Use the elimination method to solve the system of equations

The answer is:

The center of the circle is the point (-9,-2) and the circle has a radius of 6 units.

To solve the problem, we need to use the given equation which is in the general form, and then, use it transform it to the standard form in order to find the center of the circle and its radius.

So,

We are given the circle:

[tex]x^{2}+y^{2}+18x+4y+49=0[/tex]

We know that a circle can be written in the following form:

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

Where,

h is the x-coordinate of the center of the circle

k is the y-coordinate of the center of the circle

r is the radius of the circle.

So, to find the center and the radius, we need to perform the following steps:

- Moving the constant to the other side of the equation:

[tex]x^{2}+y^{2}+18x+4y=-49[/tex]

- Grouping the terms (x and y):

[tex]x^{2}+18x+y^{2}+4y=-49[/tex]

- Completing squares for both variables, we have:

We need to sum to each side of the equation the following term:

[tex](\frac{b}{2})^{2}[/tex]

Where, b, for this case, will the coefficients for both terms that have linear variables (x and y)

So, the variable "x", we have:

[tex]x^{2} +18x[/tex]

Where,

[tex]b=18[/tex]

Then,

[tex](\frac{18}{2})^{2}=(9)^{2}=81[/tex]

So, we need to add the number 81 to each side of the circle equation.

Now, for the variable "y", we have:

[tex]y^{2} +4y[/tex]

Where,

[tex]b=4[/tex]

[tex](\frac{4}{2})^{2}=(2)^{2}=4[/tex]

So, we need to add the number 4 to each side of the circle equation.

Therefore, we have:

[tex](x^{2}+18x+81)+(y^{2}+4y+4)=-49+81+4[/tex]

Then, factoring, we have that the expression will be:

[tex](x+9)^{2}+(y+2)^{2}=36[/tex]

- Writing the standard form of the circle:

Now,  from the simplified expression (after factoring), we can write the circle in the standard form:

[tex](x+9)^{2}+(y+2)^{2}=36[/tex]

Is also equal to:

[tex](x-(-9))^{2}+(y-(-2))^{2}=36[/tex]

Where,

[tex]h=-9\\k=-2\\r=\sqrt{36}=6[/tex]

Hence, the center of the circle is the point (-9,-2) and the circle has a radius of 6 units.

Have a nice day!

A triangle with angles of 30, 60, and 90 degrees is a unique and special type of right triangle known as a 30-60-90 right triangle, which has consistent properties and side ratios in Euclidean geometry.

Yes, a triangle with angles of 30, 60, and 90 degrees is a unique triangle, known as a 30-60-90 right triangle. This classification is based on the fact that in Euclidean geometry, the sum of the angles in any triangle is exactly 180 degrees. Since one of the angles is given as 90 degrees, this indicates it is a right triangle, and the remaining angles must add up to 90 degrees. Given that the other two angles are 30 and 60 degrees, this satisfies the requirement exactly, making it a specific type of right triangle with consistent properties.

For example, the sides of a 30-60-90 triangle are always in the ratio 1:√3:2. The side opposite the 30-degree angle is the shortest; the side opposite the 60-degree angle is √3 times longer; and the hypotenuse, opposite the 90-degree angle, is twice as long as the shortest side. These proportions and the angles create the unique properties of the 30-60-90 triangle, and they can be applied in trigonometric calculations and proofs. This distinct set of angles and side ratios is what makes the 30-60-90 triangle a special and unique case in geometry.

Final answer:

To calculate Trevor's total investment, multiply the number of shares of each fund by their respective offer prices and sum the results. Trevor's total investment for both Upton Group and TJH Small-Cap amounts to $2850.30.

Explanation:

To calculate Trevor's total investment, we need to multiply the number of shares he purchased by their respective offer price and then add the costs of both investments together.

For the Upton Group, the investment is:

80 shares × $18.96 per share = $1516.80

For TJH Small-Cap, the investment is:

70 shares × $19.05 per share = $1333.50

Therefore, Trevor's total investment is:

$1516.80 (Upton Group) + $1333.50 (TJH Small-Cap) = $2850.30

Answer:

12

Step-by-step explanation:

Answer:b 2(39) +2(75)

Step-by-step explanation:

Because there are four corners of a mattress your going to take the length and width of the mattress and multiply each time to then add them to get the exact size your needing

Answer:

39 × 75

Step-by-step explanation:

Since, the shape of the twin mattress is rectangular,

Given,

The length of the mattress = 75 inches,

Width of the mattress = 39 inches,

Now, the the area of the top of the mattress( which is covered by the quilt) = Area of the mattress

We know that,

The Area of a rectangle =  Length × Width

Hence, the area of the top of the mattress = 75 × 39

= 39 × 75

Third option is correct.

First you want to multiple .13 by 15 giving you 1.95 meters

Then you want to times that by 100 since there are 100 centimeters in a meter

giving you 195 centimeters

A coral reef grows 195 cm in 15 weeks.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

The unitary method exists as a technique for solving a situation by first finding the value of a single unit, and then discovering the essential value by multiplying the single unit value.

Given

in 1 week , coral grows 0.13m

in 15 weeks it grows = [tex]0.13* 15 =1.95m[/tex]

1 m = 100cm

1.95 m = [tex]1.95 * 100 = 195 cm[/tex]

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Irrational because it can not be a whole number

Answer:

The value of x is 26 degrees

Step-by-step explanation:

1: 1/4 of a circle (360 degrees) is 90 degrees.

2 90 - 64 = 26

Answer:

he has to run twice for it to be at least a mile

Answer:

12

Step-by-step explanation:

12 times 12 is 144

Answer:

12.

Step-by-step explanation:

If you were to divide 144 into 12 parts, each part would have 12 pieces. Another way to imagine it would be setting up a fraction (144/12) and then simplifying until you get 12/1.

Answer:

Part A. the x-intercepts are: x=4 and x= -1/4

Part B. The vertex of the graph is going to be a maximum

Part C. y-intercept is y=8

Step-by-step explanation:

We have the following function:

f(x) = −8x^2 + 30x + 8

Part A: What are the x-intercepts (zeros) of the graph of the f(x)?

To find the x-intercepts we have to make y=0 and solve for x. Then:

y = −8x^2 + 30x + 8

0 = −8x^2 + 30x + 8

8x^2 - 30x - 8  = 0

Dividing the whole expression by 8:

x^2 - 15/4x - 1  = 0

Using the quadratic formula we have that:

(x−4)(4x+1)

So the x-intercepts are: x=4 and x= -1/4

Part B.  Is the vertex of the graph of f(x) going to be a maximum or minimum?

The vertex of the graph is going to be a maximum, given that the quadratic term is multiplied by a negative sign.

PArt C. What is the y intercept of the graph?

To calculate the y-intercept we need to make x=0, so:

y = −8(0)^2 + 30(0) + 8 = 8

So the y-intercept is y=8

Answer:

400° F = 204.4° C

Step-by-step explanation:

We are given a temperature 400 degree in Fahrenheit and we are to convert in into another unit that is Centigrade (also known as Celsius).

We know that 0 degree Centigrade is equal to 32 Fahrenheit so we will use the following formula for conversion of units:

(32°F − 32) × 5/9 = 0°C

(400°F − 32) × 5/9 = 204.4° C

Answer:

Step-by-step explanation:

I think you are just asking for the decimal answers.

3/20 = 0.15

9/50 = 0.18

38/200 = 0.19

Answer:

106 ft²

Step-by-step explanation:

The surface area of a triangular pyramid is calculated with the following formula:

[tex]SA = \frac{H B}{2} + \frac{3 B S}{2}[/tex]

Where:

H is the height of the triangle base,

B is the side of the base triangle

S is the length of the slant.

so, if we plug in our numbers, we have:

[tex]SA = \frac{5.2 * 6}{2} + \frac{3 * 6 * 10}{2} = 15.6 + 90 = 105.6[/tex]

105.6 sq ft, which we round up to 106 square feet.

Angle sum identity:

[tex]\sin285^\circ=\sin(240^\circ+45^\circ)=\sin240^\circ\cos45^\circ+\cos240^\circ\sin45^\circ[/tex]

Now

[tex]\sin240^\circ=\sin(180^\circ+60^\circ)=-\sin60^\circ=-\dfrac{\sqrt3}2[/tex]

[tex]\cos240^\circ=\cos(180^\circ+60^\circ)=-\cos60^\circ=-\dfrac12[/tex]

[tex]\sin45^\circ=\cos45^\circ=\dfrac1{\sqrt2}[/tex]

so we end up with

[tex]\sin285^\circ=-\dfrac{\sqrt3}{2\sqrt2}-\dfrac1{2\sqrt2}=-\dfrac{\sqrt3+1}{2\sqrt2}=-\dfrac{\sqrt6+\sqrt2}4[/tex]

Answer:

6.98%

Step-by-step explanation:

To find relative frequency we divide frequency with the total number participants in that age bracket

Total number of participants age 10-19=172.....................given in the table

The frequence for those who ski at age 10-19=12---------------given in table

Relative frequency= 12/172 = 0.0697

Expressed as a percentage= 0.06976×100 =6.98%

Answer:

The correct answer option is 6.98%.

Step-by-step explanation:

We are given the results of a survey which asked  two age groups which summer sport they most preferred.

We are to find the relative frequency of 10-19 year old who preferred to ski.

For that, we will divide the number of kids aged 10-19 years who prefer to ski by the total number of people who prefer to ski and multiply by 100.

Relative frequency = 12/172 * 100 = 6.98%

Answer:

You need 30 total weeks to win at least 65% games

Step-by-step explanation:

Team have played = 20 games

Number of winning games = 3

Let x represents the number of additional weeks.

You have won 3 games per week. Therefore you will win 3x additional games.

We know that 65% = 0.65

Therefore,

3+3x/20+4x = 0.65

By cross multiplication:

3+3x= 0.65(20+4x)

3+3x = 13+2.6x

Combine the like terms:

3x-2.6x = 13-3

0.4x=10

4x/10 =10

4x = 10*10

4x=100

Divide both sides by 4

4x/4 = 100/4

x = 25

since you have already played 5 weeks...you need to play 25+5 = 30 weeks.

Therefore you need 30 total weeks to win at least 65% games....

Answer:

The volume of the figure is [tex](\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of the cone minus the volume of the square pyramid

step 1

Find the volume of the cone

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=\frac{l\sqrt{2}}{2}\ units[/tex] ----> the diagonal of the square base of pyramid is equal to the diameter of the cone

[tex]h=l\ units[/tex]

substitute

[tex]V=\frac{1}{3}\pi (\frac{l\sqrt{2}}{2})^{2}(l)[/tex]

[tex]V=\frac{1}{6}\pi (l)^{3}\ units^{3}[/tex]  

step 2

Find the volume of the square pyramid

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

we have

[tex]h=l\ units[/tex]

[tex]B=l^{2}\ units^{2}[/tex]

substitute

[tex]V=\frac{1}{3}l^{2}(l)[/tex]

[tex]V=\frac{1}{3}l^{3}\ units^{3}[/tex]

step 3

Find the volume of the figure

[tex]\frac{1}{6}\pi (l)^{3}\ units^{3}-\frac{1}{3}l^{3}\ units^{3}=(\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]

Answer:

x=0.4

Step-by-step explanation:

Answer:

x=0.4

Step-by-step explanation:

ik im good

What is the term used to describe the distribution of a data set with one mode? b. Unimodal

A.

Step-by-step explanation:

Multimodal

❤❤❤❤❤❤❤❤❤❤❤❤❤

Answer:

To find the value of the y units, u have to multiply any x unit with the first y unit given but not 0

Step-by-step explanation:

Answer:

91

Step-by-step explanation:

91 is what I think makes the most sense

The mean weight of the three reserve players is found by rearranging the formula for calculating the mean, substituting known values, and solving the equation.

Given that the mean weight of all 12 players (nine players + three reserve players) is 188 pounds. Let's denote the missing weight of the three reserve players as 'x', 'y', and 'z'.

The formula to calculate mean is the sum of all the weights divided by the number of players. Here, mean weight equals (9*188 + x + y + z) / 12.

As we know that the mean weight is 188 pounds. We can substitute it back into the formula:
9*188 + x + y + z = 188 * 12.
This simplifies to x + y + z = 188 * 12 - 9 * 188.

We divide by 3 (since we are looking for the mean weight of three players): (x + y + z) / 3 = (188*12 - 9*188) / 3. Thus, the mean weight of the three reserve players can be found by solving this equation.

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Answer:

(B) -9

Step-by-step explanation:

g(x) = 2x² - 11x

To find g(1), we substitute x = 1 into g(x).

g(x) = 2x² - 11x

g(1) = 2(1)² - 11(1) = 2 - 11 = -9

ANSWER

B) -9

EXPLANATION

The given function is

[tex]g(x) = 2 {x}^{2} - 11x[/tex]

Put x=1 into the given function to obtain;

[tex]g(1) = 2 {(1)}^{2} - 11(1) [/tex]

Simplify to get:

[tex]g(1) = 2 (1) - 11(1) [/tex]

[tex]g(1) = 2 - 11 = - 9[/tex]

The correct choice is B.

Answer:

The distributive property says that when there is a number outside of parenthesis, this means it should be distributed (or multiplied) to the values inside the parenthesis.

So in this situation, 10 x b = 10b

and 10 x 4c = 40 c

so 10(b + 4c) becomes 10b + 40c once the 10 is distributed within the parenthesis.

I hope this helps!

Answer:

They are equivalent expressions because if you use distributive property and multiply 10*b, then multiply 10*4c, you get 10b+40c

Step-by-step explanation:

See the attached picture for the solution.

Round the answer as needed.

Answer:

Step-by-step explanation:

This problem models a right triangles, where the hypothenuses is the length of the string, and one leg would be 180ft, which is the difference between the total height from the ground and the pole height (186-6=180). Also, the angle in front of the knowing leg is 60.

As, based on all given values, we can apply trigonometric reasons to the hypothenuse, which is L.

[tex]sin60=\frac{180}{L}\\ L=\frac{180}{sin60}\\ L=\frac{180}{\frac{\sqrt{3} }{2} }\\ L=\frac{360}{\sqrt{3}}=\frac{360}{1.7} \approx 211.8ft[/tex]

Therefore, the length of the kite string is around 211.8 feet.

Answer:

x = k/(y+z)

Step-by-step explanation:

We need to write a general formula to describe the variation: x varies jointly with the inverse of the sum of y and z

it can be written as

x ∝ 1/(y+z)

or can be written as

x = k/(y+z)

where k is the constant of variation introduced when we remove the ∝ sign.

It could be anything from 450 - 549 so pick a number within those two (for example, 460, 499, 523, 538, all of those work)

When rounding to the nearest hundred, any whole number from 450 to 549 will round to 500. We consider the tens place in a number to decide whether to round up or down.

In the field of Mathematics, when we are rounding a whole number to the nearest hundred, we look at the tens place. If the tens digit is 5 or above, we round up. If it's 4 or below, we round down. So, any whole number ranging from 450 to 549 will round up or down to 500 when rounding to the nearest hundred. For example, numbers like 475, 500, 525, or 543.

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6*6-(3*3)-(2*2) is the answer

Answer:

see explanation

Step-by-step explanation:

P - G

= 8[tex]w^{4}[/tex] - 3w²z² + [tex]z^{4}[/tex] - ( - 3[tex]w^{4}[/tex] + 2w²z² + 5[tex]z^{4}[/tex] )

= 8[tex]w^{4}[/tex] + 2w²z² + [tex]z^{4}[/tex] + 3[tex]w^{4}[/tex] - 2w²z² - 5[tex]z^{4}[/tex]

Collect like terms

= (8[tex]w^{4}[/tex] + 3[tex]w^{4}[/tex] ) + (- 3w²z² - 2w²z² ) + ([tex]z^{4}[/tex] - 5[tex]z^{4}[/tex] )

= 11[tex]w^{4}[/tex] - 5w²z² - 4[tex]z^{4}[/tex]