The center of a cricle ids (h,7) and the radius is 10. The circle passes through (3,-1). Find all possible values of h.

Answers

Answer 1

Answer: $center\ of\ a\ circle:(a;\ b)\n\nradius:r\n\n(x-a)^2+(y-b)^2=r^2\n\n========================\n\n(h;\ 7);\ r=10\n\n(x-h)^2+(y-7)^2=10^2\n\n========================$

$The\ circle\ passes\ throught\ (3;-1).\n\nSubstitute\ x=3\ and\ y=-1:\n\n(3-h)^2+(-1-7)^2=100\n\n(3-h)^2+(-8)^2=100\n\n(3-h)^2+64=100\ \ \ /-64\n\n(3-h)^2=36\iff3-h=\pm√(36)\n\n3-h=-6\ or\ 3-h=6\n-h=-6-3\ or\ -h=6-3\n-h=-9\ or\ -h=3\nh=9\ or\ h=-3\n\nAnswer:h=9\ or\ h=-3$

Answer 2

Answer: $equation\ of\ a\ circle:\n\n(x-h)^2+(y-7)^2=10^2\n\nif\ \ (x;y)=(3;-1),\ then\ \ (3-h)^2+(-1-7)^2=100\n\n(3-h)^2+64=100\n\n (3-h)^2=36\ \ \ \Leftrightarrow\ \ \ (3-h=6\ \ \ or\ \ \ 3-h=-6)\n\n3-h=6\ \ \ \ \ \Rightarrow\ \ \ h=-3\n3-h=-6\ \ \ \Rightarrow\ \ \ h=9\n\nAns.\ h=-3\ \ or\ \ h=9$

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Solve 4(x + 1) = 4x + 4.

Answers

The answer will be 0.
4x+4=4x+4
=0

Answer: 0

Step-by-step explanation: 4x+1=4x+4

-4x. -4x

Which of the following statement best describes the effect of replacing the graph of f(x) with the graph of f(x) - 3?A) the graph shifts 3 units up.
B) The graph shifts 3 units down. i think is correct?
C) the graph shifts 3 units left.
D)the graph shifts 3 units right.

Answers

The statement that best describes the effect of replacing the graph of f(x) with the graph of f(x) - 3 is; B) The graph shifts 3 units down.

what is graph?

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it. If we know that the function crosses x axis at some, then for some polynomial functions, we have those as roots of the polynomial.

The parent function is function of x and we the translated function is in the form f(x)-3.

Transformation Rule state that if the parent function is f(x) and if we subtract some constant 'a' in f(x) then the function will move down by 'a' units.

Thus, from the transformation rule, we can conclude that f(x) graph will shift down by 3 units.

Therefore, the correct option is; B) The graph shifts 3 units down.

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to move a graph up c units, add c to the whole function

so basicaly what you did is you subtraced 3 from the whole function

the whole graph shifts 3 units down

B is answer

1)Which system of linear inequalities is graphed?A){x<−2y≤−x−1
B){x<−3y≤−x+1
C){x≤−3y≤−x−3
D){x<−3y≤−x−1

2)Which system of linear inequalities is graphed?

A) {y≤2x+1x+y≥−2
B) {y≥2x+1x+y≤−2
C) {y<2x+1x+y>−2
D) {y>2x+1x+y<−2

Answers

Answer:

1 ) D

2 ) D

Step-by-step explanation:

The general form of the straight line is given by y=mx+c, where m is the slope and c is y-intercept.

1 ) According to the graph, we get the co-ordinates (0,-1) and (-1,0).

Using these so-ordinates, we will find the equation of the line.

i.e. Slope $m = (y_(2)-y_(1))/(x_(2)-x_(1))$

i.e. $m = (0-(-1))/(-1-0)$

i.e. m = -1

Now, substituting m and (0,-1) in general form, we get c = -1.

So, the equation of this straight line is y = -x-1.

We will now use 'Zero Test' i.e. substitute (0,0) in the required equation and since the given regions are away from the origin, this pair of points will not satisfy the equation.

So, we get y < -x-1 and as the region is given to less than x= -3.

Hence, option D is correct.

2) Now, according to the second graph, we get the points (0,-2), (-2,0) and (0,1), (-1,-1) for two lines respectively.

Solving as in 1) we get that the equations of the lines are given by x+y = -2 and y = 2x+1 respectively.

Again using 'Zero Test', we see that these pair of points does not satisfy the equations.

So, we get x+y < -2 and y > 2x+1.

Hence, option D is correct.

Answer: C and B

Step-by-step explanation:

Choose all the numbers that 84 is divisible by.2
3
4
5
6
9
10

Answers

The number 84 is divisible by 2,3,4 and 6.

What is division?

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The numbers which divide 84 completely are:-

2 ⇒ 84 ÷ 2=24

3 ⇒ 84 ÷ 3=28

4 ⇒ 84 ÷ 4=21

6 ⇒ 84 ÷ 6=13

Hence, the numbers are 2,3,4 and 6.

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2↪84:2=24
3↪84:3=28
4↪84:4=21
6↪84:6=13

What is the simplified form of the expression? 3^3 ×32+12÷4

Answers

3^3=27
27*32=864
864+12=876
876/12=73
73 is your answer

ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?

Answers

Given : - Square ABCD with side 3. E and F as midpoints.
To find : - area of EBFD

Solution : - We have, area of square ABCD = 3 x 3 = 9 units.

Thus, (ar)EBFD = ar ABCD - ar DAE - arDCF

arDAE = 1/2 x base x height

=1/2 x 1.5 x 3 ( AE is 1/2 of AB = 1.5, DA is altitude)
= 2.25

arDFC = 1/2 x base x height
= 1/2 x 1.5 x 3 (FC is 1/2 of BC, DC is altitude)
= 2.25

Thus, (ar) EBFD = arABCD - arDAE - arDCF

= 9 - 2.25 - 2.25

= 4.5 units.

Thus, area of quad EBFD is 4.5 units.

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