Mathematics High School

Marisha plots her flower garden on a computer. She determines that the circle that defines the part of the garden that gets watered by the sprinkler is (x−8)2+(y+10)2=25.

What is the diameter, in meters, of the circular area that gets watered by the sprinkler?

2.5 m

5 m

10 m

20 m

Answers

Answer 1

If the radius of the circle will be 5, then the diameter of the circle is 10 m. Then the correct option is C.

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

Marisha plots her flower garden on a computer.

She determines that the circle that defines the part of the garden that gets watered by the sprinkler is (x − 8)² + (y + 10)² = 25.

Then the equation can be written as

(x − 8)² + (y + 10)² = 5²

The radius of the circle will be 5

Then the diameter of the circle is given as

d = 2r

d = 2 x 5

d = 10 m

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Related Questions

Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280lb mixture that is 8% protein?

How many pounds of the cornmeal should be in mixture?
How many pounds of the soybean meal should be in mixture? 50 POINTS!!!!

Answers

0.14x + 0.07(280-x) = 0.08*280

0.14x + 19.6-0.07x = 22.4

0.07x + 19.6 = 22.4

0.07x = 2.8
x = 2.8 / 0.07 = 40
 x = 40 pounds of Soybean
280 -40 = 240 of cornmeal



Someone help with math?

Answers

The answer is the second one (the one on the top right)

Question 2(Multiple Choice Worth 2 points)
(10.06 MC)

Compare the functions shown below:

f(x) = 4 sin (2x − π) − 1

g(x)
x y
−1 6
0 1
1 −2
2 −3
3 −2
4 1
5 6

h(x) = (x − 2)2 + 4


Which function has the smallest minimum y-value?
f(x)
g(x)
h(x)
Both f(x) and g(x) have the same minimum y-value.

Answers

Answer:

1. f(x)=4 sin (2 x-π)-1

 =4 sin [-(π-2 x)] -1

 = -4 sin 2 x -1

-1 ≤ sin 2 x ≤1

f(x) is minimum, when, sin 2 x=1

= -4 × 1 -1

= -5→Minimum value of f(x).

2. Minimum y value of g(x) by looking at the table is ,

g(x)=-3→Minimum

3. h(x)=(x-2)²+4

As, (x-2)², will yield always a positive value.

So, minimum of h(x), will be at , x=2

h(2)=(2-2)²+4=4→Minimum

Among the three function given, f(x) has minimum y -value,equal to -5.

Option A: f(x)

quick computing company produces calculators they have found that the cost c(x),of making calculators is a quadratic function in terms of x the company also discovers that it costs $45 to produce 2 calculators, $143 to produce 4 calculators, and 869 to produce 10 calculators FIND THE TOTAL COST OF PRODUCING 1 CALCULATOR

Answers

it cost $23 to make one calculator hope this helps

Answer:

$23

Step-by-step explanation:

We will use a quadratic regression to solve this.

Using a graphing calculator, put the number of calculators into the first list (x) and the cost to produce into the second list (y).

Next we run the quadratic (x^2) regression.  Doing this gives us an equation in the form

y = ax²+bx+c.  The values we are given for a, b and c are

a = 8.9999999999; b = -4.999999999999; c = 18.999999999

These can be rounded to a = 9, b = -5 and c = 19.  This gives us the equation

y = 9x²-5x+19

Substituting 1 in place of x, we have

y = 9(1²)-5(1)+19 = 9(1)-5+19 = 9-5+19 = 4+19 = 23

Find the length of the hypotenuse of a right triangle with legs of lengths 9 and 12 If necessary round your answer to two decimal places

Answers

you can get help from Pythagoras theorem :
[tex] {x}^{2} = {9}^{2} + {12}^{2} \\ {x}^{2} = 81 + 144 = 225 \\ x = \sqrt{225} = 15[/tex]
hope this helps

How do I solve this?

Answers

In the first step, you match the pattern of
.. (-3/2)x^2 +0x +3
to the pattern of
.. ax^2 +bx +c

and you can see that
.. a = -3/2 . . . b = 0 . . . c = 3
____
Because a is negative, the parabola opens down. Because it opens down, the vertex is the high point, the maximum.

____
The y-intercept is always c. Here c=3, so the y-intercept is (0, 3).

____
The axis of symmetry is given by
.. x = -b/(2a)
.. x = -0/(2*(-3/2)) = 0

____
Because the y-intercept is on the axis of symmetry, it is the vertex.
.. vertex = (0, 3)

____
Put x=±2 in the equation and evaluate.
.. y = (-3/2)*(±2)^2 +3
.. = (-3/2)*4 +3
.. = -6 +3 = -3
The two points are (-2, -3) and (2, -3).

Polynomials are closed under the operation of subtraction.

Which statement best explains the meaning of closure of polynomials under the operation of subtraction?


A. When any two polynomials are subtracted, the coefficients of like terms are always subtracted.

B. When any two polynomials are subtracted, the result is always a polynomial with negative coefficients.

C. When any two polynomials are subtracted, the result is always a polynomial.

D. When any two polynomials are subtracted, the result is always a monomial or a binomial.

Answers

Answer: Option C. When any two polynomials are subtracted, the result is always a polynomial.

A polynomial is an expression consisting of variables and coefficients, that involves the operations of addition, subtraction, multiplication .

polynomials are closed under the operations of addition, subtraction, and multiplication.

Polynomials will be closed under an operation if the operation produces another polynomial.

The statement that best explains the meaning of closure of polynomials under the operation of subtraction is

option C. When any two polynomials are subtracted, the result is always a polynomial.


The table shows the height of an object, h(t), in meters after t seconds. Use your calculator to find the quadratic function. Find the approximate time, to the nearest hundredth of a second, after which the object will reach its maximum height.

Answers

My calculator models the function as
.. h(t) = -4.9t^2 +23.4t +120

The maximum height is reached at t=-23.4/(2(-4.9)) ≈ 2.39 seconds.

Each chef at "sushi emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. on tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. by the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten. how many chefs and how many customers were in "sushi emperor" on tuesday?

Answers

Solving the Diophantine equations for chefs (c) and customers (q) ...
.. 15c -2q = 4
.. 20c -3q = 1
we find that c=2 and q=13 are common solutions.

There were 2 chefs and 13 customers on Tuesday.


_____
It looks like this is better solved using proportions, since the ratio of roll production is different than the ratio of roll consumption. There can only be one solution.
.. (15c-4)/(20c-1) = 2/3 . . . . the ratio of rolls produced is the same as the ratio of rolls consumed
.. 3(15c -4) = 2(20c -1)
.. 45c -12 = 40c -2
.. 5c =10
.. c = 2 . . . . there were 2 chefs
They produced 30 rolls, of which 4 were left and the remaining devoured 2 at a time. Hence there were
.. (30 -4)/2 = 13 customers.

Answer:

There were  2  chefs and  13  customers.

Step-by-step explanation:

Determine if x + 3 is a factor of -3x^3+6x^2+6x+9, and how do you know?

Answers

Begin by taking out -3 as a common factor.
-3(x^3 - 2x^2 - 2x - 3)
If x + 3 is a factor, what is inside the brackets should be 0 when x = - 3 It is not. There is only one real root and that is when (x - 3) is equated to 0. Just to show the root is +3, the graph is included.  

A spinner with
9
equally sized slices is shown below. The dial is spun and stops on a slice at random. What are the odds in favor of landing on a white slice?
note their are 7 white and 2 black

Answers

If a spinner has 9 equally-sized slices, then there is an equal chance of the spinner landing on any one of those slides. If, as in this case, there are 7 white slices and 2 black slices, then the chance of the spinner landing on a black slice is 2/9. And, to answer the question, the odds of landing on a white slice are therefore 7/9, or about 78%.

This is when one word has more than one definition and its 15 letters

Answers

Notwithstanding has 2 definitions and has 15 letters

Kana earns a $25,000 salary in the first year of her career. Each year, she gets a 4% raise. How much does Kana earn in the first 10 year of her career? (Round the final answer to the nearest dollar)

Answers

The amount is $300,152.68.

Explanation:
This can be represented as a geometric sequence, with a common ratio of 1.04. This is because she earns 100% of her previous salary plus an extra 4% each year; 104%=104/100 = 1.04.

The explicit form of the sequence would be
25000(1.04)ⁿ⁻¹,

where n is the number of years. We want the sum of the first ten years, so we want
[tex]\Sigma_{n=1}^{10}25000(1.04)^{n-1}[/tex]

Using technology, this comes out to $300,152.68.

3x - 5y = 17 y = -7 Solve by substitution.

Answers

Substitute the value of y given by the second equation into the first.
.. 3x -5(-7) = 17
.. 3x +35 = 17
.. 3x = -18
.. x = -6

The solution is (x, y) = (-6, -7).

The histogram shows the number of hours volunteers worked one week.

What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?

Enter your answer in the box.


%

Answers

the answer was 45 i just took it

Answer: 45%

Step-by-step explanation:

From the given histogram, The number of volunteers worked 8 to 11 hours = 5

The number of volunteers worked 16 to 19 hours = 4

The number of volunteers worked 8 to 11 hours or 16 to 19 hours =5+4=9

Total number of volunteers = 4+2+5+4+4+1=20

The percent of volunteers worked 8 to 11 hours or 16 to 19 hours is given by :-

[tex]\frac{9}{20}\times100=45\%[/tex]

Hence, the percent of the volunteers worked 8 to 11 hours or 16 to 19 hours =45%

Please help and show all work. 20 points.

Answers

The area of the 120° sector is
.. Asector = (1/2)r^2*θ . . . . . . . angle in radians
.. = (1/2)*(24 m)^2*(2π/3)
.. = 192π m^2

The area of the white triangle in that sector is
.. Atriangle = (1/2)r^2*sin(θ)
.. = (1/2)*(24 m)^2*(√3)/2
.. = 144√3 m^2

The area of the shaded segment is the difference of these
.. Asegment = Asector -Atriangle
.. = (192π -144√3) m^2

The 2nd selection is appropriate.

This is embarrassing.. went to a Hobby Lobby job interview.. and flunked the math test.. ack! this involved percentages..how do you get 66% off of a total, and like tax % 7.5 we are not allowed to use a calculator

Answers

to get 66% off, multiply the price by 0.66 and subtract. tax is same, 0.075 of the amount but add to the price. that's crazy they don't allow a calculator. they use a cash register to compute those numbers . good luck

Final answer:

To get a percentage off of a total without a calculator, multiply the total by the percentage as a decimal. To calculate the total amount including tax, multiply the total by the tax percentage as a decimal and then add the result to the total.

Explanation:

To calculate a percentage off a total without using a calculator, you can multiply the total by the percentage as a decimal. For example, to find 66% off of a total, multiply the total by 0.66. To calculate the total amount including tax, you can add the tax amount to the original total. For a 7.5% tax, multiply the total by 0.075 and then add the result to the total.

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Dan measures an object to the nearest fourth inch. He records the length as 4 1/4 inches. Geri measures the same object the nearest half inch. Could Dan and Geri get the same measurement? Explain.

Answers

no because u cant get the same answer by measuring with a half inch
Geri's measurements will never have 1/4 inch as part of the measurement, as it will be rounded to the nearest 1/2 inch.

Dan and Geri cannot get the same measurement for whatever object it is that Dan has measured. (They may get the same measurement on other objects.)

How many 12 inch sections can you get out of 9 foot calculator?

Answers

To solve this problem, the first thing you should keep in mind is the following conversion:
 1 foot = 12 inches.
 Therefore doing the conversion:
 (12 inch) * (1 foot / 12 inch) = 1 foot.
 The number of sections is:
 N = (9 feet) / (1 foot) = 9
 Answer:
 you can get out 9, 12 inch sections of 9 foot calculator

Bailey writes 5 + 8 on the left-hand side of a paper and then writes 4 + 9 to the right of it. Which symbol should Bailey write between the two sets of numbers to show they have the same sum
a. +
b. –
c. ≠
d. =

Answers

5 + 8 = 4 + 9
13 = 13

ANSWER: D) =

The equals sign should be in between because the numbers on each side add up to the same number.

Hope this helps! :)

Elliot and Katy both bought the same lunchbox for $6. Elliot lives in Oklahoma and pays 4.5% in sales tax, while Katy lives in South Carolina and pays 6% in sales tax. How much more did Katy pay in sales tax than Elliot? A.$0.09 B.$0.27 C.$0.63 D.$0.36

Answers

The answer is A.$0.09!

the answer is A.
Elliot pays a total of $0.27 in tax
Katy pays a total of $0.36 in tax
[tex]0.36 - 0.27 = 0.09[/tex]

The relationship between the monthly fee that the cable company charges for internet service and the fee for downloading over 32KB of information is modeled by the linear function f (x) = 1.25x + 45, where x is the number of KB over 32. If the total bill for a month is $170, how many KB was in excess of 32 KB that month?

Answers

100 Kilobytes.
Because if the total is 170, then 
1.25x = 170-45
1.25x = 125
x = 100
1.25x = 170-45
1.25x = 125
x = 100

The diagram shows a line with intercepts 3 and 9 and one of many rectangles which can be inscribed under this line and within the first quadrant.
a. Write an equation for the line.
b. Determine if the rectangle can have x = 4 and y = 2 as its dimensions.
c. Find x and y if the rectangle is a square.
d. Write an expression for A, the area of the rectangle, using x as the only variable.
e. Find x if the area of the rectangle is 6.
f. Which x gives the rectangle its largest area?

Answers

a) The easiest way to write an equation for this line is to use intercept form:
.. x/x-intercept +y/y-intercept = 1
.. x/9 +y/3 = 1

b) The point (x, y) = (4, 2) does not satisfy the equation. (see the graph) These cannot be the dimensions of an inscribed rectangle.

c) The intersection with the line y=x is (x, y) = (2.25, 2.25). These are the dimensions of an inscribed square.

d) The equation can be rewritten as
.. x +3y = 9
.. y = 3 -(x/3)
Then the area can be written as
.. A = xy = x(3 -x/3)

e) For x=6, the area is
.. A = 6(3 -6/3) = 6*1 = 6 . . . . square units

f) The parabola described by A has zeros at x=0 and x=9. The vertex of that parabola is on the line of symmetry, at x = 4.5. That value of x gives the maximum area.

z varies jointly with x and y. when x=2 and y=3, z=60. what is the value of z when x=4 and y=9?
A. 360
B. 60
C. 90
D. 40,

Answers

Z $ xy then Z = Kxy. When x = 2 and y = 3, and Z = 60, our constant of variation becomes 60 = K * 2 * 3 K = 10. Our constant of proportionality equals 10. We would need that in the second part of the equation. When x = 4 and y = 9, we have Z = 10 * 4 * 9 = 360

15p for an answer please

Answers

-3/8 Divided by -1/3 becomes -3/8 x -3 which is 9/8
9/8
Hope this helps!
i believe the answer is d 
commet if i am incorrect

True or False. (0,0) is a solution to problem #1. This means that (0,0) is in the solution region.

Answers

True.

A point that is a solution is in the solution region.

Given ​ f(x)=x2+14x+40 ​.
Enter the quadratic function in vertex form in the box.
f(x)=

Answers

we know that
the quadratic function in vertex form is--------------> y=a*(x-h)²+k

we have
f(x)=x²+14x+40
y=x²+14x+40

We can convert to vertex form by completing the square on the right hand side
y-40=x²+14x
y-40-49=x²+14x-49------> subtract 49 on BOTH sides to preserve the equality
y-40=(x²+14x+49)-49
y=(x²+14x+49)-49+40---------> y=(x+7)²-9

the answer is
the quadratic function in vertex form-----------> y=(x+7)²-9
the vertex is the point (-7,-9)

Answer: f(x) = (x+7)^2 -9

Step-by-step explanation:

I know that this is late but hopefully it will help someone else.

Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (2,4) and has the origin as its vertex. what is the standard form of the equation

Answers

For the given vertex, the equation is
.. f(x) = a(x -0)^2 +0
.. f(x) = ax^2

For the given point,
.. f(2) = 4 = a*2^2 = 4a
Then a=1 and your equation is
.. f(x) = x^2

The angle of depression from D to F measures 10°. If DE = 300 m, find DF. Round your answer to the nearest tenth.


304.6 m


1,910.2 m


1,727.6 m


1,701.4 m

Answers

Answer:

Option C) 1727.6 m

Step-by-step explanation:

Given that the angle of depression from D to F measures 10°.

Also given that DE =300 m.

Since 10 is angle of depression, we can visualize a right triangle with hypotenuse DF=300 m and EF, DE two legs.

In the right triangle DEF, the angle opposite 10 is the side DE[tex]\frac{DF}{DE} =\frac{hypotenuse}{opposite side}= cosec 10\\\\DF =300 cosec 10 = 1727.6 m[/tex]

by Using trignometric ratios

Please help !!! Need fast

Answers

4x+30=90
4x = 60
  x = 15

answer is B. 15
Since b and d are perpendicular the angles they form are 90 degree angles.  Also given that a and b are parallel the angles between a and d are the same as those with b and d.

SO we can say that 4x + 30 = 90
4x = 60
x = 15
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