Which expression is equivalent to the following complex fraction? X+5/x+2-x+1/x^2+2x

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

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:

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.

First off, the length of MN is 2√10, not 8. This is because using Pythagorean Theorem, you get that MN=√4+36=2√10, which is (3).

The midpoint of MN can be found by finding the average of the coordinates of M and N. Therefore, our first part to solving this question is to find the coordinates of M and N. M is (2,5) and N is (4,-1). Finding the average of the x-coordinates gives us 3. Finding the average of the y-coordinates gives us 2, Therefore, the midpoint of MN is (3,2), or answer choice (3).

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:

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

Answer:  The probability of selecting a chip with an even number given that the chip is black = 5/6

Step-by-step explanation:

Let B represents the event of getting black chip,

While E represents the event of getting even chip.

So, according to the question,

It is given, The probability of selecting a black chip with an even number is,

[tex]P(B\cap E)=\frac{1}{2}[/tex]

And,  The probability of selecting a black chip is,

[tex]P(B)=\frac{3}{5}[/tex]

Thus, the probability of selecting a chip with an even number given that the chip is black,

[tex]P(\frac{E}{B} )= \frac{P(B\cap E)}{P(B)} = \frac{1/2}{3/5}[/tex] ( By the conditional property )

⇒ [tex]P(\frac{E}{B} )= \frac{5}{6}[/tex]

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:

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:

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:

k(x) = 4x - 2

Please refer attachment for the graph.

Step-by-step explanation:

Given :

g(x) = 3x

h(x) = 2- x

k(x) = g(x)-h(x)

k(x) =3x -(2-x) = 3x -2 +x =4x -2

∴k(x) = 4x - 2

Answer:

D

Step-by-step explanation:

A) True. Alternate interior angles are congruent so

[tex]\angle c\cong \angle e[/tex]

B) True. Considering the sum of these three angles is equal to a straight angle. Since ∠a+∠d  supplementary to ∠e

[tex]\angle a+\angle e+\angle d=180[/tex]

C) True. Since the line segments form a triangle having a (black) line as triangle base.

D) False. ∠b is congruent to its corresponding angle, and ∠e is not its corresponding angle. The corresponding angle of ∠b is the angle vertex opposed to ∠d (not identified).

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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Answer:

yes, the answer is B.

I took the practice so it is correct.

To divide fractions, multiply the first fraction (-7/10) by the reciprocal of the second one (5/2). This gives -35/20 which simplifies to -7/4 or -1 3/4.

When dividing fractions, the conventional method is to multiply the first fraction, which is the dividend, by the reciprocal of the second fraction, which is the divisor. In this case, let's take the content loaded -7/10 divided by 2/5.

The reciprocal of 2/5 is 5/2. So, to divide -7/10 by 2/5, we instead multiply -7/10 by the reciprocal of 2/5.

-7/10 * 5/2 = -35/20.

Finally, we simplify this to its simplest form, by reducing to the lowest terms. We find that, -35/20= -7/4 or -1 3/4 if expressed as a mixed number.

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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:

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

Answer:

30

Step-by-step explanation:

its 64 mannnnnnn :p sdfghjkljhgfdsdfgh

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.

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

(2, 0), (-3, 3), (9, 1), (-3, 5)  NOT

(9, 1), (-3, 4), (2, 1), (9, 2)     NOT

(2, 4), (-3, 2), (9, 1), (-7, 2)     YES

(2, 4), (-3, 6), (2, 3), (-7, 2)     NOT

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

Answer:

5000.

Step-by-step explanation:

1000 milliliter is one liter. So if you have 5 liters 5 x 1000 can fit inside.

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:

X= (300 s + 200 b + 42 d )mg

Step-by-step explanation:

Amount of spinach=300 ml

Amount of berries =200 ml

amount of dressing = 42 ml

Vitamin C in one ml of spinach = s mg

Vitamin C in 300 ml of spinach = 300 s mg

Vitamin C in one ml of berries=b mg

Vitamin C in 200 ml of berries = 200 b mg

Vitamin C in one ml of dressing = d mg

Vitamin C in 42 ml of dressing = 42 d mg

Let total vitamin C be = x

Then

X= (300 s + 200 b + 42 d )mg

is the required expression

Answer:

Step-by-step explanation:

The length can be found by setting up a proportion.  If the width is reduced by some ratio, then the length will share the same ratio.

3 / 8 =  x / 10                    Multiply both sides by 10.

3 * 10 / 8 = x                     Multiply first

30/8 = x                            Divide next. You don't need to do it in this order.

3 6/8                                 Simplify

3 3/4                                 Give another choice

3.75                                

The length = 3.75 inches

If none of these are correct, please leave a note with your choices.

Answer:

The length = 3.75 inches

Step-by-step explanation:

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.

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:

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