For f(x) = 2x+1 and g(x)=x^2-7, find (f*g)(x).

Answer:

The zeroes of the function are -3 , -1 , 1 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the meaning of the zeroes of the function

- The zeroes of the function are the values of x when f(x) = 0

- That means the coordinates of the intersection points between the

 curve and the x-axis

- Ex: If the graph of f(x) intersects the x-axis at points (p , 0) , (q , 0) ,

 (r , 0) then the zeroes of f(x) are p , q , r

* Lets solve the problem

- The graph starts at the bottom left

- It continues up through the x-axis at negative three

- That means it intersects the x-axis at point (-3 , 0)

∴ The first zero of the function is -3

- It goes to a maximum around y equals three

- It goes back down through the x-axis at negative one

- That means it intersects the x-axis again at point (-1 , 0)

∴ The second zero of the function is -1

- It goes to a minimum around y equals negative one

- It goes back up through the x-axis at one

- That means it intersects the x-axis again at point (1 , 0)

∴ The third zero of the function is 1

∴ The function has three zeroes -3 , -1 , 1

* The zeroes of the function are -3 , -1 , 1

Answer:

it is C

Step-by-step explanation:

on edge

Answer:

$45

Step-by-step explanation:

$12.50÷5=$2.50

$2.50×18=$45

or

12.50/5=n/18

Answer: Cost of 18 boxes is $45.

Step-by-step explanation:

Since we know that

Cost of 5 boxes of cereal = $12.50

We will use "Unitary method":

Cost of 1 box of cereal is given by

[tex]\dfrac{12.50}{5}\\\\=\$2.5[/tex]

So, Cost of 18 boxes would be

[tex]\$2.5\times 18\\\\=\$45[/tex]

Hence, cost of 18 boxes is $45.

Answer:

x = −1 ± √17

Hope this helps and have a nice day! :)

Answer:

B

Step-by-step explanation:

So your equation is actually x^2+2x+1=17

Left hand side is already set for rewriting it as a perfect square

So you have actually that (x+1)^2=17

Now you just take square root of both sides

x+1=(pm) sqrt(17)                        (pm) means plus or minus

x=-1 (pm) sqrt(17)                         I subtracted 1 on both sides

B

Answer:

60$ will be left

Step-by-step explanation: 30x8 = 240. subtract 300-240 and you get 60

Answer:

60

Step-by-step explanation:

30*8=240

300-240=60

Answer:

The standard form of the equation for this line can be:

l: 2x + 5y = -15.

Step-by-step explanation:

Start by finding the slope of this line.

For a line that goes through the two points [tex](x_0, y_0)[/tex] and [tex](x_1, y_1)[/tex],

[tex]\displaystyle \text{Slope} = \frac{y_{1} - y_{0}}{x_{1} - x_{0}}[/tex].

For this line,

[tex]\displaystyle \text{Slope} = \frac{(-1) - (-7)}{(-5) - 10} = -\frac{2}{5}[/tex].

Find the slope-point form of this line's equation using

The slope-point form of the equation of a line

should be [tex]l:\; y - y_{0} = m(x - x_0)[/tex].

For this line,

The equation in slope-point form will be

[tex]\displaystyle l:\; y - (-1) = -\frac{2}{5}(x - (-5))[/tex].

The standard form of the equation of a line in a cartesian plane is

[tex]l: \; ax + by = c[/tex]

where

[tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are integers. [tex]a \ge 0[/tex].

Multiply both sides of the slope-point form equation of this line by [tex]5[/tex]:

[tex]l:\; 5 y + 5 = -2x -10[/tex].

Add [tex](2x-5)[/tex] to both sides of the equation:

[tex]l: \; 2x + 5y = -15[/tex].

Therefore, the equation of this line in standard form is [tex]l: \; 2x + 5y = -15[/tex].

Answer:

x = 22/15

Step-by-step explanation:

17x - 6 + 3x - 5 = x + 11 + 4x

Combine like terms on each side.

20x - 11 = 5x + 11

Add 11 to both sides. Subtract 5x from both sides.

15x = 22

Divide both sides by 15.

x = 22/15

Answer: 20x-11=5x+11

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

f(x)= 5x-12

f(2)= 5(2)-12 = 10 - 12 = -2

Answer: -2

Step-by-step explanation: f(x)= 5x-12

f(2)= 5(2)-12 = 10 - 12 = -2

thats how i do it

Answer:

2nd one

Step-by-step explanation:

No mixing order so the second one.

You can do either

(y2-y1)/(x2-x1) or (y1-y2)/(x1-x2) which will give you rise/run in either situation

Answer:

2nd one

Step-by-step explanation:

got it right on the test and got 100%

hope this helps :)

Answer:

x > -6

The solution above is graphed correctly in the last option choice.

Step-by-step explanation:

We have been given the equation 2x + 3> -9

In order to graph the solution, we must find the value of x

2x + 3 > -9

Subtract three from both sides

-9 - 3 = -12

2x > -12

Divide both sides by 2

x > -6

To determine how to graph the solution, look at the inequality symbol. If the symbol is "greater than" then you would graph the line going left. If it was "less than" than you would graph the line going right.

In our problem, we have the "greater than" symbol which means we will be graphing our line going to the right, and since we start our line from -6 we know the last option is the correct answer.

Answer:  [tex]\bold{a.\quad \dfrac{1}{4}}[/tex]

Step-by-step explanation:

Since it is already given that the number is a 4 and each of the four colors only has one 4, then the probability for green is:

[tex]P=\dfrac{\text{number of green 4's}}{\text{total number of 4's}}=\dfrac{1}{4}[/tex]

If you wanted to find the probability that it is a four and it is green then you would calculate the probability as:

[tex]P=\dfrac{\text{number of 4's}}{\text{total number of numbers}}\times \dfrac{\text{number of greens}}{\text{total number of colors}}\\\\\\.\ =\dfrac{4}{40}\times\dfrac{1}{4}\\\\\\.\ =\dfrac{1}{40}[/tex]

Answer:

The greatest number of the two is 5

Step-by-step explanation:

Ratios = 5 : 4

Total ratio = 5 + 4 = 9

Sum = 99

To determine the greatest number, solve

5/9 × 99

495/9 = 55

and the second no.

4/9 × 99

396/9 = 44

So the numbers are 55 : 44

The greatest number is 5. ( which is 55)

The greater of the two numbers is 55.

Given:

Ratio of the two numbers is 5:4.

Let, the common factor between two numbers be x.

∴ The two numbers are 5x and 4x.

According to the given condition:

⇒ 5x + 4x = 99

⇒ 9x = 99

⇒ x = 11

The two numbers are:

5x = 5 × 11

5x = 55

4x = 4 × 11

4x = 44

Therefore, 55 is the greater of the two numbers.

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Answer:

x = - 6, x = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Assuming you require the solution to the equation

Given

2x² + 9x - 18 = 0

To factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 18 = - 36 and sum = + 9

The factors are + 12 and - 3

Use these factors to split the x- term

2x² + 12x - 3x - 18 = 0 ( factor the first/second and third/fourth terms )

2x(x + 6) - 3(x + 6) = 0 ← factor out (x + 6) from each term

(x + 6)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

Answer:

the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]

Step-by-step explanation:

We are given the series

1,-3,9,...

the common ratio is:

-3/1 = -3

9/-3 = -3

So, the common ratio in the series is -3

a₁ = 1

The formula used for geometric series is:

[tex]a_{n}= a_{1}(r)^{n-1}[/tex]

Putting values of a₁ and r

[tex]a_{n}= 1(-3)^{n-1}[/tex]

[tex]a_{n}= (-3)^{n-1}[/tex]

So, the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]

Answer:

the answer is 9

Step-by-step explanation:

Step-by-step Answer:

Topic: Points of division

There are scary looking formulas that can be used, but it is much easier to calculate by reasoning.

Given : A(-3,6), B(6,-3)

Solution:

The idea is to subdivide the DIFFERENCE in coordinates into thirds, and add onto that of A.  We choose A as the starting point, but method works equally well if we chose B.

Difference in coordinates (delta) between A & B is then

delta(Bx-Ax, By-Ay)

=(6-(-3), -3-6)

=delta(9, -9)

One third of difference (for point C)

=delta/3 = (3,-3)

So coordinates of point C

= A(-3,6)+(3,-3)

= C(0,3)

Two thirds of difference (for point D)

= (2/3)delta = (6, -6)

Coordinates for point D

= A(-3,6)+(6,-6)

= D(3,0)

If you prefer to use formulas, it would be

New coordinates = (Xa+(Xb-Xa)*k, Ya+(Yb-Ya)*k)

where

Xa,Xb = x-coordinates of points A & B respectively.

Ya,Yb = y-coordinates of points A & B respectively.

k=ratio (usually less than 1)

Here

k for point C = 1/3

k for point D = 2/3

Coordinate of C is: (0,3)

and Coordinate of D is: (3,0)

We know that if a point C(x,y) divides the given line segment A(a,b)B(c,d) into ratio of m:n

then the coordinates of points C are:

[tex]x=\dfrac{m\times c+n\times a}{m+n},\ y=\dfrac{m\times d+n\times b}{m+n}[/tex]

Here A(a,b)=A(-3,6)

and B(c,d)=B(6,-3)

This means that the coordinate of Point C are:

[tex]x=\dfrac{1\times 6+2\times (-3)}{1+2},\ y=\dfrac{1\times (-3)+2\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{6-6}{3},\ y=\dfrac{-3+12}{3}\\\\i.e.\\\\x=0,\ y=\dfrac{9}{3}\\\\i.e.\\\\x=0,\ y=3[/tex]

Hence, the coordinates of Point C are: (0,3)

Hence, the coordinates of point D is calculated by:

[tex]x=\dfrac{2\times (6)+1\times (-3)}{1+2},\ y=\dfrac{2\times (-3)+1\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{12-3}{3},\ and\ y=\dfrac{-6+6}{3}\\\\i.e.\\\\x=\dfrac{9}{3},\ y=\dfrac{0}{3}\\\\i.e.\\\\x=3,\ y=0[/tex]

Hence, the coordinate of Point D is: (3,0)

Answer:

they are the same line! hence there are infinite number of solutions

Step-by-step explanation:

y-10=3x (rearrange)

we get:  y = 3x + 10 ----------- eq. (1)

2y=6x+20 (divide both sides by 2)

we get:  y = 3x + 10 ----------- eq. (2)

We can see that (1) = (2).

i.e they are the same line! hence there are infinite number of solutions.

Answer: $75 per night and $15 per meal

Step-by-step explanation:

a 1 night cost $15

What's the equation defining?

Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of symbols that are split in the left or right sides joined by the equal sign. e.g, 2 + 4 + 5 = 11 is an equation.

Do equations always contain terms?

When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which are assumed to known, is usually known as constants, coefficients and parameters

Step-by-step explanation:

offer 1 : (1)    2*night+3*meal=195

         (2)       night=(195-3*meal)/2

offer 2:  (3)     3*night+5*meal=300

if we replace eq (2) in eq (3)

3*(195-3*meal)/2+5*meal=300

292.5+0.5meal=300

meal=$15

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Answer:

Associative property of addition

Step-by-step explanation:

The order of the addition doesn't matter. That is what the brackets show.

Answer:

Step-by-step explanation:

[tex]\bold{Commutative\ Property\ of\ Addition:}\ a+b=b+a\\\\\bold{Inverse\ Property\ of\ Addition:}\ a+(-a)=0\\\\\bold{Commutative\ Property\ of\ Multiplication:}\ a\cdot b=b\cdot a\\\\\bold{Associative\ Property\ of\ Addition:}\ a+(b+c)=(a+b)+c\\\\\text{We have}\ 7+(4+4)=(7+4)+4\\\\\text{It's Associative Property of Addition.}[/tex]

24 ounce can / 8 ounces = 3 pizzas per can.

3 pizzas per can x 4 cans = 12 total  pizzas.

The answer is D.

Answer: D.) 12 pizza

For this case we have the following quadratic equation:

[tex]3x ^ 2 + 7x + 4 = 0[/tex]

Where:

[tex]a = 3\\b = 7\\c = 4[/tex]

According to the quadratic formula we have:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Substituting:

[tex]x = \frac {-7 \pm \sqrt {7 ^ 2-4 (3) (4)}} {2 (3)}\\x = \frac {-7 \pm \sqrt {49-48}} {6}\\x = \frac {-7 \pm \sqrt {1}} {6}\\x = \frac {-7 \pm1} {6}[/tex]

We have two roots:

[tex]x_ {1} = \frac {-7 + 1} {6} = \frac {-6} {6} = - 1\\x_ {2} = \frac {-7-1} {6} = \frac {-8} {6} = - \frac {4} {3}[/tex]

Answer:

[tex]x_ {1} = - 1\\x_ {2} = - \frac {4} {3}[/tex]

Answer:

x = -4/3            x=-1

Step-by-step explanation:

3x^2 + 7x + 4 = 0

Factor the equation

(3x+4) (x+1) = 0

Using the zero product property

3x+4 =0         x+1 =0

3x+4-4=0-4    x+1-1=0-1

3x=-4                     x=-1

3x/3 = -4/3

x = -4/3            x=-1

Answer:

A. The slope is 4.

B. The y-intercept is 8.

C. The equation is y = 4x + 8

Step-by-step explanation:

We know that there is a flat $8 cost in addition to $4 per ride. We can express this by using:

y = 8 + 4x.

y is the total cost

x is the number of rides

The question wants the equation in slope-intercept form.

Slope-intercept form of a line: y = mx + b

m = slope

b = y-intercept

y = 8 + 4x ➵ y = 4x + 8

Now that we have the slope-intercept form of the line, we can answer the problems.

A. The slope is 4.

B. The y-intercept is 8.

C. The equation is y = 4x + 8

Answer:

D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.

Step-by-step explanation:

edge2021

The statement which best explains that the quadrilateral WXYZ can be a parallelogram is D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

In order to find this, we have to know the properties of the diagonals of a parallelogram.

Here given a parallelogram WXYZ.

The diagonals of a parallelogram bisect each other.

That is, if WXYZ is a parallelogram,

WC = CY and ZC = CX

But it is unknown that these are equal.

Hence the correct option is D.

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Answer:

$40.35

Step-by-step explanation:

First, solve for the sales price. Change the percentage into a decimal:

60% = 60/100 = 0.60

Next, multiply 0.60 with the original price, 97:

97 x 0.60 = 58.2

Subtract 58.2 from the original price:

97 - 58.2 = 38.8

Now, change the tax percentage into a decimal.

4% = 4/100 = 0.04

Multiply 0.04 with the sales price:

38.8 x 0.04 = 1.552

Add the sales price (rounded to nearest hundredth) to the sales price:

1.55 + 38.8 = 40.35

$40.35 is your answer.

~

Answer:

40.35

Step-by-step explanation:

First find the discount

97 * 60%

97 *.6 = 58.2

Subtract the discount to find the new price

97-58.20 =38.80

Next find the tax

38.80 * 4%

38.80 * .04

1.55

We add the tax to the sales price

38.8+1.55

40.35

Answer:

The correct option is 1, 4 and 6.

Step-by-step explanation:

The given two-way table is

                          WIN          LOSS          TOTAL

HOME GAMES     6               10               16

AWAY GAMES      3                8                11

TOTAL                   9              18               27

Total number of home games won by team is 6 and total number of away games won by team is 3. It means the team is twice as likely to win a home game as they are an away game.

The correct option is 1.

Total number of home games = 16.

Home game won by team is

[tex]\frac{6}{16}=\frac{3}{8}[/tex]

Option 2 is incorrect.

Total games = 27

Total games won by the team = 9

Total part of games won by team is

[tex]\frac{9}{27}=\frac{1}{3}[/tex]

Option 3 is incorrect.

The team played a total of 27 games.

Option 4 is correct.

The team won a total of 9 games.

Option 5 is incorrect.

Total home games loose by team = 10

Total away games loose by team = 8

The team lost more home games than away games.

Option 6 is correct.

Therefore the correct option is 1, 4 and 6.

Answer:

4 and 6

Step-by-step explanation:

took quiz

Hello There!

Your answers would be #1 and #3

If Earl jogged 5 yards forward and then jogs 9 yards back, we are subtracting 9 from 5 and we get a difference of -4. This is because he jogged backward from his position after 5 yards.

If Clarissa had $49 in her checking account, we subtract $53 because she bought a pair of shoes so we get a difference of also -4

Answer:

the first one was the answer

874.890 i think, sorry if im wrong

Answer:

The similar triangles are Δ KMJ and Δ NML

The value of x is 3

KM = 6 and NM = 3

Step-by-step explanation:

* Lets revise the cases of similarity

1) AAA similarity : two triangles are similar if all three angles in the first

  triangle equal the corresponding angle in the second triangle  

- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and  

 m∠C= m∠F then ΔABC ≈ ΔDEF by AAA  

2) AA similarity : If two angles of one triangle are equal to the

   corresponding angles of the other triangle, then the two triangles  

   are similar.

- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then  

  ΔPQR ≈ ΔDEF by AA  

3) SSS similarity : If the corresponding sides of two triangles are

   proportional, then the two triangles are similar.

- Example : In ΔXYZ and ΔLMN, if  

  then the two triangles are similar by SSS  

4) SAS similarity : In two triangles, if two sets of corresponding sides  

   are proportional and the included angles are equal then the two  

   triangles are similar.

- Example : In triangle ABC and DEF, if m∠A = m∠D and  

  then the two triangles are similar by SAS

* Now lets solve the problem

- ∠KMJ is a aright angle and M is on JL

∴ m∠JML = 180° ⇒ straight angle

∵ m∠JMK + m∠LMN = m∠JML

∴ 90° + m∠NML = 180° ⇒ subtract 90° from both sides

∴ m∠NML = 90°

- In Δ KMJ and ΔNML

∵ m∠KMJ = m∠NML ⇒ proved

∵ m∠KJM = m∠NLM ⇒ given

- By using the second case above (AA similarity)

∴ Δ KMJ ≈ Δ NML

* The similar triangles are Δ KMJ and Δ NML

- From similarity

∴ Their sides are proportion

∴ [tex]\frac{KM}{NM}=\frac{MJ}{ML}=\frac{KJ}{NL}[/tex]

∵ KJ = 10 and NL = 5

∵ KM = 3 + x and NM = x

- Substitute these values in the proportion relation

∵ [tex]\frac{KM}{NM}=\frac{KJ}{NL}[/tex]

∴ [tex]\frac{3+x}{x}=\frac{10}{5}[/tex]

- By using cross multiplication

∴ 5(3 + x) = 10(x) ⇒ simplify

∴ 5(3) + 5(x) = 10x

∴ 15 + 5x = 10x ⇒ subtract 5x from both sides

∴ 15 = 5x ⇒ divide both sides by 5

∴ 3 = x

* The value of x is 3

∵ KM = 3 + x

∵ x = 3

∴ KM = 3 + 3 = 6

∵ NM = x

∴ NM = 3

* KM = 6 and NM = 3

- Check the ratio

∵ KM/NM = 6/3 = 2

∵ KJ/NL = 10/5 = 2

∴ The sides are proportion

Answer:

Triangle JMK is similar to triangle LMN.

[tex]x = 3[/tex].

[tex]\rm \overline{KM}= 6[/tex].

[tex]\rm \overline{NM} = 3[/tex].

Step-by-step explanation:

The angle [tex]\rm N\hat{M}L[/tex] is a right angle for it is complementary with another right angle, [tex]\rm K\hat{M}J[/tex].

The diagram also indicates that angle [tex]\rm \hat{J}[/tex] is equal to angle [tex]\rm \hat{L}[/tex]. As a result, [tex]\rm \triangle JMK \sim \triangle LMN[/tex] for two of their angles are equal.

Consequently,

[tex]\displaystyle \rm \frac{(\overline{MN})}{(\overline{MK})} = \frac{(\overline{LN})}{(\overline{JK})}[/tex].

Let [tex]x[/tex] be the length of segment [tex]\rm MN[/tex].

[tex]\displaystyle \frac{x}{3+x} = \frac{5}{10}[/tex].

Cross multiply. In other words, multiply both sides by [tex]10(3 + x)[/tex].

[tex]10x = 5(3 + x)[/tex].

[tex]x = 3[/tex].

[tex]\rm \overline{KM} = 3 + \mathnormal{x} = 6[/tex].

[tex]\rm \overline{MN} = \mathnormal{x} = 3[/tex].

Answer:

25747 is all you mentioned except irrational

Step-by-step explanation:

Whole numbers are counting numbers or also 0. If you can count to it and you can but no one wants to in this cases because that's a big number, then it is a whole number for sure. So 25747 is a whole number which means it is also an integer and also a rational number.  It is definitely not irrational.

25,747 is a positive whole number and thus is classified as an integer. It is also a rational number, but it is not an irrational number. Therefore, 25,747 is both a whole number and a rational number.

The number 25,747 is an example of a positive whole number and can also be classified as an integer. In mathematics, an integer is defined as any whole number without a fractional or decimal component, which can be positive, negative, or zero. Since 25,747 is a whole number greater than zero, it is specifically a positive integer.

A rational number is a number that can be expressed as the ratio of two integers, such as fractions or any number that has a finite or repeating decimal expansion. Clearly, 25,747 qualifies as a rational number since it can be written as 25,747/1.

An irrational number, on the other hand, cannot be expressed as a simple fraction - examples include π (pi) and √2 (the square root of 2), both of which have non-repeating, non-terminating decimal expansions. Therefore, 25,747 is not irrational.

In conclusion, 25,747 is a positive whole number, which means it is an integer and a rational number, but not an irrational number.

Answer:

[tex]2x-3y=-12[/tex]

Step-by-step explanation:

We can use the point-slope formula given by:

[tex]y-y_1=m(x-x_1)[/tex]

The given line passes through the

point (-3,2) and having slope [tex]m=\frac{2}{3}[/tex].

We substitute the given point and slope to get:

[tex]y-2=\frac{2}{3}(x--3)[/tex]

[tex]y-2=\frac{2}{3}(x+3)[/tex]

we clear the fraction to get;

[tex]3y-6=2(x+3)[/tex]

[tex]3y-6=2x+6[/tex]

[tex]3y-2x=6+6[/tex]

[tex]3y-2x=12[/tex]

Or in standard form:

[tex]2x-3y=-12[/tex]

The correct equation for a line passing through the point (-3,2) with a slope of 2/3 is y = 2/3x + 4, which corresponds to option C in the provided choices.

To find a correct equation for a line passing through a specific point with a given slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point through which the line passes.

In this problem, we have the point (-3, 2) and a slope of 2/3. Substituting these values into the point-slope form gives us:

y - 2 = 2/3(x + 3).

After multiplying both sides by 3 to eliminate the fraction, the equation becomes:

3(y - 2) = 2(x + 3).

Expanding and simplifying this equation further, we end up with:

3y - 6 = 2x + 6,

or

y = 2/3x + 4, which matches option C.

Therefore, the correct equation for the line passing through the point (-3, 2) with a slope of 2/3 is y = 2/3x + 4.