Simplify the expression -2x^2(4x − 3).
-8x3 − 6x2
-8x3 + 6x2
8x3 − 6x2
8x3 + 6x2

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)

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]

Answer: The answer is B

Step-by-step explanation:

The smaller the coefficient, the wider the graph would be. So the smallest number, if positive, 1/5 is the widest and the largest 7 is the narrowest.

Answer:

b is ur answer

Step-by-step explanation:

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.

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.

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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The distance between two points (x₁,y₁),(x₂,y₂) = d
[tex]d = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} } [/tex]

Answer:

90 ft

Step-by-step explanation:

Given,

The 6 ft tall man casts 4 ft long shadow,

So, the ratio of the height of the man and its shadow = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]

Now, suppose the height of the tree that casts the shadow of 60 ft long is h ft,

So, the ratio of the height of tree and its shadow = [tex]\frac{h}{60}[/tex]

At the same time,

[tex]\frac{h}{60}=\frac{3}{2}[/tex]

[tex]h=60\times\frac{3}{2}=30\times 3=90[/tex]

Hence, the height of the tree is 90 ft

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:

  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.

__

Additional comment

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

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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For this case, the first thing we must do is define variables.

We have then:

x: time in seconds

y: number of ounces

We then have an equation of the form:

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

Where,

b: initial amount of juice

m: amount of juice added every second.

Substituting values we have:

[tex] y = 1.75x + 9.5
[/tex]

For 6 seconds later we have:

[tex] y = 1.75 (6) +9.5

y = 20
[/tex]

Answer:

20 ounces of juice are in the container after 6 seconds

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!

⛈

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 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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yes there is because there is 8 flute players and there are 4 trumpets and 8 is double then 4

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.