Write an equation of a line containing (2, 1) and (3, 4) in point-slope form.

Answer:

  10√269 ≈ 164.012 yd

Step-by-step explanation:

You want the length of the diagonal of a 100 yd by 130 yd soccer field.

The diagonal of the field is the hypotenuse of the right triangle created by that diagonal and the sides of the field. The length of the hypotenuse is given by the Pythagorean theorem.

  c² = a² +b²

  c² = 100² +130² = 10,000 +16,900 = 26,900

  c = √26900 = 10√269 ≈ 164.012

The length of the diagonal is 10√269 ≈ 164.012 yards.

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Additional comment

As a practical matter, it would be difficult to measure this distance with an accuracy better than 0.1 yards.

We have to write

[tex] 2^2 =4 [/tex]

In log form

To convert exponential equation to log equation, we have to use the following rule[tex] If \ a^b = c, \ then \ b=log_{a} c [/tex]

So we will get

[tex] If \ 2^2 =4, \ then \ 2 = log_{2} 4 [/tex]

or

[tex] log_{2}4=2 [/tex]

And that's the required log form .

I will try my best to assist you with your question.

We can to write

2^2 =4

In log form

To convert exponential equation to log equation, we have to use the following rule If \ a^b = c, \ then \ b=log_{a} c

So we will get

If \ 2^2 =4, \ then \ 2 = log_{2} 4

or

log_{2}4=2

Hope I helped!

Good Luck!

⛈

Part A:

The most expensive item on the menu is roast beef wrap at $4.50

6% tax on it becomes: [tex]4.50+(0.06\times4.50)=4.77[/tex] dollars

15% tip on it becomes: [tex]4.77+(0.15\times4.77)=5.485[/tex] dollars

The least expensive item on the menu is coffee at $0.90

6% tax on it becomes: [tex]0.90+(0.06\times0.90)=0.954[/tex] dollars

15% tip on it becomes: [tex]0.954+(0.15\times0.954)=1.097[/tex] dollars

So, the difference between roast beef wrap and coffee cost is :

[tex]5.485-1.097=4.388[/tex] dollars nearest to $4.36

Option B is the answer.

Part B:

You and your friend ordered two roast beef wraps, one soup, one fries, and two coffees.

Total becomes:

[tex](2\times4.50)+(2.25)+(1.50)+(2\times0.90)[/tex]

= [tex]9+2.25+1.50+1.8=14.55[/tex] dollars

Sales tax of 5% and 15% tip means 20% more on $14.55

[tex]14.55+(0.20\times14.55)=17.46[/tex] dollars

Change you will receive = [tex]20-17.46=2.54[/tex]dollars

Option D is the answer.

The area of the slice of pie that was cut, rounded to the nearest hundredth is; D: 98.83 ft²

We are given the angle of the sector of the circle as θ = 37°.

We are given;

Diameter; d = 35 ft

Thus;

Radius; r = 35/2 = 17.5 ft

Now, the formula for area of a sector of a circle is;

A = (θ/360) * πr²

Thus;

A = (37/360) * π * 17.5²

Approximating to the nearest hundredth gives;

A = 98.883 ²

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Answer:   C. (-1, 2)

Step-by-step-explanation:

The center is the midpoint of the endpoints

  →          [tex]\bigg(\dfrac{x_1+x_2}{2}[/tex]       ,      [tex]\dfrac{y_1+y_2}{2}\bigg)[/tex]

    →           [tex]\bigg(\dfrac{-7+5}{2}[/tex]         ,       [tex]\dfrac{3+1}{2}\bigg)[/tex]

    →               [tex]\bigg(\dfrac{-2}{2}[/tex]             ,          [tex]\dfrac{4}{2}\bigg)[/tex]

    →                (-1              ,            2)

The midpoint is (-1, 2)

The [tex]\angle[/tex]C is [tex]77^o[/tex] in the triangle ABC inscribed in the circle as evident from the figure.

A triangle is a polygon with three angles, three edges, and three vertices. It's one of the most introductory and abecedarian shapes in geometry.

Triangles can be classified by their side lengths, their angles, or their symmetry.

As the angle on the circumference is double the angle on the semicircle,

therefore,

[tex]\angle[/tex]B = [tex]\frac{110^o}{2}[/tex]

     = [tex]55^o[/tex].

As the sum of a triangle is [tex]180^o[/tex],

So,

[tex]\angle[/tex]A + [tex]\angle[/tex]B + [tex]\angle[/tex]C =  [tex]180^o[/tex],

Given that [tex]\angle[/tex]A = [tex]48^o[/tex],

[tex]48^o[/tex] + [tex]55^o[/tex] + [tex]\angle[/tex]C = [tex]180^o[/tex],

[tex]\angle[/tex]C = [tex]180^o[/tex] - [tex]48^o[/tex] - [tex]55^o[/tex],

[tex]\angle[/tex]C = [tex]77^o[/tex]

So, the [tex]\angle[/tex]C is [tex]77^o[/tex].

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For this case we have the following expression:

[tex] \frac{c-5}{c^2-5} [/tex]

To simplify the expression, the first thing to do is factor the denominator.

We have then:

[tex]\frac{c-5}{(c-5)(c+5)}[/tex]

Then, canceling similar terms we have:

[tex]\frac{1}{(c+5)}[/tex]

From here, we must find any value that should be excluded from the expression.

We must exclude values of c that make the denominator equal to zero.

We have then:

[tex] c+5=0

c=-5 [/tex]

Answer:

The simplified expression is:

[tex]\frac{1}{(c+5)}[/tex]

The value to be excluded from the expression is:

[tex] c=-5 [/tex]

The required dimensions of the rectangular field are 34 yards by 136 yards.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

Let's represent the width of the field x. Since the field is four times as long as it is wide, the length of the field is 4x.

The perimeter of the field is the sum of all four sides of the field. This can be written as:

2(x) + 2(4x) = 340

Solving this equation for x, we find that the width of the field is x = 34 yards.

Since the length of the field is four times the width of the field, the length of the field is 4 × 34 = 136 yards.

Therefore, the width of the field is 34 yards, and the length of the field is 136 yards.

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Answer:

Simple Random answer

Step-by-step explanation:

It says that he divided town into eight regions and randomly chose 10. The sample she formed was the Simple Random Answer.

Answer:

Adult dinosaurs=4

Baby Dinosaurs=12

Step-by-step explanation:

You only have to put an X to a certain number, in this case it will be like this:

Adult dinosaurs=x

Baby Dinosaurs= 3x

So the equation will be:

15(3x)+7(x)=208

You multiply it and add it and it will end up like this:

52x=208

x=4

So there were 4 adult dinosaurs.

And baby dinosaurs there are 3x which equals 12.

The cylinder has base diameter of 6 centimeters and the height, [tex] h [/tex], of 8 centimeters.

Since the base diameter of the cylinder is 6 cm, therefore, it's radius, [tex] r [/tex], will be 3 cm.

Now, we know that the volume, [tex] V [/tex], of such a cylinder will be:

[tex] V=\pi r^2h [/tex]

Plugging in the values given we get the volume to be:

[tex] V=\pi(3)^2\times 8=3.14\times9\times8=226.08 [/tex] [tex] cm^3 [/tex]

Since Rene needs to make 2000 [tex] cm^3 [/tex] of ice and one cylinder's volume is 226.08 [tex] cm^3 [/tex], Rene would need...

[tex] \frac{2000}{226.08}\approx8.846\approx\boldsymbol{9} [/tex] such identical cylindrical containers.

Final answer:

To make 2000 cm3 of ice, Rene would need a minimum of 9 identical containers, given the volume of one container is 226.08 cm3.

Explanation:

To determine the number of identical cylindrical containers needed to make 2000 cm3 of ice, we must first calculate the volume of one container. Given that the diameter of the base is 6 centimeters, the radius (r) is half of that, which is 3 centimeters. We're also given the height (h) of 8 centimeters. We can use the formula for the volume of a cylinder, V = πr2h.

Plugging in the values, we get:

V = 3.14 × (3 cm)2 × 8 cm

which simplifies to V = 3.14 × 9 cm2 × 8 cm = 226.08 cm3.

Now we can divide the total volume of ice Rene wants to make by the volume of one container:

2000 cm3 ÷ 226.08 cm3 = approx 8.85.

Since Rene cannot use a fraction of a container, she would need a minimum of 9 identical containers to make at least 2000 cm3 of ice.

Final answer:

Switching the axes of two hyperbolas affects the equations of the asymptotes.

Explanation:

When the transverse axis and conjugate axis are switched in two hyperbolas, it affects the equations of the asymptotes. The equations of the asymptotes are determined by the ratio of the coefficients of x² and y² in the hyperbola equation. When the axes are switched, this ratio changes, resulting in different equations for the asymptotes.

For example, let's consider two hyperbolas with equations:

1) 8x² + 10xy - 3y² - 2x - 4y - 2 = 0

2) 8y² + 10xy - 3x² - 2x - 4y - 2 = 0

In the first hyperbola, the ratio of the coefficients of x² and y² is 8/(-3), which determines the equation of the asymptotes. In the second hyperbola, the ratio is (-3)/8, leading to different equations for the asymptotes.

Answer:

Option: A is the correct answer.

The equation of parabola is:

                              [tex]x^2=8y[/tex]

Step-by-step explanation:

Clearly we could observe that the parabola opens upward with vertex at (0,0) this means that the general equation of the parabola is:

          [tex]x^2=4ay[/tex]

The focus of parabola is: (0,a) and equation of directrix is: y= -a

From the image provided to us we get:

                 a=2

             and directrix is: y= -2

           Hence, the equation of  a parabola is:

                       [tex]x^2=8y[/tex]