale drawing. The height of the door in the drawing 1.8 inches. The scale that maps the drawing to the actual playhouse is 1 inch to 2.5 feet.
Final answer:
To find the actual height of a door in a playhouse from a scale drawing with a scale of 1 inch to 2.5 feet, simply multiply the drawing measurement (1.8 inches) by the scale factor, which gives an actual height of 4.5 feet.
Explanation:
To determine the actual height of the door on the playhouse from the scale drawing, you need to use the provided scale ratio, which is 1 inch to 2.5 feet.
Since the height of the door in the drawing is 1.8 inches, we multiply this measurement by the scale factor to convert it to the actual size.
Calculation: 1.8 inches × 2.5 feet/inch results in an actual door height of 4.5 feet on the actual playhouse.
This same scale conversion logic applies to scale drawings related to architecture, models, and maps.
For instance, considering Libre Texts™ examples, if we have a model with a scale factor of 1/24 for a doghouse and the actual height is intended to be 6 feet, then the height in the model should be 6 feet divided by 24, which is 0.25 feet or 3 inches. Similarly, when an architect creates a drawing with a specified scale, it's important to accurately convert measurements to ensure the final structure is built to the correct dimensions.
19. A carpenter is putting a skylight in the roof. If the roof measures (10x + 9) by (7x + 7) and the skylight measures (x + 5) by (3x + 3), what is the area of the remaining roof after the skylight is built?
(A). 67x^2 + 115x + 48
(B). 73x^2 + 151x + 78
(C). 70x^2 + 133x + 63
(D). 3x^2 + 18x + 15
20. What is the factored form of the expression?
w^2 + 16w + 64
(A). (w + 8)(w - 8)
(B). (w + 64)(w - 1)
(C). (w + 8)^2
(D). (w - 8)^2
21. What is the factored form of the expression?
d^2 + 22d + 121
(A). (d + 11)^2
(B). (d - 11)^2
(C). (d - 11)(d + 11)
(D). (d - 121)(d - 1)
22. What is the factored form of the expression?
r^2 - 49
(A). (r - 7)(r + 7)
(B). (r + 7)(r + 7)
(C). (r - 7)(r - 7)
(D). (r - 7)(r + 9)
Hence, option (A) is correct.
Hence, option (C) is correct.
Hence, option (A) is correct.
Hence, option (A) is correct.
What is a factor?
A factor is a number that divides another number, leaving no remainder.
In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division.
Here given that,
19)
The area of the ceiling is given by [tex](10x+9)(7x+7)[/tex].
[tex]10x(7x)+7(10x)+9(7x)+9(7)\\=70x^2+70x+63x+63\\=70x^2+133x+63\\[/tex]
The area of the skylight is of the form [tex](x+5)(3x+3)[/tex].
[tex]x(3x)+3(x)+5(3x)+5(3)\\=3x^2+3x+15x+15\\=3x^2+18x+15\\[/tex]
We subtract to find out the remaining ceiling:
[tex](70x^2+133x+63)-(3x^2+18x+15)\\=70x^2+133x+63-3x^2-18x-15\\=67x^2+115x+48[/tex]
Hence, option (A) is correct.
20)
For the factor, we find factors of
[tex]8(8)=64\\8+8=16[/tex]
Therefore we have:
[tex](w+8)(w+8)[/tex]
Hence, this is the same binomial twice, we write it as [tex](w+8)^2[/tex]
Hence, option (C) is correct.
21)
Again we look for the factors
[tex]11(11)=121\\11+11=22[/tex]
so it is of the form [tex](d+11)(d+11)[/tex].
Hence this is the same binomial twice, we have [tex](d+11)^2[/tex].
Hence, option (A) is correct.
22)
Factors [tex]-49[/tex] that sum to [tex]0[/tex]
As
[tex]-7(-7)=49\\-7-7=-14[/tex]
So:
[tex](r-7)(r+7)[/tex]
Hence, option (A) is correct.
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You are buying a $14.95 item that has 4.5% sales tax. You give the cashier a $20 bill. How much change do you get back?
Answer:
4.38 is the aount you get back
Step-by-step explanation:
14.95*.045=.67
14.95+.67=15.62
20-15.62=4.38
Brainleist plz
You give the cashier a $20 bill. $4.38 you get back.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
You are buying a $14.95 item that has 4.5% sales tax.
That means,
the total price = 14.95 + 4.5% of 14.95.
= 14.95 + 0.67
= 15.62
You give the cashier a $20 bill.
You get in return,
= 20 - 15.62
= $4.38
Therefore, you get back $4.38.
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The graph of quadratic function f(x) has a minimum at (-2,-3) and passes through the point (2,13). The function g(x) is represented by the equation g(x)=-(x+2)(x-3)
How much greater is the y-intercept of g(x) than f(x)?
I really need some help soon ((:
Lots of points given
The y-intercept of function g(x) is 9 greater than the y-intercept of function f(x).
Explanation:The question is asking for the difference in the y-intercepts of two quadratic functions f(x) and g(x). The minimum point of a function gives us both the x-value of the vertex and the y-intercept. Here, for f(x), the minimum point is given as (-2,-3) which means the y-intercept is -3. Similarly, for the function g(x)=-(x+2)(x-3), expanding this equation gives us g(x) = -x^2 + x + 6. Here, we see that the constant term, 6, is the y-intercept. Therefore, the difference in the y-intercepts of g(x) and f(x) is 6 - (-3) = 9.
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Solve for x: -2.3(x - 1.2) = -9.66
Answer:
x = 5.4Step-by-step explanation:
[tex]-2.3(x-1.2)=-9.66[/tex] use the distributive property a(b + c) = ab + ac
[tex]-2.3x+2.76=-9.66[/tex] subtract 2.76 from both sides
[tex]-2.3x=-12.42[/tex] divide both sides by (-2.3)
[tex]x=5.4[/tex]
Which is an equation of the line graphed below?
A. y=2x-3
B. y=1/2x-3
C. y= -1/2x-3
D. y= -2x-3
You have 1500 and want to invest it for the future. Bank of westminster has a saving account with an interest rate of 3% compounded yearly, but a local credit union is offering 2% compounded continuously. Which account would give you more money if you leave the money in the account for 10 years? How much more? Show all calculation and label everything
Which expression is equivalent to square root of 2x^5/18? Assume
Answer with explanation:
The Meaning of equivalent expression is those expressions, in which when you replace the variables by some constant values , in the original expression and the reduced expression,the both expression produce the same numerical value.
The expression which is equivalent to:
[tex]\rightarrow\sqrt {\frac{2x^5}{18}}\\\\=\sqrt{\frac{x^5}{9}}\\\\=\frac{x^2}{3}\times\sqrt{x}[/tex]
This can be illustrated by
Original Expression
[tex]A=\sqrt {\frac{2x^5}{18}}\\\\ \text{put, x=1}\\\\A=\sqrt{\frac{2 \times 1^5}{18}}\\\\A=\sqrt{\frac{1}{9}}\\\\A=\frac{1}{3}\\\\\text{Equivalent Expression B}\rightarrow \frac{x^2}{3}\times \sqrt{x}\\\\\text{put,x=1}\\\\B=\frac{1^2}{3}\times \sqrt{1}\\\\B=\frac{1}{3}[/tex]
Which statement describes the transformation of the graph of function f onto the graph of function g?
The area of a rug, which is shaped like a rectangle,is 4x²+4x square feet. Factor this polynomial to find expressions for the dimensions of the rug
Final answer:
The expressions for the dimensions of a rectangular rug with an area of 4x²+4x square feet are 4x feet and (x + 1) feet after factoring the polynomial.
Explanation:
To find the expressions for the dimensions of the rug with an area of 4x²+4x square feet, we need to factor the polynomial. Factoring out the greatest common factor (GCF), we get:
4x² + 4x = 4x(x + 1).
This indicates that one dimension of the rug is 4x feet and the other dimension is (x + 1) feet. The rug can be visualized as a rectangle where one side is 4 times a certain length x, and the other side is that length plus one.
Which is a solution of x2 – x – = 0?
[tex]x^2-x=0\\\\x(x-1)=0\iff x=0\ \vee\ x-1=0\\\\\boxed{x=0\ \vee\ x=1}[/tex]
The school store started selling music CDs five years ago. They sold $22,600 worth in the first year. But, since MP3 players became so popular, the total yearly sales of CDs have dropped 14% per year since then. What is the total money collected for music CDs sold in the school store over the last five years? Use the geometric series formula to calculate your answer.
The total money collected for music CDs sold in the school store over the last five year is $85,557
Geometric Series Formula:
To calculate the total money collected for music CDs sold in the school store over the last five years, we can use the formula for the sum of a geometric series: Sum = a * (1 - r^n) / (1 - r), where a is the initial value, r is the common ratio, and n is the number of terms.
Given Data:
Initial sales in the first year = $22,600
Annual decrease rate = 14%
Duration = 5 years
Calculation Steps:
Calculate the common ratio: r = 1 - 0.14 = 0.86
Plug the values into the formula: Sum = $22,600 * (1 - 0.86^5) / (1 - 0.86) = $85,557
if you were to solve the following system by substitution what would be the best variable to solve and from what equation? 2x+8y=12 3x-8y=11
Answer:
X in 1st
Step-by-step explanation:
A rental car costs a one time fee of $150 and then an additional $80 for each day it is rented. If the Nawa family's total bill was $470, how many days did they rent the car?
Nawa family rented the car for 2 days.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
A rental automobile costs $150 for the first day and an extra $80 for each consecutive day booked. If the entire bill for the Nawas family was $470.
The total cost of the rental car per day is :
⇒ one-time fee + additional fee
⇒ $150 + $80
Apply the addition operation,
⇒ $230 per day.
The Nawas paid $470 for the rental car, so they rented the car for $470 / $230 per day = 2 days.
Therefore, his family rented the car for 2 days.
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A reflection of the pink triangle is shown. Which transformation makes this reflection?
A) (x', y') = (y, x)
B) (x', y') = (x, -y)
C) (x', y') = (-x, y)
D) (x', y') = (-x, -y)
Answer:
(x, y) → (-x, y).
Step-by-step explanation:
(x, y) → (-x, y). is correct. For example, the point (-3, 5) on triangle 1 goes to (3, 5) on triangle 2.