The equation x^2+ y^2+ 8x - 12y + 43 = 0 is the equation of a circle. Complete the square to change this
equation to standard form. Find the radius and the coordinates of the center of the circle and then graph the
circle.

Answer:

[tex]{ \bf{a).}} \\ { \tt{( \sqrt{6} + \sqrt{3} )( \sqrt{6} - \sqrt{3}) }} \\ { \tt{ = ( { \sqrt{6} )}^{2} - {( \sqrt{3}) }^{2} }} \\ { \tt{ = 6 - 3}} \\ { \tt{ = 3}} \\ \\ { \bf{b).}} \\ { \tt{( \sqrt{5} - \sqrt{2})( \sqrt{2} + \sqrt{5} )}} \\ { \tt{ = ( { \sqrt{5} }^{2}) - { (\sqrt{2} }^{2}) }} \\ { \tt{ = 5 - 2}} \\ { \tt{ = 3}}[/tex]

Answer:

(6-3)(5-2)=3×3=9

Step-by-step explanation:

[tex]x ^{2} - {y}^{2} = (x - y)(x + y)[/tex]

[tex]( \sqrt{6} - \sqrt{3} )( \sqrt{6} + \sqrt{3} ) = ( { \sqrt{6} }^{2} - { \sqrt{3} }^{2} ) = 6 - 3 = 3[/tex]

Answer:

[tex](\frac{6}{11} )*(\frac{6}{11} )[/tex] = 36/121 =.297

Step-by-step explanation:

Answer:

36/121

Step-by-step explanation:

We have 5+6 = 11 marbles

P(red) = number of red/ total = 6/11

We replace the marble so we still have 11 marbles

P(red) = number of red/ total = 6/11

P(red, red) = 6/11*6/11 = 36/121

Answer:

640 feet.

Step-by-step explanation:

Let d represent the distance required to stop and let s represent the speed of the car.

The distance required to stop varies directly as the square of its speed. In other words:

[tex]d=ks^2[/tex]

Where k is the constant of variation.

250 feet are required to stop a car traveling 60 miles per hour. Substitute:

[tex](250)=k(60)^2[/tex]

Simplify and solve for k:

[tex]\displaystyle 3600k=250\Rightarrow k=\frac{250}{3600}=\frac{25}{360}=\frac{5}{72}[/tex]

So, our equation is:

[tex]\displaystyle d=\frac{5}{72}s^2[/tex]

Then the distance required to stop a car traveling 96 miles per hour will be:

[tex]\displaystyle d=\frac{5}{72}(96)^2=\frac{5}{72}(9216)=640\text{ feet}[/tex]

Answer:

59 is prime ... 1 & 59 are the only factors

Step-by-step explanation:

Answer:On June 17

the explanation is in the picture

Answer:

<K ≅ <N

Step-by-step explanation:

JKL ≅ MNP

That means the angles are the same

<J ≅< M

<K ≅ <N

<L ≅<P

The sides are also congruent

JK ≅ MN

KL ≅ NP

JL ≅ MP

Answer:

(x + 4)(x + 3)

Step-by-step explanation:

x^2 + 7x + 12

In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term. Factor each pair by finding common factors.

so we need two number that gives 12 when multiplied and 7 when added

4 and 3 are the numbers because 4*3 = 12 and 4+3 = 12

=x^2 + (4 + 3)x + 12

=x^2 + 4x + 3x + 12

=x(x + 4) + 3(x + 4)

take (x + 4) as common

=(x + 4) (x*1 + 3*1)

=(x + 4)(x + 3)

Answer:

Step-by-step explanation:

[tex]6\sqrt{20} + 8\sqrt{5} -5\sqrt{45}[/tex]

[tex]12\sqrt{5} + 8\sqrt{5} -15\sqrt{5}[/tex]

[tex]5\sqrt{5}[/tex]

Answer:

Step-by-step explanation:

I imagine that you are simplifying this, since there is nothing else you can do with it. You are in the section in algebra where you're learning how to simplify radicals. ALWAYS think prime factorization when it comes to numbers. For example, the square root of 5...the prime factorization of 5 is simply 5 * 1. So we know that √5 is as simple as it can be. It would benefit us if we could simplify either of the other 2 radicals down to the same radicand so we could add or subtract them.

The prime factorization of 20 is

20--> 5   *   4

                  4--> perfect square (2×2). So the simplification of 6√20 is 6×2√5 which is 12√5.

The prime factorization of 45 is

45--> 5   *   9

                   9--> perfect square (3×3). So the simplification of 5√45 is 5×3√5 which is 15√5.

Put it all together to get

12√5 + 8√5 -15√5 which simplifies to

5√5

Answer:

let the ages of the brothers be 2x and 3x

2x +3x=35

5x=35

x=35÷5

x=7

now,

A=2x=2×7=14

B=3x=3×7=21

this is the answer

Answer:

D = [tex]\sqrt{\frac{216W}{35L} }[/tex]

Step-by-step explanation:

From the given question, the expression showing the relationship among the weight, length and diameter of the metal bar is;

W [tex]\alpha[/tex] L[tex]D^{2}[/tex]

W = kL[tex]D^{2}[/tex]

where k is the constant of proportionality.

When W = 140, D = 4 and L = 54, then;

140 = k(54)[tex](4)^{2}[/tex]

      = 864k

k = [tex]\frac{140}{864}[/tex]

  = [tex]\frac{35}{216}[/tex]

k = [tex]\frac{35}{216}[/tex]

⇒ W = [tex]\frac{35LD^{2} }{216}[/tex]

So that;

35L[tex]D^{2}[/tex] = 216W

[tex]D^{2}[/tex] = [tex]\frac{216W}{35L}[/tex]

D = [tex]\sqrt{\frac{216W}{35L} }[/tex]

Answer:

the third graph is the answer

Answer:

It's A.

Step-by-step explanation:

Since 175-87 is 88, there is 88 or less available tickets left. So it is A.

Hope this helps.

Answer:

x = 25

Step-by-step explanation:

The angles in a triangle add up to 180°, so we can write an equation to model the situation:

55 + 75 + 2x = 180

Now, we can simplify and solve:

130 + 2x = 180

2x = 50

x = 25

Answer:

x = 25

Step-by-step explanation:

The angles in a triangle add up to 180 degrees.

Using this, create an equation:

55 + 75 + 2x = 180

Solve for x:

55 + 75 + 2x = 180

130 + 2x = 180

2x = 50

x = 25

So, x = 25

Answer:

2nd option

Step-by-step explanation:

Using the rule of exponents/ radicals

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex](\sqrt[n]{a}) ^{m}[/tex] , then

[tex]\sqrt{10} ^{\frac{3x}{4} }[/tex]

= [tex](\sqrt[4]{10}) ^{3x}[/tex]

Answer:

Step-by-step explanation:

That exterior angle is equal to the sum of the remote interiors, specifically:

2x + 3 = 45 + x + 8 and

x = 50

So the angles inside the triangle...we already know one of them is 45. If x = 50, then x + 8 is 50 + 8 = 58. That means that the third angle is 180 - 45 - 58 which is 77.

Hope this helps

Answer:

£21

€28 = £21

Answer:

175°

Step-by-step explanation:

If angle x = 058° and angle y = 127° then the bearing A from point O is 360 minus angle x plus angle y.

Solution:

360° - (058° + 127°) = 175°

This is because the complete turn from north to north is 360°.

Answer:

4762 N/m^2

Step-by-step explanation:

Find area.

30x5.6=168

Convert to m^2

168cm^2=0.0168m^2

Use pressure formula to get answer

P=F/A

P=80/0.0168

P=4762 N/m^2

Answer:

A, C are both solutions

Step-by-step explanation:

B will not work because:

-1 = 4(-1/4)² + 4(-1/4) - 1

-1 = 1/4 - 1 - 1

-1 ≠ -1 3/4

D will not work because:

1 = 4(1/4)² + 4(1/4) - 1

1 = 1/4 + 1 - 1

1 ≠ 1/4

Answer:

[tex]\text{C. }60[/tex]

Step-by-step explanation:

Question from image:

"The digits 1, 2, 3, 4, and 5 can be formed to arrange 120 different numbers. How many of these numbers will have the digits 1 and 2 in increasing order? For example, 14352 and 51234 are two such numbers."

Let's start by taking a look with the number 1. There are four possible places 1 could be, because there needs to be space for the 2 after it.

Checkmarks mark where the 1 can be, the x marks where it cannot be.

[tex]\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{X}[/tex]

Let's start with the first position:

[tex]\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]

There are four places the 2 can be. For each of these four places, we can arrange the remaining 3 digits in [tex]3!=6[/tex] ways. Therefore, there are [tex]4\cdot 6=\boxed{24}[/tex] possible numbers when 1 is the first digit of the number.

Continue this process with the remaining possible positions for 1.

Second position:

[tex]\underline{X}\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]

There are three places the 2 can be, since the 2 must be behind the 1. For each of these three places, the remaining 3 digits can be arranged in [tex]3!=6[/tex] ways. Therefore, there are [tex]3\cdot 6=\boxed{18}[/tex] possible numbers when 1 is the second digit of the number.

The pattern continues. Next there will be 2 places to place the 2. For each of these, there are [tex]3!=6[/tex] ways to rearrange the remaining 3 digits for a total of [tex]2\cdot 6=\boxed{12}[/tex] possible numbers when 1 is the third digit of the number.

Lastly, when 1 is the fourth digit of the number, there is only 1 place the 2 can be. For this one place, there are still [tex]3!=6[/tex] ways to rearrange the remaining three numbers. Therefore, there are [tex]1\cdot 6=\boxed{6}[/tex] possible numbers when 1 is the fourth digit of the number.

Thus, there are [tex]24+18+12+6=\boxed{60}[/tex] numbers that will have the digits 1 and 2 in increasing order, from a set of 120 five-digit numbers created by the digits 1 through 5, where no digit may be repeated.

10235

I just typed it in a calculator

the answer is in the above image

Answer:

Step-by-step explanation:

5* (2⁰ + 2¹ + 2 ²+ 2³+ ........+ 2¹⁰)

Sum of geometric series = [tex]a*\frac{r^{n}-1}{r-1}[/tex]

a -> first term = 1

r- ratio = 2

n --> number of terms = 11

5* (2⁰ + 2¹ + 2 ²+ 2³+ ........+ 2¹⁰)=

 [tex]5*[1*\frac{2^{11}-1}{2-1}]\\\\=5 *[1*(2048-1)]\\\\= 5 * 2047\\= 10235[/tex]

Step-by-step explanation:

4(2.8*4.5)=50.4

50.4/12= 4.2

4.2 means 5 tins of paint

£52.5 =price

Step-by-step explanation:

i have explained in the paper.

Goodluck

Answer:

Step-by-step explanation:

4/9 on the number line would be 0.44.

-7/9 on the number line would be -0.77

Answer:

9 pounds

Step-by-step explanation:

1 lb = 16 ounces

144/16 = 9 pounds

Answer:

∠ BCD = 111°

Step-by-step explanation:

Since AB = BC then the triangle is isosceles and the 2 base angles are congruent.

∠ ACB = ∠ A = 69°

∠ ACB and ∠ BCD are adjacent angles and sum to 180° , that is

∠ BCD + ∠ ACB = 180°

∠ BCD + 69° = 180° ( subtract 69° from both sides )

∠ BCD = 111°

Step-by-step explanation:

The first president of the United States was

[tex]\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}[/tex]

Answer:

x=9

y=12

Step-by-step explanation: