From the table below, determine whether the data shows an exponential function. Explain why or why not.

x: 3, 1, -1, -3
y: 1, 2, 3, 4

(A) No; the domain values are at regular intervals and the range values have a common sum 1.
(B) No; the domain values are not at regular intervals.
(C) Yes; the domain values are at regular intervals and the range values have a common factor 2.
(D) Yes; the domain values are at regular intervals and the range values have a common sum 1.

Answers

Answer 1

x        Δx                                 y             Δy

3                                               1

1        1 - 3 = - 2                        2             2 - 1 = 1

-1        -1 - 1 = -2                      3            3 - 2 = 1

-3        -3 - (-1) = -2                  4               4 - 3 = 1

So, as you see y in increasing in regular constant intervals, when x also increases in regular constant intervals. => Δy / Δx = constant.

That is the result of a linear function, not an exponential one.

So, the true statement is given by the option (A) No; the domain values are at regular intervals and the range values have a common sum 1.

Answer 2

Answer:

Step-by-step explanation:

Related Questions

Find the midpoint of segment below

Answers

The midpoint of any two points is the average of the coordinates of the two points:

mp=((x1+x2)/2, (y1+y2)/2)

The correct answer here would be (0, 2) because to find the mid point, you take the mean of both x-coordinates and y-coordinates.

Please help me I'm so confused and it's due at 7:30

Answers

Alright, so from what I understand, you need to create an equation with the solution x=5. One of the steps must include the distributive property. The distributive property essentially means that in x(y+z) with each letter representing a number, it turns into xy+xz. Since 5 is a prime number, we could work backwards. Just tossing out ideas, 5*4=20, so one step in your equation could be 20/4=x and dividing the 4. What's 4? 2 times 2, so we can make it 20/(2*2)=x. 1+1=2, so we can add that step. 20/((1+1)(2))=x, since 1+1=2 ,2*2=4, and 20/4=5. How do we extend 20? 20 equals 2*10, so we can make it (2*10)/((1+1)(2)). For a random thing to add, we can add 20-20 to the equation - it essentially does nothing but add a step since it equals 0, making our equation 20-20+(2*10)/((1+1)(2)).=x. In addition, since x is 5 and positive, we can square 5 (25) and find the square root of 25 to get 5, making our equation now sqrt(((20-20+(2*10)/((1+1)(2))))^2) =x. To decode it, we first cancel the sqrt (square root) and square. Now we know it is positive due to all square roots are positive. The equation is then ((20-20+(2*10)/((1+1)(2))) After that, we can multiply 2 and 10, making it 20-20+(20/((1+1)(2))). Next, we can use the distributive property to multiply 2*1 and 2*1, making it (20/(2+2))-20+20. Adding 2+2 and subtracting 20 from 20, we then get (20/4)=5=x. I challenge you to use something similar, but not the exact thing!

(08.02)How many solutions are there for the system of equations shown on the graph?
No solution
One solution
Two solutions
Infinitely many solutions

Answers

There is no solution since the lines never intersect.

Answer:

The system of equations has no solution

Step-by-step explanation:

We have to find the number of solutions of system of equations shown in the graph.

Since, the number of solutions of system of equations is that point of thew graph on which the graph of two equations meet.

Since, we can see from the graph the two lines are parallel

Hence, they can never meet.

Hence, the system of equations has no solution.

Hence, first option is correct.

What can you say about the nature of any other zeros of the quadratic equation ax^2+bx+c=0 , which has one complex zero? Explain your answer.

Answers

The roots of a quadratic equation are given by :

[tex] \frac{-b+ \sqrt{D} }{2a} [/tex] and [tex] \frac{-b- \sqrt{D} }{2a} [/tex]

so if one of these roots (zeros) is complex, it means that D<0.

This makes the other zero complex as well.

so if one of the roots is complex, the other is also complex, and these complex roots are the conjugates of each other.

Which number sentence below matches this word problem?
Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore. How far did they get? A.15 - 6 = 9
B. 9 + 15 = 24 C.15 - 9 = 6
D. 135 9 = 15

Answers

15 up, 9 back, so 15-9 = 6.
I'd say C.

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore

so, distance they travel before they ran out of gas = 15 miles

distance they floated back down river = 9 miles

So, they are at

[tex]15-9\\\\=6\ miles[/tex]

Hence, They are 6 miles far.

Therefore, Option 'C' is correct.

Line PQ has endpoints at P (-2,3) and Q (4,1). The center of dilation is (-1,4) and the scale factor is 2. What are the coordinates of the endpoints of P'Q'?

Answers

The dilation of line PQ to P'Q' is shown in the diagram below.

The trick is to double the distance from the centre of dilation to each point, P and Q to get the point P' and Q'

P' (-3, 2)
Q' (9, -2)

80 POINTS!
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (give the polynomial with the GCF of 2 AND give two more forms and explain how you got it.

Answers

4y Squared. Turns to 2y * 2y. Another way is 2*2*y*y

4y².

You can rewrite this as 2y * 2y or 4 * y * y

a machine fills 150 bottles of water every 8 minutes. How many minutes will it take this machine to fill 675 bottles?

Answers

All you have to do is put this in your calculator (if your allowed one):
150 minus 8 divide by 675

150 bottles --- 8 minutes
675 bottles --- x minutes

x = 675*8 / 150 = 36 minutes

The photo printed has length of 6 imams width of 4. A smaller picture is printed the ratio of the new picture to the size of the first picture is 1.5 to 2. What's the length and width of the new picture?

Answers

we know the width of the first picture, is 4
we know the ratio from smaller to larger is 1.5:2

thus [tex]\bf \cfrac{\textit{width of small}}{\textit{width of large}}\qquad 1.5:2\implies \cfrac{1.5}{2}=\cfrac{w}{4}[/tex]

solve for "w".

we know the length of the first picture, 6

[tex]\bf \cfrac{\textit{length of small}}{\textit{length of large}}\qquad 1.5:2\implies \cfrac{1.5}{2}=\cfrac{L}{6} [/tex]

solve for "L".

The new picture will have a length of 4.5 inches and a width of 3 inches.

There is asking about the size of a scaled-down photo in comparison to the original photo that has a length of 6 inches and a width of 4 inches. Given the ratio of the new picture to the size of the first picture is 1.5 to 2, we need to calculate the new dimensions.

The scale factor from the original to the new photo is 1.5 / 2, which simplifies to 0.75. Thus, we multiply the original dimensions by 0.75 to find the dimensions of the new picture:

Length of new picture = 6 inches * 0.75 = 4.5 inches

Width of new picture = 4 inches * 0.75 = 3 inches

A first grader measures 1 meter high how much bigger is a first grader compared to the height of a book

Answers

To solve this problem, we would be needing the actual height or size of the book which is not given in the problem. However for the sake of calculation let us assume that the average height of a book is 8.5 inches.

Then the next step we have to do is to convert the height of the first grader from units of meter to units of inches. We know that:

1 meter = 39.37 inches

Therefore the height of the first grader is 39.37 inches.

Taking the ratio with the bigger number in the numerator (height of the 1st grader / height of the book):

ratio = 39.37 inches / 8.5 inches

ratio = 4.63

Therefore this means that the first grader is about 4.63 times taller than the book.

How many pints of blood does a person have for every 14 pounds of body weight?

Answers

there is 8 pints of blood for every 14 pounds of body weight

Answer:

[tex]1[/tex] units.

Step-by-step explanation:

Here body weight is 14 pounds =[tex]\frac{14}{2.205}[/tex] kg =[tex]6.35[/tex] kg (∵ 1 kg ≈ 2.205 ponds ).

Normally, 75 ml of blood needs, if the body weight is 1 kg. Therefore total amount of blood for the body weight 14 pounds [tex](6.35 kg) = 6.35*75 ml=476.25 ml[/tex] [tex]=.47625 l[/tex] and we know that 1 litter of blood =2.11338 point of blood.

Hence total amount of blood = [tex]0.47625*2.11338[/tex] points =[tex]1.006497[/tex] units≈ [tex]1[/tex] units.

He ratio of the lengths of the corresponding sides of two rectangles is 8:3. the area of the larger rectangle is 320 ft2. what is the area of the smaller rectangle? 120 ft2 30 ft2 90 ft2 45 ft2

Answers

The answer is: [A]: " 120 ft² " .
_______________________________________________________
Explanation:
_______________________________________________________
Set up a ratio as a fraction:
_______________________________________________________

8/3 = 320/x ;
_______________________________________________________
Cross-multiply:
_____________________________________________________

8x = 3 * 320 ;

8x = 960 ;

Divide each side of the equation by "8" ;
to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________________
8x / 8 = 960 / 8 ;

to get: x = 120 .

The answer is: [A]: " 120 ft² " .
______________________________________________________

which equation of a circle represents the graph?

Answers

equation of the circle centered on the origin is x²+y²=r²
r=5

x²+y²=5²
x² + y² = 25 ← answer

The equation of circle will be;

⇒ x² + y² = 25

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle is shown in figure.

Centre of circle = (0, 0)

Radius of circle = 5

Now,

We know that;

The standard form of circle with radius 'r' and center (h, k) is,

⇒ (x - h)² + (y - k)² = r²

Hence, The equation of circle with radius '5' and center (0, 0) is,

⇒ (x - 0)² + (y - 0)² = 5²

⇒ x² + y² = 25

Thus, The equation of circle will be;

⇒ x² + y² = 25

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ2

One of the acute angles of a right triangle is 50° and its hypotenuse is 7 inches. find the lengths of its legs to the nearest tenth of an inch.

Answers

Final answer:

To determine the lengths of the legs of a right triangle with a hypotenuse of 7 inches and an acute angle of 50°, we use the trigonometric functions cosine and sine. The adjacent leg (A) is approximately 4.5 inches and the opposite leg (B) is approximately 5.4 inches, both to the nearest tenth.

Explanation:

The student asked: "What are the lengths of the legs of a right triangle if one of the acute angles is 50° and the hypotenuse is 7 inches?"

To find the lengths of the legs of a right triangle, we can use trigonometry. The cosine of an angle in a right triangle is equal to the adjacent leg divided by the hypotenuse, and the sine of an angle is equal the opposite leg divided by the hypotenuse.

Since we know the hypotenuse (7 inches) and one acute angle (50°), we can find:

the length of the opposite leg (leg B) using sine (sin(50°) = leg B / 7 inches).

By solving these equations:

leg A = cos(50°) × 7 inches

leg B = sin(50°) × 7 inches

After calculating, we find:

leg A ≈ 4.5 inches (to the nearest tenth)

leg B ≈ 5.4 inches (to the nearest tenth)

Prove that for any x in the reals 5 divides x if and only if 5 divides x squared

Answers

I think we can do this by taking the contrapositive of the statement.

if the statement is true then the contrapositive is also true:-

If, for any real x, 5 does not divide x^2 then 5 does not divide x.

Any number that 5 will divide into must end in 0 or 5 so the above is evidently true.

So the original statement is also true.

Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).

Answers

check the picture below. So, more or less looks like so.

notice, the center is clearly at the origin, and notice how long the "a" component is, also, bear in mind that, is opening towards the y-axis, that means the fraction with the "y" variable is the positive one.

Also notice, the "c" distance from the center to either foci, is just 5 units.

[tex]\bf \textit{hyperbolas, vertical traverse axis }\\\\ \cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}, {{ k}}\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{{{ a }}^2+{{ b }}^2} \end{cases}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=0\\ k=0\\ a=4\\ c=5 \end{cases}\implies \cfrac{(y-{{ 0}})^2}{{{ 4}}^2}-\cfrac{(x-{{ 0}})^2}{{{ b}}^2}=1\implies \cfrac{y^2}{16}-\cfrac{x^2}{b^2}=1 \\\\\\ c=\sqrt{a^2+b^2}\implies c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \\\\\\ \sqrt{5^2-4^2}=b\implies \boxed{3=b} \\\\\\ \cfrac{y^2}{16}-\cfrac{x^2}{3^2}=1\implies \boxed{\cfrac{y^2}{16}-\cfrac{x^2}{9}=1}[/tex]

Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day. If the original amount of room freshener in the bottle was 40 grams, which of the following graphs best represents the amount of room freshener f(x) that would remain in the bottle after x days?

graph of function f of x equals 30 multiplied by 0.88 to the power of x

graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis

graph of function f of x equals 50 multiplied by 0.82 to the power of x

graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis

Answers

The decay rate is 100% - 15% = 75% = 0.75

The decay equation is f(x) = 40(0.75)ˣ
Where f(x) is the mass of air freshener left after x days of use

The graph of this function is given below

The correct description of the graph is statement 2:

graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis

The person under is wrong but there chart is right. 100%-15%=85%

85%=.85

F(x)= 40(.85)^x

Write that in desmos graphing and you will get the chart.

(Please mark me brainiest)

What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. Thank you!

Answers

Answer with explanation:

⇒A game will be fair , if there is equal chance of winning and losing.

→The game would be fair , if

Landing on Blue sector gives 3.5 points.

Then the, Expected value will be

[tex]E(x_{i})=x_{i} \times P(x_{i})\\\\E(x)=x_{1} \times P(x_{1})+x_{2} \times P(x_{2})+x_{3} \times P(x_{3})+x_{4} \times P(x_{4})\\\\E(x)=-1 *\frac{2}{7}+(0) *\frac{2}{7}+(1) *\frac{2}{7}+(3.5) *\frac{1}{7}\\\\E(x)=(3.5) *\frac{1}{7}\\\\E(x)=0.50[/tex]

→→By Assigning, Blue sector =3.5 points, the game will become fair, Gives, E(x)=0.50.

Final answer:

A game is considered fair if the expected value for all players is zero, balancing the potential wins and losses over the long run. By adjusting winnings and losses so that the sum of the expected values of all outcomes is zero, and recalculating these expected values, we can prove the fairness of the game.

Explanation:

To make a game fair using expected values, one must ensure that the expected value for all players is zero, meaning that there's no advantage or disadvantage to playing the game in the long run. The expected value is calculated by multiplying the value of each possible outcome by its probability and summing these products.

Let's consider the card and coin flipping game and determine its fairness. The expected value (EV) for this game can be expressed as:

EV(face card and heads) = P(face card) * P(heads) * winnings from face card and headsEV(face card and tails) = P(face card) * P(tails) * winnings from face card and tailsEV(non-face card) = P(non-face card) * (P(heads) + P(tails)) * loss from non-face card

To avoir long-term loss, the sum of the expected values for all outcomes should be zero. If the current values do not result in a fair game, we can adjust the winnings and losses such that the expected value is balanced. By recalculating these probabilities with new values, we can verify if the game is fair or not.

Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius round to the nearest hundredth

Answers

volume for cylinder = pi x r^2 x h

radius = half the diameter = 8/2 =4

height = 3 times the radius = 3*4 =12

using 3.14 for pi

volume = 3.14 x 4^2 x 12 = 602.88 cubic inches

Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.

According to the given information, quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles measure 90°. Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the Converse of the Same-Side Interior Angles Theorem. Quadrilateral RECT is then a parallelogram by definition of a parallelogram. Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent. Therefore, one can say that segment ER is congruent to segment CT. Segment TR is congruent to itself by the Reflexive Property of Equality. The _______________ says triangle ERT is congruent to triangle CTR. And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.

Which of the following completes the proof?

A (ASA) Theorem
B (HL) Theorem
C (SAS) Theorem
D (SSS) Theorem

Answers

Consider the triangles ERT and CTR.

|ER|=|CT| shown

(Therefore, one can say that segment ER is congruent to segment CT.)

m(R)=m(T)= 90°shown

(By the definition of a rectangle, all four angles measure 90°)

|RT|=|TR|

so we have Side Angle Side congruence.

By the (SAS) Theorem, the triangles are congruent.

Answer: C (SAS) Theorem

The answer is (SAS) Theorem. Because we know triangle ERT is congruent to triangle CTR, it has the sides ( C& E and R&T, and the angle T&R).

Hope its correct.

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. B = 137°, c = 9, b = 14

Answers

Yes; a triangle is formed:
______________________________________________________
m∡A = 17° ;
m∡B = 137° (given) ;
m∡C = 26° ;
   a = 6 ;
   b = 14 (given) ;
   c = 9 (given) .
______________________________________________________
Explanation:
______________________________________________________
Note:

The law of sines:

(sin A) / a = (sin B) / b = (sin C) / c ;
______________________________________________________
Given:
______________________________________________________
B = 137 ;
c = 9 ;
b =14 ;
______________________________________________________
(sin B) / b = (sin C) / c ;

(sin 137) / 14 = (sin C) / 9 ;

(0.681998360062) / 14 = 0.0487141685758571 = (sin C) / 9 ;
______________________________________________________

sin C = (0.0487141685758571) * (9) ;

sin C =  0.4384275171827139 ;

        Take the "arc sin" of each side of the equation; to isolate "C" on one side of the equation; and to solve for "C" ;

arc sin (C) = arc sin ( 0.4384275171827139) ;

           C = 26.003593520741 ; round to 26.

If all angles of a triangle add up to 180 degrees: then:

A + B + C = 180 ;

A + 137 + 26  = 180 ;

A + 163 = 180 ;

Subtract "163" from each side of the equation; to isolate "A" on one side of the equation; and to solve for "A" ;

A + 163 − 163 = 180 − 163 ;

      A = 17 ;

Now, to solve for "a" ;

(sin A) / a = (sin B)/ b ;

(sin 17) / a = 0.0487141685758571 ;

(0.0487141685758571) a = (sin 17) ;

Divide EACH SIDE of the equation by: "(0.0487141685758571)" ;
______________________________________________________
           to isolate "a" on one side of the equation; and to solve for "a" ;
______________________________________________________
[(0.0487141685758571)a ] / (0.0487141685758571) =

                   (sin 17) / (0.0487141685758571) ;
_________________________________________________________
                   a = (sin 17) / (0.0487141685758571) ;

                      = (0.292371704723) / (0.0487141685758571) ;

                   a = 6.0017796314787227112 ; round to "6" .
_________________________________________________________

Final answer:

Explanation of units for trigonometric functions and how to apply the Law of Sines in triangle problems.

Explanation:

The units for sine, cosine, and tangent must be dimensionless. These trigonometric functions relate angles to side lengths in a triangle.

The Law of Sines can be used to solve triangles when you have a known angle and the opposite side length. It states that the ratio of the length of a side to the sine of its opposite angle is constant.

When given measurements may or may not form a triangle, you can apply the Law of Sines to determine if a triangle can be solved. If not, it means no triangle can be formed.

Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (9, 0), and a co-vertex at (0, 1).

Answers

The standard for of an ellipse is:

(x-h)²/a² + (y-k)²/b² = 1, where h and k are the coordinate of its center.

Since its center is at the origin, then the formula becomes:

x²/a² = y²/b² = 1

The vertex being at (9,0) then a = 9
The co-vertex being at (0.1). then b =1
Hence, the final equation:

x²/9² + y²/1² = 1

x²/81 + y²/1 = 1 ↔ x²/81 + y² = 1 (1st answer)

Find the area of the circle. Leave your answer in terms of pi diameter is 4.1 m

Answers

area= pir^2
r=d/2
4.1/2=2.05
pi(2.05)^2
final answer: 4.2pi

Answer:

Area of the circle will be (4.20 [tex]\pi[/tex])

Step-by-step explanation:

We have to find the area of the circle with diameter given is 4.10 m.

Since radius of a circle is represented by [tex](\frac{diameter}{2})[/tex]

Therefore, radius of the circle = [tex](\frac{4.1}{2})[/tex] = 2.05 m

Formula of the area of a circle is A = [tex]\pi r^{2}[/tex]

So area of the circle with radius 2.05 m will be

A = [tex]\pi (2.5)^{2}[/tex]

= 4.20 [tex]\pi[/tex]

Area of the circle will be (4.20 [tex]\pi[/tex])

a segment is divided into two parts having lengths in the ratio of 5:3. if the difference between the lengths of the parts is 6 " find the length of the longest part

Answers

2 parts.....ratio is 5:3...added = 8.....so one of the parts is 5/8 of the total...5/8x....and the other part is 3/8 of the total...3/8x

the difference is 6...
5/8x - 3/8x = 6
2/8x = 6
x = 6 * 8/2
x = 48/2
x = 24

so the total length is 24
with the longest being : 5/8(24) = 15 <==
and the shortest being : 3/8(24) = 9

The length of the longest part is 15 units.

The length of the longest part in a segment divided into parts in the ratio of 5:3 with a difference of 6 units is 15 units.

The length of the longest part is 15 units.

Let the lengths of the two parts be 5x and 3x.Since the difference between them is 6, we can set up the equation 5x - 3x = 6.Solving for x gives x = 3, so the longest part is 5x = 5 * 3 = 15 units.

HELP PLEASE THANKS (;

Answers

You have 2 equations that are both equal to y. If they are both equal to y, then by the transitive property of equality, they are equal to each other (if a = b, and b = c, then a = c).
5x - 17 = x + 3 and
4x = 20 and x = 5. Now sub in that x value of 5 to solve for y:
y = 5 + 3 and y = 8. So the ordered pair is (5, 8)

In four to five sentences, explain some of the factors that cause shifts in supply and demand and what the effects of these shifts are.

Answers

In the real world, businesses base all their projections to the law of demand and supply. The law of demand states that as the quantity of demand rises, the price of the product falls, and vice versa. On the other hand, as the quantity of supply rises, the price of the product also rises.

Let's take a situation for example. Company A's demand has decreased because a new product from Company has just been launched. Because of their advertisements in blockbuster movies, the product of Company B was bought by many people. Because of this, Company A decides to decrease their price so that people will opt to buy it. To do this, Company A has to reduce their supply. The qualitative graph is shown in the picture. S1&D1 and D2&D2 are supply and demand before and after Company B launched their product, respectively.

From the graph, we can say that from S1 and D1 to S2 and D2, the price decreases and the quantity of products also decreases.

Answer:

Sample Response: Shifts in supply and demand occur when the amount of goods available increases or decreases, or when the demand for a particular good increases or decreases. Shifts in supply can happen when consumers change their spending habits, when competitors produce similar goods, or when the availability of labor or resources changes. Shifts in demand occur when the price changes or when the number of people trying to buy the good changes. It can also happen when people's tastes change.

can anyone help me calculate AC, AD, and EC?

Answers

AC = sqrt(56^2 + 33^2) = 65cm

EC = sqrt(65^2 - 16^2) = 63 cm

to find AD 33-25 = 8

8^2 + 56^2 = AD^2

64 + 3136=3200^2

square root (3200) = 56.5685 round off to 56.6cm

John received $0.76 change from a purchase in the drugstore. if he received eight coins, and five of the coins are the same denomination, how many quarters did he receive?

Answers

5 nickels , 2 quarters, and 1 pennies = 8 coins.

he received 2 quarters

Which graph represents the function of f(x) = 9x 2 -36/3x+6 Please help

Answers

The function is:

         (9x^2 - 36)
f(x) = ---------------------
                3x + 6

You can simplify that function to a linear function for all x for which 3x + 6 ≠ 0

=> x ≠ - 2.

So, for x ≠ - 2, you can do:

         (9x^2 - 36)
f(x) = --------------------- =
               3x + 6

          9(x^2 - 4)
f(x) = ---------------------
                3(x + 2)

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

So, the graph is a right line that intercepts the y-axis at - 6 and the x-axis at x = 2, excluding x = -2 as the function is not defined for x = -2. That is the second graph of the second picture.

Final answer:

The given function is a quadratic equation, not a linear one, and so it would be represented by a parabolic curve on a graph, not a straight line.

Explanation:

The function you're asking about, f(x) = 9x² - 36/3x + 6, is a quadratic equation. Quadratic equations are represented by parabolas on the graph not a straight line. Parabolas usually have a shape like a U (or an upside down U, depending on the equation).

The equation you've given should result in a parabolic graph. The straight line equations and graphs you’re referring to, like y = 9+3x, would not represent your function. The line graph with a y-intercept of 9 and a slope of 3 is not a representation of your function.

Also, it's important to note that the equation you provided, f(x) = 9x² - 36/3x + 6, can be simplified to f(x) = 9x² - 12x + 6.

Learn more about Quadratic Equations here:

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which of the diagram below represents the statement. if it is an insect then it has wings

Answers

The diagram that represent the statement is a Venn diagram in which:

An inner circle labeled "insects" is completely included inside an outer circle which is labeled "has wings".

In such diagram all the insects are inside the bigger set of things that have wings. That means that all the insects have wings but not all the things that have wings are insects.

That is exactly what the proposition if it is an insect then it has wings.

As per the proposition, having wings is a necessary condition to be insect, but it is not sufficient.

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