simplify this expression 7x(9x^2)

Final answer:

To find the width of a rectangle with an area of 45 square inches and a length of 9 inches, divide the area by the length, resulting in a width of 5 inches (Option A).

Explanation:

The area of a rectangle can be calculated by multiplying its length by its width. In this case, we know the area is 45 square inches and the length is 9 inches. To find the width, we divide the area by the length.

Width = Area ÷ Length = 45 sq in ÷ 9 in = 5 in

Therefore, the width of the rectangle is 5 inches, which corresponds to option A.

Answer:

1 nanosecond = 1 billionth of a second

Step-by-step explanation:

A nanosecond (ns) is an SI unit of time equal to one billionth of a second, that is, ​1⁄1 000 000 000 of a second, or 10^−9 seconds. The term combines the prefix nano- with the basic unit for one-sixtieth of a minute. A nanosecond is equal to 1000 picoseconds or ​1⁄1000 microsecond.

To find the points where the tangent is horizontal on the given curve, find the values of x for which the derivative is zero.

To find the points on the given curve where the tangent is horizontal, we need to find the values of x for which the derivative of the curve is equal to zero. This is because the derivative represents the slope of the tangent line. Setting the derivative equal to zero and solving for x will give us the x-coordinates of the points.

The given curve is y = 7x³ + 6x² - 8x + 7. To find the derivative of this curve, we use the power rule of differentiation. The derivative is dy/dx = 21x^2 + 12x - 8.

Setting dy/dx equal to zero, we have 21x² + 12x - 8 = 0. To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). Using this formula, we can find the values of x that make the derivative equal to zero.

Keywords: curve, tangent, horizontal, derivative, quadratic equation

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Answer:  The required solution for p is [tex]p=2mr+q.[/tex]

Step-by-step explanation:  We are given to solve the following equation for the variable p :

[tex]2m=\dfrac{p-q}{r}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for p, we must take p on one side of the equation and all other terms on the other side.

From equation (i), we get

[tex]2m=\dfrac{p-q}{r}\\\\\Rightarrow 2mr=p-q~~~~~~~~~~~~~~[\textup{Cross-multiplication}]\\\\\Rightarrow p=2mr+q.[/tex]

Thus, the required solution for p is [tex]p=2mr+q.[/tex]

Answer:

Hence, the probability is:

0.296

Step-by-step explanation:

This can be solved with the help of the binomial probability as:

[tex]P(x=r)=n_C_rp^r(1-p)^{n-r}[/tex]

where n denote the quantity which are chosen.

r denote the quantity whose probability is to be determined or success.

and p denote the probability of success.

with n=4 since 4 trucks are randomly selected.

p=5/15=1/3 ( As 5 have brake problems out of total 15 trucks)

1-p=10/15=2/3

r=2 ( since we are asked to find the probability that 2 of those tested have defective brakes)

Hence, the probability is:

[tex]P(x=2)=4_C_2(\dfrac{1}{3})^2(\dfrac{2}{3})^2\\\\\\P(x=2)=\dfrac{4!}{2!\times (4-2)!}\times \dfrac{1}{9}\times \dfrac{4}{9}\\\\\\P(x=2)=0.296[/tex]

Hence, the probability is:

0.296

The actual distance between two cities that are 4.2 cm apart on a map with a scale of 1 cm : 50 mi is 210 miles. The distance was calculated using a direct proportion based on the map's scale.

To determine the actual distance between two cities that are 4.2 cm apart on a map with a scale of 1 cm : 50 mi, you can use the following method:

First, understand that the scale means for every 1 cm on the map, the actual distance is 50 miles. Therefore, you can set up a direct proportion to solve for the actual distance.

Scale of map: 1 cm : 50 mi
Distance on map: 4.2 cm

Setting up the proportion, we get:

Now, solve for 'x' which represents the actual distance between the two cities.

The actual distance between the two cities is 210 miles.

Answer:

C, B, D, E, A.

Step-by-step explanation:

Experimental value = 10 km
accepted value = 12 km

Step 1: Deduct the accepted value from the experimental value.

10 km – 12km = -2 km

Step 2: Take the absolute value of step 1

|--2km| = 2km

Step 3: Divide that answer by the accepted value. 2km/10km = 0.2%

To find the value of y for the point (-1, y) in the equation y = 3x + 4, plug in -1 for x and solve: y = -3 + 4, which simplifies to y = 1. Thus, the value of y is 1.

The student needs to determine the value of y when x is -1 for the equation y = 3x + 4. To find y, we substitute -1 in place of x and solve the equation:

y = 3(-1) + 4

y = -3 + 4

y = 1

Therefore, the value of y for the point (-1, y) is 1.

Sketch  a right triangle having adjacent side(A) is given as “3”, hypotenuse side (H) is “x” and assigning angle “a” as the angle between A and H. Using Pythagorean theorem, you will get “square root of x-squared minus 9” as the opposite side (O). Using SOH CAH TOA function, and since secant is the reciprocal of cosine, sec(a) = x/3. Thus, a = arcsec(x/3). The remaining expression tan(a) is Opposite side over Adjacent side which is equal to “square root of x^2 - 9” over "3". Therefore, the algebraic expression would be: tan(arcsec(x/3)) = “sqrt (x^2 -9)” /3. Different answers can be made depending on which side you consider the “3” and “x”.

The lines l1 and l2 are perpendicular to each other. They form a 270° angle which means they form three right angles. Hence they are indeed perpendicular due to the fact they intersect at a point if one line is extended by 180°.

In this case, we are asked to determine if the lines l1 and l2 are parallel, perpendicular or neither. One critical information presented is that the two lines are perpendicular and form a 270° angle between each other.

Typically, when two lines are perpendicular, they form a right angle, which is 90°. However, a 270° angle suggests they make three right angles, meaning they do not directly intersect at a right angle, but do meet at a point if you extend one line 180° further. Hence, they are indeed perpendicular.

So, although it might seem a bit unusual, based on this information, the lines l1 and l2 are perpendicular to each other.

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Answer:

Speed of sound, v = 340 m/s

Step-by-step explanation:

It is given that,

A exploded 1360 meters away, d = 1360 meters

time taken, t = 4 seconds

We need to find the speed of the travelled sound. Speed of sound is equal to the distance covered divided by total time taken i.e.

[tex]v=\dfrac{d}{t}[/tex]

[tex]v=\dfrac{1360\ m}{4\ s}[/tex]

v = 340 m/s

So, the speed with which sound is travelled is 340 m/s. Hence, this is the required solution.

Answer:

f(2) = 9.

Step-by-step explanation:

Given : f(x) = 2x² – 3x + 7.

To find : What is the value of the function when x = 2.

Solution : We have given that f(x) = 2x² – 3x + 7.

For, x = 2

f(2)  = 2(2)² – 3(2) + 7.

f(2) = 2 *4 -6 +7

f(2) = 8 - 6 +7.

f(2) = 2 +7

f(2) = 9.

Therefore, f(2) = 9.

The answer should be B.

Decimal number equal to 2/3 is 0.67.

Decimal numbers include those numbers which have a whole number and the fractional part separated by a decimal point. Example -

2.33, 4.55, 5.6

A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. Example -

2/5, 5/6, 7/9

We have a fraction 2/3.

The decimal number equal to 2/3 is 0.67.

Hence, decimal number equal to 2/3 is 0.67.

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Answer:

B. y=-2x+8

Step-by-step explanation:

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