Analyze the following pattern
1, 2, 5, 10, 17,....

what's the 8th term of the pattern ​

Chevy has some yarn that he wants to use to make hats and scarves. Each hat uses 0.2 kilograms of yarn and  each scarf uses 0.1 kilograms of yarn. Chevy wants to use 2 kilograms of yarn to make a total of 15 items.

Let h be the number of hats Chevy makes and s be the number of scarves he makes.

Which system of equations represents this situation?​

The system of equations represents this situation are:

h + s = 15

0.2h + 0.1s = 2

5 hats and 10 scarves are made

From given,

Let "h" be the number of hats Chevy made

Let "s" be the number of scarves made

They made a total of 15 items

Therefore, we get,

h + s = 15 --------- eqn 1

Also given that,

Each hat uses 0.2 kilograms of yarn

Each scarf uses 0.1 kilograms of yarn

Chevy wants to use 2 kilograms of yarn

Therefore, we frame a equation as:

[tex]0.2 \times h + 0.1 \times s = 2[/tex]

0.2h + 0.1s = 2 --------- eqn 2

Thus eqn 1 and eqn 2 represents the system of equations

Let us solve eqn 1 and eqn 2

From eqn 1,

h = 15 - s ------ eqn 3

Substitute eqn 3 in eqn 2

0.2(15 - s) + 0.1s = 2

3 - 0.2s + 0.1s = 2

0.1s = 1

s = 10

Substitute s = 10 in eqn 3

h = 15 - 10

h = 5

Thus 5 hats and 10 scarves are made

Answer:

1/2 and 2/4

Step-by-step explanation:

To make an equivalent fraction, you have to multiply or divide the numerator (top number) and denominator (bottom number) by the same number. For 6/12, we can divide the numerator and denominator by 6, which gives us 1/2. We can also divide the numerator and denominator by 3, and we get 2/4. 1/2 and 3/4 are 2 equivalent fractions, but there are tons more of equilalent fractions to 6/12.  

Final answer:

To find equivalent fractions for 6/12, divide both the numerator and the denominator by 2 to get 3/6, and by 3 to get 2/4. These operations demonstrate creating equivalent fractions through division.

Explanation:

The question asks us to use division to write 2 equivalent fractions to 6/12. Equivalent fractions are fractions that represent the same value. To find equivalent fractions, we can divide both the numerator and the denominator by the same number, provided that number does not equal zero.

Let's divide the numerator and denominator by 2:

Therefore, one equivalent fraction of 6/12 is 3/6.

Now, let's divide the numerator and the denominator by 3:

Thus, another equivalent fraction of 6/12 is 2/4.

Both fractions represent the same value as the original fraction 6/12, showcasing the concept of equivalent fractions through division.

Answer: i dont see expressions but it would be 5

Step-by-step explanation:

Answer:

|-4-1|

Step-by-step explanation:

i got it right

Answer:

Option D) (k − 12)/m                          

Step-by-step explanation:

We have to write an expression:

the quotient of the quantity k minus 12 and m.

k minus 12 can be written as:

[tex]k - 12[/tex]

The quotient of (k-12) and m means (k-12) is divided by m.

This can be written as:

[tex]\dfrac{k-12}{m}[/tex]

Thus, the correct answer is

Option D) (k − 12)/m                                                                      

Final answer:

The expression for the quotient of 'k minus 12' and 'm' is correctly written as (k - 12) ÷ m, making option D the accurate choice.

Explanation:

The expression for the quotient of the quantity k minus 12 and m should be written as a fraction where the numerator is k minus 12 and the denominator is m. This is mathematically represented by the fraction (k - 12) ÷ m, which indicates the division of the expression k minus 12 by m. Therefore, the correct expression from the given options is D) k - 12 ÷ m.

Answer:

16 feet.

Step-by-step explanation:

Given:

Ben’s living room is a rectangle measuring 10 yards x 168.

Question asked:

How many feet does the legs of the room exceed the width ?

Solution:

By applying unitary method:

Length of rectangle = 10 yards = 30 feet (1 yard = 3 feet)

                                                                    (10 yard = [tex]3\times10 = 30)[/tex]

Breadth of  rectangle = 168 inch = 14 feet   (12 inch = 1 feet)

                                                                       (1 inch = [tex]\frac{1}{12}[/tex])

                                                                       ( 168 inch = [tex]\frac{1}{12}[/tex][tex]\times168 = 14 feet)[/tex]

By subtracting the breadth from the length of rectangle,

30 feet - 14 feet = 16 feet

Therefore,  by 16 feet, length of the room exceed the width.

Answer:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

Step-by-step explanation:

Errors in Algebraic Operations

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

The first expression is

[tex]1-x / (5-x)(-x)=x-1 / x(x-5)[/tex]

Let's arrange into format:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}[/tex]

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

Now for the second expression

[tex]5/s+2/5=2/s[/tex]

Let's arrange into format

[tex]\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}[/tex]

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

The sentence 'The product of b and 6 is less than -16' translates to the inequality '6b < -16' in Mathematics.

In mathematics, translating a sentence into an inequality involves identifying the mathematical symbols and operations represented by the words in the sentence. In this case, 'the product of b and 6' translates to '6 * b' and 'is less than' translates to '<'. So, the sentence 'The product of b and 6 is less than -16' translates to the inequality '6 * b < -16' or '6b < -16' in simplified form.

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Answer:

-2x + 4

Step-by-step explanation:

First off, rename your equation as -6x=5x+22

You solve the equation by subtracting 5x on both sides to get:

-11x=22

Now divide both sides by -11 to get x=-2

So the answer is C: -2

Hope this helped! This is my first time answering!

Answer:

It is -2 (B)

Because you add  -5x to both sides and you get -11x=22 and 22 divided by -11 is -2

Answer:

1/6

Step-by-step explanation:

1/3 divided by 2 people= 1/6 each

Answer:

Step-by-step explanation:

1/3

Answer:

Therefore,

[tex]x=\dfrac{1}{2}[/tex]

Step-by-step explanation:

Given:

[tex]4x-2=0[/tex]

To Find:

x = ?

Solution:

[tex]4x-2=0[/tex]

Step 1 : Add 2 on both the side we get

[tex]4x-2+2=0+2\\4x=2[/tex]

Step 2 : Dividing  by 4 on both the side we get

[tex]\dfrac{4x}{4}=\dfrac{2}{4}\\\\x=\dfrac{1}{2}[/tex]

Step 3 :The final  solution is

[tex]x=\dfrac{1}{2}[/tex]

Therefore,

[tex]x=\dfrac{1}{2}[/tex]

Step-by-step explanation:

The given absolute value expression is

[tex]f(x) = |x + 3| - 1[/tex]

This absolute value function is of the form

[tex]f(x) = |x + h| + k[/tex]

where (h,k)=(-3,-1) is the vertex.

This function opens upwards, hence the the minimum point is (-3,-1)

The domain is the values of x for which the function is defined.

The domain is all real numbers.

The range is the values of y for which x is defined.

The is y≥-1 because the minimum value is -1.

The graph is shown in attachment.

The constant of proportionality for the given ratios is 1.5.

The constant of proportionality for the given ratios can be found by dividing the second value of each ratio by the first value. Let's take the first ratio (2,3) as an example:

Constant of proportionality = 3 / 2 = 1.5

Following the same steps for the other ratios, we can find the constant of proportionality for each of them. For the second ratio (4,6), the constant of proportionality is 6 / 4 = 1.5. For the third ratio (6,9), the constant of proportionality is 9 / 6 = 1.5. And for the fourth ratio (8,12), the constant of proportionality is 12 / 8 = 1.5.

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Final answer:

The constant of proportionality for the given ratios is 1.5, as each second number in the ratio is 1.5 times the corresponding first number.

Explanation:

To find the constant of proportionality for the given set of ratios, we first look at each pair to determine if there is a common constant that each first number is multiplied by to result in the second number. Inspecting the given ratios (2, 3), (4, 6), (6, 9), and (8, 12), we can see that in each case, the second number is 1.5 times the first number.

For example, for the ratio (2, 3), if you multiply 2 by 1.5, you get 3. Similarly, for the ratio (4, 6), multiplying 4 by 1.5 gives you 6, and so on. This consistency across the ratios confirms that the constant of proportionality is 1.5.

Answer:

110°

Step-by-step explanation:

the supplement of an angle is 30 degrees less than twice the measure of the angle itself. find the angle and its supplement.

Let the angle be A, then its supplement = (180 - A)

Now, since the supplement is 30 degrees less than twice the measure of the angle itself, then we'll have:

180 - A = 2A - 30

-3A = - 210

A, or the angle = [tex]\frac{-210}{-3}[/tex]= 70 °

Its supplement, (180 - A) = 180 - 70 = 110°

Answer:

0.004 or 1/250

Step-by-step explanation:

the word "of" means multiply. so just multiply 1/0 by 0.04. :)

Answer:

0.004

Step-by-step explanation:

you move the decimal a place to the left

Option C:

Surface area of the three dimensional figure is 166 unit².

Solution:

Let us find the area of the net of the figure.

Length = 7, Width = 5, Height = 4

Area of the bottom = length × width

                                = 7 × 5

                                = 35 unit²

Area of the Top =  length × width

                          = 7 × 5

                          = 35 unit²

Area of the left = width × height

                         = 5 × 4

                         = 20 unit²

Area of the right = width × height

                         = 5 × 4

                         = 20 unit²

Area of the front = length × height

                            = 7 × 4

                            = 28 unit²

Area of the back = length × height

                            = 7 × 4

                            = 28 unit²

Surface area = 35 + 35 + 20 + 20 + 28 + 28

                     = 166 unit²

Surface area of the three dimensional figure is 166 unit².

Make two equations:

Carlos: y=10x+85

Michael: y=5x+120

Set them equal to each other and solve:

10x+85=5x+120

5x+85=120

5x=35

x=7

So therefore, B is the correct answer

Hope this helped!

Final answer:

To determine when Carlos and Michael will have the same number of baseball cards, set up an equation based on their weekly acquisitions. After solving the equation, it is revealed that they will have the same amount in 7 weeks.

Explanation:

The subjects of interest are Carlos and Michael's baseball card collections.

Carlos starts with 85 cards and adds 10 each week, while Michael starts with 120 and receives 5 more weekly.

To find when they will have the same amount, set up an equation:

Carlos's cards: 85 + 10x (x representing the number of weeks)Michael's cards: 120 + 5xSolve the equation: 85 + 10x = 120 + 5xTherefore, x = 7 weeks, so the answer is B: in 7 weeks.

To combine like terms, group terms with the same variable and combine their coefficients. The simplified expression is -3y + 7x^2 + 9.

To combine like terms, we group terms with the same variable and combine their coefficients. In this case, we have:

2y - y + 7 - 1 + 3 + 7x2 - 4y

Combining the like terms:

2y - 4y - y + 7 - 1 + 3 + 7x2

Combining the coefficients:

(2 - 4 - 1)y + (7 - 1 + 3) + 7x2

-3y + 9 + 7x2

So, the simplified expression is -3y + 7x2 + 9.

Learn more about Combining like terms here:

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Answer:

ab + ac

Step-by-step explanation:

a (b+c)

a is multiplying everything in the bracket

axb + axc

ab + ac

Answer:

ab + ac

Step-by-step explanation:

a (b + c) *multiply

a x b + a x c

ab + ac

Answer:

105

Step-by-step explanation:

The number that is 25% more than 84 is 105.

To find 25% more than a given number, one can calculate 25% of that number and then add it to the original number. Here's the step-by-step calculation:

1. First, calculate 25% of 84:

[tex]\[ 25\% \text{ of } 84 = \frac{25}{100} \times 84 = \frac{1}{4} \times 84 = 21 \][/tex]

2. Then, add this value to the original number to find the increased amount:

[tex]\[ 84 + 21 = 105 \][/tex]

Therefore, 25% more than 84 is 105.

Answer:

93

Step-by-step explanation:

9      8 3 7

− 0    

 8 3  

− 8 1  

   2 7

 − 2 7

     0

f(x) * g(x) = 4 (x² + 5x + 6)

Step-by-step explanation:

f(x) * g(x) = (4x + 8) (x + 3)

              = 4x² + 12x + 8x + 24

              = 4x² + 20x + 24

              = 4 (x² + 5x + 6)

Probably too late, but still need to know how to do this.

Formula for the area of a circle: A = πr²     [pi times radius(r) squared]

The radius is half of the diameter. [diameter would be a line that would go through the whole circle, the radius would be a line that would stop/end halfway through the circle - see attached image]

They gave you the diameter, which is 3, so divide it by 2 or multiply by 1/2 to get the radius, which will be 1.5.

A = πr²    Plug in 1.5 for r

A = π(1.5)²         Find 1.5²  [or 1.5 x 1.5 = 2.25]

A = 2.25π meters²

First off, use carats so its more clear that there's exponents (I'm using parentheses for simplicity):

(4*a^3*b^5)-(16*a^5*b^2)+(12*a^2*b^3)

It's best to divide the whole expression by 4a^2b^2 because it's the least common factor.

So we get (a*b^3)-(4*a^3)+(3b)

I hope this helped. It's been a while since I've done problems like these!

Answer:

105 is the least common denominator

Step-by-step explanation:

Since 7, 5 and 3 are all prime.

LCM would be 7×3×5 = 105

Answer:

I think its 226800.

Step-by-step explanation:

8% of 210,000 is 16800. I added that to 210,000 and got my answer.

Answer: 3.12:16

Step-by-step explanation:

Answer:

2, 3 and 4

Step-by-step explanation:

6:8

3:4

1. 36/40 = 9/10

2. 9:12 = 3:4

3. 12 to 16 = 3/4 = 3:4

4. 15/20 = 3/4 = 3:4

5. 24:36 = 2/3

6. 16 to 24 = 2/3

t = 1.33 sec

Solution:

Given data:

Velocity [tex](v_0)[/tex] = 17.5 ft/s

Height [tex](h_0)[/tex] = 5 ft

The height can be modeled by a quadratic equation

[tex]h(t)=-16t^2+v_0t+h_0[/tex]

where h is the height and t is the time

[tex]h(t)=-16t^2+17.5t+5[/tex]

[tex]-16t^2+17.5t+5=0[/tex]

a = –16, b = 17.5, c = 5

It looks like a quadratic equation. we can solve it by quadratic formula,

[tex]$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

[tex]$\Rightarrow t=\frac{-17.5 \pm \sqrt{(-17.5)^{2}-4\times (-16)(5)}}{2 (-16)}[/tex]

[tex]$\Rightarrow t= \frac{-17.5 \pm \sqrt{306.25+ 320}}{-32}[/tex]

[tex]$\Rightarrow t= \frac{-17.5 \pm 25.025}{-32}[/tex]

[tex]$\Rightarrow t= \frac{-17.5 - 25.025}{-32}, \ t= \frac{-17.5 + 25.025}{-32}[/tex]

[tex]$\Rightarrow t= 1.33, \ t= -0.24[/tex]

Time cannot be in negative. So neglect t = –0.235.

t = 1.33 sec

Hence Amy have to react  1.33 sec before the volleyball hits the ground.

Answer:

In order to be a quadrilateral, a polygon must have 4 sides, and parallelograms always have 4 sides. In order to be a parallelogram, a polygon must have 4 sides with opposite sides parallel. Quadrilaterals always have 4 sides, but do not always have opposite sides parallel.

Step-by-step explanation:

In order to be a quadrilateral, a polygon must have 4 sides, and parallelograms always have 4 sides. In order to be a parallelogram, a polygon must have 4 sides with opposite sides parallel. Quadrilaterals always have 4 sides, but do not always have opposite sides parallel.

Answer:

80

Step-by-step explanation:

8(3+7)

8*3=24

8*7=56

24+56=80

Answer: 80

Step-by-step explanation: To solve this problem, we first substitute 7 in for x inside the parentheses and we have 8 (3 + 7).

Following your order of operations, you should simplify what's inside the parentheses first. So 3 + 7 simplifies to 10.

Bring down your 8 and you have 8 (10) which equals 80.