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Write the equation of a parabola with vertex (-5,8) and directrix x=2. Show all of your work and put your equation in graphing/vertex form.

o see what is going on, we simply draw a triangle. Since the tower is 125 feet high, but the guy wire is 20 feet from the top, the triangle is 125 - 20 = 105 feet high, then 80 feet long.

Using the pythagorean theorem, 105^2 + 80^2 = g^2

g^2 = 11025 + 6400 = 17425

g = sqrt(17425)

g = 132.0038 feet = 132 feet

Hope this helps!

The length of the guy wire is 132 ft, determined by using the Pythagorean theorem with the given vertical and horizontal distances.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Therefore, the length of the guy wire is 132 ft.

Complete question:

The top of an antenna tower is 125 ft. above level ground. The tower is to be guyed 20 ft. from its top to a point on the ground 80 ft. from the base of the tower· What is the length of the guy wire?

Answer:

fadsfdaskfgadsghkfdsaghfjdasbmncvxzgwgriuewryhdkewghdfskljghdfsgdfgasdgdfsgfdagdfsjkjbkb,kbnkbhkjbh

Step-by-step explanation:

dsafdasfdasdfasghdfsghdfshdfashndsfgndfgadgbadfgbafddryhbbgdrfbdf

The value of Kayleigh's investment in 7 years is approximately $930.05.

To find the value of Kayleigh's investment in 7 years, we can use the given equation A = d(1.005)^12t. Let's substitute the values: d = $850, t = 7.

Plugging in these values, we have A = 850(1.005)^(12*7).

Evaluating the expression, the value is approximately $930.05 when rounded to the nearest cent.

This implies that Kayleigh's initial investment of $850, compounded monthly at a rate of 0.5%, will grow to around $930.05 after 7 years.

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Alright first get the sector formula which is

(3.14)(r)^2(measure of the degrees / 360) now plug it in the formula

(3.14)(8.91)^2(81/360)

3.14 x 79.4 x 81 = 20,194.596/360 = 56.1 cm squared and that I believe should be the answer to that :)

ANSWER

B. 700 units^2

EXPLANATION

The surface area of the pyramid is the area of the four triangular faces plus the area of the square base.

The area of the four triangular faces is

[tex] = 4 \times \frac{1}{2} \times bh[/tex]

We substitute b=14 and h=18.

[tex] = \frac{1}{2} \times 14 \times 18 \times 4[/tex]

[tex] =504 {units}^{2} [/tex]

The area of the square base

[tex] = {14}^{2} = 196 {units}^{2} [/tex]

The surface area of the pyramid is

[tex] = 196 + 504 = 700 {units}^{2} [/tex]

Answer:

WR = 26

Step-by-step explanation:

Givens

UT = 10

VS = 18

WR = ??

Formula

(WR + UT) / 2 = VS

Solution

Substitute

(WR + 10) /2 = 18

Multiply both sides by 2

(WR + 10/2 * 2 = 18 * 2

Do the multiplication

WR + 10 = 36  

Subtract  10 from both sides

WR + 10 - 10 = 36 - 10

WR = 26

Use Pythagorean theorem

[tex]y=\sqrt{6+10}=\boxed{4}[/tex]

You can solve this using Pythagorean theorem

[tex]\sqrt{10^{2} -6^{2} }[/tex] = 8

Answer:

Shifts the graph left 2, would look like  

(x+2)^2

Step-by-step explanation:

Answer:

5,5

Step-by-step explanation:the slope is going up 1 and to the right 3 3/1

Answer:

Step-by-step explanation:

5,5 that is the answer my frienddd

Answer:

See below in bold.

Step-by-step explanation:

Area of a circle with radius 2 cm = πr^2 =  π * 2^2 = 4π cm^2.

Area of a circle with radius  4 cm = πr^2 =  π * 4^2  = 16π cm^2.

Answer: D.

Step-by-step explanation: Your Answer Is D. This Does Not Represent A Function.

A table that does not represent a function include the following; D. table D.

In Euclidean Geometry, a function refers to a mathematical expression which is used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set P) to an output variable (Set Q).

In this context, we can logically deduce that table D does not represent a function because the same input value is mapped to different output values;

0 ↔ -1

0 ↔ 4

0 ↔ 6

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Answer:

option A

2/4 = 0.5

Step-by-step explanation:

Given in the questions that,

number of student in chess club = 4

P(B) = 4/10

number of student in karate club = 6

P(A) = 6/10

number of students who are both in chess and karate club = 2

P(A∩B) = 2/10

total number of students 10

Formula to use

Answer:

P(A/B) = P(A∩B) / P(B)

          = 2/10 / 4/10

          = 2/4

          = 1/2

          = 0.50

Step-by-step explanation:

Answer:

14 square units

Step-by-step explanation:

There are several ways we can find the area.  Probably the easiest is to cut the kite in half vertically and find the area of each triangle.  The area of the kite will be double that.

The height of the kite is 7 units, and the width is 4 units.  So each triangle will have a base of 7 and height of 2.

A = 1/2 bh

A = 1/2 (7) (2)

A = 7

The area of the kite is double that, so:

2A = 14

The area of kite WXYZ in the coordinate plane given is: C. 14 square units.

Area of a kite = pq/2, where p and q are the diagonal lengths of the kite.

The dimensions of the kite are:

Area of the kite = (7×4)/2

Area of the kite = 14 square units

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-11a^2+1ab+4b^2; P-Q would mean you rearrange the equation to where (-4a^2-2ab+9b^2)-(7a^2-3ab+5b^2). Don't forget to distribute the negative for Q since you plugged it into a variable.

-4a^2-2ab+9b^2-7a^2+3ab-5b^2

Add/Subtract like terms

-11a^2+1ab+4b^2

Bar graphs are easy to understand, widely used, and can show changes over time. That gives them an advantage over other graphs that are difficult to read or can only show a single data set.

They use vertical or horizontal bars to represent data along both an x-axis and a y-axis visually. Each bar represents one value, so it'll be an advantage for Peter because he can add as many colours he wants and the graph would still be easy to read. When the bars are stacked next to one another, the viewer can compare the different bars, or values, at a glance.

The area of w is 289 pi m². Find the circumference of w A. c=17 pi m B. c= 34 pi m C. c=68 pi m D. c=289 pi m

Answer: 34 pi

Step-by-step explanation:

Answer:

Step-by-step explanation:

The last three situations involve "descriptive statistics," which could mean measures of central tendency and measures of the spread of data.  The first one does not, since no exploratory work has yet been done.  

It's important that you look up terms such as this one and be able to come up with examples on your own.

Answer:

Step-by-step explanation:

Let x represent the amount (in ounces) of 24% alloy in the mix. Then the amount of 12% alloy is (50 -x). The amount of silver in the mix is ...

  24%·x + 12%·(50 -x) = 21%·50

  12x = 450 . . . . . . simplify, multiply by 100 (to eliminate %), and subtract 600

  x = 37.5 . . . . . . . divide by 12

The jeweler needs to mix 37.5 ounces of 24% silver alloy with 12.5 ounces of 12% silver alloy to make 50 ounces of 21% silver alloy.

Answer:

196

Step-by-step explanation:

edg 21

The formula for the surface area of a sphere is explained step by step using the given diameter to calculate the surface area in terms of pi. The result is that the surface area of the sphere with a 14 ft diameter is 196π ft².

To calculate the surface area of a sphere:

Therefore, the surface area of the sphere with a diameter of 14 ft is 196π ft².

Answer:

$126

Step-by-step explanation:

First, use the general percent equation (y is x% of z, y being your part percentage, x being your percent, and z being your whole base).

y = 40% x 90 --> .4 x 90 = 36

y = 36

Now, simply add the part percentage (36) to the original whole base.

90 + 36 = 126

The markup price of the model is equal to $126.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a toy store's per cent of markup is 40%. A model train costs the store $90.

First, use the general per cent equation (y is x% of z, y being your part percentage, x being your per cent, and z being your whole base).

y = 40% x 90 --> .4 x 90 = 36

y = 36

Now, simply add the part percentage (36) to the original whole base.

90 + 36 = 126

The markup price of the model is $126.

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Answer:

Subtraction Property on Equality.

Step-by-step explanation:

2. 15x + 6 = -24

15x + 6 - 6 =  -24-6

15x = -30

Subtraction Property on Equality.

Answer:

Option A. is even so both ends of the graph go in the same direction.

Step-by-step explanation:

Graphing the function give we can recognize the factor is even, but at the same time both the ends go in the same direction.

Answer:

y = -x + 2

Step-by-step explanation:

We first need to find the derivative of the equation x² + xy + y² = 3. this is done with implicit differentiation

2x + y + xy' + 2yy' = 0

Get terms with y' to one side, and the other terms to the other side of the equals sign...

xy' + 2yy' = -2x - y

Factor out y'...

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

Divide both sides by x + 2y

y' = (-2x - y)/(x + 2y)

This is the formula for the slope of the lines tangent to the curve of the original function.

Plug in the given point (1, 1) to find the slope of this

y' = (-2[1] - 1)/(1 + 2([1])

y' = -3/3

y' = -1

To find the equation of the line:

The general form for a linear equation in slope-intercept form is  

y = mx + b where m is the slope and b is the y-intercept

Use what we know about our line to solve the rest. By using one of the given points, we have 3 of the 4 variables in the above equation. Pick either point, it doesn't matter which one. We'll use (1, 1), which is (x, y), and we know that  

m = -1

The equation becomes...

1 = -1(1) + b (now solve for b)

1 = -1 + b

2 = b  

Plug that value into the general form...

y = -x + 2

See attached photo for the graphs of the original equation, and the graph of the tangent line at (1, 1)

Answer:

12, 13, 4

Sum of the squares of the smaller 2 sides < longest side squared - OBTUSE SCALENE TRIANGLE

6, 4, 11

LONGEST SIDE GREATER THAN OR EQUAL TO THE SUM OF THE OTHER TWO SIDES - NO TRIANGLE.

7, 6, 5

Sum of the squares of the smaller 2 sides > longest side squared - ACUTE SCALENE TRIANGLE

3, 14.5, 17

Sum of the squares of the smaller 2 sides < longest side squared - OBTUSE SCALENE TRIANGLE

Step-by-step explanation:

Final answer:

To determine if a set of three lengths can be the side lengths of a triangle, we need to apply the triangle inequality theorem.

Explanation:

In order for a set of three lengths to be the side lengths of a triangle, they must satisfy the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This can be represented as:

a + b > c

a + c > b

b + c > a

For example, if the given lengths are 3, 4, and 7, we can check if they satisfy the inequality:

3 + 4 > 7

3 + 7 > 4

4 + 7 > 3

Since all of these inequalities are true, the lengths 3, 4, and 7 can indeed be the side lengths of a triangle.

Answer: Option A.

Step-by-step explanation:

You need to use this formula for calculate the surface area of the right cylinder:

[tex]SA=2\pi r^2+2\pi rh[/tex]

Where "r" is the radius and "h" is the height.

You can identify in the figure that:

[tex]r=8units\\h=3units[/tex]

Knowing this, you can substitute these values into the formula [tex]SA=2\pi r^2+2\pi rh[/tex], therefore you get that the surface area of this right cylinder is:

[tex]SA=2\pi (8units)^2+2\pi (8units)(3units)[/tex]

[tex]SA=176\pi\ units^2[/tex]

Answer:

x^2 + y^2 = 8^2

Step-by-step explanation:

The general equation in standard form here is x^2 + y^2 = r^2.

Replace r with 8, obtaining:

x^2 + y^2 = 8^2

The standard form equation of a circle with a radius of 8 and centered at the origin is x² + y² = 64.

The equation for a circle centered at the origin with a given radius can be written in standard form. For a circle with a radius of 8, which is centered at the origin, the standard form equation is x² + y² = 64. This equation is derived from the general formula for a circle's equation in standard form, which is (x - h)² + (em)(y - k)² = R², where (h, k) is the center of the circle and R is the radius. Since the center is at the origin, h and k both equal zero.

Answer:

  7:30 pm

Step-by-step explanation:

The difference in speed is 20 mph, half as fast as the truck's speed. This is the speed at which the gap is closed. So, the head start that the truck has will be closed in a time after the car started that is twice as long as the time before the car started. That is, they will meet at ...

  10:00 + 3:10 + 2×3:10

  = 13:10 + 6:20 = 19:30 . . . . . 7:30 pm

Answer:

7:30 pm that is the answer i solved it

ANSWER

[tex]p = - 2[/tex]

EXPLANATION

The given equation is

[tex]x = - \frac{1}{8}{y}^{2} [/tex]

Multiply both sides by -8

[tex] \implies \: {y}^{2} = - 8x[/tex]

We now compare this to the general equation of the parabola:

[tex] {y}^{2} = 4px[/tex]

This implies that,

[tex]4p = - 8[/tex]

Divide both sides by 4.

[tex]p = \frac{ - 8}{4} [/tex]

[tex]p = - 2[/tex]

Answer:

  B.  1/392 cubic yard

Step-by-step explanation:

The volume is the product of base area and height:

  V = Bh = (1/28 yd²)·(1/14 yd) = 1/(28·14) yd³ = 1/392 yd³

Answer:

B. 1/392 cubic yard

Step-by-step explanation:

Given,

The base area of the pillar, B = [tex]\frac{1}{28}[/tex] square yard ,

Its height, h = [tex]\frac{1}{14}[/tex] yd

Thus, the volume of the pillar would be,

[tex]V=B\times h[/tex]

[tex]=\frac{1}{28}\times \frac{1}{14}[/tex]

[tex]=\frac{1}{28\times 14}[/tex]

[tex]=\frac{1}{392}\text{ square yard}[/tex]

Since, the concrete he needs to cast the pillar = Volume of the pillar

= [tex]\frac{1}{392}\text{ square yard}[/tex]

Option 'B' is correct.

Answer:

[tex]g(x)=8(2^x)[/tex]

Step-by-step explanation:

Here we are given with parent function [tex]f(x)=2^x[/tex] and the graph which shows that the function g(x).

We are asked to guess the function g(x).

We are given the two coordinates on g(x)

(0,8) and (2,32)

Hence for x = 0 , g(x)= 8

And for x=2, g(x)= 32

Let us say that the translated function is represented by

[tex]g(x)=a2^x+b[/tex]

[tex]g(0)=a\times 2^0+b[/tex]

Hence

[tex]a \times 2^0+b=8[/tex]

[tex]a +b=8[/tex] --------------- (i)

also

[tex]g(2)=32[/tex]

Hence

[tex]a\times 2^2+b=32[/tex]

[tex]4a+b=32[/tex] -------------------(ii)

Subtracting (i) from (ii) we get

[tex]3a=34[/tex]

Hence a = 8

Now putting this value of a in (i)

[tex]8+b=8[/tex]

B=0

Hence [tex]g(x)=8 \times 2^x +0[/tex]

[tex]g(x)=8(2^x)[/tex]

Answer:

The length of the hypotenuse is 4.1 in

Step-by-step explanation:

By definition, the sine of an angle is:

[tex]sin(x) = \frac{opposite\ side}{hypotenuse}[/tex]

In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.

With this information we can find the length of the hypotenuse h

[tex]sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in[/tex]

Finally the length of the hypotenuse is 4.1 in

Answer:

B: 4.1 in.

Step-by-step explanation:

on edge! hope this helps!!~ ⊂((・▽・))⊃