Grace starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 1/4 each week for a number of weeks, w. She writes the expression 100(1/4)w to find the amount of radioactive substance remaining after w weeks.

Answer:

it is a polynomial

3a^2+a^2= 4a^2

4a^2+6

Step-by-step explanation:

3a^2 +a^2 = 4a^2+6

=4a^2+6

The student's question simplifies to 4a^2 + a + 6 after combining like terms.

This problem draws upon the concepts of linear equations and variables in mathematics. When you encounter 3a^2 + a^2 added to a + 6, you want first to combine like terms. In this case, 3a^2 and a^2 are like terms, meaning they can be added together. So, this results in 4a^2 + a + 6.

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This is what i did to get the answer.

225/ 4.5 = 50 seconds to finish the slushy.

Answer:

(a) 225 mm

(b)50 seconds

Step-by-step explanation:

Let the equation that represents this situation is y = mx+ b

Here, y represents the amount left in  milliliters and x represents the time in seconds.

It has been given that she drank the slushy at a rate of 4.5 milliliters per second.

So, m = -4.5        (negative because the amount decreases)

And after 17 seconds, 148.5 milliliters of slushy remained

So, when x = 17, y = 148.5

Substituting these values in the above model y = mx +b

148.5 = -4.5(17) + b

148.5 = -76.5 +b

b = 225

Therefore, the model is y = -4.5x + 225

(a)

When x = 0, we have to find y

y = -4.5 (0) + 225

y =225

Thus, 225 mm of slushy was originally in the cup.

(b)

Now, we have to find x for y =0

0= -4.5x + 225

4.5 x = 225

x = 50

So, Mariana took 50 seconds to drink all the slushy.

Answer:

26.4= 26 2/5 millimeters

Step-by-step explanation:

All you do for this problem is see how many times 1/3 goes into 1. Since 1 means a full load of dishes. Which is three times. So you also do 8 4/5 times three too to get your answer.

Answer:

addition property of equality.

Step-by-step explanation:

4(3 x^2 + 2) - 9 = 8 x^2 + 7

We can add 9 to each side, by using the addition property of equality.

a=b  then a+c = b+c

Okay # 1

Y = 6x (I don't know why there's two answer choices)

# 2

Uhh it should be increasing linear but the (3,8) kinda threw it off

The rule for the first set of ordered pairs is y = 6x, representing a linear, increasing function.

The relationship between the number of college courses and time spent on homework is increasing and non-linear.

The ordered pairs (1, 6), (2, 12), (3, 18), (4, 24), and (5, 30) show that for each value of x, y is always six times as much.

Thus, the rule that represents this function is y = 6x.

When you plot these points on a graph, the line will be straight, showing it's a linear function, and because y increases as x increases, it is an increasing function.

Looking at the other set of ordered pairs for the number of college courses versus the time spent on homework, we can see that as the number of courses increases, the time spent also increases, showing that the relationship is increasing.

However, the increase in time is not consistent (3, 6, 8, 12), which suggests the relationship is non-linear.

Answer:

30

Step-by-step explanation:

its 64 mannnnnnn :p sdfghjkljhgfdsdfgh

Answer:

560x^3

Step-by-step explanation:

The formula is

(r + 1)th term of (a + x)^n = nCr a^(n-r)x^r

So 5th term = (4 + 1)th term

= 7C4 x^(7-4) (-2)^4

=  35x^3*16

= 560x^3

To graph the equation 2x + 3y + z = 6, which represents a three-dimensional plane, isolate one variable (e.g. z = 6 - 2x - 3y) and choose arbitrary values for the other two variables, then calculate z. The obtained ordered triplets (x, y, z) represent points on the plane and can be plotted to give a visual of the plane.

In order to graph the equation 2x + 3y + z = 6, we first need to understand that this is a linear equation in three variables representing a plane in three-dimensional space. Unfortunately, it's challenging to graph a three-dimensional plane manually without specific technology or software.

However, I can explain how you'd approach plotting this. The general process involves initially isolating one variable then choosing arbitrary values for the other two variables. Let's isolate z, for example:

z = 6 - 2x - 3y.

Now, you can choose values for x and y, and subsequently calculate z. You can form ordered triplets (x, y, z) and these would be points of the plane that satisfies the equation. A sufficient number of these points, plotted and confined, will depict a visual of the plane.

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To graph the equation 2x + 3y + z = 6, find the intercepts by setting two variables to zero and solving for the third. Plot these intercepts (0,2,0), (3,0,0), and (0,0,6) on a 3D coordinate system and draw a plane through these points.

To graph the equation 2x + 3y + z = 6, you need to understand that this is an equation of a plane in three-dimensional space. Unlike graphing a line, where you only need two points, graphing a plane requires you to find at least three non-collinear points (points not on the same line) to form a flat surface.

Here is a step-by-step method to graph this plane:

Set z = 0 and solve for y when x = 0 to find the y-intercept. (2(0) + 3y + 0 = 6 gives y = 2).

Set z = 0 and solve for x when y = 0 to find the x-intercept. (2x + 3(0) + 0 = 6 gives x = 3).

Set x = 0 and solve for z when y = 0 to find the z-intercept. (2(0) + 3(0) + z = 6 gives z = 6).

Plot these intercepts on a three-dimensional coordinate system.

Draw a plane that passes through these three points.

These three intercepts, (0,2,0), (3,0,0), and (0,0,6), are enough to define the plane uniquely. Connect these points to form a triangular shape which implies the plane extending infinitely in all directions within the given slope constraints.

Problem 6)

Scale factor is 1:6, so you are correct

Ratio of perimeters is also 1:6 because the perimeters are just the sum of the linear parts. The larger figure has a perimeter that is 6 times longer than the smaller figure.

The ratio of the areas is 1:36, you simply square both parts of the scale factor ratio. Imagine you had 2 squares. One is 1x1 and the other is 6x6. The first square has an area of 1 square unit. The second square has an area of 36 square units. We see that the larger square is 6 times larger in terms of linear side length, and 36 times larger in area compared to the smaller square.

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Problem 7)

You have the correct scale factor when you write 3:5

The ratio of perimeters is also the same at 3:5

The ratio of areas (small to big) is 9:25 after you square both parts of the scale factor.

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Problem 8)

The scale factor is 3:1 after you reduce the ratio 6:2

The ratio of perimeters is also 3:1

The ratio of areas is 9:1

Answer:

The system of linear inequalities is equal to

[tex]4x+10y\leq 100[/tex]

[tex]y\geq 5[/tex]

Step-by-step explanation:

Let

x-----> the number of bags of salt

y-----> the number of bags of sand

we know that

[tex]4x+10y\leq 100[/tex] -----> inequality A

[tex]y\geq 5[/tex] ------> inequality B

Using a graphing tool

see the attached figure

The solution of the system of inequalities is the triangular shaded area

Answer:

2*2*3*3*5

Step-by-step explanation:

Factor 180 into prime numbers that multiply together to give 180

180 = 20 *9

  =  4*5 * 3*3

  = 2*2* 5 * 3*3

Now rewrite them from smallest to largest

2*2*3*3*5

PQ because it corresponds by order.

Answer:

a < -11 (picture included)

Step-by-step explanation:

To solve an inequality, you work it like a regular equation, with a few exceptions, such as flipping the inequality sign when you multiple or divide a number by a negative. Let's solve.

-6a > 66

Divide both sides by -6 and flip the inequality sign because we divided by a negative number.

a < -11

On a number line, it should look like the picture. It has an open hole because the inequality sign does not have a line under it.

-6a > 66      change the signs

6a < -66     divide both sides by 6

a < -11

Answer:

Option A, C and D are correct choices.

Step-by-step explanation:

Let x be the number of rides that Tomas has been on so far. Each ride costs 5 tickets. This means that cost of x rides will be 5x.

We are told that Tomas bought 80 tickets for rides at an amusement park.

To find the number of of tickets that Tomas has left we will subtract cost of x rides from total number of tickets that Thomas bought.

We can represent this information in an expression as: [tex]80-5x[/tex]

Now let us see which of our given choices in equivalent to our expression.

A. [tex]80-5x[/tex]

Upon looking at option A we can see that it is same as our expression, therefore, option A is the correct choice.

B. [tex]80+5x[/tex]

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option B is not a correct choice.

C. [tex]5(16-x)[/tex]

Upon distributing 5 we will get,

[tex]80-5x[/tex]

Now this expression is same same as our expression, therefore, option C is the correct choice.

D. [tex]-5x+80[/tex]

This expression is also same as our expression as we can rearrange the terms in this expression as: [tex]80-5x[/tex], therefore, option D is a correct choice as well.

E. [tex]5(16+x)[/tex]

Upon distributing 5 we will get,

[tex]80+5x[/tex]

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option E is not a correct choice.

Answer:

A D

Step-by-step explanation:

Answer:

6 roots

Step-by-step explanation:

f(x)=3x^6+2x^5+x4-2x^3

The number of roots is determined by the degree of the polynomial.  They may be real or complex.

Since this is a 6th degree polynomial, it will have 6 roots

f(x)=3x^6+2x^5+x4-2x^3

Answer:

6 is the total number of roots

Answer:

slope = [tex]\frac{1}{3}[/tex], y- intercept = - 1

Step-by-step explanation:

to calculate the slope m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 0) ← 2 points on the line

m = [tex]\frac{0+1}{3-0}[/tex] = [tex]\frac{1}{3}[/tex] → B

the y-intercept c is where the line crosses the y- axis

that is c = - 1 ← y- intercept

[tex]\left\{\begin{array}{ccc}2x+7y=1\\2x-4y=12&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+7y=1\\-2x+4y=-12\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad11y=-11\qquad\text{divide both sides by 11}\\.\qquad\qquad \boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\2x+7(-1)=1\\2x-7=1\qquad\text{add 7 to both sides}\\2x=8\qquad\text{divide both sides by 2}\\\boxed{x=4}\\\\Answer:\ \boxed{x=4\ and\ y=-1\to(4,\ -1)}[/tex]

Answer:

y = 4.25x

Step-by-step explanation:

Answer:

y = 4.25x

Step-by-step explanation:

Cheddar cheese cost 4.25 per pound . This means the cost of cheddar cheese is 4.25 for every pound in weight. Assuming we put a currency to the value we can say 1 pound of cheddar cheese is equals to 4.25 dollars($4.25). Mathematically, it can be represented as

4.25 is the cost for 1 pound of Cheddar cheese

Let the cost of the equation be y as required from the question.

y = cost of the cheddar cheese

x is the weight value in pounds of the Cheddar cheese.

The equation can be best represented as

y = 4.25x

In the equation above if the amount in pounds is 3 pound . the value will be inputted for x and the cost will be gotten which is y.

Answer:

The sum of the interior angles of a triangle is 180 degrees.

d. Scalene

e. Isosceles

f. Isosceles

g. Equilateral

h. Scalene

i. Equilateral

j. Right

l. Acute

m. Obtuse - doesn't add to 180 not a triangle

n. Acute - doesn't add to 180 not a triangle

o. Obtuse

Step-by-step explanation:

The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.

Side lengths: Compare the side lengths and see if any are equal to determine the type.

Angle Measures: Compare the angles measures to 90 degrees.

Answerthe answer is b

Step-by-step explanation:

Answer:

1/4 (n-64)

Step-by-step explanation:

1/4  n-16

We need to factor out 1/4 from each term which means divide each term by 1/4

1/4 ( 1/4 n / (1/4) - 16 / (1/4))

Remember copy dot flip when dividing fractions)

1/4 ( n - 16 * 4/1)

1/4 (n-64)

Answer:

Step-by-step explanation:O would say the first answer choice

Answer:

The first one.

Step-by-step explanation: Well it is simple, the total has to be 36, none of the other ones show 36 as the total.

Answer:

yes, the answer is B.

I took the practice so it is correct.

Substitute the values of x, y and z to the expression:

[tex]x=5,\ y=3,\ z=14\\\\\dfrac{5x-6y+20z}{4yz}=\dfrac{(5)(5)-(6)(3)+(20)(14)}{(4)(3)(14)}=\dfrac{25-18+280}{(12)(14)}\\\\=\dfrac{7+280}{168}=\dfrac{287}{168}=1\dfrac{119}{168}=1\dfrac{119:7}{168:7}=1\dfrac{17}{24}[/tex]

Answer:

(A) m=0   y intercept =-4

(B)  m=1/3     y intercept = 5

(C) M=5          y intercept = -11

Step-by-step explanation:

Answer:

Correct choice is C

Step-by-step explanation:

Let x be unknown number.

Three times a number x is [tex]3\cdot x=3x.[/tex]

Three times a number is no less than negative six means that the number [tex]3x[/tex] can be equal to -6, can be greater than -6, but cannot be less than -6.

Thus,  the inequality that could be used to solve the  problem is

[tex]3x\ge -6.[/tex]

Answer:

3x ≥ -6

Step-by-step explanation:

The correct graph representing the total cost for a group to visit the zoo with an admission fee of $15 per person is a linear graph starting at the origin and increasing by $15 on the y-axis for each additional visitor on the x-axis.

The question asks which graph correctly represents the total cost for a group to visit the zoo, with an admission fee of $15 per person. To depict this scenario correctly, we would look for a linear graph that starts at the origin (0, 0), indicating that no cost is incurred without visitors, and then increases positively and linearly as the number of visitors increases. This is because the total cost is directly proportional to the number of visitors, with each additional visitor adding $15 to the total cost.

For example, if 1 person visits, the cost is $15; for 2 people, it's $30, and so on. This relationship would be represented graphically by a straight line, where the slope of the line represents the cost per person ($15). Therefore, the correct graph is one that shows a linear relationship with a slope of $15, where the y-axis represents the total cost and the x-axis represents the number of visitors.

Answer:

A

Step-by-step explanation:

the days are at the bottom 1-7. each day does up by 15 (cost of the tickets)

Answer: The minimum is 16, probably arranged in 4 rows of 4 buttons.

Step-by-step explanation: just grab a calculator lol

Answer: tens

Step-by-step explanation:

Answer: $36.69

Step-by-step explanation:

Okay, so let's first write the equation:

2.59*10 + 3d = 135.97

Now, let's work on isolating d by first simplifying the equation:

25.9 + 3d = 135.97

25.9 + 3d - 25.9 = 135.97 - 25.9

3d = 110.07

3d/3 = 110.07/3

d = 36.69

Okay, now let's check:

2.59*10 + 3*36.69  = 135.97

25.9 + 110.07 = 135.97

135.97 = 135.97

Okay, so so it costs $36.69 per pair of shoe.

The correct possible numbers of players on the soccer team and the baseball team that maintain the ratio of 4 to 7 are 4 soccer players to 7 baseball players.

To find possible numbers of players on the soccer team and the baseball team, we can use the given ratio 4:7. This means that for every 4 soccer players, there are 7 baseball players. To maintain this ratio, we can multiply both numbers by a common factor to find a set of possible numbers of players.

Let's denote the common factor by 'k'. Then, the number of soccer players would be 4k and the number of baseball players would be 7k. Here are a few examples with different values of k:

1. If k = 1, then we have:

Soccer players: 4 × 1 = 4

Baseball players: 7 × 1 = 7

2. If k = 2, then we have:

Soccer players: 4 × 2 = 8

Baseball players: 7 × 2 = 14

3. If k = 3, then we have:

Soccer players: 4 × 3 = 12

Baseball players: 7 × 3 = 21

4. If k = 4, then we have:

Soccer players: 4 × 4 = 16

Baseball players: 7 × 4 = 28

And so on. The numbers of players on the soccer and baseball teams can be any multiple of 4 and 7, respectively, while still maintaining the ratio of 4:7.