What are the center and radius of the circle defined by the equation x^2+y^2-6x+4y+4=0

Answer:

X=5, X=1

Step-by-step explanation:

Okay so the | means absolute value and it is similar to a parentheses, except everything inside it becomes positive. Since there is a variable (x) inside it, you will have two scenarios then, one where everything inside is positive and where it's negative (so -3x +9 = -6 and 3x -9 =-6) You then solve for x in both equations.

Answer:

x=5   x=1

Step-by-step explanation:

-3|x - 3|= -6

Divide each side by -3

-3|x - 3|/-3= -6/-3

|x - 3|= 2

To get rid of the absolute value signs, we get two equations, one positive and one negative

x-3 =2           x-3 = -2

Add 3 to each side

x-3+3 = 2+3        x-3+3 = -2 +3

x =5                         x = 1

See attachment for the answer.

Answer:

360 ft^2

Step-by-step explanation:

The surface area of a right square pyramid can be found using the formula: [tex]a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex]

In this formula:

In this diagram, the base edge length is 10 ft and the height of the square pyramid is 12 ft. Substitute these values into the formula to find the surface area.

Simplify this expression. Start by evaluating the exponents then rewrite the expression.

Now evaluate inside the radical sign.

Multiply 2 and 10 together (we're following the rules of PEMDAS).

Find the square root of 169 then multiply that by 20.

Finish the problem by adding 100 and 260 together.

The surface area of the pyramid is [tex]\boxed{\text {360 ft}^2}[/tex].

If there was a graphical representation, I would be happy to assist you.

Answer: 8x^4+x^3-4x^2+1

Step-by-step explanation:

To simplify this polynomial expression, we first combine like terms. The simplified expression will be 8x^4 - x + 1.

The expression provided in your question is a polynomial that contains terms with variables raised to different powers. In simplifying this kind of polynomial, you first need to combine like terms, which are those terms that have the same variable and the same exponent.

Therefore, let's organize and combine like terms: x4 - 2x + x and 3x2 - 5x2 + x2 and . As a result, we get 8x4, or 8x to the power of 4, -x, and 1. Thus, the final simplified expression is: 8x4 - x + 1

Hope this helps in your understanding of simplifying polynomials!

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Answer

I think its Rational

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers

Given

x² = 55 ( take the square root of both sides )

x = ± [tex]\sqrt{55}[/tex] ← irrational

[tex]\sqrt{55}[/tex] cannot be expressed as a rational number

Answer:

5

Step-by-step explanation:

Let's just pretend the 6 numbers are: a,b,c,d,e,f.

Then (a+b+c+d+e+f)/6 =4 (given by first statement.)

Let's pretend the average of 2 numbers is 2 means they are talking about the a and b.

So (a+b)/2=2.

Now we want to find (c+d+e+f)/4 as requested by their question.

So first step multiply both sides of our first equation by 6 giving us:

a+b+c+d+e+f=24

So the second step multiply both sides of our second equation by 2 giving us:

a+b=4.

Now if a+b+c+d+e+f=24 and a+b=4, then c+d+e+f=20 since 20+4=24.

So the average of the four numbers c,d,e, and f is 20/4=5.

Answer:

Opposite sides are congruent; All right angles are congruent

Step-by-step explanation:

the correct answer is B) (-5, 7), which represents the center point of the circle.

The equation of a circle in standard form is given by:

[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]

Where:

- (h, k) is the center of the circle

- r is the radius of the circle

Comparing this standard form to the given equation [tex]\( (x + 5)^2 + (y - 7)^2 = 36 \)[/tex], we can identify the center and radius of the circle.

For the given equation:

- Center of the circle: (-5, 7) because the term [tex]\( (x + 5)^2 \)[/tex] means the x-coordinate of the center is -5, and the term [tex]\( (y - 7)^2 \)[/tex]means the y-coordinate of the center is 7.

- Radius of the circle: [tex]\( r = \sqrt{36} = 6 \)[/tex] because the equation is already in the form [tex]\( r^2 = 36 \), so \( r = 6 \).[/tex]

So, the correct answer is B) (-5, 7), which represents the center point of the circle.

Answer:

The perimeter can be found by calculating lengths of sides using distance formula and then adding up the lengths

Step-by-step explanation:

If the vertices of a quadrilateral are known in the coordinate plane, the vertices can be used to determine the lengths of sides of quadrilateral. The distance formula is used for calculating the distance between two vertices which is the length of the side

[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

after calculating all the lengths of four sides using their vertices, they can be summed up to find the perimeter ..

Answer:

V=1884 Cubic mm

Step-by-step explanation:

We know that the volume of the Sphere is given by the formula

[tex]V= \pi r^2h[/tex]

Where r is the radius and h is the height of the cylinder

We are asked to determine the radius of the hollow cylinder , which will be the difference of the solid cylinder and the cylinder being carved out.

[tex]V=V_1-V_2[/tex]

[tex]V=\pi r_1^2 \times h-\pi r_2^2 \times h[/tex]

[tex]V=\pi \times h \times (r_1^2-r_2^2)[/tex]

Where

[tex]V_1[/tex] is the the volume of solid cylinder with radius [tex]r_1[/tex] and height h

[tex]V_2[/tex] is the volume of the cylinder being carved out with radius [tex]r_2[/tex] and height h

where

[tex]r_1 = 7[/tex] mm ( Half of the bigger diameter )

[tex]r_2 = 5[/tex] mm ( Half of the inner diameter )

[tex]h=25[/tex] mm

Putting these values in the formula for V we get

[tex]V=\pi \times 25\times (7^2-5^2)[/tex]

[tex]V=3.14 \times 25 \times(49-25)[/tex]

[tex]V=3.14 \times 25 \times 24[/tex]

[tex]V= 1884[/tex]

Answer:

[tex]\large\boxed{x=-8\pm5\sqrt2}[/tex]

Step-by-step explanation:

[tex](x-2)^2+12(x+2)-14=0\\\\\text{Substitute}\ (x+2)=t:\\\\t^2+12t-14=0\qquad\text{add 14 to both sides}\\\\t^2+2(t)(6)=14\qquad\text{add}\ 6^2=36\ \text{to both sides}\\\\\underbrace{t^2+2(t)(6)+6^2}=14+36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(t+6)^2=50\Rightarrow t+6=\pm\sqrt{50}\qquad\text{subtract 6 from both sides}\\\\t=-6\pm\sqrt{25\cdot2}\\\\t=-6\pm5\sqrt2[/tex]

[tex]\text{we're going back to substitution}\\\\x+2=-6\pm5\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-8\pm5\sqrt2[/tex]

Answer:

D. Every integer is also a rational number

Step-by-step explanation:

Every integer is also a rational number would be FALSE about a rational statement.

Answer:

1. multiply (2) by -2 and add to (1)

-2x-2y=-1320

add to (1) we get

4y-2y=1440-1320

2y=120

y= $60 cost of silver ring.

2. Multiplying (distributive property, we get the equivalent equation

x+72=3x-216

Adding 216 to both sides of the equal sign, we get

x+72+216=3x-216+216 --> x+288=3x

Subtracting x from both sides, we get

x+288-x=3x-x --> 288=2x

Logan and Izzy had initially had 188 stickers between the two of them.

3.

a = d before Anna gives away 50 marbles.

5 (a-50) = a +50 after Anna gives away 50 marbles.

5a - 250 = a + 50

4a = 300

a = 75

Anna has 75 marbles at the beginning and so did David.

Together they have 150 marbles.

Answer:

The function g(x) has smallest minimum y-value.

Step-by-step explanation:

The given functions are

[tex]f(x)=4(x-6)^4+1[/tex]

[tex]g(x)=2x^3+28[/tex]

The degree of f(x) is 4 and degree of g(x) is 3.

The value of any number with even power is always greater than 0.

[tex](x-6)^4\geq 0[/tex]

Multiply both sides by 4.

[tex]4(x-6)^4\geq 0[/tex]

Add 1 on both the sides.

[tex]4(x-6)^4+1\geq 0+1[/tex]

[tex]f(x)\geq 1[/tex]

The value of f(x) is always greater than 1, therefore the minimum value of f(x) is 1.

The minimum value of a 3 degree polynomial is -∞. So, the minimum value of g(x) is -∞.

Since -∞ < 1, therefore the function g(x) has smallest minimum y-value.

The function f(x)=4(x-6)^4+1 has the smallest minimum y-value as its minimum value can be directly located at y=1 while g(x)=2x^3+28, being a cubic function, continues infinitely in the negative direction.

In this mathematical problem, we are tasked to determine which of the functions, f(x)=4(x-6)^4+1 or g(x)=2x^3+28, has the smallest minimum y-value. Each of these functions represent distinct types of polynomials which have different properties. The function f(x) is a quartic function that is even, or symmetric around the y-axis, while g(x) is a cubic function.

The minimum value of f(x) can be determined directly by setting the expression (x - 6)^4 to 0, yielding the minimum value 1 because any real number to the power of 4 is always non-negative and the smallest non-negative number is 0. For cubic functions like g(x), they do not have absolute minimum or maximum. They go from negative to positive infinity as x ranges over all real numbers. Therefore, the function f(x)=4(x-6)^4+1 has a smaller minimum y-value.

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Answer:

The perimeter of Δ WXY is 14.50 cm ⇒ the last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- There is a fact in any triangle; the segment joining the midpoints of

  two side of a triangle is parallel to the 3rd side and half its length

* Lets use this fact to solve the problem

- In Δ WXY

∵ Q is the midpoint of WX

∵ R is the midpoint of XY

∵ S is the midpoint of YW

- By using the fact above

∴ QR = 1/2 WY

∴ RS = 1/2 WX

∴ SQ = 1/2 XY

- Lets calculate the length of the sides of Δ WXY

∵ QR = 1/2 WY

∵ QR = 2.93

∴ 2.93 = 1/2 WY ⇒ multiply both sides by 2

∴ WY = 5.86 cm

∵ RS = 1/2 WX

∵ RS = 2.04

∴ 2.04 = 1/2 WX ⇒ multiply both sides by 2

∴ WX = 4.08 cm

∵ SQ = 1/2 XY

∵ SQ = 2.28

∴ 2.28 = 1/2 XY ⇒ multiply both sides by 2

∴ XY = 4.56 cm

- Lets find the perimeter of Δ WXY

∵ The perimeter of Δ WXY = WX + XY + YW

∴ The perimeter of Δ WXY = 5.86 + 4.08 + 4.56 = 14.50

* The perimeter of Δ WXY is 14.50 cm

In this exercise we have to use the knowledge of the perimeter of a figure to calculate its value, and then:

Letter D

So from some information given in the statement and in the image, we can say that:

So solving, you will have to:

[tex]QR = 1/2 WY\\RS = 1/2 WX\\SQ = 1/2 XY[/tex]

Now with both information we can calculate the perimeter value as:

[tex]QR = 1/2 WY\\QR = 2.93\\2.93 = 1/2 WY\\ WY = 5.86 cm\\RS = 1/2 WX\\ RS = 2.04\\2.04 = 1/2 WX\\WX = 4.08 cm\\SQ = 1/2 XY\\SQ = 2.28\\2.28 = 1/2 XY \\XY = 4.56 cm\\ WXY = WX + XY + YW\\WXY = 5.86 + 4.08 + 4.56 = 14.50[/tex]

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Answer:

126.5 ft

Step-by-step explanation:

It's further for the catcher to throw to

The catcher must throw approximately 127.3 feet to get a runner out at second base on a square baseball diamond. The Pythagorean theorem is used to calculate the diagonal from home plate to second base. Runners often try to steal second base due to the longer throw required and being in scoring position.

The question involves calculating the distance a catcher must throw the ball to get a runner out at second base on a baseball diamond, which is a square with sides of 90 feet. To find this distance, we must determine the diagonal of the square, as the catcher throws the ball from one corner (home plate) to the opposite corner (second base). Applying the Pythagorean theorem to the square, the diagonal distance D is given by D = √(90² + 90²). So, D = √(8100 + 8100) = √16200 feet, which approximately equals 127.3 feet. Runners are inclined to steal second base more often because it is generally easier to steal with the catcher having to make a longer throw, and once on second base, the runner is in scoring position with two bases potentially available to advance.

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Simplified form of expression is,

⇒ - 3√3

We have to given that,

An expression is,

⇒ 2√27 + √12 - 3√3 - 2√12

We can simplify it as,

⇒ 2√27 + √12 - 3√3 - 2√12

⇒ 2 √9×3 + √3×4 - 3√3 - 2√3×4

⇒ 2 × 3 √3 - 2√3 - 3√3 - 2 × 2√3

⇒ 6√3 - 2√3 - 3√3 - 4√3

⇒ - 3√3

Therefore, Simplified form of expression is,

⇒ - 3√3

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Final answer:

The expression simplifies to 4sqrt(3) after breaking down the square roots of 27 and 12 into 3√(3) and 2√(3), respectively, and combining like terms.

Explanation:

To simplify the expression 2√(27) + √(12) - 3√(3) - 2√(12), we should first simplify √(27) and √(12) individually.

Square root of 27 can be written as √(9*3). Since 9 is a perfect square, we get 3√(3). Similarly, √(12) can be simplified to √(4*3). As 4 is a perfect square, this simplifies to 2√(3).

Now, substituting back into the original expression, we get 2(3√(3)) + 2√(3) - 3√(3) - 2(2√(3)), which simplifies to 6√(3) + 2√(3) - 3√(3) - 4√(3).

Combining like terms, we obtain 6√(3) - 2√(3), which simplifies further to 4√(3).

Therefore, the simplified form of the original expression is 4√(3).

Answer:

Yep your correct, 3 east 5 north.

Step-by-step explanation:

He first walks 6 east and 2 north

He then walks 3 west and 3 north

East and west are opposites so 6-3=3 east (not west because he walked more blocks east than west)

North and north are the same so 2+3=5 north

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Answer:

2b2t

Step-by-step explanation:

2b2t

Answer:

x = 3, x = - 3, x = - 1 with multiplicity 2

Step-by-step explanation:

Given that x = 3 and x = - 3 are zeros then

(x - 3) and (x + 3) are factors and

(x - 3)(x + 3) = x² - 9 ← is a factor

Using long division to divide the polynomial by x² - 9 gives

quotient = x² + 2x + 1 = (x + 1)² and equating to zero

(x + 1)² = 0 ⇒ x + 1 = 0 ⇒ x = - 1 with multiplicity 2

Hence the zeros of the polynomial are

x = 3, x = - 3, x = - 1 with multiplicity 2

Answer: 3y/2 - 5

Step-by-step explanation:

Expand

-(-3y/2 + 5)

Simplify the brackets

3y/2 - 5

Answer:

Monthly Payment = $457.5

Total amount Henry end up paying for the boat overall = $35,960

Step-by-step explanation:

Total Amount to be paid = $32,000

Down Payment = $ 14,000

Interest rate = 5.5%

Total time for Amount to be paid = 4 years

Rest of the payment to be paid = 32,000 - 14,000

= 18000

Amount of interest = P*r*t

P= Principal Amount

r = rate

t = time

Putting values

Amount of interest= 0.055 *18000*4 = 3960

Total Remaining payment = 18000+3960 = 21,960

As Payment to be paid in 4 years, So number of months = 4*12 = 48 months

Monthly payment = Total Payment / Months = 21,960/48 = 457.5

So, Monthly Payment = $457.5

Total amount Henry end up paying for the boat overall = Down Payment + Remaining Payment

=14,000+21960

= 35960

So, Total amount Henry end up paying for the boat overall = $35,960

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation

[tex]y-36x-1=0[/tex]     add 36x and 1 to both sides

[tex]y-36x+36x-1+1=36x+1[/tex]

[tex]y=36x+1[/tex]

Therefore

the slope: m = 36

the y-intercept: b = 1

Answer:

x=-2/9 or

x = negative 2 over 9

Step-by-step explanation:

We need to solve:

[tex]\frac{2}{5}(x-2)=4x[/tex]

and find the value of x.

Solving:

[tex]\frac{2}{5}(x-2)=4x\\\frac{2x}{5}-\frac{4}{5}=4x\\ Adding \,\,4/5\,\,on\,\,both\,\,sides\\\frac{2x}{5}-\frac{4}{5}+\frac{4}{5}=4x+\frac{4}{5}\\\frac{2x}{5}=4x+\frac{4}{5}\\subtract \,\,4x\,\,from both sides\\\frac{2x}{5}-4x=\frac{4}{5}\\\frac{2x-20x}{5}=\frac{4}{5}\\\frac{-18x}{5}=\frac{4}{5}\\-18x=\frac{4}{5}*5\\-18x=4\\x=\frac{4}{-18}\\x=\frac{-2}{9}[/tex]

x=-2/9 or

x = negative 2 over 9

Answer:

Step-by-step explanation:

The y value has to be 0, so neither of those 2 answers look correct.

factor the quadratic

x^2 + 8x +7 = 0

(x + 7)(x + 1) = 0

x + 7 = 0

x = - 7

========

x + 1 = 0

x = - 1

========

The two points that solve this equation are

(-1,0)

(-7,0)

Answer:

The answer for the equation is {-1,-7}

Step-by-step explanation:

This is found by using the quadratic equation.

Answer:

m=4

n=-2

Step-by-step explanation:

(7z^m) (nz^3) = -14z^7

7*n z^(m+3) = -14 z^7

We know the constants have to be the same

7n = -14

Divide each side by 7

7n/7 = -14/7

n = -2

And the exponents have to be the same

m+3 = 7

Subtract 3 from each side

m+3-3 = 7-3

m =4

The values that satisfy the equation (7z^m) (nz^3) = -14z^7 are m = 4 and n = -2, found by equating coefficients and exponents.

To find the values for m and n that would make the given equation true, we need to equate the coefficients and the exponents of the similar terms on both sides of the equation. The original equation is (7zm) (nz3) = -14z7.

First, let's look at the coefficients: 7 * n should equal -14. This gives us the value of n directly, n = -2.

Now, let's look at the exponents of z. To equate the exponents, we use the property that when multiplying similar bases, the exponents are added: m + 3 equals 7. Solving for m gives us m = 4.

Therefore, the values that satisfy the equation are m = 4 and n = -2.

[tex]\bf V=\cfrac{1}{3}s^2h\implies V=\cfrac{s^2h}{3}\implies 3V=s^2 h\implies \cfrac{3V}{h}=s^2\implies \sqrt{\cfrac{3V}{h}}=s[/tex]

Answer:

s = sqrt(3V/h)

Step-by-step explanation:

To put this in terms of s, we must first isolate the s^2. So we can multiply by 3/h on both sides. So we get s^2 = 3V/h. Taking the square roots of both sides, we get s = sqrt(3V/h).

Answer:

B 3 ^ (1/9)

Step-by-step explanation:

We know that a^b^c = a ^ (b*c)

3 ^ (2/3)^1/6

3^ (2/3*1/6)

3^ (2/18)

3^(1/9)

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle.

So, we have that the area of the shaded region is given by:

[tex]\pi * (2x) ^ 2- \pi * 6 ^ 2 = 288 \pi\\4x ^ 2-36 = 288\\4x ^ 2 = 288 + 36\\4x ^ 2 = 324[/tex]

We divide between 4 on both sides of the equation:

[tex]x ^ 2 = 81[/tex]

We apply root to both sides:

[tex]x = \pm \sqrt {81}[/tex]

We choose the positive value of the root:

[tex]x = \sqrt {81}\\x = 9[/tex]

Finally, the value of "x" is 9

Answer:

[tex]x = 9[/tex]

Answer:

B

Step-by-step explanation:

Using the rule of exponents

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

f(x) = [tex]16^{x}[/tex], then when x = [tex]\frac{1}{2}[/tex]

f([tex]\frac{1}{2}[/tex] ) = [tex]16^{\frac{1}{2} }[/tex] = [tex]\sqrt[2]{16}[/tex] = 4