use synthetic division
PLEASE HELP 30 PTS

Answer:

Step-by-step explanation:

To find the equation of a circle given three non-collinear points, we can use the following steps:

Find the equations of the perpendicular bisectors of the line segments connecting the pairs of points.

Find the intersection point of the two perpendicular bisectors. This point is the center of the circle.

Find the distance between the center and any one of the three points. This distance is the radius of the circle.

Let's apply these steps to the given points:

Find the midpoint and slope of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18+(-7))/2, (-5+(-16))/2) = (-12.5, -10.5)

Slope of (-18, -5) and (-7, -16): (-16 - (-5))/(-7 - (-18)) = -11/11 = -1

Midpoint of (-18, -5) and (4, -5): ((-18+4)/2, (-5+(-5))/2) = (-7, -5)

Slope of (-18, -5) and (4, -5): (-5 - (-5))/(4 - (-18)) = 0

Midpoint of (-7, -16) and (4, -5): ((-7+4)/2, (-16+(-5))/2) = (-1.5, -10.5)

Slope of (-7, -16) and (4, -5): (-5 - (-16))/(4 - (-7)) = 11/11 = 1

The equations of the perpendicular bisectors passing through the midpoints are:

x + 12.5 = -1(y + 10.5) or x + y + 23 = 0

y + 5 = 0

Find the intersection point of the two perpendicular bisectors:

Solving the system of equations:

x + y + 23 = 0

y + 5 = 0

yields: x = -18, y = -5

So, the center of the circle is (-18, -5).

Find the distance between the center and any one of the three points:

Using the distance formula:

Distance between (-18, -5) and (-18, -5): sqrt(((-18)-(-18))^2 + ((-5)-(-5))^2) = 0

Distance between (-18, -5) and (-7, -16): sqrt(((-18)-(-7))^2 + ((-5)-(-16))^2) = sqrt(221)

Distance between (-18, -5) and (4, -5): sqrt(((-18)-4)^2 + ((-5)-(-5))^2) = 22

The radius of the circle is sqrt(221).

Therefore, the equation of the circle in standard form is:

(x + 18)^2 + (y + 5)^2 = 221

The standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5) is:

(x + 13)² + (y + 1)² = 41

From the question, we are to determine the standard equation of a circle with the given points

The given points are:

(-18;-5), (-7;-16) and (4;-5)

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

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

and r is the radius.

Using the given points (-18, -5), (-7, -16), and (4, -5), we can find the equation of the circle as follows:

Find the midpoint of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18 + -7)/2, (-5 + -16)/2) = (-12.5, -10.5)

Midpoint of (-7, -16) and (4, -5): ((-7 + 4)/2, (-16 + -5)/2) = (-1.5, -10.5)

Midpoint of (-18, -5) and (4, -5): ((-18 + 4)/2, (-5 + -5)/2) = (-7, -5)

Find the equations of the perpendicular bisectors of the line segments:

Perpendicular bisector of the line connecting (-18, -5) and (-7, -16):

Slope of the line: (−16 + 5)/(-7 + 18) = -11/5

Slope of the perpendicular bisector: 5/11

Midpoint: (-12.5, -10.5)

Equation: y + 10.5 = (5/11)(x + 12.5)

Perpendicular bisector of the line connecting (-7, -16) and (4, -5):

Slope of the line: (-5 + 16)/(4 + 7) = 11/7

Slope of the perpendicular bisector: -7/11

Midpoint: (-1.5, -10.5)

Equation: y + 10.5 = (-7/11)(x + 1.5)

Perpendicular bisector of the line connecting (-18, -5) and (4, -5):

Slope of the line: 0

Slope of the perpendicular bisector: undefined (perpendicular bisector is a vertical line)

Midpoint: (-7, -5)

Equation: x + 7 = 0

Find the point of intersection of any two perpendicular bisectors:

Intersection of perpendicular bisectors 1 and 2:

y + 10.5 = (5/11)(x + 12.5)

y + 10.5 = (-7/11)(x + 1.5)

Solving for x and y, we get:

x = -13

y = -1

Thus,

The center of the circle is (-13, -1).

Find the radius of the circle:

Using the center (-13, -1) and one of the given points, say (-18, -5):

r² = (-18 - (-13))² + (-5 - (-1))²

r² = 25 + 16

r² = 41

Hence, the equation of the circle is:

(x + 13)² + (y + 1)² = 41.

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Answer:

C

Step-by-step explanation:

The area of a rectangle is 2 dimensions so it would be measured in square meters.

a = lwh

26241 = lw(17)  Divide both sides by 17

1542 = lw

The lw is he area of the base.

Helping in the name of Jesus.

Answer:

x = 67

Step-by-step explanation:

The two triangles are identail.

Answer:

x = 67

because 67 and x the same

Answer:

The true statements:

6 is an element of D

12 is an element of D

Answer: [tex]\frac{-3}{4}[/tex]

Step-by-step explanation:

   To find the slope of the line, we will use change in y over change in x.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{-4--1}{3--1} =\frac{-4+1}{3+1} =\frac{-3}{4}[/tex]

The value of B is 6 when the value of sin x degrees equals to 4/5.

In the given triangle diagram, the opposite side of x = 3b

The hypotenuse of the given triangle = 22.5

Given triangle is a right-angled triangle, in trigonometry, we know that in a right-angled triangle the sin x = opposite side of x / hypotenuse side

So, sin x = 3b/22.5

But, the given value is 4/5. So,

3b/22.5 = 4/5

3b = 90/5

3b = 18

b = 18/3

b = 6

From the above explanation, we can conclude that the value of b is 6.

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Answer:

Step-by-step explanation:

To estimate the monthly cost of electric, gas, and water utilities as 0.1% of the price of your house, you can multiply the price of your house by 0.001. For example, if the price of your house is $300,000, then the estimated monthly cost of these utilities would be $300,000 * 0.001 = $300.

It’s important to note that this is just an estimate and the actual cost of these utilities can vary depending on factors such as the size of your house, the number of people living in it, and your usage habits.

Answer:

y= 50x + 150

Step-by-step explanation:

Answer:

Here’s a piecewise function that represents the total cost C (in dollars) for a photoshoot that lasts h hours:

                     150            for 0<h≤1

C(h)= {150 +100⌈2(h−1) ⌉ for 1<h≤3​

Step-by-step explanation:

The first part of the function represents the cost for a photoshoot that lasts up to 1 hour. The second part represents the cost for a photoshoot that lasts more than 1 hour but no more than 3 hours. The ceil function rounds up to the nearest integer.

I hope this helps you! Have a nice day. (゜▽゜)つ Bye -

The rate of change is 4/1

Answer:

93 + 7 = 100

Step-by-step explanation:

I would assume positive because 100 is above the x-axis not below it.

Answer:

5,340x.095=507.3

507.3÷5=101.46

101.46÷12=$8.45 interest

5,340÷5=1068

1068÷12= $89

89+8.45=$97.45

answer $97.45 a month

A 3:5 scaled version means that the dimensions of the new version are proportional to the original dimensions in a ratio of 3:5.

A scaled version is a version of a shape where every size in the original shape is multiplied by the same number.

In this situation, a 3:5 scaled version means that the dimensions (or sizes) of the new version are proportional to the original dimensions in a ratio of 3:5.

For example, if we have a circle with radius 20 cm, we can create a 3:5 scaled version by multiplying the radius by the ratio 3/5. That is:

scaled version radius = 3/5 * 20 = 12 cm

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The number of bacteria present at 5 hours is (b) 148.413

From the question, we were given,

f(t) = eᵗ

Then  f(t) = number of bacterials present at a particular time t.

f(5) = number of bacterial present at 5 hours

So, we have

f(5) = e⁵

f(5) = 148.413

Then this can be written in the whole number as 148  which implies that the second option is correct because using f(t) = eᵗ to describes the growth of a colony of bacteria will provide us with the answer

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Answer:

Step-by-step explanation:

(a)  currently the  mode is pink.  Mode means which one occurs the most.

If you take a pink out.  Now P=3  G=3 and Y=3

(a) PINK

(b) Yellow, you want yellow to be the most/mode  so they put a yellow back in

The part of the cake with vanilla or lemon frosting is 1/5 by using arithmetic and algebraic expression.

Let's start by defining the variable "x" as the part of the cake with vanilla or lemon frosting.

According to the problem, Jonah uses vanilla frosting on 1/5 of the cake, which can also be written as x = 1/5.

Similarly, he uses lemon frosting on 2/5 of the cake, which can be written as x = 2/5.

We know that the sum of the parts of the cake with vanilla, lemon, and chocolate frosting should equal the whole cake. Since there are only three types of frosting, we can write:

x + x + chocolate frosting = 1

2x + chocolate frosting = 1

We also know that chocolate frosting covers the remaining part of the cake, which is 3/5. Therefore, we can write:

chocolate frosting = 3/5

Substituting this value into the previous algebraic expression, we get:

2x + 3/5 = 1

Subtracting 3/5 from both sides of the equation, we get:

2x = 2/5

x = 1/5

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Answer:

The answer for <M is 28°

Step-by-step Explanation:

<P=180-48

<P=132°

base angles in an isosceles are equal

<M+<N+<P=180

3y+1+2y+2+132=180

3y+2y+3+132=180

5y+135=180

5y=180-135

5y=45

divide both sides by 5

5y/5=45/5

y=9

<M=3(9)+1=27+1=28°

Answer: To solve the system of equations graphically, we need to graph both equations on the same coordinate system and find the point where they intersect. This point will give us the values of x and y that satisfy both equations.

First, we can rewrite the two equations in slope-intercept form:

y = 4x - 1 (equation 1)

y = -x + 4 (equation 2)

Now we can graph both equations on the same coordinate system. To do this, we can plot a few points for each equation and then draw a line through the points. Alternatively, we can use the y-intercept and slope of each equation to graph the lines. For equation 1, the y-intercept is -1 and the slope is 4. For equation 2, the y-intercept is 4 and the slope is -1.

We can see that the two lines intersect at the point (1, 3). Therefore, the solution to the system of equations is x = 1.

Let x be the length of each of the equal sides of the isosceles triangle. Then the length of the base is x - 4. The perimeter of the triangle is the sum of the lengths of the three sides, which is:

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

We know that the perimeter is 32, so we can set 3x - 4 equal to 32 and solve for x:

3x - 4 = 32

Adding 4 to both sides gives:

3x = 36

Dividing by 3 gives:

x = 12

Therefore, one of the equal sides of the triangle is 12 inches long, and the length of the base is 12 - 4 = 8 inches.

So the three sides of the triangle are 12 inches, 12 inches, and 8 inches.

The correct equation to solve the problem is (C) 3x - 4 = 32.

Answer:

Y=-10x+1 with x being -5

y = -10 *-5 +1

y = -50+1

y =-49

Answer: To evaluate this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) and work from left to right:

(49)^(-2) * (34)^(-2)

First, we can simplify the exponents:

1/(49^2) * 1/(34^2)

Next, we can calculate the values of 49^2 and 34^2:

1/2401 * 1/1156

Then, we can multiply the fractions:

1/2785456

Therefore, the value of the expression (49)^(-2) * (34)^(-2) is approximately 0.000000359.

Step-by-step explanation:

The Taylor polynomial T3(x) for the function f centered at the number a.

f(x) = e^x, a = 1 is

[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]

A polynomial is  described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:

[tex]pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....[/tex]

In this formula, f'(1), f''(1), f'''(1), and f^(n)(1) are the first, second, third, and nth derivatives of f(x), respectively, evaluated at a.

The symbol n! denotes the factorial of n, which is the product of all positive integers from 1 to n.

In the scenario above, we are given the function f(x) = e and a = 1.

The first derivative of e^x is e^x,

the second derivative is e^x,

and the third derivative is also eˣ.

We then evaluate these derivatives at a = 1, we get:

f(1) = e¹ = e

f'(1) = e¹ = e

f''(1) = e¹ = e

f'''(1) = e¹ = e

We substitute  these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:

[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]

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According to the given question, Alice should use this equation f(t) = [tex]24,000(0.945)^t[/tex] to represent the value of the car after t years.

Depreciation is the expected decrease in the value of fixed assets over the course of a fiscal year. For physical assets like real estate, machinery, vehicles, and other items, large lump sum acquisitions are made.

The equation[tex]f(t) = 24,000(0.945)^t[/tex] represents the value of the car after t years, where 0.945 represents the remaining value of the car after one year of depreciation at a rate of 5.5%.

To calculate the value of the car after two years, for example, we would substitute t = 2 into the equation:

f(2) = [tex]24,000(0.945)^2[/tex]

f(2) = 24,000(0.893025)

f(2) ≈ 21,433.80

Therefore, the value of the car after two years would be approximately $21,433.80.

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The value of x in the triangle to the nearest tenth is 2.6.

The figure in the image is a right triangle.

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( H ) = opposite / adjacent

Plug in the given values and solve for x.

tan( 43° ) = x / 2.8

Cross multiply

x = tan( 43° ) × 2.8

x = 2.6 units

Therefore, the value of x is 2.6.

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Thw correct option based on the information given about the parabola will be B. X.

The observed parabola has its vertex situated at (0, 0), declining until (0, 0) then again rising. Its equation falls in the form of f(x) = a(x - 0)² + 0, which simplifies to ax².

In order to detect the value of 'a' we can utilize any point on the parabola itself. Let's take (1, 1):

1 = a(1)²

1 = a

Therefore, the formula for the presented parabola is exsiting in the form of f(x) = x².

Now consider g(x) = (x + 1)² such that it's merely a horizontal movement of function f(x) = x². The vertex of g(x) stands at (-1, 0) and linearly declines until (-1, 1) prior to onching higher again. All this leaves us with option X as the only conceivable graph for g(x).

Therefore, the answer is B) X.

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The adjusting entry that Tanning Company will make for Allowance for Doubtful Account will be:

Data:

Total credit sales = $1,000,000

Accounts receivable balance = $310,000

Estimated uncollectible receivables = $21,700

The adjusted balance for allowance for doubtful accounts will be:

= Credit balance + Estimated uncollectible receivables

= $2,200 + $21,700

= $23,900

So, the Company will make an adjusting entry by debiting Bad Debt Expense for $21,500 and crediting Allowance for Doubtful Accounts for $21,500 which will increase the balance of the allowance for doubtful accounts to $23,900.

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Answer:

t ≈ 37.76 seconds (rounded to the nearest hundredth)

Step-by-step explanation:

To solve the problem, we can use the equation for the height of a projectile at time t: h(t) = - 16 * t^2 + v0 * t + y0

where v0 is the initial velocity and y0 is the initial height.

In this case, we have:          v0 = 600 ft/sec (upward)

                                             y0 = 160 ft (above the ground)

We want to find the time at which the projectile hits the ground, which is when h(t) = 0.

So we can set up the equation:   0 = -16 * t^2 + 600 * t + 160

We can solve for t using the quadratic formula:

                                           t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -16, b = 600, and c = 160.

Plugging in the values, we get:

                   t = (-600 ± sqrt(600^2 - 4(-16)(160))) / 2(-16)

                   t = (-600 ± sqrt(360000 + 10240)) / (-32)

                   t = (-600 ± sqrt(370240)) / (-32)

We can simplify this expression by taking the negative root since the positive root would give a negative time, which is not physically meaningful in this context: t = (-600 - 608.47) / (-32)

t ≈ 37.76 seconds (rounded to the nearest hundredth)

Therefore, the projectile will be in flight for about 37.76 seconds before hitting the ground.

The equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit is 15 in - (1.25 in/hr)t

Given  the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h

L(t) is a function of time, t:

L(t) = 15 in - (1.25 in/hr)t

Note that when the candle has burned down to nothing, L(t) = 0.

Set 15 in - (1.25 in/hr)t equal to zero and solve for t:

(1.25 in/hr)t = 15 in, or

t = 15/  1.25 in/hr

t = 12 hrs

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The total number of chickens the farmer owns is 35.

A quantity or proportion can be expressed as a percentage of 100 by using the word "percentage." It is represented by the sign %.

For instance, when we state that 50 percent of a group of people are women, we mean that 50 out of every 100 people in the group are women.

We can deduce here the total chickens the farmer owns in % = 100%

Hens placed in a new coop = 20% = 7

Let the total number of chickens = x

Thus,

7 / x = 20 / 100

To solve for x, we can cross-multiply and simplify:

7 × 100 = 20 × x

700 = 20x

x = 35

Thus, the total number of chickens = 35.

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