The centre of the circle is (-2,7) and the radius is √7 , Option D is the right answer.
What is the standard equation of a Circle ?The standard equation of a Circle is
(x-h)² +(y-k)² = r²
where h and k is the centre of the circle , r is the radius
The given equation is
x² + y² + 4x – 14y + 46 = 0
x² +4x +4 -4 +y² -2.7y + 49-49+46 = 0
(x + 2)² + (y-7)² -4-49+46 = 0
(x + 2)² + (y-7)²= 7
Therefore the centre of the circle is (-2,7) and the radius is √7 ,
Therefore Option D is the right answer.
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Analia is a school district manager. Here are some details about two schools in her district for the last school year:
School A School B
Number of students 300030003000 400040004000
Number of teachers 190190190 380380380
Graduation rate 86\%86%86, percent 90\%90%90, percent
Budget per student \$10{,}500$10,500dollar sign, 10, comma, 500 \$10{,}000$10,000dollar sign, 10, comma, 000
% of students in sports club 62\%62%62, percent 68\%68%68, percent
Number of sports medals won 999 777
SAT average 120012001200 105010501050
SAT range (max-min) 900900900 700700700
Analia wants to know which school has higher athletic achievements relative to the SAT average.
1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
% of students in sports club divided by SAT average
(Choice B)
B
Graduation rate divided by SAT average
(Choice C)
C
Number of sports medals won
(Choice D)
D
Number of sports medals won divided by SAT average
2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average.
(Choice B)
B
Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average.
(Choice C)
C
No. The definitions have opposite results.
Answer is in this link:
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Please help!!! I will give 20 points to the correct answer!! Thanks so much
Answer:
either it's 7 and 3 but not sure
Step-by-step explanation:
7x3 =21
now for the negative -10 it would basically be -7+-3=-10
A line of best fit was drawn for 16 data points. What is the maximum number
of these data points that may not actually be on the line?
OA. 14
OB. 13
O C. 15
OD. 16
The maximum number of data points that may not actually be on the line is 16. so, the correct option is D.
How to find the line of best fit?We know that a line of best fit is basically a straight line drawn for a given data that may or may not pass through data points.
It is given that the line is drawn for 16 data points.
Hence, the line may or may not pass through all these 16 points.
Therefore, the maximum number of data points that may not actually be on the line is 16.
so, the correct option is D.
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A researcher believes that singing to plants causes them to grow an extra 0.5 inches on average per month. She tests this with 20 of her own plants by bringing 10 to work and leaving 10 at home. The ones at home she sings to each day, and she does not sing to the ones at her work.
The control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.
How to depict the control variable?According to the information, the researcher wants to seek whether singing to plants causes them to grow taller.
The explanatory variable is singing. Therefore, the researcher can control some of the variables to determine the explanatory variable on the growth of the plant.
Hence, the control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.
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i give brainliest to first person who gets it correct
Answer:
(-4,-3)
Step-by-step explanation:
The point where those 2 equations intersect is (-4,-3)
Thaddeus models the number of hours of daylight in his town as
D(t) = 3sin(t) + 12, where D is the number of daylight hours and t is the
time in months since January 1.
What are the least and greatest numbers of daylight hours over the course of
a year?
Answer:
(π2,15)(π2,15) is a local maximal
(3π2,9)(3π2,9) is a local minimal
Step-by-step explanation:
Dan sold 40 concert tickets in 5 days.
Each day he sold 3 tickets MORE than the
previous day. The number of tickets he
sold on the third day is?
Step-by-step explanation:
The number of tickets sold by Dan the first day is x.
Tickets sold on the 2nd day: x+3
on the 3rd day: x+6
on the 4th day: x+9
on the 5th: x+12
Since the total of tickets sold by Dan is 40:
x+(x+3)+(x+6)+(x+9)+(x+12)=40
5x+30=40
5x=10
x=2
number of tickets sold on the third day: 8
determine weather y varies directly with x. if so find the constant of variation and write the equation
This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The correct option is B.
What is the directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
Since the graph of the equation is a line, therefore, it can be concluded that the relationship is linear as a result y varies directly with x.
Therefore we can write the relationship as,
y ∝ x
y = k x
The line goes through the point (-2,3), thus, substitute the points in the equation formed above,
3 = k × (-2)
k = -3/2
Now, substitute the value of k in the equation,
y = -(3/2)x
Hence, the correct option is B.
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yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
X
x
Inverse
Answer:
Sike
Step-by-step explanation:
That's the wrong number only 123
What is 43.808 in written form
Answer:
fourty-three.(point) eight zero eight
Step-by-step explanation:
hope it helps...
Quick please!
Will give brainliest
100 points
3(4j + 7 + 2j) or 3(6j +7) b. Use the distributive property to create an equivalent expression.
Answer:
3(4j + 7 + 2j)
12j + 21 + 6j
12j + 6j + 21
18j + 21 ----- (1)
3(6j +7)
18j + 21 --------(2)
eq 1 = eq. 2
both are equal
For which value(s) of xwill the rational expression below equal zero? Check
all that apply.
(x - 3)(x + 6)/x +7
A. -6
B. -7
C. 7
D. 3
E. 6
F. -3
Answer:
A. -6
D. 3
Step-by-step explanation:
Is 7/7 a proper fraction, an improper fraction, a mixed number, or decimal fraction?
None of these choices are correct.
O a decimal number
an improper fraction
O a mixed number
O a proper fraction
7/8 yard of material is needed to make a blanket, how many blankets can be made from 21 yards of material?
Answer:
24
Step-by-step explanation:
the question translates to asking how many times does 7/8 fit in 21, so 21 divided by 7/8.
when we divide by a fraction, we can multiply by it's inverse, so 21 divided by 7/8, is 21 multiplied by 8/7. so:
21×8/7 = (21×8)/7 = (21/7)×8 = 3×8 = 24
height of 24cm with a radius of 7cm. What is the total surface area of the cone?
Answer:
the answer to this problem is 703.7 in^2
The number 900 is increased by 20% and then decreased by 20%. Find the new number.(the ans is 864 apparently:/ I need steps)
Step-by-step explanation:
if 900 is increased by 20% then
120/100×900=1080
Decreasing it by 20% then
80/100×1080=864
Urgent!!!
Use the Law of Sines to find all missing sides and angles of the following triangle (side b, side
c, and angle C). Approximate your answers to the nearest tenths. a = 35.0 km, A = 13.0°, B =
65.3°
Answer:
A = 13 degrees
B = 65.3 degrees
C = 180 - (13 + 65.3) = 101.7 degrees
Side a = 35 km
Side b = 141.4 km
Side c = 152.4 km
What is the point of intersection of the lines represented by these equations
Jy = -2x + 2
y = x - 4
A. (-2, 2)
B. (1, -3)
c. (2,-2)
D. (3,-4)
To find the point of intersection of two lines, we can use substitution to find the x and y coordinates.
Solving the QuestionWe're given:
[tex]y = -2x + 2[/tex][tex]y = x - 4[/tex]Use substitution to find x:
[tex]-2x + 2=x-4\\-2x=x-6\\-3x=-6\\x=2[/tex]
Use substitution to find y:
[tex]y=x-4\\y=2-4\\y=-2[/tex]
AnswerThe point of intersection is (2,-2).
Determine the next three terms in the following sequence: Negative 1, one-half, negative one-fourth, StartFraction 1 Over 8 EndFraction,____, ____, ____,... a. StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, StartFraction 1 Over 48 EndFraction b. StartFraction 1 Over 16 EndFraction, StartFraction 1 Over 32 EndFraction, StartFraction 1 Over 64 EndFraction c. Negative StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, Negative StartFraction 1 Over 48 EndFraction d. Negative StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, Negative StartFraction 1 Over 48 EndFraction
The next three terms will be -1/16, 1/32, and -1/64. Then the correct option is B.
What is the geometric sequences?Let a be term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
The sequence is given below.
-1, 1/2, -1/4, 1/8,....
The common ratio will be -1/2.
Then the next three terms will be
a₅ = a₄ x (-1/2)
a₅ = (1/8) x (-1/2)
a₅ = -1/16
a₆ = a₅ x (-1/2)
a₆ = (-1/16) x (-1/2)
a₆ = 1/32
a₇ = a₆ x (-1/2)
a₇ = (1/32) x (-1/2)
a₇ = -1/64
Then the next three terms will be -1/16, 1/32, and -1/64.
Then the correct option is B.
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Answer:
C
Step-by-step explanation:
An investor decides to invest some cash in an account paying 13% annual interest, and to put the rest in a stock fund that ends up earning 7% over the course of a year. The investor puts $1300 more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1270. How much money was invested at each of the two rates? Round to the nearest integer.
A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,
x - y =1300
x = 1300 + y
Also, at the end of the year the total interest from the two investments was $1270. Therefore, we can write,
0.13x + 0.07y = 1270
Substitute the value of x from the above,
0.13(1300 + y) + 0.07y = 1270
169 + 0.13y + 0.07y = 1270
0.20y = 1101
y = 5505
substitute the value of y in the first equation,
x - y = 1300
x = 6805
Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
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The stock of Company A gained 6% today to $87.45. What was the opening price of the stock in the beginning of the day?
The opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
The stock of Company A gained 6% today to $87.45.
Let x be the opening price of the stock in the beginning of the day.
(x + 0.06x) = 87.45
Because gained 6% today to $87.45
1.06x = 87.45
x = $82.5
Thus, the opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.
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help me pleaseeeeeeeeeeee i need the answer fast because it is limited
i will mark as brainiest
Answer:
D
Step-by-step explanation:
Original area = x * x = x^2
New area = x ( x +3.5) = x^2 + 3.5x <====the underlined is the increase in area
The repeating decimal z=0.142857142857142857 as fraction
Answer:
[tex] \frac{1}{7} [/tex]
For all a and b, what is the sum of (a-b)² and (a+b)²
Answer:
2a² + 2b²
Step-by-step explanation:
(a - b)² + (a + b)² ← expand both factors using FOIL
= a² - 2ab + b² + a² + 2ab + b² ← collect like terms
= 2a² + 2b²
Step-by-step explanation:
Expand both classic quadratics and combine like terms to find the sum:
(a−b)2+(a+b)2
Based on the graph of g (x), on which intervals
are the function's values positive? Select all that
apply.
Answer:
[tex]\text{A}) \text{ } -\infty < x < 3\\\\\text{C}) \text{ } -1 < x < 2\\\\[/tex]
Step-by-step explanation:
The graph lies above the x-axis for these intervals.
144 to the 1/2 power
Answer:
(144)^1/2
(12^2)^1/2
12 is the answers
Step-by-step explanation:
please mark me as brainlest
Answer:
12
Step-by-step explanation:
Rewrite 144 as 12²
(12²)^1/2
Apply the power rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
12^2(1/2)
Cancel the common factor of 2.
Cancel the common factor.
Rewrite the expression
12^1
Evaluate the exponent.
12
Solve x:
3x + 99x= 1224
10 pts
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]The figure below is a scatterplot for paired data (x, y), with x values on the horizontal axis and y on the vertical axis. The tick marks are spaced 10 units apart on both axes. (Note that to answer the following questions you don't need the actual values for each tick mark, only differences between them.) 00 00 Oo oo 8 Oo oo (1) What are plausible values for the standard deviations of x and y, respectively? (2) What is a plausible value for the slope of the SD line? (3) Given your answer to part (b), what is a plausible value for the slope of the regression line?
The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.
What is a scatter plot?Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.
We have a scatter plot shown in the table:
1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:
Standard deviation = SD
6SD(x) = 40
SD(x) = 40/6 = 6.67
6SD(y) = 20
SD(y) = 20/6 = 3.37
2) Slope of the line:
= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5
3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.
Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.
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Which of the following is a correctly written algebraic equation?
2 + 0.2x
5b - 5x + 2
a - 3x=0
3(x/5)
Expand:
4(5x+5) - 3(2x + 4)
Answer:
14x + 8
Explanation:
⇒ 4(5x+5) - 3(2x + 4)
distribute inside parenthesis
⇒ 4(5x) + 4(5) - 3(2x) - 3(4)
multiply the variables
⇒ 20x + 20 - 6x - 12
collect like terms
⇒ 20x - 6x + 20 - 12
subtract like term
⇒ 14x + 8
4 x 5x = 20x
4 x 5. = 20
-3 x 2x = - 6x
-3 x 4 = - 12
Line them up, collect like terms & simplify
20x + 20 - 6x - 12
20x - 6x = 14x
20 - 12 = 8
Thus, answer is 14x + 8
Hope this helps!
