Mr. Jones asks his students to generate the next two numbers in the sequence beginning –5.5, 11, ....

Taquan suggests that the sequence is geometric and the next two numbers are –22 and 44. Julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44.

Which best explains which student is correct?

Taquan is correct. When the signs change in a sequence, the sequence is geometric. Each successive term is generated by multiplying by –22 .
Julia is correct. When the numbers alternate between decimals and whole numbers, the sequence is arithmetic. Each successive term is generated by adding 16.5.
Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways.
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

Answer:

4 19/32

Step-by-step explanation:

convert into improper fractions

6 1/8= 49/8

1 x 3/4= 3/4

49/8 x 3/4 = 147/32

reduce into mixed number

4 19/32

To convert the mixed numbers 6 1/8 and 1 3/4 to improper fractions, resulting in 49/8 and 7/4, respectively. Then, perform the division as multiplication with the reciprocal of the second fraction, which yields 3 1/2.

Firstly, it's essential to convert the mixed numbers into improper fractions. The given mixed numbers are 6 1/8 and 1 3/4. We can convert 6 1/8 to an improper fraction by multiplying 6 (the whole number) by 8 (the denominator) and then adding 1 (the numerator) to get 49/8. With 1 3/4, we multiply 1 (the whole number) by 4 (the denominator), then add 3 (the numerator), which gives us 7/4.

Now, the division 49/8 ÷ 7/4 can be performed. To divide fractions, we multiply the first fraction by the reciprocal of the second. Therefore, we will multiply 49/8 by 4/7. The result is 196/56. This simplifies to 3 1/2 when converted back to a mixed number.

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Answer:

Option A   ∠RWQ, ∠WPS and ∠PWU

Step-by-step explanation:

we know that

Two angles are supplementary if their sum is equal to 180 degrees

Part 1)

∠OPW+∠WPS=180° ------> by supplementary angles

we have

∠OPW=110°

substitute

110°+∠WPS=180°

∠WPS=180°-110°=70°

Part 2) we know that

∠RWQ+(50°+60°)=180° ------> form a linear pair

∠RWQ=180°-(50°+60°)=70°

so

∠OPW+∠RWQ=180° -----> by supplementary angles

Part 3) we know that

∠PWU=∠RWQ -------> by vertical angles

so

∠OPW+∠PWU=180° -----> by supplementary angles

therefore

The angles that are supplements to angle ∠OPW are

∠WPS, ∠RWQ and ∠PWU

Answer:

25.9

Step-by-step explanation:

12+7x−(1−3) (evaluate parentheses first)

= 12+ 7x - (-2)

= 12+ 7x + 2

= 14+ 7x

When x = 1.7, equation becomes

14+ 7(1.7)

= 14 + 11.9

= 25.9

Answer:

y = x² ⇒ answer C

Step-by-step explanation:

* Lets explain the problem

∵ The function is y = 1/2 x² + 3 , that means the parent function is

  transformed by some transformation

- If the parent function is y = x²

- y = x² is a quadratic function represented graphically by upward

 parabola with vertex (0 , 0)

∵ y = x² changed to y = 1/2 x² that means we multiply each

  y-coordinates of the points on the graph of the function by 1/2

∴ The graph of the function is  compressed vertically by scale

   factor 1/2

- That means the graph is squeezing toward the x-axis

∵ y = 1/2 x² changed to y = 1/2 x² + 3 that means we add each

  y-coordinates of the points on the graph of the function by 3

∴ The function translated 3 units up

- That means the vertex of the parabola changed to (0 , 3)

∴ The new function is y = 1/2 x² + 3

* The parent function of y = 1/2 x² + 3 is y = x²

# Look to the attached graph for more understand

- y = x² ⇒ the red graph (parent function)

- y = 1/2 x² + 3 ⇒ the blue graph

Answer: 3 losses

Step-by-step explanation: The win to loss ratio is 4:1. Their losses are 1/4 of their wins. Multiply 12, their number of wins, by 1/4.

12 x 1/4 = 3

They have lost 3 games.

Given the ratio of 4:3:1 for wins, ties, and losses, and the information that the team has won 12 games, you calculate that '1 part' of the ratio equals 3 games by dividing 12 by 4. As losses are represented by '1 part' in the ratio, the team has lost 3 games.

In this baseball team scenario, the ratio of wins to ties to losses is 4:3:1 respectively. You know that the team has won 12 games. In a ratio, every part represents something equivalent, so we need to find what '1 part' is. Since '4 parts' represents 12 wins, you divide 12 by 4 to get '1 part', which is 3 games. Therefore, since losses represent '1 part' of your ratio, the team has lost 3 games.

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Answer:

[tex]f(x) = 7x + 30[/tex]

Step-by-step explanation:

We need at least two points to write the equation of a straight line.

The recursive formula that Elijah wrote is:

[tex]f(0) = 30[/tex]

[tex]f(n + 1) = f(n) + 7[/tex]

When we substitute n=0, we get:

[tex]f(0 + 1) = f(0) + 7[/tex]

[tex]f(1) = 30 + 7[/tex]

[tex]f(1) = 37[/tex]

The points (0,30) and (1,37) lies on this line.

The equation of this line is of the form:

[tex]f(x) = mx + b[/tex]

where b =30 is the y-intercept and m=7 is the slope.

We plug in these values to get:

[tex]f(x) = 7x + 30[/tex]

Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.

You could also use the two points to find the slope:

[tex]m = \frac{37 - 30}{1 - 0} = 7[/tex]

Answer:

2x^3 - 6x^2 - 4x + 12.

Step-by-step explanation:

(p*q) (x)  = (2x^2 - 4)(x - 3)

= 2x^3 - 6x^2 - 4x + 12.

For this case we have the following functions:

[tex]p (x) = 2x ^ 2-4\\q (x) = x-3[/tex]

We must find [tex](p * q) (x).[/tex] For definition, we have to:

[tex](p * q) (x) = p (x) * q (x)[/tex]

So:

[tex](p * q) (x) = (2x ^ 2-4) (x-3)[/tex]

We apply distributive property:

[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]

Answer:

[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]

Answer:

18

Step-by-step explanation:

We can use a proportion to find out the number of teachers that are needed.

3/70 = x/14,700

70x = 3 * 14,700

70x = 44,100

x = 630

630 teachers are needed altogether. Since there are already 612 teachers, the number of more teachers who are needed is the difference between 630 and 612.

630 - 612 = 18

Answer: 18

Answer:

A.

5 ^ (5/6)

Step-by-step explanation:

5 ^ (1/2)  * 5 ^ (1/3)

We know that a^b * a^ c = a ^ (b+c)

5 ^ (1/2 + 1/3)

5^ (3/6+2/6)

5^ (5/6)

Answer:

5^(5/6)

Step-by-step explanation:

5^(1/2)*5^(1/3)=5^(1/2+1/3)=5^(5/6)

When multiplying numbers with same base you add the exponents.

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{-6},\stackrel{y}{5})~~ \begin{cases} x=-6\\ y=5 \end{cases}\implies 5=k(-6)\implies \cfrac{5}{-6}=k~\hfill \boxed{y=-\cfrac{5}{6}x}[/tex]

Answer:

B. -2√2 - 5

C. 2√2 - 5

Step-by-step explanation:

The left side of the equation is already a perfect square.

Let us factorize it first.

x²+10x+25=8

x(x+5)+x(x+5)=8

(x+5)²=8

Let us take the square roots of both sides.

x+5=±√8

But √8=±2√2

Therefore in surd form, the two solutions become:

x+5=2√2 or x+5=-2√2

Therefore x= 2√2-5 and -2√2+-5

Answer:

They must mix

_44_ pounds of the Organic Free Trade Blend

_36__ pounds of the Rift Valley Blend.

Round your answers to the nearest whole number of pounds.

Step-by-step explanation:

The formula you are using is:

Total price * total amount= Organic price * amount organic + Rift price * amount rift

First we will simplify it by calculating it for each pound of final mix.

So this is 10.82 * 1 = 8.30 * x + 13.90 * y.

Since the total amount should be 1 pound, you could say that x+y = 1, or that y = 1-x.

If you fill this in you get

10.82 * 1 = 8.30 * x + 13.90 * (1-x)

Which you can solve as follows.

10.82 * 1 = 8.30 * x + 13.90 - 13.90x

10.82 = 13.90 - 5.6x

-5.6x = -3.08

x = -3.08/-5.6 = 0.55

So you will need 0.55 of Organic coffee for each pound of the final mix.

So in total you will need 0.55 * 80 = 44 pounds of Organic coffee.

So you need 80 - 44 = 36 pounds of Rift Valley Coffee.

To produce the desired coffee blend, the coffee distributor needs to mix approximately 51 pounds of Organic Free Trade Blend with 29 pounds of Rift Valley Blend.

This problem falls under a category of Mathematics known as Algebra. We'll start by defining two variables: x, representing the weight of the Organic Free Trade Blend, and y, representing the weight of the Rift Valley Blend.

From the total weight of the mix, we get our first equation: x + y = 80

Then, by weighing the cost of each part against the total, we get our second equation: 8.3x + 13.9y = 10.82 * 80.

Solving these two equations simultaneously, we find that approximately 51 pounds of Organic Free Trade and 29 pounds of Rift Valley blend are needed to create the desired mixture.

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Given that area of circle is 64cm we can assume we will need to first find radius and then calculate circumference.

First we know that area of a circle is [tex]A=\pi r^2[/tex] hence [tex]r=\sqrt{\dfrac{A}{\pi}}[/tex]

We can now put in our area,

[tex]r=\sqrt{\dfrac{64}{\pi}}\approx20.37[/tex]

Then we use the formula for circumference,

[tex]C=2\pi r\Longrightarrow C=2\pi\cdot20.37\approx\boxed{128\mathbf{cm}}[/tex]

Hope this helps.

r3t40

Answer:

(6,∞)

x > 6

Step-by-step explanation:

Solve by adding 4 to both sides.

[tex]x-4>2\\x>6[/tex]

To put this in interval notation for your solution set, consider your sign.

You have a greater than sign, which means that 6 is not a solution. In interval notation, that means that you should use parentheses " ( " instead of brackets " [ ".

Your solution set goes on infinitely, and infinity also uses parentheses rather than brackets.

You can write your solution set in interval notation as follows:

(6, ∞)

Rewrite the equation in slope-intercept form:

y+5=2(x+1)

Use the distributive property:

y+5 = 2x +2

Subtract 5 from each side:

y = 2x -3

The slope is the value with the X

The slope = 2

Answer:

2.5

Step-by-step explanation:

2(x+1)=y+5

2x+1=y+5

y+5=6

in addtion y can be add

so we have now...

2x+1=6

minus 1 from 6 and get 5

2x=5

5 divide by 2 = 2/5

Hope it helps

[tex]\bf \underset{\textit{\Large 18 + 8 = 26 units}}{\stackrel{\textit{18 units}}{\boxed{-18}\rule[0.35em]{10em}{0.25pt}}0\stackrel{\textit{8 units}}{\rule[0.35em]{5em}{0.25pt}\boxed{8}}}[/tex]

Answer:

Step-by-step explanation:

The ruler Postulate:

the distance between number A and number B

AB = |B - A|

We have A = -18 and B = 8. Substitute:

|8 - (-18)| = |8 + 18| = |26| = 26

Answer:

About 405

Step-by-step explanation:

570 CDs were sold the first quarter.

The second quarter CDs had dropped 29% from the first quarter (570).

Dropped, you should think you are subtracting.

So we need to

simplify 570-.29(570):

570(1-.29)

570(.71)

404.7

404.7 --> 405 (when rounded)

In order to find the answer to your question, we would need to find how much of 570 is 29%, and subtract that number to 570.

The reason why we would do this is because in the question, it says that the sales dropped 29% for one quarter to the next. This means that the next quarter would drop 29%.

We know that they sold 570 units, so we would use 570 in our calculations.

We know that the sales decrease by 29%, so we would multiply 570 by 0.29 to find how much of 570 is 29%.

[tex]570*0.29=165.3[/tex]

29% of 570 is 165.3

What we would do now is subtract 570 by 165.3 in order to fin how much sales they made in the next quarter.

[tex]570-165.3=404.7[/tex]

Once you're done solving, you would get the answer of 404.7

This means that they sold 404.7 (405 when rounded) CDs in the next quarter.

Answer:

sin²x

Step-by-step explanation:

we have

(1 − cos x)(1 + cos x)=1-cos²x

Remember that

sin²x+cos²x=1 ------> i-cos²x=sin²x

therefore

(1 − cos x)(1 + cos x)=sin²x

Answer:

[tex]sin^2x[/tex]

Step-by-step explanation:

Given expression,

[tex](1 - cos x)(1 + cos x)[/tex]

By using [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex](1 - cos x)(1 + cos x)=1^2 - cos^2x = 1 - cos^2x[/tex]

[tex]\because sin^2x+cos^2x=1[/tex]

[tex]\implies (1 - cos x)(1 + cos x)=sin^2x+cos^2x - cos^2x=sin^2x[/tex]

Since, further simplification is not possible,

Hence, the simplified form of the given expression is [tex]sin^2x[/tex]

A (x=y)

By vertical angles, the angle opposite y is equal to y, and x = y because it would transform isometrically onto x (as can be seen by the parallel lines because the transversal can be treated as parallel to itself)

Answer:

Step-by-step explanation:

Add all 8/20 marbles multiply Times 5 40/100 = 40%

Answer =40%

Answer:

[tex]\large\boxed{-mn+10m+5n}[/tex]

Step-by-step explanation:

[tex](14mn - 12m +7n)-(15mn - 22m +2n)\\\\=14mn-12m+7n-15mn-(-22m)-2n\\\\=14mn-12m+7n-15mn+22m-2n\qquad\text{combine like terms}\\\\=(14mn-15mn)+(-12m+22m)+(7n-2n)\\\\=-mn+10m+5n[/tex]

Answer:

it is not possible that Brayden made it back to his starting point.

Step-by-step explanation:

Part 1: Step 1: Define the map scale

REAL:MAP

1 km : 1 cm

5 km : 5 cm

14 km : 14 cm

8 km : 8 cm

Step 2: Sketch the map according to the scale.

Shown on the map in the picture attached.

Part 2: As shown on the map, it is not possible that Brayden made it back to his starting point.

!!

Answer:

5 12/24 -> -0.5 -> -5 6/20

Step-by-step explanation:

Negatives are lasts and positive goes first! Since the order is greatest to least.

-5 6/20 is less than -0.5 because *think of a number line -5 6/20 will be all the way to the left because it large in negative value

Answer:

Option A. The measure of angle C is 140°

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The triangle OAB is an isosceles triangle

Because

OA=OB=radius

m∠BAO=m∠ABO=20°

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

m∠BAO+m∠ABO+m∠C=180°

substitute the given values

20°+20°+m∠C=180°

m∠C=180°-40°=140°

Answer:

The quotient is x³+x²+x+1

Step-by-step explanation:

=(x^4-1) ÷ (x-1)

=(x^4-1)/ (x-1)

Solve the numerator by using perfect square formula:

⇒x^4-1 = (x²-1)(x²+1)

=(x²-1)(x²+1)/(x-1)

Further solve the numerator by using perfect square formula:

=(x+1)(x-1)(x²+1)/(x-1)

Cancel the like terms of numerator and denominator

We get;

=(x+1)(x²+1)

Multiply the terms:

=x³+x+x²+1

Re-arrange the terms:

=x³+x²+x+1

Hence the quotient is x³+x²+x+1....

Answer:

C

Step-by-step explanation:

Answer: Not sure if I’m correct but I’m pretty sure

x = 90

Step-by-step explanation:

Total figure = 360 degrees

107+72+91=270

360-270=90

Answer:

x=90 degrees

Step-by-step explanation:

The sum of the 4 angles of a quadrilateral add to 360 degrees

Add the 4 angles

72+107+x+91 = 360

Combining like terms

270 +x = 360

Subtract 270 from each side

270+x-270 = 360-270

x = 90

The unknown angle is 90

Answer:

D) 160π/3 units²

Step-by-step explanation:

Step 1: Write the formula for area of sector

Area of sector = 1/2 x r² x angle in radians

Step 2: Substitute values in the formula

Area of sector = 1/2 x 8² x 5π/3

Step 3: Solve to find the value of area of sector

Area of sector = 160π/3 units²

Therefore, the correct option is D

!!

Answer:

m = 200

Step-by-step explanation:

30 m = 6000 Divide both sides by 30

30 m / 30 = 6000 / 30

m = 200