If f(x) = 3x? - 4 and g(x) = x+2, find (f - g)(x).
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A. 3x2 - *-6
B. 3x2 - x-2
C. 3x -8
D. *- 3x - 2

Answer:

Step-by-step explanation:

Calculate slopes.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Line m:

(3, 7), (6, 12)

[tex]m=\dfrac{12-7}{6-3}=\dfrac{5}{3}[/tex]

Line n:

(-5, 1), (-2, 6)

[tex]m=\dfrac{6-1}{-2-(-5)}=\dfrac{5}{3}[/tex]

The lines have the same slope. That is why they are parallel.

Answer:

y=3x+3 is slope-intercept form

y-6=3(x-1) is point-slope form

I don't know the form your equation(s) are in. There are other forms.

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

So the slope of y=3x+2 is 3.

Parallel lines have the same slope.  So the slope of the line we are looking for has a slope of 3.

Therefore, our equation his this form y=3x+b.

We need to now find b.

We know a point (x,y) on the line.

y=3x+b using (x,y)=(1,6).

6=3(1)+b

6=3+b

Subtract 3 on both sides:

3=b

So the equation is y=3x+3

Point-slope form is another form we can put our line into

y-y1=m(x-x1)

where m is the slope and (x1,y1) is a point on the line.

We have m=3 and a point (x1,y1) on the line is (1,6).

y-6=3(x-1)

[tex]\huge{\boxed{y=3x+3}}[/tex]

It could also be [tex]\boxed{y-6=3(x-1)}[/tex]

We can use point-slope to find this.  Parallel lines have the same slope, and the given line has a slope of 3 ([tex]m[/tex] in [tex]y=mx+b[/tex]).  This means that the parallel line will also have a slope of 3.

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a known point on the line.

Plug in the values. [tex]\boxed{y-6=3(x-1)}[/tex] (point-slope form)

Distribute. [tex]y-6=3x-3[/tex]

Add 6 to both sides. [tex]\boxed{y=3x+3}[/tex] (slope-intercept form)

Answer:

2 ( 24 ) + 2 a = 215

Step-by-step explanation:

Perimeter of the rectangle is 215 feet, the short sides are 24 feet long and we need to work out the long sides (we will call a long side 'a') so,

24 + 24 + a + a = 215

For this case we have to:

Let "a" be the variable that represents the length of the rectangle and let "b" be the variable that represents the width of the rectangle. Then the perimeter is given by:

[tex]P = 2a + 2b[/tex]

We have as data that:

[tex]P = 215 \ feet\\b = 24 \ feet[/tex]

Then, replacing:

[tex]215 = 2a + 2 (24)[/tex]

Answer:

Option B

Answer:

5/3 units  or 1 2/3 units

Step-by-step explanation:

P =2 (l+w)

We know the length = 1/3 and the width = 1/2

P = 2 (1/3+1/2)

Get a common denominator of 6

1/3 *2/2 = 2/6

1/2 *3/3 = 3/6

Therefore

P = 2(2/6+3/6)

  = 2(5/6)

   = 10/6

    =5/3 units

Changing from an improper fraction

  = 1 2/3 units

Answer:

We have a geometric series in which:

a = 20

r = 1/2

Now, we know that: S2 = 20(1-r^2)/(1-r)  and S12 = 20(1-r^12)/1-r

Therefore:  sigma(3,12) = S12-S2  = 20[(1-r^12)/(1-r) - (1-r^2)/(1-r)]  =5115/512  = 9.99023438

Therefore, the answer is: 9.99

Answer: Is D

Step-by-step explanation:

A quadrilateral is a polygon with 4 number of sides and 4 vertices. The correct figure is figure B.

A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.

For the above-given condition,  "If it is a square, then it is a quadrilateral" figure B is correct because, as per the first diagram, not all the squares are quadrilateral, while as per the figure B every square is a quadrilateral.

Hence, the correct figure is figure B.

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Answer:

Option d. the initial amount of money placed in the savings account

Step-by-step explanation:

we have

[tex]f(x)=3,005(1+0.03)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(1+r)^{x}[/tex]

where

a is the initial value

r is the growth rate

(1+r) is the base

x is the number of years

f(x) is the amount of money in a savings account

In this problem we have

a=$3,005

r=0.03=3%

(1+r)=1.03

therefore

3,005 represent the initial value ( the amount of money for the value of x equal to zero)

Answer:

d. The initial amount of money placed in the savings account

Step-by-step explanation:

Given function that represents the amount of money after x years,

[tex]f(x)=3005(1+0.03)^x[/tex]

Which is an exponential growth function,

Since, in a growth function,

[tex]f(x)=ab^x[/tex]

a represents the initial value,

b is the growth rate per period,

x is the number of periods,

By comparing,

a = 3005,

Hence, 3005 must be represent the initial amount of money placed in the savings account,

Option 'd' is correct.

Step-by-step explanation:

here is the answer for your question

Answer:

20x^4 + 23x^3 – 21x^2

Step-by-step explanation:

other answer was a bit hard to read, sorry

Answer:

Rhombus

Step-by-step explanation:

The given points are A(−5, 6), B(−1, 8), C(3, 6), D(−1, 4).

We use the distance formula to find the length of AB.

[tex]|AB|=\sqrt{(-1--5)^2+(8-6)^2}[/tex]

[tex]|AB|=\sqrt{16+4}[/tex]

[tex]|AB|=\sqrt{20}[/tex]

The length of AD is

[tex]|AD|=\sqrt{(-1--5)^2+(6-4)^2}[/tex]

[tex]|AD|=\sqrt{16+4}[/tex]

[tex]|AD|=\sqrt{20}[/tex]

The length of BC is:

[tex]|BC|=\sqrt{(-1-3)^2+(8-6)^2}[/tex]

[tex]|BC|=\sqrt{16+4}[/tex]

[tex]|BC|=\sqrt{20}[/tex]

The length of CD is

[tex]|CD|=\sqrt{(-1-3)^2+(6-4)^2}[/tex]

[tex]|CD|=\sqrt{16+4}[/tex]

[tex]|CD|=\sqrt{20}[/tex]

Since all sides are congruent the quadrilateral could be a rhombus or a square.

Slope of AB[tex]=\frac{8-6}{-1--5}=\frac{1}{2}[/tex]

Slope of BC [tex]=\frac{8-6}{-1-3}=-\frac{1}{2}[/tex]

Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be  a square. It is a rhombus

Answer:

answer is Rhombus

Step-by-step explanation:

Charlene will need 286 square inches of wrapping paper to cover all six sides of the box with dimensions of 7 inches by 9 inches by 5 inches. This is found by calculating the surface area of each side and then adding them together.

To determine how much wrapping paper Charlene will need to wrap a box with dimensions 7 inches by 9 inches by 5 inches, we calculate the surface area of the box. The box has 6 sides, with each side being a rectangle. The dimensions of the sides are 7x9 inches (two sides), 7x5 inches (two sides), and 9x5 inches (two sides).

To find the total surface area, we calculate the area of each of these rectangles and then sum them together:

Area for two 7x9 sides: 2 * (7in * 9in) = 2 * 63in2 = 126in²

Area for two 7x5 sides: 2 * (7in * 5in) = 2 * 35in2 = 70in²

Area for two 9x5 sides: 2 * (9in * 5in) = 2 * 45in2 = 90in²

Adding these together gives:

Total surface area = 126in² + 70in² + 90in² = 286in²

Charlene will need 286 square inches of wrapping paper to wrap the box.

Answer:

565.5 in^3

Step-by-step explanation:

To find the full volume of the tank

V = l*w*h

We know 12 inches high, 14.5 inches long, and 6.5 inches wide.

Substituting in

V = 12 * 14.5*6.5

V =1131 in ^3

He is filling it 1/2 full, that would be 1/2 of the volume

1/2 V = 1131/2 = 565.5 in^3

Answer:

answer is 565.5 in^3

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{7*(-3) * (-2)(2) = ?}[/tex]

[tex]\huge\text{7 * (-3) = -21}[/tex]

[tex]\huge\text{-21 * (-2)2 = ?}[/tex]

[tex]\huge\text{-21 * -2 = 42}[/tex]

[tex]\huge\text{42(2) = ?}[/tex]

[tex]\huge\text{42 * 2 = 42 + 42 = 84}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: 84}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

A figure formed by 3 segments connecting 3 non-colinear points.

Answer:

Hi there!

The answer to this question is: C

A figure formed by three segments connecting three noncollinear points

Answer:

Explanation:

A two way table permits to represent the situation clearly and find the answser is an easy way.

The two way table is that results from the given information is:

Initial information:

                     Blue           Green         Total

Fit well             4                  1                 ?

Too big            ?                   ?                ?

Total               5                   7                12

Now by subtraction and addition you can fill the unknown fields:

                     Blue           Green         Total

Fit well             4                  1                5

Too big            1                   6                7

Total                5                   7                12

Now, you can see that there are 5 blue and 7 too big shirts, but the total number of them is 5 + 7 - 1 (because one of the too big shirts is also blue).

Then, the number of shirts being blue or too big is 5 + 7 - 1 = 11.

And the probability is :

You can also realize that there is only 1 green shirt that fits well, and that is the only option of not being blue of too big, so 1 /12 is the probability of not being blue or too big, and its complement (being blue or too big) is 1 - 1/12 = 11 / 12.

Answer:

The value x=-5 makes the quotient undefined

Step-by-step explanation:

When we are looking for undefined values, we want values that make the denominator zero

x+5 =0

Subtract 5 from each side

x+5-5 =0-5

x=-5

The value x=-5 makes the quotient undefined

2/1000

0.002%

2/6

0.33%

0.002%×0.33%

The percentage of yall being in the same class is 0.00066%

[tex]\huge{\boxed{\text{1750 units}^{3}}}[/tex]

[tex]\begin{array}{cc}\text{First, multiply 12.5 by 10.}&125*14\\\text{Then, multiply 125 by 14.}&1750\end{array}[/tex]

Answer:

Step-by-step explanation:

=4⁴ · 4³

=4^{7}

=16 384

=2² · 2⁻⁴

=2^{-2}

=1/2^{2}

=1/4

Answer:

Algebraic expressions are useful because they represent the value of an expression for all of the values a variable can take on

Answer:

y=2x

100 miles

Step-by-step explanation:

The slope is determined by change of y/ change of x

when using the points (0,0)-(50,100) is

100-0/50-0= 100/50=2

so the slope is 2.

Also there is no Y intercept on the equation bc it goes through the origin.

100 miles is the y point for 50 miles per hour

Answer:

The equation of the best line of fit is y = 2x

Step-by-step explanation:

The relationship between y and x is

y = mx + c

Where m = slope of the line

And c = intercept

At 50 miles per hour she has already covered a distance of 100 miles ---- from the graph

We can use this to calculate the slope of the line using the coordinates (0,0) (50,100)

Slope m is calculated as;

m = (y2 - y1)/(x2 - x1)

Where y2 = 100, x2 = 50

y1 = x1 = 0

Substitute these values

So m = (100 - 0)/(50 - 0)

m = 100/50

m = 2

Since there's no intercept, c = 0

The equation y = mx + c becomes

y = 2x + 0

y = 2x

[tex]\huge{\boxed{6(3)+6(0.05)}}[/tex]

The distributive property shows that you need to multiply the [tex]6[/tex] separately by each term in the parentheses. This means you multiply [tex]6*3[/tex] and [tex]6*0.05[/tex], then add them together to get [tex]6*3+6*0.05[/tex], or in the terms of your answer choices, [tex]\boxed{6(3)+6(0.05)}[/tex].

Option C is correct. The required equivalent expression will be  6(3)+6(0.05)

Given three values A, B and C expressed as A(B+C)

Using the law of distribution

A(B+C) = AB + AC

Applying this law on the expression 6(3+0.05)

6(3+0.05) = 6(3) + 6(0.05)

hence the required equivalent expression will be  6(3)+6(0.05)

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Answer:

{2, 3, 4, 5}

Step-by-step explanation:

3x + 1 > 4

3x > 3

x > 1.

If x = 1 the inequality is not true,

- but  2 3 4 and 5 will make the inequality true.

The numbers in 1, 2, 3, 4, 5} make the inequality 3x + 1 > 4 true is{2, 3, 4,5}

The answer is option D.

     ⇒3x + 1 > 4

     ⇒ 3x > 3

      ⇒  x > 1.

  If x = 1 the inequality is not true,

Therefore   2 3 4 and 5 will make the inequality true.

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Answer:

Explanation:

The graph has the following properties:

        (0.5, 1.6), (0.8, 1), (1.6, 0.5), and (2, 0.4)

The equation represented by the graph is an inverse variation:

From that equation, you can solve for the contstant:

Now, you can take any ordered pair to find the constant:

Thus, you have obtained that the constant is 0.8.

This triangle has no sides which are the same, so this is classified as a scalene triangle.

After we have classified this triangle type, we look at the angles.

If you see the angles, all of the angles have no more than 90°. Acute is less than 90°, right is 90°, and obtuse if more than 90°.

All of the angles in this triangle is less than 90°. This means it's acute.

In conclusion, the triangle is scalene and it is acute, which means it is a scalene acute.

Answer:

1. C.

2. $15.75

Step-by-step explanation:

To find the total cost of lures, multiply your cost of lures (4.25) against your total amount of lures (p).

[tex]4.25p[/tex]

To find the total cost of bobbers, multiply your cost of bobbers (1.50) against your total amount of bobbers (b).

[tex]1.5b[/tex]

To find the total cost of everything, add these two together and you'll have your equation.

[tex]4.25p+1.5b[/tex]

To find the cost given that Jake purchases 3 lures and 2 bobbers, simply plug in your numbers of lures and bobbers to the equation.

[tex]4.25(3)+1.5(2)\\12.75+3\\15.75[/tex]

Answer:

c. 4.25 *p + 1.50 b

15.75

Step-by-step explanation:

lures are 4.25 a pack and bobbers are 1.50

We want to buy p packers of lures and b  bobbers

Take the cost per each item and multiply by the number of each item

Add them together to the total cost

4.25 *p + 1.50 b

This is the cost

Let p =3 and b=2

4.25 *3 + 1.50 (2)

12.75 +3

15.75

Answer:

27 N

Step-by-step explanation:

Since force varies directly with acceleration, we can introduce a constant, k, and write  [tex]F=ka[/tex]

When force is 15, acceleration is 5, so plug it into the equation and solve for k:

[tex]F=ka\\15=k(5)\\k=\frac{15}{5}\\k=3[/tex]

Now, to find force, we use a = 9 and k = 3, so

[tex]F=ka\\F=(3)(9)\\F=27[/tex]

The force is 27 N

Answer:From the box plot, it can be seen that for grade 7 students,

The least value is 72 and the highest value is 91. The lower and the upper quartiles are 78 and 88 respectively while the median is 84.

Thus, interquatile range of the resting pulse rate of grade 7 students is upper quatile - lower quartle = 88 - 78 = 10

Similarly, from the box plot, it can be seen that for grade 8 students,

The least value is 76 and the highest value is 97. The lower and the upper quartiles are 85 and 94 respectively while the median is 89.

Thus, interquatile range of the resting pulse rate of grade 8 students is upper quatile - lower quartle = 94 - 85 = 9

The difference of the medians of the resting pulse rate of grade 7 students and grade 8 students is 89 - 84 = 5

Therefore, the difference of the medians is about half of the interquartile range of either data set.

Step-by-step explanation: i hope it helps it took a long time to write!

Answer:

I hope this helps

Step-by-step explanation:

Answer:

y = - 2x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x - 7 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2, hence

y = - 2x + c ← is the partial equation of the perpendicular line

To find c substitute (4, - 3) into the partial equation

- 3 = - 8 + c ⇒ c = - 3 + 8 = 5

y = - 2x + 5 ← equation of perpendicular line

Answer: 65

Step-by-step explanation:

F(x)=5x+40 and x=5

Enter 5 for x in the equation...

F(x)=5(5)+40

F(x)=25+40

F(x)=65