Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4

Answer:

vertex is (4,-4) and another point is (6,0) or you could use (2,0) or many other options :)

Step-by-step explanation:

The cool thing about this question your quadratic is in factored form so your x-intercepts are easy to figure out, they are 2 and 6.

So you can plot (6,0) and (2,0).

The vertex will lie half between x=2 and x=6... so it lays at (6+2)/2=4

We just have to find the y-coordinate for when x=4.

Plug in 4 gives you (4-2)(4-6)=(2)(-2)=-4.

So the vertex is at (4,-4).

Answer:

ST, RS, and RT

Step-by-step explanation:

A line is tangent to a circle if it intersects it at only one point.

ST, RS, and RT are all tangent to circle A.

AP intersects the circle at two points when extended.

XT intersects the circle at two points as well.

Answer:

A. [tex]\overline{ST}[/tex]

B. [tex]\overline{RS}[/tex]

D. [tex]\overline{RT}[/tex]

Step-by-step explanation:

We have been given that triangle RST is circumscribed about circle A. We are asked to choose that tangent of our given circle fro the provided choices.

We know that tangent of circle is a straight line that touches the circle exactly at one point. This point is known as point of tangency.

Upon looking at our given diagram, we can see that line segment RX touches circle A exactly at one point that is X. Line segment SX touches circle A exactly at one point that is X, therefore, line segment RS is tangent to our given circle.

Similarly, line segments SQ and TQ touch circle A exactly at one point that is Q, therefore, line segment ST is tangent to our given circle.

We can see that line segments RP and TP touch circle A exactly at one point that is P, therefore, line segment ST is tangent to our given circle.

AP is radius of circle, therefore, AP is not a tangent for our given circle.

If we draw a line joining points XT, it will intersect circle at two points, therefore, XT is not a tangent for our given circle.

Answer:

Option 2  

Step-by-step explanation:

Given : Equation [tex]\log_2(3x-1)=2[/tex]

To find : Which graph shows the solution to the equation?

Solution :

First we distribute the equation into two equation.

Let  Equation 1 be [tex]y=\log_2(3x-1)[/tex]

and Equation 2 be [tex]y=2[/tex]

Plot these two equation,

The equation 1 with purple line and equation 2 with orange line.

As these equation are equal there intersection point is given by,

Intersection point (1.667,2)

From the given graph only option 2 gives the correxct intersection point.

So, option 2 is correct.

Refer the attached figures below.  

Answer:

graph 2

Step-by-step explanation:

edg '23

[tex]\dfrac{a^2}{b}[/tex] is an integer, where [tex]a,b\in\mathbb{Z_+}[/tex], therefore [tex]b|a^2[/tex] and [tex]b\leq a^2[/tex]

[tex]a=pq[/tex] therefore [tex]a^2=p^2q^2[/tex]

[tex]b>a\wedge b\leq a^2[/tex], therefore [tex]pq<b\leq p^2q^2[/tex]

So,

[tex]b\in\{p^2q,pq^2,p^2q^2\} \\|\{p^2q,pq^2,p^2q^2\}|=3 \implies \text{B}[/tex]

Answer:

The best estimate for the solution is the point (0.5,-3.5)

Step-by-step explanation:

we have

-----> equation A

-----> equation B

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

The intersection point is

see the attached figure

therefore

The solution of the system of equations is the point

The best estimate for the solution is the point

Answer:

Part 1) [tex]y=-x^{2}[/tex]  ---> Translated up by 1 units

Part 2) [tex]y=x^{2}+1[/tex]  ---> Reflected across the x-axis

Part 3) [tex]y=-(x+1)^{2}-1[/tex]  ---> Translated left by 1 unit

Part 4) [tex]y=-(x-1)^{2}-1[/tex] ----> Translated right by 1 unit

Part 5) [tex]y=-x^{2}-1[/tex]  ----> Reflected across the y-axis

Part 6) [tex]y=-x^{2}-2[/tex]  ----> Translated down by 1 unit

Step-by-step explanation:

we know that

The parent function is

[tex]y=-x^{2}-1[/tex] ----> this is a vertical parabola open downward with vertex at (0,-1)

Calculate each case

Part 1) Translated up by 1 unit

The rule of the translation is

(x,y) -----> (x,y+1)

so

(0,-1) ----> (0,-1+1)

(0,1) ----> (0,0) ----> the new vertex

The new function is equal to

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

Part 2) Reflected across the x-axis

The rule of the reflection is

(x,y) -----> (x,-y)

so

(0,-1) ----> (0,1) ----> the new vertex

The new function is equal to

[tex]y=x^{2}+1[/tex]

Part 3) Translated left by 1 unit

The rule of the translation is

(x,y) -----> (x-1,y)

so

(0,-1) ----> (0-1,-1)

(0,1) ----> (-1,-1) ----> the new vertex

The new function is equal to

[tex]y=-(x+1)^{2}-1[/tex]

Part 4) Translated right by 1 unit

The rule of the translation is

(x,y) -----> (x+1,y)

so

(0,-1) ----> (0+1,-1)

(0,1) ----> (1,-1) ----> the new vertex

The new function is equal to

[tex]y=-(x-1)^{2}-1[/tex]

Part 5) Reflected across the y-axis

The rule of the reflection is

(x,y) -----> (-x,y)

so

(0,-1) ----> (0,-1) ----> the new vertex

The new function is equal to

[tex]y=-x^{2}-1[/tex]

Part 6) Translated down by 1 unit

The rule of the translation is

(x,y) -----> (x,y-1)

so

(0,-1) ----> (0,-1-1)

(0,1) ----> (0,-2) ----> the new vertex

The new function is equal to

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

Area of a triangle = height x base ÷ 2

When ever you have an isosceles triangle, remember that you can split it in half to form two right angled triangles - which allow you to use Pythagoras' Theorem.

So we split 10cm in half to get 5cm.

We can then use 13cm and 5cm to work out the height:

Height = √(13²  - 5²)      (Note: you subtract because you are using the    

           = √144              (hypotenuse)

           =  12

---------------------------------------------------------

Now to get the area, we just multiply the base (which is 10) by the height (which is 12) and divide by 2:

Area = 12 x 10 ÷ 2

        = 6 x 10               (note: 12 ÷ 2 = 6 )

        = 60 cm²

_____________________________________

Answer:

60 cm²

Final answer:

By setting up an equation where the total costs for both electricians are equal and solving for h, we find that the number of hours for which the costs are the same is 4 hours.

Explanation:

To determine the number of hours, h, for which the cost would be the same for hiring both electricians, we set up an equation where both cost expressions are equal. The equation, which expresses the total cost for each electrician's services, is:

First electrician: Cost = $60 + $55h

Second electrician: Cost = $20 + $65h

We now equate the two expressions and solve for h:

$60 + $55h = $20 + $65h

$55h - $65h = $20 - $60

-$10h = -$40

Divide each side by -10: h = 4

Thus, the number of hours for which the costs are the same is 4 hours.

Final answer:

The number of hours for which both electricians would charge the same is 4 hours. We find this by setting up an equation based on their fees and hourly rates, solving this equation yields the result of 4 hours.

Explanation:

To determine the number of hours, h, for which the cost would be the same for hiring both electricians, we can set up an equation based on their charges. The first electrician charges a service call fee of $60 and $55 per hour. Therefore, the cost for the first electrician, C1, can be expressed as:

C1 = 60 + 55h

The second electrician charges a service call fee of $20 plus $65 per hour, which means the cost for the second electrician, C2, is:

C2 = 20 + 65h

To find when the costs are the same (C1 = C2), we set the two expressions equal to each other:

60 + 55h = 20 + 65h

Now we solve for h:

60 + 55h = 20 + 65h

55h - 65h = 20 - 60

-10h = -40

h = 4

The costs are the same when the electricians work for 4 hours.

Answer:

19 1/2 or 19.5

Step-by-step explanation:

you could either:

break it up

6*3=18

1/2*3=1 1/2 = 1.5

18+1.5=

and get 19.5

or

just multiply it as decimal

6 1/2 = 6.5

                6.5

               x  3  

                1 5

           +1 8 0  

             1 9 5

or

multiply it as a improper fraction

6 1/2= 13/2

3= 3/1

     13    x     3      =    39   =?

      2    x     1       =      2   =?

?=19.5=39/2

*sorry if format or placement is not placed right because I did this in computer*

Answer:

Part 1) Option A. f of x equals one half times x plus 16

Part 2) Option  A. x = 5

Part 3) Option C. x − 4y = −9

Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.

Step-by-step explanation:

Part 1)

Let

x -----> the number of months

y ----> vertical jump in inches

step 1

Find the slope

we have the points

(0,16) and (2,17)

[tex]m=(17-16)/(2-0)=\frac{1}{2}[/tex]

The equation of the line in slope intercept form is

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

we have

[tex]m=\frac{1}{2}[/tex]

[tex]b=16[/tex] -----> the point (0,16) is the y-intercept

substitute

[tex]y=\frac{1}{2}x+16[/tex]

convert to function notation

f(x)=y

[tex]f(x)=\frac{1}{2}x+16[/tex]

Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?

step 1

Find the slope

we have the points

(5, 0) and (5, −2)

[tex]m=(-2-0)/(5-5)=\frac{-2}{0}[/tex]

the slope is undefined

This is a vertical line (parallel to the y-axis)

therefore

The equation is

x=5

Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)

step 1

Find the slope

we have the points

(−1, 2) and (3, 1)

[tex]m=(1-2)/(3+1)=-\frac{1}{4}[/tex]  

step 2

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{1}{4}[/tex]

[tex]point\ (3, 1)[/tex]

substitute

[tex]y-1=-\frac{1}{4}(x-5)[/tex]

Convert to standard form

Multiply by 4 both sides to remove the fraction

[tex]4y-4=-(x-5)[/tex]

[tex]4y-4=-x+5[/tex]

[tex]x-4y=-4-5[/tex]

[tex]x-4y=-9[/tex]

Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario

we know that

The independent variable is the variable whose change isn’t affected by any other variable (An example the age and time)

The dependent variable it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))

Let

x ----> the number of rides

y ----> the total cost in dollars

In this problem

The independent variable or input is the number of rides

The dependent variable or output is the total cost

The correct linear function for Maryann's vertical jump is f(x) = ½x + 16. The equation of the line containing points (5, 0) and (5, −2) is x = 5. For the line through points (−1, 2) and (3, 1), the correct equation is 4x − y = −6, and in Jewels' scenario, the number of ferry rides is the independent variable, and the total cost is the dependent variable.

Answer:

Equation = x²+(y+3)²=5²

Step-by-step explanation:

The question is on equation of a circle in a center-radius form

The general equation is

(x-h)² + (y-k)² = r² where the center is at (h,k) and the radius is r

Given

point P=(3,1) and point Q= (-3,-7)

Find the diameter PQ

[tex]d=\sqrt{(X2-X1)^2 + (Y2-Y1)^2\\[/tex]

[tex]d= \sqrt{(-7-1)^2 + (-3-3)^2}[/tex]

[tex]d=\sqrt{-8^2 + -6^2}[/tex]

[tex]d= \sqrt{64+36}  = 10[/tex]

d= 10 units hence radius is 10/2 =5 units

Find the center of the circle

center =[ (x₁+x₂)/2, (y₁+y₂)/2]

center=[ (3+-3)/2 , (1+-7)/2]

center= [ 0/2 ,-6/2]

center= [0,-3]

Equation = x²+(y+3)²=5²

Answer:

5^2

Step-by-step explanation:

Answer:

next = 2 x now + 2, starting at 50

Step-by-step explanation:

Step-by-step explanation :

Sam : 0.25 = [tex]\frac{25}{100}[/tex] = [tex]\frac{1}{4}[/tex]  (Answer)

Mark : 0.30 = [tex]\frac{30}{100}[/tex] = [tex]\frac{3}{10}[/tex]  (Answer)

Jill : 0.35 = [tex]\frac{35}{100}[/tex] = [tex]\frac{7}{20}[/tex]  (Answer)

Total amount of pizza eaten = 0.25 + 0.30 + 0.35 = 0.9

Amount of pizza left = 1.0 - 0.9 = 0.1 = [tex]\frac{10}{100}[/tex] = [tex]\frac{1}{10}[/tex] (Answer)

Answer:

B

Step-by-step explanation:the other corner is 75 so that leaves the other corner to be 50. 75+55+50=180

Hello There!

Other corner to be 50. 75+55+50=180

ANSWER[tex]q(x) = 7x + 4[/tex]

EXPLANATION

We want to find the quotient when [tex]7{x}^{2}-3x-9[/tex] is divided by x-1

We can quickly perform a synthetic division.

We write out the coefficients of the polynomial

[tex]7{x}^{2}-3x-9[/tex]

   7     -3     -9

1|         7      4

  7      4       -5

To obtain the top row.When we equate the divisor to zero, we get;[tex]x - 1 = 0[/tex][tex]\implies\:x=1[/tex]

This gives the 1 in the far left.The first two numbers in the last row are the coefficients of the quotient. The last number in the last row is the remainder.Therefore the quotient is [tex]7x + 4[/tex] and the remainder is -5

Remember this polynomial can be written as:

Dividend= Divisor * Quotient     + Remainder

[tex]7x^2-3x-9=(x-1)(7x+4)-5[/tex]

Therefore Quotient=7x+4

Answer:

  {52}

Step-by-step explanation:

The calculator function appears to be ...

  f(x) = {3x -1, x odd; x/2 +1, x not divisible by 4; x/4, x divisible by 4}

The inverse of the first function is ...

  x = 3y -1

  (x+1)/3 = y . . . . (y must be odd)

For x = 13, this is 14/3, which is not an integer.

__

The inverse of the second function is ...

  x = y/2+1

  2(x-1) = y . . . . (y must not be divisible by 4)

For x = 13, this is 2·12 = 24, which is divisible by 4, so 24 is not the input value.

__

The inverse of the third function is ...

  x = y/4

  4x = y . . . . (y must be, and is, divisible by 4)

For x = 13, this is 4·13 = 52.

The only possible input value for an output of 13 is 52.

Answer:

csc0

Step-by-step explanation:

Answer:

it is c

Step-by-step explanation:

For this case we have to:

n: It's the variable that represents the number of lawns that mowed Wally last week.

If you tell us as a fact that this week Wally mowed two more lawns, then we have the following expression:

[tex]n + 2[/tex]

Finally, the expression is:

[tex]n + 2[/tex]

Answer:

[tex]n + 2[/tex]

Option A

Answer:

  3022.08 . . . dollars per square meter

Step-by-step explanation:

The slope is multiplied by the factor that changes units:

  (280.76 dollars/ft²)×(1 ft²)/(.092303 m²) ≈ 3022.08 dollars/m²

To make predictions for house prices in square meters, you would have to multiply the given slope of 280.76 by the conversion factor of 1/0.092903, which will give an estimated slope of approximately 3017.9

The problem here is related to the conversion of units from square feet to square meters. Your friend gives you a simple regression fit for predicting house prices from square feet with an estimated intercept of -44850 and the estimated slope is 280.76.

Given that there are 0.092903 square meters in 1 square foot, a square foot equals to 1/0.092903 square meters. When you are making a prediction based on square meters rather than square feet, you need to consider this factor. This means the new slope would be calculated by multiplying the old slope with this conversion factor as:

Slope for prediction in square meters = Old slope * (1/0.092903) = 280.76 / 0.092903 = 3017.9 approximately.

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Answer:

B

Step-by-step explanation:

Under a reflection in y = x

a point (x, y) → (y, x)

Given

H(17, 34 ) → H'(34, 17)

I(- 5, 10) → I'(10, - 5)

J(28, - 14) → J'(- 14, 28)

B represents the image coordinates of H, I, J

For the given figure with vertices H(17,34), I(-5,10), and J(28,-14) across the line y=x, the reflection will appear at H(34,17), I(10,-5), J(28,-14). This is because at y=x the reflection will have the coordinates with interchanged values.

Across y=x, the reflection will have interchanged coordinates.

that is (x, y) → (y, x)

For the given vertices across the line y=x,

H(17,34) → H'(34,17)

I(-5,10) → I'(10,-5)

J(28,-14) → J'(-14,28)

So, option (2) is correct that is H(34,17), I(10,-5), J(-14,28) which undergoes reflection across y=x.

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Answer:

h = 9 and k = -8

Step-by-step explanation:

Answer: Option D

Step-by-step explanation:

By definition if we have a function F (x) and perform a transformation of the form

[tex]G (x) = F (x + c)[/tex]

Then it is true that:

If c is negative the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the right

If c is positive, the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the left.

Note that in this case the transformation is:

[tex]G (x) = F (x + 9)[/tex]

Then [tex]c = 9[/tex] and [tex]c> 0[/tex]

Therefore the graph of G(x) will be equal to the graph of F(x) displaced horizontally 9 units to the left

The answer is the option D.

ANSWER

D. The graph of G(x) is the graph of F(x) shifted 9 units to the left.

EXPLANATION

The given functions are F(x) and G(x).

The function, G(x) is obtain by translating or shifting the graph of F(x).

This translation is of the form.

[tex]G(x) = F(x+ 9)[/tex]

The '+9' within the parenthesis tells us that the shift is 9 units to the left.

Remember that for horizontal shift:

+ means a shift to the left.

The correct answer is D.

Answer:

[tex]y=-\frac{1}{7}x+\frac{37}{7}[/tex]

Step-by-step explanation:

Your equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.  Your line has a slope of 7.  In order to find the line perpendicular to this line, we have to take the opposite reciprocal of the slope.  The perpendicular slope to m = 7 is m = -1/7.  Now we go through x = -5 and y = 6 to find the new equation.

6 = -1/7(-5) + b gives us

6 = 5/7 + b and

b = 37/7

Therefore, the equation of the line perpendicular to your original line is

[tex]y = -\frac{1}{7}x + \frac{37}{7}[/tex]

Answer:a or b

Step-by-step explanation:

Answer:

B. 3 sqrt 2

Step-by-step explanation:

got oit right on edge

Answer:

x=225

Step-by-step explanation:

\sqrt{x} + (-13 + 13) = 2 + 13

\sqrt{x} = 15

√x-13=2

x=225

If you meant to write...

[tex]\sqrt{x - 13} = 2[/tex]

Then the following is the answer:

To solve this you must get rid of the square root. The opposite of square root is square. You must square both sides since what you do to one side you must do to the other...

([tex]\sqrt{x-13} )^{2}[/tex] = [tex]2^{2}[/tex]

x - 13 = 4

Finish completely isolating x. To do this first add 13 to both sides (what you do on one side you must do to the other). Since 13 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

x + (-13 + 13) = 4 + 13

x + 0 = 17

x = 17

If you meant to write...

[tex]\sqrt{x}[/tex] - 13 = 2

Then the following is the answer:

To isolate [tex]\sqrt{x}[/tex]. To do this first add 13 to both sides (what you do on one side you must do to the other). Since 13 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

[tex]\sqrt{x}[/tex] + (-13 + 13) = 2 + 13

[tex]\sqrt{x}[/tex] = 15

To completely isolate x you must get rid of the square root. The opposite of square root is square. You must square both sides since what you do to one side you must do to the other...

[tex](\sqrt{x})^{2} = 15^{2}[/tex]

x = 225

Hope this helped!

~Just a girl in love with Shawn Mendes

The answers are:

[tex]MaximumDistance=1200.1ft\\MinimumDistance=1199.9ft[/tex]

Since we are given the margin of error and it's equal to ±0.1 feet, and we know the surveyed distance, we can calculate the maximum and minimum distance. We must remember that margin of errors usually involves and maximum and minimum margin of a measure, and it means that the real measure will not be greater or less than the values located at the margins.

We know that the surveyed distance is 1200 feet with a margin of error of ±0.1 feet, so, we can calculate the maximum and minimum distances that the reader could assume in the following way:

[tex]MaximumDistance=ActualDistance+0.1feet\\\\MaximumDistance=1200feet+0.1feet=1200.1feet[/tex]

[tex]MinimumDistance=ActualDistance-0.1feet\\\\MaximumDistance=1200feet-0.1feet=1199.9feet[/tex]

Have a nice day!

Answer:

  24.5 cubic inches

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

A can with a diameter of 2.5 inches has a radius of 1.25 inches. Filling in the given values, the volume is ...

  V = π(1.25²)(5) = 7.8125π ≈ 24.54 . . . . cubic inches

The approximate volume is 24.5 cubic inches.

The volume of a cylinder is 24.54 inches³

The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.

We know that the volume of cylinder is

V = πr²h

Given that:

diameter = 2.5 inches

radius = 1.25 inches.

Height= 5 inches

V = π(1.25²)(5)

= 7.8125π

≈ 24.54 inches³

Hence, the volume of cylinder is 24.54 inches³

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The green square is 15 ft wide by 15 ft tall.

The area of one green square is 15 x 15 = 225 square feet.

There are 4 sides plus the base : 225 x 5 = 1125 square feet for the green part.

One triangle has a base 15 feet wide and a height of 9 feet.

The area for one triangle is 1/2 x 15 x 9 = 67.5 square feet.

There are 4 triangles: 67.5 x 4 = 270 square feet.

Total: 1125 + 270 = 1,395 square feet.