Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?

The expression sin(2x) − sinx is equivalent to 2sin (3x/2) sin(x/2) therefore option (D) is correct.

Recall the formula of sine

[tex]\sin x-\sin y=2 \sin (\frac{x+y}{2}) \sin (\frac{x-y}{2})[/tex]

The given expression is sin (2x) − sin x.

Apply the formula

[tex]\sin (2x) - \sin x =2 \sin (\frac{2x+x}{2}) \sin (\frac{2x-x}{2})[/tex]

                      [tex]=2 \sin (\frac{3x}{2}) \sin (\frac{x}{2})[/tex]

Hence the expression is equivalent to 2sin (3x/2) sin(x/2)

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The bottom answer is incorrect

The answer is C.$28.14 for 14 gal

To solve the linear system given by -14x + 11y = 23 and 7x - 3y = 37, we used the elimination method, which resulted in finding the solution x = 13.6 and y = 19.4.

To solve the system of linear equations given by -14x + 11y = 23 and 7x - 3y = 37, you can use the method of substitution or elimination. Here, I'll demonstrate the elimination method:

Therefore, the solution to the system of equations is x = 13.6 and y = 19.4.

The woman's average speed is 49 miles per hour, so in 7 hours she will travel 343 miles.

To solve how far a woman will drive in 7 hours at the same rate as she did for 245 miles in 5 hours, we need to calculate her average speed and then use that to find the distance for 7 hours. The average speed is calculated by dividing the total distance by the total time of travel. So in this case, the average speed is 245 miles divided by 5 hours, which is 49 miles per hour.

Next, to find out how far she will travel in 7 hours, we multiply her average speed by the total time of travel. Therefore, 49 miles per hour multiplied by 7 hours equals 343 miles.

The first four terms of the function f(x) = 3n - 1 are 2, 5, 8, and 11.

Given,

f(n) = 3n - 1

We need to find the first four terms.

A function has an input and an output.

Example:

f(x) = x + 1

x = 1,2,3 are inputs.

f(1) = 1 + 4 = 5

f(2) = 2 + 4 = 6

f(3) = 3 + 4 = 7

5, 6, and 7 are the outputs.

We have,

f(n) = 3n - 1

We can assume that the first four terms can be found with n= 1,2,3,4.

f(1) = 3 x 1 - 1 = 3 - 1 = 2

f(2) = 3 x 2 - 1 = 6 - 1 = 5

f(3) = 3 x 3 - 1 = 9 - 1 = 8

f(4) = 3 x 4 - 1 = 12 - 1 = 11

Thus the first four terms of the function f(x) = 3n - 1 are 2, 5, 8, and 11.

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The area of rectangle is 60 yd²

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangle is 4 yd longer than its width.

Let, the length = x

And, width = y

Now,

Perimeter of rectangle = 2(x+y)

the area of rectangle = xy

x = y+ 4

2(x+y) = 32

Subtract x by equation (1) in (2), we get;

2(y+4+y) = 32

2y+8 +2y = 32

4y = 24

y= 24\4

y  =6yd

And, x = 6+4

x  = 10yd

Thus, Area of rectangle = xy

                                   = 10 × 6

                                   = 60yd²

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The roots of any equation, always satisfies that equation.

Values of  ,   a = - 2   and  b = 22

Other factor of given function is  (x - 3/2)

The given function  [tex]f(x) = ax^3 -x^2 + bx -24[/tex]

Since,  (x - 2) and (x + 4) are factors of given function

Therefore,  x = 2 and x = -4 satisfies the given function.

[tex]f(2)=8a-4+2b-24=0\\8a+2b=28\\\\f(-4)=-64a-16-4b-24=0\\-64a-4b=40\\-16a-b=10[/tex]

Now , solving above two equation by elimination method

We get,   a = -2  and  b = 22

So,   [tex]f(x) = -2x^3 -x^2 + 22x -24[/tex]

To find other factors , we divide above function by multiplication of (x - 2)(x+4).

So we get other factors,    (x - 3/2)

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 all the coordinates of the original triangle have been multiplied by 1/2

A (-4,-6) x 1/2 = -2,-3

B (-8,2) * 1/2 = -4,1

C (-2,4)  *1/2 = -1,2

 so the scale factor is 1/2

 Answer is B

there are 3600 seconds per hour

15 * 3600 = 54000 meters per hour

54000/ 1609 = 33.56

 round to 33.6 miles per hour

The speed of Hummingbird's in miles per hour is 8,153.6463 mph.

       Distance = Speed X Time, and

Given:

A hummingbird can travel up to 15 meters per second.

As,

1 m/s= 2.23694 mph

So, 15 m/s= 15 * 2.23694

                = 8,153.6463 mph

Hence, the speed in mph is 8,153.6463.

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Answer: b. 300 feet

Step-by-step explanation:

We know that 1 yard = 3 feet

Given : The length of a football playing field is 100 yards between the opposing goal lines.

Then, the length of the football field in feet will be :-

[tex]100\times3=300[/tex]

Therefore, the length of the football field in feet = 300 feet

Hence b is the correct option.

Answer:

IF the other line is parallel you use the same slope (m) as the line given then find the y intercept (b) by plugging in the (x,y) and m into y = mx + b

Step-by-step explanation:

So the other guy has the right work but at the end he messed up. The real answer is 10 miles.

By establishing the relationship between Ted's uphill and downhill travel times, we can set up an equation to solve for the one-way distance D of the hike. We find that the one-way distance D is 5 miles, making the total length of the hike 10 miles.

On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40 minutes longer to climb up than run-down, we need to figure out the total length of Ted's hike.

First, let's establish the relationship between the times it takes Ted to hike up and run down the hill. If T is the time it takes to run down, then the time to hike up is T + 40/60 hours (since 40 minutes is two-thirds of an hour).

Let D be the distance of the hike one way. As Ted climbs up at a rate of 3 miles per hour, the uphill time is D/3. Running down at a rate of 5 miles per hour, the downhill time is D/5. We can set up the following equation:

D/3 = D/5 + 40/60

Multiplying through by 15 to eliminate fractions, we get:

5D = 3D + 10

This simplifies to:

2D = 10

Dividing by 2:

D = 5 miles

Since the total hike involves going up and then down the same distance, the total length of the hike is:

Total Length = 5 miles + 5 miles = 10 miles.

The triangle's base measures 82 in length.

What is the Permeter of a traingle?

According to our question,

IF (3X+2) & (5X-14) ARE THE EQUAL SIDES THEN

3X+2=5X-14

-2X=-16

X=-16/-2

X=8

THUS THE EQUAL SIDES ARE

3*8+2=24+2=26

5*8-14=40-14=26

SO

82=BASE+26+26

BASE=82-52

B=30 CM.

30+26+26=82

82=82

Hence we can say that the triangle's base measures 82 in length.

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Final answer:

The lengths of the two legs of the isosceles triangle are equal, and by setting the expressions for these lengths equal to each other and solving for 'x', we find that the length of the base of the triangle is 30 cm.

Explanation:

The perimeter of an isosceles triangle is given as 82 cm. The two legs are represented by the expressions (3x + 2) and (5x - 14). Since it is isosceles, these two expressions must be equal because the lengths of the legs are equal, as stated by the theorem.

First, set the expressions equal to each other to find the value of 'x':

3x + 2 = 5x - 14

We then solve for 'x' by subtracting 3x from both sides and adding 14 to both sides:

16 = 2x
x = 8

After finding 'x', we can determine the length of one of the equal sides by substituting 'x' back into either of the original expressions:

Length of one side = 3x + 2 = 3(8) + 2 = 26 cm

Since we have two sides of the same length, we multiply by 2 to find the total length of the two legs:

Total length of two legs = 26 cm  imes 2 = 52 cm

To find the length of the base, subtract the total length of the two legs from the perimeter:

Length of the base = 82 cm - 52 cm = 30 cm.

Therefore, the length of the base of the isosceles triangle is 30 cm.