The ratio pens to pencils in the pencil case is 2 to 3. If there are 18 pens, how many PENS AND PENCILS are there in the pencil case

Answer:

3m4 + 5m3 - 5m2 + m - 3  

            3          

Step-by-step explanation:

Step-by-step explanation:

step by step

STEP

1

:

Equation at the end of step 1

((((3•(m3))+5m2)-5m)+1)

(———————————————————————•m)-1

3

STEP

2

:

Equation at the end of step

2

:

(((3m3+5m2)-5m)+1)

(——————————————————•m)-1

3

STEP

3

:

3m3 + 5m2 - 5m + 1

Simplify ——————————————————

3

Checking for a perfect cube :

3.1 3m3 + 5m2 - 5m + 1 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 3m3 + 5m2 - 5m + 1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -5m + 1

Group 2: 5m2 + 3m3

Pull out from each group separately :

Group 1: (-5m + 1) • (1) = (5m - 1) • (-1)

Group 2: (3m + 5) • (m2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(m) = 3m3 + 5m2 - 5m + 1

Polynomial Roots Calculator is a set of methods aimed at finding values of m for which F(m)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers m which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 3 and the Trailing Constant is 1.

The factor(s) are:

of the Leading Coefficient : 1,3

of the Trailing Constant : 1

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 8.00

-1 3 -0.33 3.11

1 1 1.00 4.00

1 3 0.33 0.00 3m - 1

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

3m3 + 5m2 - 5m + 1

can be divided with 3m - 1

Polynomial Long Division :

3.4 Polynomial Long Division

Dividing : 3m3 + 5m2 - 5m + 1

("Dividend")

By : 3m - 1 ("Divisor")

dividend 3m3 + 5m2 - 5m + 1

- divisor * m2 3m3 - m2

remainder 6m2 - 5m + 1

- divisor * 2m1 6m2 - 2m

remainder - 3m + 1

- divisor * -m0 - 3m + 1

remainder 0

Answer is 3

Answer:

1. 25 envelopes

2. 82 words per minute

3. 27 Miles per gallon

Step-by-step explanation:

Answer:

a = 132

b = 132

d = 29

e = 29

f = 151

g = 24

h = 24

Answer: -64

Step-by-step explanation:

flip the fraction, and then change the sign so it turns into multiplication.

-8 x 8

multiply them after that.

-64

Answer:

The values of x is -30 degrees and undefined

None of these values fall within the given range

Thus, no value within the given range is the solution to the equation

Step-by-step explanation:

Here, we want to find the value of x that works for the equation in the selected range

2cot^2x = -3csc x

Mathematically, from trigonometry;

cot^2x = csc^2x - 1

Substitute this above

2(csc^2x - 1)= -3csc x

let csc x = b

2(b^2-1) = -3b

2b^2 - 2 + 3b = 0

2b^2 + 3b - 2 = 0

2b^2 + 4b - b - 2 = 0

2b(b+ 2) - 1( b + 2) = 0

(2b-1)(b + 2) = 0

2b = 1

b = -2

b = 1/2 = 0.5

or b = -2

Recall;

csc x = b

x = csc^-1 b

x = csc^-1 0.5

x = undefined

Secondly;

b = -2

x = csc^-1 (-2)

x = -30 degrees

As we can see , between the points

0 ≤ x < 360

None of our answers fall in these range

Answer:

Step-by-step explanation:

The sum of angle in the triangle BCD is 180 degrees

Given;

<B = 4x  -14

<C = x - 1

<D = 6x + 8

Required

Find x

Since <B + <C + <D = 180, hence;

4x - 14 + x - 1 + 6x + 8 = 180

11x -7 = 180

11x = 180+7

11x = 187

x = 187/11

x = 17

Hence the value of x is 17

Answer:

Jack eat 3/8 pounds of the blueberries.

Step-by-step explanation:

Jane had 3/4 of a pound of blueberries.

Jack eat 1/2 of the blueberries.

How many pounds of blueberries did Jack eat?

= 1/2 of 3/4 pounds of blueberries

= 1/2 × 3/4

= (1*3) / (2*4)

= 3/8 pounds

Jack eat 3/8 pounds of the blueberries.

Answer:

Looks like at (3,21) the graph intersects, meaning both values are equal to one another.

Answer:

x= 2.4

Step-by-step explanation:

Answer:

2.4 or 12/5

Step-by-step explanation:

1.2/0.96=3/x

convert the decimal into a fraction---- 6/5 /0.96= 3/x

Simplify the complex fraction-----5/4 = 3/x

simplify the equation using cross-mulitpication----- 5 x = 12

divide both sides of the equation by 5--- x= 12/5

Check if the solution is in the defined range

Alternitive form:

x=2 2/5, x =2.4

Answer: Angle TUV = 57 degrees

Explanation:

The diagram shows Angle TSV = 57 degrees.

Opposite angles of any parallelogram are always congruent, so angle TUV is equal to angle TSV. This makes angle TSV to be 57 degrees. The other values are not needed.

Answer:

Step-by-step explanation:

To get a length of any side 8+10=18

the area= L^2=

                18^2=324m

Answer: 1.18 OR 0.18

Step-by-step explanation:

Answer:

It would depend of what your bill is.

Step-by-step explanation:

Here is how to find the tip of a bill.

Move the decimal, then double the number.

Move the decimal point in your pretax bill one place to the left to get $5.375 from $53.75.

Round up to the next easy number: $5.40.

Double that number to get $10.80, which is 20% of your original bill.

Answer:

The equivalent expressions are;

9x + 9

and

9(x + 1)

Step-by-step explanation:

Mathematically, we should understand that an equilateral triangle has all of its sides equal

So if one side is 3x+ 3, the other sides too measures same

Therefore, the length of the rope represents the perimeter of the triangle

This is obtainable by adding all the side lengths together

This will be;

3x + 3 + 3x + 3 + 3x + 3 = 9x + 9

This is also same as 9(x + 1)

Answer:

sussi baker!!!

Step-by-step explanation:

Median = 5

Mean = 5.4444444444444

Mode: 3

Range = 9

Minimum =   1

Maximum =  10

How to find Median:

Arrange your numbers in numerical order.  Then the second step is to have an odd number, divide by 2 and round up to get the position of the median number.  The last step is to find the even number and if you have it, divide it by 2.

Answer: 5

Hope this helps.

Answer:

x = 67

Step-by-step explanation:

180 - 113 = 67

Answer:

x=67 degrees

Step-by-step explanation:

113+x=180--->linear pair

x=67--->subtractioin property

Answer:

D

Step-by-step explanation:

I had this on my quiz and said it was right. Hope this helps!

Answer:

x = -22

Step-by-step explanation:

x + 9 = -13

  -9     -9

x = -13 - 9

x = -22

Answer:

B

Step-by-step explanation:

The triangle which shows the new location would be Triangle B.

From the coordinates of XYZ transformed to coordinates of triangle X'Y'Z', we can see that the transformation pattern is;

(x, y) -----> (-y, x)

Consider the point be having coordinates (x,y).

Case 1: If the point is in first quadrant:

Subcase: Clockwise rotation, Then (x,y) → (y, -x)

Subcase: Counterclockwise rotation:

Then (x,y) → (-y, x)

Case 2: If the point is in second quadrant:

Subcase: Clockwise rotation, Then (x,y) → (y, -x)

Subcase: Counterclockwise rotation:

Then (x,y) → (-y, x)

On origin, No effect as we assumed rotation is being with respect to origin.

Now, this pattern of transformation occurs when Triangle A is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure.

However, the other rotation that can be used to achieve this is a 270° counterclockwise rotation. so the correct option triangle is B.

Read more about rotation at;

brainly.com/question/4289712

#SPJ6

Answer:

1 gallon = 30 milles

×5

=5 gallon = 150 milles

×10

=10 gallon =300 milles

Step-by-step explanation:

1 gallon = 30 milles

×5

=5 gallon = 150 milles

×10

=10 gallon =300 milles

Answer:

8% compounded monthly has higher yield

Step-by-step explanation:

Here, we want to compare which of the two options would give a higher yield

An interest rate of 8% compounded monthly or 8% compounded annually

Let us say we are looking at a time frame of two years

If compounded monthly, since there are 12 months in a year, there would have been a compounding of 12 * 2 = 24 times

While if it is annual, we would have only twice

The higher the number of times we compound, the more the return

Answer:

Step-by-step explanation:

Let football cost be f and basketball cost be b

We have two equations as per given:

We need to find b, therefore we'll eliminate f

To do so we'll double the first equation and subtract the second one:

Each basketball costs $6.25

Question:

Coach purchased footballs and basketballs from two different stores.

Each football costs the same amount, and each basketball costs the same amount.

At the first store, the coach paid $110 for 5 footballs and 14 basketballs.

At the second store, the coach paid $82.50 for 10 footballs and 6 basketballs.

What was the cost in dollars of Each basketball?

Answer:

Probably 7

REAL Answer:
6.25

Your Welcome! (^·^)

#TeamTrees #TeamSeas #TeamEducation #TeamWorkMakesDreamWork #TeamSpirit #NoSleep #TeamIPhone #TeamBrainly

Given:

The measurement of the angles of a triangle are 3b,2b,and 4b.

To find:

The smallest angle.

Solution:

According to the angle sum property, the sum of all angles of a triangle is 180 degrees.

[tex]3b+2b+4b=180^{\circ}[/tex]           [Angle sum property]

[tex]9b=180^{\circ}[/tex]

Divide both sides by 9.

[tex]b=20^{\circ}[/tex]

Now,

[tex]3b=3(20^{\circ})=60^{\circ}[/tex]

[tex]2b=2(20^{\circ})=40^{\circ}[/tex]

[tex]3b=4(20^{\circ})=80^{\circ}[/tex]

Therefore, the smallest angle is 40 degrees.

Answer:

hope this helps

Step-by-step explanation:

2,995,384 - 89

==2,995,295

Answer:

the answer is 2,995,295

Answer:

0.039

Step-by-step explanation:

Multiply.

1.3 x 0.03 = 0.039

Answer:

Sally is not right

Step-by-step explanation:

Given the two sequences which have their respective [tex]n^{th}[/tex] terms as following:

Sequence A. [tex]3n - 2[/tex]

Sequence B. [tex]10 - 2n[/tex]

As per Sally, there exists only one number which is in both the sequences.

To find:

Whether Sally is correct or not.

Solution:

For Sally to be correct, we need to put the [tex]n^{th}[/tex] terms of the respective sequences as equal and let us verify that.

[tex]3n-2=10-2n\\\Rightarrow 3n+2n=10+2\\\Rightarrow 5n=12\\\Rightarrow n = \dfrac{12}{5}[/tex]

When we talk about [tex]n^{th}[/tex] terms, [tex]n[/tex] here is a whole number not a fractional number.

But as per the statement as stated by Sally [tex]n[/tex] is a fractional number, only then the two sequences can have a number which is in the both sequences.

Therefore, no number can be in both the sequences A and B.

Hence, Sally is not right.