Let f(x) = - 5x + 6. Find and simplify f(3a-5).f(3a –5)=(Simplify your answer.)

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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Answer:

the standard deviation of the speeds of cars travelling on California freeways is 6.0 miles per hour

Step-by-step explanation:

The computation of the standard deviation of the speeds of cars is shown below;

The z score for the top 1% is 2.326

So,

= (75 - 61) ÷ standard deviation = 2.326

Standard deviation is

= 14 ÷ 2.326

= 6.0 miles per hour

Hence, the standard deviation of the speeds of cars travelling on California freeways is 6.0 miles per hour

Answer: B & C

Edg2021

Answer:

D) 8x+5

Step-by-step explanation:

3(2x-1)+2(x+4)

6x-3+2x+8

6x+2x-3+8

8x-3+8

8x+5

Rοn wοuld make salary $43,460 in the secοnd year.

The answer is οptiοn (a) 43,460.

Arithmetic οperatiοns are the basic mathematical calculatiοns used tο manipulate numerical values.

Tο find Rοn's salary in the secοnd year, we need tο calculate the 6 percent increase frοm his starting salary οf $41,000 and add it tο his starting salary:

Salary in the secοnd year = Starting salary + 6% οf starting salary

                         = $41,000 + 0.06 * $41,000

                         = $43,460

Hence, Rοn wοuld make $43,460 in the secοnd year.

The answer is οptiοn (a) 43,460.

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer:

10+8y-9y-12 is equivalent to H.

Answer:

27 cupcakes left

In percentage of the number of cupcakes left after she ate 4 = 75%

In percentage of the total number of cupcakes she baked = 67.5%

Step-by-step explanation:

Given that Nora baked 40 cupcakes and ate 4 cupcakes then, the remainder

= 40 - 4

= 36 cupcakes

If she gave 25% of the remaining, the number of cupcakes given

= 25% * 36

= 25/100 * 36

= 9 cupcakes

the number of cupcakes left

= 36 - 9

= 27 cupcakes

In percentage of the number of cupcakes left after she ate 4, this will be

= 100% - 25%

= 75%

In percentage of the total number of cupcakes she baked

= 27/40 * 100%

= 67.5%

From the circle the value of angle x is 90 degrees

We have to find the value of x

The radius of the circle is 18.5

As we observe the figure the angle x is opposite to the 90 degrees

The angle x and angle 90 degrees are vertical angles

We know that the vertical angles are equal or same

∠x = 90 degrees

Hence, the value of angle x is 90 degrees from the circle

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When the Richter scale is 4.3, the value of x, which represents the radius of destruction, is approximately 4.53 kilometers. Rounded to the nearest hundredth, x ≈ 4.53.

The Richter scale measures the magnitude or energy release of an earthquake. It is a logarithmic scale, which means that each whole number increase on the Richter scale represents a tenfold increase in the amplitude of seismic waves and approximately 31.6 times more energy release.

To determine the value of x when the Richter scale is 4.3, we need to understand the relationship between the Richter scale and the radius of destruction caused by an earthquake.

The formula commonly used to estimate the radius of destruction (R) in kilometers is:

R = 10^(0.5 * (M - 3))

Where M is the magnitude of the earthquake.

Substituting M = 4.3 into the formula, we can calculate the radius of destruction:

R = 10^(0.5 * (4.3 - 3))

R = 10^(0.5 * 1.3)

R ≈ 10^(0.65)

R ≈ 4.53

Therefore, when the Richter scale is 4.3, the value of x, which represents the radius of destruction, is approximately 4.53 kilometers. Rounded to the nearest hundredth, x ≈ 4.53.

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Answer:

The critical value for a 99% confidence interval is T = 2.9768

Step-by-step explanation:

We have the standard deviation of the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

Critical value

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.99}{2} = 0.995\). So we have T = 2.9768

The critical value for a 99% confidence interval is T = 2.9768

Answer:

Co-ordinates of the focus is; (0, -4)

Step-by-step explanation:

We are given;

Vertex at origin; (0, 0)

Equation of parabola; y = x²/4p

4p = -16

Now,in parabola with vertex at origin, the coordinates of the focus is usually at (0, p)

Now, from 4p = -16 we can find p

p = -16/4

p = -4

Thus coordinates of the focus is; (0, -4)

Answer:

8^6 is your answer

Step-by-step explanation:

since you are dividing the exponents you subtract the exponents

Answer:

A.3

Step-by-step explanation:

\(increase = 13.25 - 12.50 \\ increase = 0.75 \: dollars\)

\(12.50 = 100\% \\ 0.75 = x\%\)

\(12.50x = 100(0.75) \\ x = \frac{100(0.75)}{12.50} = \frac{75}{12.5} = 6\%\)

Answer:5

Step-by-step explanation:

a2+b2=c2

a2+12squared=13 squared

169-144=a2

a2=25, now that we have 25 we have to find the square root which is 5.

After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.

To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.

The terms involved in this calculation are:
Time (t): 4.5 seconds.

Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times  (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.

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Answer:

B

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .

Answer:

B. \(-\frac{1}{5} x+\frac{4}{5}\)

Step-by-step explanation:

1. Rewrite the function as a linear equation:

y = -5x - 4

2. Swap x and y:

x = -5y - 4

3. Solve for y:

x+4 = -5y - 4+4

x + 4/-5 = -5y/-5

\(\frac{x+4}{-5}\) = y  can be rewritten as \(-\frac{1}{5} x+\frac{4}{5}\)

4. Write in inverse notation:

f(x) = \(-\frac{1}{5} x+\frac{4}{5}\)

Therefore, B is the answer.

Answer:

C

Step-by-step explanation:

the answer is c

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

768

Step-by-step explanation:

64*12

Answer:

768

Step-by-step explanation:

12x64=768

Answer:

7 < x < 12

Step-by-step explanation:

To solve this inequality, solve it the same way you do a normal function. Perform the same actions on both sides of the inequality.

\(10 < 2x-4 < 20\\14 < 2x < 24\\7 < x < 12\)

Answer:

300+ 80+6

Step-by-step explanation:

i think i not sure

Answer:

x = 7

Step-by-step explanation:

In this question, we need to find what the value of x is.

To do so, we need to find the value of the change of the triangle, since the triangles are basically the same

We know to get from 18 to 27, we would need to multiply 18 by 1.5.

This means that the triangle "BCD" is increasing from 1.5 to get "JKL"

With this knowledge, we also know that side CB, 10, needs to increase by 1.5

When you multiply 10 by 1.5, you get 15.

The triangle side "JK" is the same side as "CB", so we need to find what makes the value of 15 for the "JK" side.

To do this, solve 3x-6 for 15.

3x - 6 = 15

Add 6 to both sides.

3x = 21

Divide both sides by 3

x = 7

The x-variable would be 7.

Answer:

Step-by-step explanation:

angle ∠DEF = 180 - 28 - 47

                   = 105°

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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