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3 years ago

The equation below describes a circle. x^2+14x+y^2=70. what are the center and radius of the circle?

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

5 0

Answer:

Step-by-step explanation:

center(-7,0)

radius= radical 119

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Graph each absolute value function. State the domain, range, and y-intercept.

grandymaker [24]

Answer:

i) D: All real numbers

ii) R: $y\le5$

iii) Y-int: b=2

Step-by-step explanation:

i) The given absolute value function is

$y=-|x+3|+5$

The domain is all values of x that makes the function defined.

The absolute value function is defined for all values of x.

The domain is all real numbers.

ii) The given function is $y=-|x+3|+5$

The function has vertex $(-3,5)$ .

The function is reflected in the x-axis.

This means the vertex is the maximum point on the graph of the function.

The maximum y-value is 5.

The range is therefore $y\le 5$ or $(-\infty,5]$

iii) To find the y-intercept, put $x=0$ into the function.

$y=-|0+3|+5$

$y=-|3|+5$

$y=-3+5$

$y=2$

The y-intercept is (0,2) or $b=2$

See attachment for graph.

6 0

3 years ago

The side length of a square S can be determined by the formula S equals the square root of a where a represents the area of the

kakasveta [241]

Answer:the side length of a square with the area 0.09 square meter is 0.3 meter.

Step-by-step explanation:

The side length of a square S can be determined by the formula S equals the square root of a where a represents the area of the square. It means that

S = √a

Therefore, the side length of a square with the area 0.09 square meter would be

S = √0.09 = 0.3 meter

7 0

3 years ago

How large is one side of the square garden plot in meters

ruslelena [56]

the correct question in attached figure

Let
A1 -------------------------> area rectangular plot=4*9=36 m²
A2 ------------------------- > area square plot=x²

we have that
A1=A2
A2=x²=36---------------> x=√36=6 m

the answer is 6 m

4 0

2 years ago

Find the solution of the system of equations 3x+4y=10 and x−y=1. Give the x value followed by the y value, separated by a comma.

Burka [1]

Answer:

x,y =2,1

Step-by-step explanation:

3x+4y=10 ................equ1

x-y=1 ................equ2

This system of equations forms a quadratic equation.

Lets use the substitution method in solving this set of equations

from equ 2; x=y+1

substitute x=y+1 into equ 1

3(y+1) +4y=10

3y+3+4y=10

7y=10-3

7y=7

y=7/7

y=1

but x=y+1

substitute the value of y into this equation to get x

x= 1+1

x=2

x,y=2,1

5 0

3 years ago

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2

Basile [38]

Answer:

$f(x) = x^3 - 2x^2 -3x + 6$

Step-by-step explanation:

According to the Factor Theorem, if (x - k) is a factor of a polynomial P(x), then P(k) must equal zero.

We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let k = 2, √3, -√3.

So, according to the Factor Theorem, P(2), P(√3) and P(-√3) must equal 0.

Testing each choice, we can see that only A is true:

$\displaystyle f(x) = x^3 - 2x^2 - 3x + 6$

Testing all three values yields that:

$\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \end{aligned}$

Hence, our answer is A.

3 0

2 years ago