Help me with this problem please

The domain of the function is  (-∞,∞) and the simplified expression is x²-6x-40 .

A function's domain and range are its constituent parts. A function's  range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.

The given functions are

f(x)=6x+24

g(x)=x²-16

Now we have to find (g-f)(x) .

(g-f)(x)=x²-16-6x-24

or,(g-f)(x)=x²-6x-40

or,(g-f)(x)=x²-10x+4x-40

or,(g-f)(x)=x(x-10)+4(x-10)

or,(g-f)(x)=(x-10)(x+4)

So the domain of the function (g-f)(x) are the values for which the function exists. we can see that the function exists for all values of x.

Domain in set builder notation={x|x∈R}

Domain in interval notation=(-∞,∞)

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Answer:

B

Step-by-step explanation:

use the formula x = [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]x= \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

according to the known condition, a = 1, b = -5-2/5 c = -3

you can input these values into the above two.

Answer:

1

Step-by-step explanation:

the answer is 1.21576655000000000.

the unit of this no. is 1.

Answer:

3 : 2 : 1

Step-by-step explanation:

Simplest ratio

6oz : 4oz : 2 oz

Divide each by 2

6oz/2 : 4oz/2 : 2 oz/2

3 oz:  2 oz:  1 oz

3 : 2 : 1

The solution to the given inequality (-4 < 16 - 4x) is x < 5.

Hence, option B) x < 5  is the correct answer.

Given the in equality in the question;

-4 < 16 - 4x

First, rewrite the inequality such that x is on the left side.

-4x + 16 > -4

Subtract 16 from both sides

-4x + 16 - 16 > -4 - 16

-4x > -20

Divide both sides by -4

Note that when dividing both sides of an inequality by a negative value, the inequality sign flips direction.

-4x/-4 < -20/4

x < -20/-4

x < 5

The solution to the given inequality (-4 < 16 - 4x) is x < 5.

Hence, option B) x < 5  is the correct answer.

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Answer: its not equal.

Step-by-step explanation:

-6y + 4 = 2 (-3y + 2)

|4y + 12| = 4 (y + 3)

Suppose [tex]x>0[/tex]; then the curves meet when

[tex]x^2 + \dfrac5{12} = 2 - \dfrac83 x \implies x^2 + \dfrac83 x - \dfrac{19}{12} = \left(x + \dfrac{19}6\right) \left(x - \dfrac12\right) = 0 \\\\ \implies x = \dfrac12[/tex]

By symmetry, they intersect at [tex]x=\pm\frac12[/tex].

We also see that [tex]\min\left\{f(x):|x|\le\frac34\right\} = \frac5{12}[/tex] and [tex]\max\left\{g(x):|x|\le\frac34\right\} = 2[/tex] at [tex]x=0[/tex]. [tex]f[/tex] and [tex]g[/tex] are continuous, so it follows that

[tex]\min\left\{f(x),g(x) :|x|\le\frac34\right\} = \begin{cases} f(x) & \text{if } |x| < \frac12 \\ g(x) & \text{if } |x| > \frac12 \\ f\left(\pm\frac12\right) = g\left(\pm\frac12\right) = \frac23 & \text{if } x = \pm\frac12 \end{cases}[/tex]

Compute the area [tex]\alpha[/tex]. Taking advantage of symmetry again, we have

[tex]\alpha = \displaystyle 2 \int_0^{1/2} \int_0^{f(x)} dy\,dx + 2 \int_{1/2}^{3/4} \int_0^{g(x)} dy \, dx \\\\ ~~~~ = 2 \int_0^{1/2} f(x) \, dx + 2 \int_{1/2}^{3/4} g(x) \, dx \\\\ ~~~~ = \left. 2 \left(\frac{x^3}3 + \frac{5x}{12}\right) \right\vert_0^{1/2} + \left. 2 \left(2x - \frac{8x^2}6\right) \right\vert_{1/2}^{3/4} \\\\ ~~~~ = \left(\frac12 - 0\right) + \left(\frac32 - \frac43\right) = \frac23[/tex]

and it follows that [tex]9\alpha = \boxed{6}[/tex].

The solution to the given inequality is -10 < x < 5.

To solve a compound inequality involving the and operation, we solve each inequality, then find the intersection of these solutions.

For this problem, the inequality is given by:

-12 < 0.5(4x + 16) < 18.

Multiplying all the terms by 2:

-24 < 4x + 16 < 36

Hence:

4x + 16 > -24

4x > -40

x > -10.

4x + 16 < 36

4x < 20

x < 5

The intersection of these two solutions is:

-10 < x < 5.

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Eigenvalues are the special set of scalar values that is associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed as characteristic roots. It is a non-zero vector that can be changed at most by its scalar factor after the application of linear transformations.

0 Eigenvalue

3 Eigenvalue

The y values of any nxn matrix A that adhere to the following criteria are considered to be its eigenvalues.

When I is the order n identity matrix, det(A - yI) = 0.

In this case, A = [1 2; 1 2], I = [1 0; 0 1], and yI = [y 0; 0 y]. I've added a new line in this notation with ;.

A - yI = [1-y 2; 1 2-y]

det(A - yI) = 1 - y* In other words, - 2 = = 2 - y - 2y + y2 - 2 = 0 = y2 - 3y = 0 = y(y-3) = 0.

y = 0 or y - 3 = 0

y = 3

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Answer:Not there yet

Step-by-step explanation: Think about it your close 2/9 = nothing why do numbers determine our grades so don't answer if anything flunk out of school

Answer: hope this help

step-step explanation:

Answer: -5,9

Step-by-step explanation:

Perimeter = 18 units; Area = 9 sq. units

GH = √(-4-4)²+(1-1)² = 8 units

HI = √(4-0)²+(1+2)² = 5 units

IG = √(0+4)²+(-2-1)² = 5 units

Perimeter of the given triangle = 8+5+5=18 units

Semi-perimeter of triangle = 18÷2=9 units

Using Heron's formula; √[s(s-a)(s-b)(s-c)]=Area of triangle;

A= √(9)(9-8)(9-5)(9-5)

  = √(9)(3)(3)

  = 9 sq. units

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Answer:

9 9 years 9999999999999

Answer:

277g / 40cm³

Step-by-step explanation:

Density = mass / volume

In this case:

volume = 8cm*5cm*4cm = 160cm³

then:

Density = 1088g / 160cm³ = 544g/80cm³ = 277g/40cm³

Answer:

d I'm leaning towards d

Step-by-step explanation:

a doesn't make sense B can't be because we went adding d is phrased wrong

Answer:$49.50

Step-by-step explanation:

First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.

Answer:

the answer will be c....

The correct option is The x-intercept is the point where the graph intersects the x-axis and hence the y-coordinate of that point will be 0.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Given that, we are asked to find the x-intercept of the graph given its equation, we substitute y = 0 into the equation,

So, if we are asked to find the x-intercept, so simply by the definition of intercepts we are asked to find where is the line cutting the x-axis, and as we know that, when a line cuts x-axis its y-intercept we automatically be 0.

So, the answer to this will be, the line cut the x-axis is its x-intercept thus, making y-intercept zero.

Hence, the correct option is the x-intercept is the point where the graph intersects the x-axis and hence the y-coordinate of that point will be 0

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There are 5,000 nails in five boxes. The first and second boxes have 2,700 nails altogether. The second and third boxes have 2,000 nails altogether. The third and fourth boxes have 1,800 nails altogether. The fourth and fifth boxes have 1,700 nails altogether. How many nails are in each box

Purchases of both small and large boxes total:

two little boxes.

six huge boxes

Two equations must be created with the given data in order to answer the unknowns:

150X + 400Y = 2700 (the price of the boxes and the total number of nails, where X is the small boxes and Y the large boxes)

Y = 3X

Equation one is then changed to equation 2, and variable X is eliminated:

150X + 400 (3X) = 2700

150X + 1200X = 2700 1350X = 2700 X = 2700/1350 X = 2

In order to determine the number of big boxes, equation 2's value of X is finally changed:

Y = 3X

Y = 3

Y = 6

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Answer:

(n ÷ 4) + 6 = 8

Step-by-step explanation:

Pretty sure I answered this before, but here you go.

Quotient means The answer when you divide' So we are working in the division.

n ÷ 4 is the division part

It says 'and' which can also mean addition. So we add 6. So far our equation is: (n ÷ 4) + 6 (Brackets are needed as we are dividing n by 4 and not dividing n by 4+6)

Lastly it says the answer must be 8 so we add that at the end. So the answer is:

(n ÷ 4) + 6 = 8

Answer:

B

Step-by-step explanation:

I am not sure what kind of help you need here. the answer is kind of obvious, already revealed by the names of the lines (AB and CB). they meet or intersect at their joined point B.

Answer:

linear

Step-by-step explanation:

because they're are all in a vertical vay

Answer:  36. Substitute: - 32 - 6 * - 3 + 9 Remove the parentheses: 32 + 6 * 3 + 9 Calculate the power:9 + 6 * 3 + 9.

Step-by-step explanation: I hope this help

Answer:

= 1

Step-by-step explanation:

m² + 6m + 9

m = -4

= -4² + 6*-4 + 9

= 16 -24 + 9

= 25 - 24

= 1

Answer:x/5 + 2b/5

Step-by-step explanation:

9a-2b=c+4a solve for a

9a-2b=c+4a

add -4a to both sides

9a-4a-2b=x+4a-4a

5a-2b=x

add 2b to both sides

5a-2b+2b=x+2b

5a= x+2b

divide by 5

5a/5 = x/5 +2b/5

a= x/5 + 2b/5

The measurement of the given angle is a 90 degree.

According to the statement

We have to find that the measurement of this angle.

So, For this purpose, we know that the

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

From the given information:

In the given figure, the measurement of the angle we have to find.

A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.

And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.

Then the angle is 90 degree.

So, The measurement of the given angle is a 90 degree.

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Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer:

x=5

Step-by-step explanation:

so after five months, the costs would equal each other.

Explanation:

You'd have to write equations for the price per month for each club.

Let x equal the number of months of membership, and y equal the total cost. Club A's is y=25x+40 and Club B's is y=30x+15.

Because we know that the prices, y, would be equal, we can set the two equations equal to each other.

25x+40=30x+15.

We can now solve for x by isolating the variable.

25x+25=30x.

25=5x.

5=x

After five months, the total cost would be the same.

Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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True Cash Balance As on June 30  is mathematically given as $ 52588

This is further explained below.

As of the Bank Statement dated June 30th, the Unadjusted Balance A = $53,382.

Deposit in Transit June B = $2,545.

Outstanding Check June 30 C = $3,339

Generally, the equation for the true cash balance is mathematically given as

cash balance = A-(C-B)

Therefore

cash balance= 53,382-(3,339-2,545.)

cash balance= 52588

In conclusion, True Cash Balance As on June 30 = $ 52588

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