If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

Answer:

True

Step-by-step explanation:

Answer:

The answer is false.

Step-by-step explanation:

Given line segments are :

AC = 9

CB = 8

AB = 17

As per the triangle inequality theorem the sum of any 2 sides should be greater than the third side. This should be true to all the three combinations.

[tex]AC+CB>AB[/tex] => [tex]9+8>17[/tex] => [tex]17>17[/tex] (not true)

[tex]AC+AB>CB[/tex] => [tex]9+17>8[/tex] => [tex]26>8[/tex] ( true)

[tex]AB+CB>AC[/tex] => [tex]17+8>9[/tex] => [tex]25>9[/tex] (true)

As we can see only two conditions are fulfilled not the third one, so the triangle cannot be formed.

The answer is false.

Answer: B. 20/30

Step-by-step explanation: 20/30 simplified to 2/3. Multiply each number by 2 to get 4/6. 4/6 is not the same number as 5/6.

Answer:

B. 20/30

Step-by-step explanation:

Answer:

(g − f) ( 3 ) = 23

Step-by-step explanation:

( g − f ) ( x ) = g ( x ) − f ( x )

= 6 x − ( 4 − x 2 )

= x 2 + 6 x − 4

to evaluate ( g - f ) ( 3 ) substitute x = 3 into ( g − f ) ( x )

( g − f ) = ( 3 ) 2 + ( 6 x 3 ) - 4 =23

For this case we have the following functions:

[tex]f (x) = 4-x ^ 2\\g (x) = 6x[/tex]

By definition we have to:

[tex](f-g) (x) = f (x) -g (x)\\(g-f) (x) = g (x) -f (x)[/tex]

Then, we find [tex](f-g) (x):[/tex]

[tex]f (x) -g (x) = 4-x ^ 2-6x = -x ^ 2-6x 4[/tex]

We evaluate the function in 3:

[tex](f-g) (3) = - (3) ^ 2-6 (3) 4 = -9-18 4 = -27 4 = -23[/tex]

Now we find[tex](g-f) (x):[/tex]

[tex]g (x) -f (x) = 6x- (4-x ^ 2) = 6x-4 x ^ 2 = x ^ 2 6x-4[/tex]

We evaluate the function in 3

[tex](g-f) (3) = 3 ^ 2 6 (3) -4 = 9 18-4 = 23[/tex]

Answer:

[tex](f-g) (3) = - 23\\(g-f) (3) = 23[/tex]

Note that if [tex]i^2=-1[/tex] than [tex]i=\sqrt{-1}[/tex],

Also note that [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

So we have,

[tex]\sqrt{-49}=\sqrt{-1}\sqrt{49}=\boxed{7i}[/tex]

and,

[tex]\sqrt{-4}=\sqrt{-1}\sqrt{4}=\boxed{2i}[/tex]

Hope this helps.

r3t40

Answer:

A. 37

Step by step explanation:

The median is the middle value with high to low frequency and low to high frequency. How to determine the median is to sort the numbers from the smallest to the big number and the largest number to the smallest number, then count using two hands (one finger left hand and one finger right hand).

Method:

22, 37, 49, 15, 82 then sorted: 82, 49, 37, 22, 15 means the median is 37

The median of this data set is 49.

Option A is correct.

The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. Given a small data set, count the number of data points (n) and arrange them in increasing order.

We have the data: 22, 37, 49, 15, 82

Now, arranging the data in Ascending order as

15, 22, 37, 49, 82

Now, the median is the middle term of the data.

Here there are 5 terms.

So, the median of data is 37.

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Answer:

The first one should be right. Since the teacher is charging $15 per hour of the piano lesson then it can't be any of the answers of $100h. The answer can't be C, the third one, since you're adding the enrollment fee to the cost of every piano lesson it would be wrong to subtract the $100. Hope that helps!

Step-by-step explanation:

The answer will the answer on the top $25=$100+$15h over h

Answer: The number of hours is 10 hours.

Step-by-step explanation:

Since we have given that

Average cost of lessons = $25

let h be the number of hours a student spends in lessons.

Since each student has fee of $100 plus $15 per hour.

So, According to question, it becomes,

[tex]25=\dfrac{100+15h}{h}\\\\25h=100+15h\\\\25h-15h=100\\\\10h=100\\\\h=\dfrac{100}{10}\\\\h=10[/tex]

Hence, the number of hours is 10 hours.

Answer:

[tex]\large\boxed{\dfrac{27}{80}}[/tex]

Step-by-step explanation:

Put x = 3, y = 2 and z = 5 to the given expression [tex]10x^3y^{-5}z^{-2}[/tex]:

[tex]10(3^3)(2^{-5})(5^{-2})\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{10(27)}{(2^5)(5^2)}=\dfrac{270}{(32)(25)}=\dfrac{270}{800}=\dfrac{27}{80}[/tex]

Answer:2x-5

Step-by-step explanation:-(x+5)+3x

-x-5+3x=(3x-x) -5

=2x-5

Answer:

[tex]\large\boxed{y=-\dfrac{3}{4}x-3}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

Parallel lines have the same slope.

===========================================

We have the equation of the line: [tex]y=-\dfrac{3}{4}x-5[/tex]

The slope is [tex]m=-\dfrac{3}{4}[/tex].

Put the value of the slope and the coordinates of the point (4, -6) to an equation of a line:

[tex]-6=-\dfrac{3}{4}(4)+b[/tex]

[tex]-6=-3+b[/tex]           add 3 to both sides

[tex]-3=b\to b=-3[/tex]

Finally:

[tex]y=-\dfrac{3}{4}x-3[/tex]

Answer:

-21

Step-by-step explanation:

For this case we must evaluate the following expression:

[tex]\frac {-66} {(- 3)} + (- 4) - (- 5) =[/tex]

We solve the division:

[tex]22 + (- 4) - (- 5) =[/tex]

We eliminate parentheses keeping in mind that:

[tex]+ * - = -\\- * - = +[/tex]

So:

[tex]22-4 + 5 =[/tex]

Different signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:

[tex]18 + 5 =\\23[/tex]

Answer:

23

Answer:

k= - 2.5

Step-by-step explanation:

If the graph is the attached picture then according to this:

The graph is in V- shape. So if the corners of the graph are not at (0,0) than there must be a constant.

k is the constant which means that it is the amount the function is vertically shifted. The graph is shifted 2.5 units down, therefore the value of k is -2.5.

Thus option 1 is correct....

Answer:

After the 12th Stop

Step-by-step explanation:

2nd stop 1+2=3

3rd 3+3=6

4th 6+4=10

5th 10+5=15

6th 15+6=21

7th 21+7=28

8th 28+8=36

9th 36+9=45

10th 45+10=55

11th 55+11=66

12th 66+12=78

After the 12th stop.

The train will be full after 12 full stops. If we include the 13th stop, the train would exceed its capacity. Therefore, the train can handle 12 full stops if it picks one passenger at the first stop and increases the number of passengers picked by one at each stop.

The problem you're describing is a summation problem in mathematics. You're incrementing the number of passengers at each stop starting at one and increasing by one each time. This can be summed up using the formula for the sum of the first n positive integers (including one), which is n*(n+1)/2. To find out after how many stops the train will be full, you'll need to solve this formula for n such that this sum is less than or equal to 78 (the capacity of the train). You can do this by substitution or by solving the quadratic equation, n² + n - 156 = 0. The result is roughly 12.421, which means that after 12 full stops, the train will have 78 passengers (since we can't have a fraction of a stop). After the 13th stop, the train will exceed its capacity.

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Answer:

4x - 1 and x + 6 are the factors of given Trinomial

Step-by-step explanation:

The given Trinomial is:

[tex]4x^{2}+23x-6[/tex]

We can factorize this trinomial by mid-term splitting. The mid-term(23x) can be split up in two terms (24x and -x) such that their sum is 23x and their product(-24x²) is equal to the product of other two terms (4x² and -6)

So, the above expression can be written as:

[tex]4x^{2}+23x-6\\\\ =4x^{2}+24x-x-6\\\\\text{Taking out commons, we get}\\\\=4x(x+6)-1(x+6)\\\\ =(4x-1)(x+6)[/tex]

Therefore, 4x - 1 and x + 6 are the factors of given Trinomial

Answer: 4x-1 and x+6

Step-by-step explanation: a p e x

Answer:

D is correct

Step-by-step explanation:

Step 1 : Find equation of function A in y = mx + c

2 more than 5 times x

f(x) = 2 + 5x or y = 5x + 2

Step 2 : Identify slope and y-intercept of function A

y = mx + c

y = 2 + 5x

Slope = m = 5

Y-intercept = c = 2

Step 3 : Find the equation of function B in y = mx + c

From my understanding, the number given in the question are coordinates

(-1, 2) , (0, 5) , (1, 8)

Slope = y2-y1/x2-x1

Lets take two coordinates : (-1, 2) , (0, 5)

Slope = 5-2/0-(-1)

Slope = 3/1 = 3

For y-intercept

Lets take (1, 8)

y = mx + c

8 = 3(1) + c

c = 5

The equation is f(x) = 3x + 5 or y = 3x + 5

Step 4 : Lets write both equations with their slope and y-intercept and check with the statements

y = 5x + 2

y = 3x + 5

A) Their slopes are equal but y-intercepts are not equal. Incorrect

B) Their slopes are not equal but y-intercepts are equal. Incorrect

C) Both slopes and y-intercepts are equal. Incorrect

D) Neither slopes nor y-intercepts are equal. Correct

!!

Answer:

D. Taylor correctly found the distance between –4 and 45, but this number represents the total distance the team moved in both directions, not the team’s total gain.

Step-by-step explanation:

The team only ended up gaining the 45 yards on the second play and had gained -4 on the first play.  45-4≠49, but the total distance between -4 and 45 is 49.

Answer:

D.

Step-by-step explanation:

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \qquad \qquad a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-64\implies x^3-4^3\implies (x-4)(x^2+4x+4^2)\implies (x-4)(x^2+4x+16)[/tex]

Answer:

Option C.

Step-by-step explanation:

If k<0, the function g(x) = f(x) + k represents the function f(x) shifted k units downwards.

In this case, given that k=-3 (k<0). The graph was shifted 3 units down. Therefore, the correct option is Option C.

Answer:

The irrational number could be √30

Step-by-step explanation:

An irrational number is a number which can not be written as a ratio between two numbers and it can not be written as a simple fraction. In simple words we can not write it in p/q form.

Find an irrational number that is between 5.2 and 5.5.

Mostly irrational numbers are square root numbers.

So square the both numbers.

(5.2)^2 (5.5)^2.

27.04 , 30.25

It means that the number is between 27.04 and 30.25

We will pick number 30

Square root 30

√30 = 5.48

The irrational number could be √30

It is 5.48 to the hundredth....

Answer:

d. 1134 inches squared

Step-by-step explanation:

The formula for the area of a circle is [tex]\pi r^2[/tex]

where r is the radius.

You are given r=19 here so replace r in [tex]\pi r^2[/tex] with 19 giving us:

[tex]\pi (19)^2[/tex]

Then it is to the calculator we go:

1134 inches squared

Choices A and C are both true statements.  

But C is trivial.  It's CALLED a perpendicular "bisector" of the chord, so OF COURSE it bisects the chord ... otherwise it would be silly to CALL it a "bisector".

The choice that's surprising but true is A .

The perpendicular bisector of a chord passes through the center of the circle.

A chord in plane geometry is a line segment that connects two points on a curve. A line segment whose endpoints are on a circle is frequently described using this phrase. A cycle chord of a graph cycle is an edge that is not in and whose endpoints are in, according to graph theory, which also uses the phrase.

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Answer:

A. The function is linear and is growing by equal differences over equal intervals.

Answer:

A. The function is linear and is growing by equal differences over equal intervals.

Step-by-step explanation:

As you can see in the graph, the function is linear since if draw a line that conects the dots, the graph would turnout linear, and as you can see it is growing 100 orders every 2 weeks, so it is growing by equal differences, over equal intervals.

Answer:

let the integers be x, x+2, x+4 and x+6

therefore,

x + x+2 + x+4 + x+6 = -72

=> 4x + 12 = -72

=> 4x = -72 - 12

=> x = -84/4

=> x = -21

therefore the integers are: -21, -19, -17, -15

[tex]\huge\boxed{\text{-21, -19, -17, -15}}[/tex]

Represent this mathematically. [tex]x+(x+2)+(x+4)+(x+6)=-72[/tex]

Combine like terms. [tex]4x+12=-72[/tex]

Subtract 12 from both sides. [tex]4x=-84[/tex]

Divide both sides by 4. [tex]x=-21[/tex]

Find the numbers by adding 2 each time. [tex]-21, -19, -17, -15[/tex]

Answer:

y = - 0.5x + 4

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (4, 2) ← 2 points on the line

m = [tex]\frac{2-4}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - 0.5

Note the line crosses the y- axis at (0, 4) ⇒ c = 4

y = - 0.5x + 4 ← equation of boundary line

Answer:

y = -0.5 x + 4.

Step-by-step explanation:

Slope-intercept form of the equation of a line on a Cartesian Plane:

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

[tex]m[/tex] is the slope of the line.

If two different points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] on the line are given, the slope of the line will equal

[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].

For this line, the two points are:

As a result,

[tex]\displaystyle m = \frac{2 - 4}{4 - 0} = - \frac{1}{2}[/tex].

[tex]b[/tex] is the [tex]y[/tex]-coordinate (the second coordinate) of the point at the intersection of the line and the [tex]y[/tex]-axis (the vertical axis.) The [tex]x[/tex]-coordinate (the first coordinate) of that point shall equals [tex]0[/tex]. For this line, the coordinates of the intersection is [tex](0, 4)[/tex]. As a result, [tex]b = 4[/tex].

The slope-intercept form of the equation of this line will thus be

[tex]\displaystyle y = -\frac{1}{2}x + 4[/tex].

Answer:

Tanya is 20 years old

Step-by-step explanation:

Let the age of Vera = x years

The age of Linda is twice the age of Vera = 2x years

Tanya  is four less than four times the age of Linda = 4(2x)-4 = 8x-4

Total age of Vera, Linda and Tanya is:

x+2x+8x-4

Combine the like terms:

11x-4

But now their total age is two more than nine times the age of Vera:

11x-4 = 9x+2

Solve the expression

Combine the like terms:

11x-9x=2+4

2x=6

Divide both the sides by 2

2x/2 = 6/2

x= 3

Thus the age of Vera is 3 years.

The age of Linda is 2x= 2*3 = 6 years

The age of Tanya is 8x-4 = 8*3 - 4 = 24-4 = 20years....

Answer:

1) multiplicative inverse of i = -i

2) Multiplicative inverse of i^2 = -1

3) Multiplicative inverse of i^3 = i

4) Multiplicative inverse of i^4 = 1

Step-by-step explanation:

We have to find multiplicative inverse of each of the following.

1) i

The multiplicative inverse is 1/i

if i is in the denominator we find their conjugate

[tex]=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i[/tex]

So, multiplicative inverse of i = -i

2) i^2

The multiplicative inverse is 1/i^2

We know that i^2 = -1

1/-1 = -1

so, Multiplicative inverse of i^2 = -1

3) i^3

The multiplicative inverse is 1/i^3

We know that i^2 = -1

and i^3 = i.i^2

[tex]1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i[/tex]

so, Multiplicative inverse of i^3 = i

4) i^4

The multiplicative inverse is 1/i^4

We know that i^2 = -1

and i^4 = i^2.i^2

[tex]=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1[/tex]

so, Multiplicative inverse of i^4 = 1

Answer:

395

You are 100% right! You go!

Step-by-step explanation:

We are given f(x)=5x^2-2x+8 and are asked to find the value of the function at x=9.

So replace x with (9):

f(9)=5(9)^2-2(9)+8

f(9)=5(81)-18+8          I did the exponent 9^2 and 2(9) in this step:

f(9)=405-18+8           I did 5(81) in this step

f(9)=405-10               I did -18+8 in this step

f(9)=395

Answer:

The break- even point is attained when n=75

Step-by-step explanation:

The break-even point is defined as the point where revenue is equal to cost.

We take the equation for revenue r=15n, and set it equal to the equation c=9n+450

15n=9n+450

Subtract 9n from both sides:

6n=450

Divide both sides by 6.

6n/6=450/6

n=75

The break- even point is attained when n=75....

Final answer:

To determine Amanda's store's break-even point, set the revenue equal to the cost function and solve for n to find 75 shirts.

Explanation:

To find the break-even point of Amanda's store:

Set the revenue function equal to the cost function: 15n = 9n + 450

Solve for n: n = 75

Therefore, the break-even point is when Amanda sells 75 graphic t-shirts.