Find the equation of a circle with center at (5, 6) and radius 8.

Here, Given

Area of Equilateral triangle = 3cm2

therefore, we know;

Area of Equilateral triangle =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]

so,

3 =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]

3÷( [tex]\sqrt{3}[/tex]÷4) = [tex]a^{2}[/tex]

2.63 cm = a .

The area of ​​an equilateral triangle is the area covered by an equilateral triangle on a two-dimensional plane. An equilateral triangle is a triangle with all sides equal and all angles at 60 degrees. The area of ​​the shape is the number of unit squares that fit inside.

Here, "unit" refers to 1, and a unit square is a square with one side. Alternatively, the area of ​​an equilateral triangle is the total amount of space it surrounds in a two-dimensional plane.

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The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables.

The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.

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The system of inequalities x > 2 · y + 3 and - 2 · x < y + 1 includes the point (x, y) = (10, 0).

The solution area of the two inequalities given in the statement does not contain the point (x, y) = (10, 0) as we can see in the first figure.

But if we change the sign "<" for ">" in the first inequality, then the solution area includes the point mentioned above. Please see the second figure for further details.

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Statements is TRUE

Based on the graph of the general solution to the differential equation dy over dx equals 2 times x - 2 times y = dy/dx=2x-2y.

A differential equation's solution is an expression for the dependent variable in terms of one or more independent variables that satisfy the relationship.

The statement which is true is the slopes are all positive in quadrant I.

Given the differential equation is dy/dx=2x-2y

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

Given dy/dx=2x-2y

now slope=2x-2y

Along x-axis, y=0. So, slope=2x+0.

Since it depends upon x hence the slope along the y-axis are not horizontal.

Along y-axis, x=0. So, slope -2y+0.

The slope along the x-axis are also not horizontal.

In quadrant I:

x,y≥20

So, dy/dx ≥20

Therefore, the slopes are all positive in quadrant I. In quadrant IV,

x≥0,y≤0

so, dy/dx is not always positive.

The slope are not all positive in quadrant IV:

Therefore, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.

General solution to the differential equation =

dy/dx=2x-2y.

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Complete Question:

Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?

The slopes along the y-axis are horizontal.

The slopes along the x-axis are horizontal.

The slopes are all positive in Quadrant 1.

The slopes are all positive in Quadrant 4.

Answer: base = 12, altitude = 16

Step-by-step explanation:

If the growth rate is 0.469 per member per day and in the beginnning there are 5 members then the population size after eight days is 108.42.

Given growth of population of protozoa 0.469 per member per day and population in beginninng is 5 members.

We have to find the population afte eight days.

First of all we have to find the function or equation showing sum of population after t days.

Because it is given that the rate is 0.469 per member per day it means it is like compounding.

The equation which shows the sum after compounding is P[tex](1+r)^{n}[/tex]

where P is the amount in beginning, r is the rate and n is the number of years.

In this problem the equation will be 5[tex](1+0.469)^{t}[/tex] where t is number of days.

We have to put the value of t=8 to find the population after 8 days=

=5[tex](1.469)^{8}[/tex]

=5*21.68

=108.42

Hence the population of protozoa after 8 days is 108.42.

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Using proportions, it is found that the fraction of each candy bar that each friend will get is:

[tex]\frac{2}{3}[/tex].

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the three friends that were there initially and the three that arrived later, 4 candy bars will be split between 6 friends, hence the fraction that each will get is:

[tex]\frac{4}{6} = \frac{2}{3}[/tex]

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Answer:G

Step-by-step explanation:

4/9 times 2/8= 1/9

Answer:

G 1/9

Step-by-step explanation:

add all of the cards together that will get you 9 then you take the hearts overing it by total then times it by 2 overing by 8 or

4/9x2/8

Answer:

a. The free throw percentage obtained by the Lions is of 81.25%.

b. The free throw percentage for the Eagles was of 37.04%.

c. The field goal percentage for the Lions was of 56.01%.

d. The field goal percentage for the Eagles was of 34.43%.

e. The Lions scored 96 points.

f. The Eagles scored 64 points.

Solution:

a. The lions attempted 16 free throws and made 13, which means lions scored 13 out of 16,

The free throw percentage obtained by the Lions = [tex]\frac{13}{16}[/tex] × 100 = 81.25%

The free throw percentage obtained by the Lions is 81.25%

b. The eagles attempted 27 free throws and made 7 which means 7 out of 27, so:

The free throw percentage obtained by the eagles = [tex]\frac{7}{27}[/tex] × 100 = 25.92 %

The free throw percentage obtained by the eagles is 25.92 %

c. The lions attempted 51 two-point shots and made 22, and attempted 16 three-point shots and made 10.

Total attempted = 51 + 16 = 67

Total shots made = 22 + 10 = 32

The field goal percentage (two-point and three-point shots combined) for the Lions = [tex]\frac{32}{67}[/tex] × 100 = 47.76 %

The field goal percentage for the Lions was of 47.76 %.

d. The eagles attempted 41 two-point shots and made 19, and attempted 16 three-point shots and made 7.

Total attempted = 41 + 19 = 60

Total shots made = 19 + 7 = 26

The field goal percentage (two-point and three-point shots combined) for the eagles= [tex]\frac{32}{67}[/tex] × 100 = 43.33 %

The field goal percentage for the eagles was of 43.33 %.

e. Total goals secured by lions 13 free throws, 22 two's and 10 three's. So

Total points = 10 × 1 + 22 × 2 + 10 × 3 = 84

The Lions scored 84 points.

f. Total goals secured by eagles 7 free throws, 19 two's and 7 three's. So

Total points = 7 × 1 + 19× 2 + 7 × 3 = 66

The eagles scored 66 points.

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.

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Applying multiplication of functions, the total number of seats in the auditorium is given by:

h(x) = 80x² + 560x.

They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.

In this problem, the functions are given as follows:

Then the multiplication is:

h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.

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Answer:

The answer is b

Step-by-step explanation:

:)

Answer:

16 slices

Step-by-step explanation:

24* 2/3 = 16

The correct property of the quadratic parent function is given by:

B. Its vertex is at the origin.

The quadratic parent function is modeled by:

y = x².

It has the vertex at the origin and increases to the left and to the right, into quadrants I and II, forming a function that is graphed by a parabola.

Hence the correct option regarding a property of the quadratic parent function is given by:

B. Its vertex is at the origin.

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Third option Base angles theorem is the correct answer as it contains the information that statement 4 is missing.

About The Base Angle Theorem

The two base angles in an isosceles triangle that are opposite the congruent sides must be identical in measure or congruent, according to the base angle theorem.

As a result, JKL and MLK are the base angles of the recognized isosceles triangle. Thus, the two angles, ∠JKL and ∠MLK are congruent or equal to each other by the means of the base angles theorem, and third option -   base angles theorem - the missing justification for statement 4.

About the other options

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Answer: option c

Step-by-step explanation:

Answer:

Step-by-step explanation:

A parallel line will have the same slope as the line on the graph. A perpendicular line will have a slope that is the opposite reciprocal of the slope of the graphed line.

The line on the graph rises 1 grid square for each run of 2 grid squares to the right. Its slope is ...

  m = rise/run = 1/2

The opposite reciprocal of this slope is ...

  -1/(1/2) = -2

A perpendicular line will have a slope of -2.

The slope-intercept form of the equation for a line is ...

  y = mx +b

where the slope is m and b is the y-intercept. For the purpose here, we don't care about the y-intercepts of any of the lines. We only care about the slope: the coefficient of x.

This means the equations we're looking for are of the form ...

  parallel line: y = 1/2x + b

  perpendicular line: y = 2x +b . . . . . for some constant b

Of the equations offered, the only one with an x-coefficient of 1/2 is ...

  y = 1/2x +3

Of the equations offered, the only one with an x-coefficient of -2 is ...

  y = -2x +1

Answer:

Step-by-step explanation:

you are welcome

Answer:

2x/19

Quotient = division

Product = multiplication

Difference = subtraction

Sum = addition

Answer:

Step-by-step explanation:

 yes I believe it is an quartic binomial

Answer:

yes

Step-by-step explanation:

If because it has two terms, it is a binomial, therefore it also qualifies as a polynomial.

Hope this helps

Answer: A

Step-by-step explanation:

[tex]m\angle ABC=59^{\circ}[/tex] by the inscribed angle theorem.

Answer:

A=120

B=165

C=240

Step-by-step explanation:

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{2x}{x+1}+\dfrac{3(x+1)}{x}=5[/tex]

Make the denominators the same:

[tex]\implies \dfrac{2x}{x+1} \cdot\dfrac{x}{x}+\dfrac{3(x+1)}{x} \cdot \dfrac{x+1}{x+1}=5[/tex]

[tex]\implies \dfrac{2x^2}{x(x+1)}+\dfrac{3(x+1)^2}{x(x+1)} =5[/tex]

Combine the fractions:

[tex]\implies \dfrac{2x^2+3(x+1)^2}{x(x+1)} =5[/tex]

Multiply both sides by x(x+1):

[tex]\implies 2x^2+3(x+1)^2 =5x(x+1)[/tex]

Expand the brackets:

[tex]\implies 2x^2+3(x^2+2x+1) =5x^2+5x[/tex]

[tex]\implies 2x^2+3x^2+6x+3 =5x^2+5x[/tex]

Combine like terms:

[tex]\implies 5x^2+6x+3=5x^2+5x[/tex]

Subtract 5x² from both sides:

[tex]\implies 6x+3=5x[/tex]

Subtract 5x from both sides:

[tex]\implies x+3=0[/tex]

Subtract 3 from both sides:

[tex]\implies x=-3[/tex]

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Answer:

The measure of the acute angle = 90 - a

Leg 1 = a cos(a)

Leg 2 = a sin(a)

Step-by-step explanation:

In a right triangle ,the two acute angles are complementary

We are given that the measure of one of the acute angles is ‘a’

Then

The measure of the other one is ‘90 - a’

Now, we use the law of sine to determine the length of the legs :

Let x and y be respectively the length of the two legs.

[tex]\frac{x}{\sin \left( 90-a\right) } =\frac{a}{\sin \left( 90\right) }[/tex]

[tex]\Longleftrightarrow \frac{x}{\sin \left( 90-a\right) } =a[/tex]

[tex]\Longleftrightarrow x = a \times\sin \left( 90-a\right)[/tex]

[tex]\Longleftrightarrow x = a \times\cos \left( a\right)[/tex]

On the other hand,

[tex]\frac{y}{\sin \left( a\right) } =\frac{a}{\sin \left( 90\right) }=a[/tex]

Then

[tex]y = a \times \sin(a)[/tex]

The period of simple harmonic motion is T = 4.19 seconds:

For given question,

A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft.

So, we have mass (m) = 16 pounds

spring constant (k) = 36 lb/ft.

Let T be the period of simple harmonic motion.

Using the formula for the period of simple harmonic motion,

⇒ T = 2π√(m/k)

⇒ T = 2 × π × √(16/36)

⇒ T = 2 × π × √(0.444)

⇒ T = 2 × π × 0.666

⇒ T = 1.333 × π

⇒ T = 4.19 seconds

Therefore, the period of simple harmonic motion is T = 4.19 seconds

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Ms. Sanchez paid 150 dollars more than Mr. Roland.

Let's say that the electrician worked for x hours in Mr. Roland's home, then worked for (x + 2) hours in Ms. Sanchez home.

Then we need to find the difference between the linear equations:

C(x + 2) - C(x) = (75*(x + 2) + 125) - (75*x + 125)

If we simplify that, we get:

75*x + 75*2 + 125 - 75*x - 125

= 75*2 = 150

This means that Ms. Sanchez paid 150 dollars more than Mr. Roland.

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Using a system of equations, the weight of 5 apples, 2 oranges are 4 bananas is given as follows:

B. 1147 gm.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Considering the data given, the equations are:

From the first equation:

3x = 928 - 5y.

x = 309.33 - 1.667y.

From the second equation:

6z = 1088 - 4y

z = 181.33 - 0.667y

Replacing in the third equation:

5x + 3z = 799

5(309.33 - 1.667y) + 3(181.33 - 0.667y) = 799

10.336y = 12961.64

y = 1291.64/10.336

y = 125 gm.

The other weights are:

The weight of 5 apples, 2 oranges are 4 bananas is:

5x + 2y + 4z = 5 x 101 + 2 x 125 + 4 x 98 = 1147 gm, option B.

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The equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.

In the question, we are given that Scarlett made a profit of $250.00 with her mobile car wash company. She charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car.

We are asked to represent the situation with an equation.

We assume the number of cars washed by the company to be x.

Charge for washing 1 car = $75.00.

Cost for cleaning supplies for 1 car = $5.00.

Thus the profit on the wash of 1 car = $75.00 - $5.00 = $70.00.

The total profit received by the company, on washing x number of cars = $70x.

The tips received = $35.00.

Thus, the total profit of the company = $(70x + 35).

But, the total profit is given to be $250.00.

Thus, we get an equation, 250 = 70x + 35.

Thus, the equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.

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Answer:

Step-by-step explanation:

The triangle would end up back where it started.  It is hard to explain without a graph.  If you have graph paper, you might want to try drawing this out.  Say that the original points are at A (1,2) B (2,0) and C(0,0).  Now, when we reflect the points over the x axis, they will be the same distance below the x that the points original were about the x axis.  Since A was 2 units above the axis, it will now be 2 units below at (1, -2).  Points B and C will stay on the x axis and will remain in place at B(2.0) and C(0,0).  Since these points are on the line, they were not above the x axis, so they will now not be below the x axis.

Now, we are going to reflect the triangle over the y axis.  Since C (0,0) is already on the y axis, it will not move.  It will remain there.  Since B(2,1) is two units to the right of the y axis, when we flip it, it will now be 2 units to the left of the y axis B (-2,0).  Point C will move one unit to the left of the y axis to become (-1,2).

The last thing left it to rotate this final triangle 180 degrees.  Since a circle is 360 degrees and 180 is half of a circle, it does not matter if we rotate clockwise or counter-clockwise.  If you could trace our new triangle and put a plus sign at the origin (0,0).  You would put your pencil on the origin  and rotate the two turns at the plus sign.  This would put your triangle right back to the beginning.  So the original value of B would be the same.  In this case C ((2,0)

The point B' would be at point B. The position of point won't change.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees.

Let (x, y) be the coordinates of B.

To find B':

If a figure reflected over x-axis, then

(x, y) → (x, -y)

So, let point B₁ is  (x, -y).

If a figure reflected over y-axis, then

(x, y) → (-x, y)

So, (x, -y) → (-x, -y)

So, let point B₂ is  (-x, -y).

If a figure rotated 180 degrees about the origin, then

(x, y) → (-x, -y)

(-x, -y) → (x, y)

So the B' is (x, y).

Therefore, the position of point won't change.

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what help? how can i help you?

Given the 6 pound weight of the new seasoning having ingredients that cost $8, and $11, the amount she should charge for 1 ounce is $0.53125

The ingredients in the new seasoning are;

5 pounds of dried rose hips + 1 pounds of five-spice powder

Cost of the ingredients are;

1 pound of dried rose hips = $8

1 pound of five-spice powder = $11

The cost of combined spice, C, is therefore;

C = $8 × 5 + $11 × 1 = $51

The weight of the new combined seasoning = (5 + 1) pounds = 6 pounds

Cost of 1 pound of the new seasoning is therefore;

[tex]1 \: lb = \frac{51}{6} = 8.5[/tex]

Therefore;

[tex]1 \: ounce = \frac{8.5}{16} = \mathbf{0.53125}[/tex]

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Answer: $2.25

Step-by-step explanation:

5 lbs = 80 oz, so the mixture is worth

80(8/16) + 16(11) = 96x

x = $2.25/oz

Hope this helps!!

1. The given function is growth.

The percent of growth is 43%.

The initial value is 1500.

2. The rate of decay is 20% per day.

3. a. The exponential equation representing the sales after x months for the given situation is 3500000(0.97ˣ).

b. The monthly sales after 8 months will be $274,310.1758.

4. Between months 5 and 6, the website gains more members. The difference between the two sites for this period is 2700 members.

An exponential function is of the form f(x) = (a)(bˣ), where a is the initial value, and b is the exponential factor.

When b > 1, we have growth, and when b < 1, we have decay or depreciation.

1. Given function, f(x) = 1500(1.43ˣ).

The exponential factor in this function is 1.43, which is greater than 1, thus we have growth.

The percent of growth = (1.43 - 1)*100% = 43%.

The initial value = 1500.

2. Given an equation, y = 75(.8ˣ).

The exponential factor in this function is 0.8, and x signifies the days passed.

Thus, the rate of decay = (1 - 0.8)*100% per day = 20% per day.

3. Initial value = $350,000.

Rate of depreciation = 3% per month.

a. Thus, the equation for the sales after x months can be given as:

f(x) = 350000(1 - 0.03)ˣ = 350000(0.97ˣ).

b. To find the monthly sales after 8 months, we substitute x = 8.

Sales = 350000(0.97⁸) = $274,310.1758.

4. Initial members for both sites = 100.

For site a:-

Members double each month.

This makes an exponential equation, f(x) = 100.(2ˣ), where x is the number of months.

The growth between months 5 and 6 can be calculated as:

f(6) - f(5) = 100.(2⁶) - 100.(2⁵) = 6400 - 3200 = 3200.

For site b:-

500 new members are added each month.

This makes a linear equation, f(x) = 100 + 500x, where x is the number of months.

The growth between months 5 and 6 can be calculated as:

f(6) - f(5) = (100 + 500*6) - (100 + 500*5) = 3100 - 2600 = 500.

Thus, between months 5 and 6, the website a gains more members. The difference between the two sites for this period is 2700 members.

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Answer: ) (2a+7)(3b- 4)

Step-by-step explanation:

The requried simplified expression for  [tex]y^{5/4}[/tex]  is given by [tex]y^{5/4}= 32 * 10^{10k}[/tex]

To find an expression for [tex]y^{5/4}[/tex] in terms of k, we'll substitute the given value of y into the expression and then apply the exponent (5/4).

Given: [tex]y = 16 *10^{8k}[/tex]

Now, let's calculate [tex]y^{5/4}[/tex]:

[tex]y^{5/4} = (16 *10^{8k})^{5/4}[/tex]

To apply the exponent (5/4), we raise each factor to the power of (5/4):

[tex]y^{5/4}= 16^{5/4} * (10^{8k})^{5/4}[/tex]

Since [tex](10^8)^k[/tex] is [tex]10^{(8k)}[/tex], we have:

[tex]y^{5/4}= 16^{5/4}* 10^{8k * 5/4)[/tex]

[tex]y = 16*10^{8k}[/tex]

[tex]y^{5/4}= 2^5 * 10^{10k}[/tex]

Finally, we can write the expression in terms of k:

[tex]y^{5/4}= 32 * 10^{10k}[/tex]

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Answer:

x² + 5x - 14 = (x + 7)(x - 2)

x² - 3x - 54 = (x - 9)(x + 6)

x² + 8x + 12 = (x + 2)(x + 6)

x² - 11x + 30 = (x - 5)(x - 6)

x² - 25 = (x + 5)(x - 5)

x² + 8x - 9 = (x - 1)(x + 9)

Step-by-step explanation:

To factor x² + ax + b, look for two numbers whose sum is a and whose product is b.

The factorization of x² - a² is (x + a)(x - a).

x² + 5x - 14 = (x + 7)(x - 2)

x² - 3x - 54 = (x - 9)(x + 6)

x² + 8x + 12 = (x + 2)(x + 6)

x² - 11x + 30 = (x - 5)(x - 6)

x² - 25 = (x + 5)(x - 5)

x² + 8x - 9 = (x - 1)(x + 9)

The factored form of the given expressions are

y = (x -2)(x +7)

y = (x +6)(x -9)

y = (x +2)(x +6)

y = (x -5)(x -6)

y = (x +5)(x -5)

y = (x -1)(x +9)

y = (x +4)(x -4)

From the question we are to factor the given quadratic expressions

y = x² +7x -2x - 14

y = x(x +7) -2(x +7)

y = (x -2)(x +7)

y = x² -9x +6x - 54

y = x(x -9) +6(x -9)

y = (x +6)(x -9)

y = x² +6x +2x +12

y = x(x +6) +2(x +6)

y = (x +2)(x +6)

y = x² -6x -5x +30

y = x(x -6) -5(x -6)

y = (x -5)(x -6)

y = (x +5)(x -5)

y = x² +9x -x -9

y = x(x +9) -1(x +9)

y = (x -1)(x +9)

y = (x +4)(x -4)

Hence, the factored form of the given expressions are

y = (x -2)(x +7)

y = (x +6)(x -9)

y = (x +2)(x +6)

y = (x -5)(x -6)

y = (x +5)(x -5)

y = (x -1)(x +9)

y = (x +4)(x -4)

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