expand and simplify (2x+5)(3x+1`)

Answers

Answer 1

Answer:

6x^2 + 17x + 5

Step-by-step explanation:

(2x + 5)(3x + 1)

= 6x^2 + 2x + 15x + 5

= 6x^2 + 17x + 5

Answer 2

The expression (2x+5)(3x+1) is a product of two binomials. To expand this product, we multiply each term in the first binomial by each term in the second binomial, using the distributive property of multiplication.

When we multiply 2x by 3x, we get 6x^2.

Then we multiply 2x by 1, which gives us 2x.

Next, we multiply 5 by 3x, which gives us 15x.

Finally, we multiply 5 by 1, which gives us 5.

Putting these terms together gives us the expanded form of the expression:

(2x+5)(3x+1) = 6x^2 + 2x + 15x + 5

Simplifying, we can add the 2x and 15x terms to get 17x, giving us the final simplified expression:

(2x+5)(3x+1) = 6x^2 + 17x + 5.


Related Questions

Simplify 8 − (14). plsss help

Answers

Answer:

(-6)

Step-by-step explanation:

Integer subtraction:

If two numbers have different sign, subtract and the result will have the sign of the bigger number.

 8 - 14 = (-6)

Subtract 8 from 14 and the bigger number is 14 and sign of 14 is (-).

So, the answer is  (-6)

(11-8)x3+7+27-3
(18÷3)+6+(14-8)x5
(11-7)x6+4+32-4

Answers

The results of the arithmetic evaluations as given in the task content are; 40,42 and 62.

What are the results of the arithmetic evaluations?

The arithmetic operations above can be evaluated and simplified as follows;

(11-8)x3+7+27-3 = (3×3)+7+27-3 = 40.

(18÷3)+6+(14-8)x5 = (6)+6+(6)x5 = 42.

(11-7)x6+4+32-4 = (5×6) +4 +32-4 = 62.

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Ariana scored 89% out of 600 in Exam what could be the marks she had scored? ​

Answers

Answer:

534

Step-by-step explanation:

The solution is in the image

please answer me I will f0ll0w u​

Answers

Step-by-step explanation:

1. let n=2, then, n+2= 2+2=4 so 2^2= 4 and 4^2=16 then 16-4=12 which is an even number

2. let n=4, the. n+3=4+3=7, and 4^2=16 and 7^2=49 then 49-16 =33 which is an odd number

please follow me

Detailed Solution:

1) Let ‘n’ be 5
Therefore, (n + 2) = 5 + 2 = 7

=> 5^2 = 25
=> 7^2 = 49


Difference of Squares
= 49 - 25
=> 24

24 is an Even Number.
Hence, proved.

1) Let ‘n’ be 5
Therefore, (n + 3) = 5 + 3 = 8

=> 5^2 = 25
=> 8^2 = 64


Difference of Squares
= 64 - 25
=> 39

39 is an Odd Number.
Hence, proved.

The side of an equilateral triangle is given as 8 cm, correct to the nearest centimetre. What is the least possible length of its perimeter?​

Answers

[tex]\textsf {21 cm}[/tex]

[tex]\textsf {If it is correct to the nearest centimeter, then the least side length}\\\textsf {would be 8 - 1 = 7 cm. }[/tex]

[tex]\textsf {Then, the least possible perimeter would be :}[/tex]

[tex]\mathsf {7 \times 3}[/tex]

[tex]\textsf {21 cm}[/tex]

write an equation for the line that passes through the given point and has the given slope m (4,-5);m= -1/4

Answers

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{y = -1/4x - 4}[/tex]

-------------------------------------------------------------------------------------------------------------

Given: [tex]\textsf{Slope = -1/4, Point through = (4, -5)}[/tex]

Find:  [tex]\textsf{Equation for the line that passes through the given point}[/tex]

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

Plug in the values

[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-5) = -1/4(x - 4)}[/tex]

Simplify and solve for y

[tex]\textsf{y + 5 = -1/4(x - 4)}[/tex][tex]\textsf{y + 5 = -1/4x + 1}[/tex][tex]\textsf{y + 5 - 5 = -1/4x + 1 - 5}[/tex][tex]\textsf{y = -1/4x - 4}[/tex]

Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

Suppose that F(x) = x² and G(x) = 3x^2 + 8. Which statement best compares the graph of G(x) with the graph of F(x)?

A. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units to the left.

B. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units to the left.

C. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units up.

D. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units up.

Answers

Answer:

The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.

Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
-3x+3y=9
2x-7y=-14
Alse please don't take long
Choices are attached

Answers

Answer:

[tex]\sf C) \ x = -1\dfrac{2}{5} , \ y = \ 1\dfrac{3}{5}[/tex]

Given equations:

a) -3x + 3y = 9b) 2x - 7y = -14

Make x the subject in equation 1:

-3x + 3y = 9-3x = 9 - 3yx = y - 3

Substitute this into equation 2:

2(y - 3) - 7y = -14

2y - 7y = -14 + 6

-5y = -8

  y = -8/-5

  y = 1.6

Then x = y - 3

           = 1.6 - 3

           = -1.4

Solution: (x, y)(-1.4, 1.6)

Given that x is an even number, express, in terms of x, the product of the next two odd numbers.

Answers

Answer:

Odd is the answer.

Step-by-step explanation:

An even number can be written in the form 2x, where x is an integer.

An odd number can be written in the form 2x + 1, where x is an integer.

So two odd numbers can be represented by 2a +1 and 2b +1, the product would be:

(2a + 1)(2b +1) = 4ab + 2a + 2b + 1 = which can be written as 2(2ab + a +b) + 1, but 2ab +a + b represents some integer, so 2ab + a + b = x.

So (2a + 1)(2b + 1) = 2(2ab + a + b ) + 1 = 2x +1 which is odd.

A bookshelf has 96 books. 64 of the books are fiction and the rest are non-fiction. (a) What fraction of the books are fiction? Give your answer in its simplest form. (b) What fraction of the books are non-fiction?​

Answers

(a) The fraction of books that are fiction is 2/3.

(b) The fraction of books that are non-fiction is 1/3.

To find the fraction of fiction and non-fiction books on a bookshelf:

Given: A bookshelf has 96 books. 64 of the books are fiction and the rest are non-fiction books. (a)Fraction of fiction books =?

(b)Fraction of non-fiction books =?

Now,

As given, we have,

The total number of books on a bookshelf = 96

Out of 96, the total number of fiction books = 64

So,

The remaining number of books = non-fiction books = 96-64 = 32

(a) Fraction of fiction books = fiction books/total books

= 64/96

On simplification,

= 2/3

(b) Fraction of non-fiction books = non-fiction books/total books

= 32/96

= 1/3

Therefore, the fraction of fiction and non-fiction books is 2/3 and 1/3 respectively.

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Please help me solve problems a - d.

Answers

By defining and solving systems of equations, we will see that:

a) the fraction is 40/56

d) the fraction is 15/21.

How to write the equations?

We have the fraction 5/7 and we want to write it in different ways.

a) First we want to find a number a/b such that:

a/b = 5/7

a + b = 96

This is a little system of equations, to solve this, first we can rewrite the first equation as:

7a = 5b

Now we can isolate a on the second equation:

a = 96 - b

And replace that on the other equation:

7*(96 - b) = 5b

And now we can solve this for b.

672 - 7b = 5b

672 = 5b + 7b = 12b

672/12 = b = 56

And we know that:

a = 96 - b = 96 - 56 = 40

Then the fraction is 40/56

d) This time we want the denominator to be 9 less than twice the numerator.

in a/b, a is the numerator and b is the denominator.

So this time we have:

a/b = 5/7

b = 2a - 9

We can rewrite the first equation again:

7a = 5b

And then replace the other equation in the right side:

7a = 5*(2a - 9)

And now solve this for a.

7a = 10a - 45

45 = 10a - 7a = 3a

45/3 = a = 15.

And:

b = 2a - 9 = 2*15 - 9 = 21

Then the fraction is 15/21.

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help please I need alot of help ​

Answers

Answer:

HI i no  answer of this quetion but what grade are in school

Please help with this question

Answers

Answer:

4

Step-by-step explanation:

the second column and the second row so, the answer is 4

I need these answers ASAP would be very grateful for these if you would like to help me out I would appreciate it and give a good amount of points!

Answers

Answer:

5. 8π 6. 18π 7. 8.6π 8. 11/4π

Step-by-step explanation:

8. 2 3/4

2*4+3 = 11/4

disributivity of multiplication over addition for rational numbers solve : -3/4 , 2/3 and -5/6 = 1/8 ? how ?​

Answers

The distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

Complete question

Which of the following is an example of distributive property of multiplication over addition for rational numbers

(a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

(b) -3/4 × {2/3 + (-5/6)} = [3/4 × 2/3] - (-5/6)

(c) -3/4 × {2/3 + (-5/6)} = 2/3 + (-3/4) × -5/6

(d) -3/4 × {2/3 + (-5/6)} = {2/3 + (-5/6)} - 3/4

How to determine the correct distributive property?

The distributive property of multiplication states that:

a * (b + c) = (a * b) + (a * c)

From the given question, we have:

-3/4 × {2/3 + (-5/6)}

This means that:

a = -3/4

b = 2/3

c = -5/6

Recall that a * (b + c) = (a * b) + (a * c)

So, we have:

-3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

Hence, the distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

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If a = 2√3, then the exact value of b is...

Answers

Answer:

b = 2

Step-by-step explanation:

using the tangent ratio in the right triangle and the exact value

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{a}[/tex] = [tex]\frac{b}{2\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

b × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

b = 2

Answer:

C. b = 2Step-by-step explanation:

Given that a = 2√3.

Let's find value of b...

[tex]\bf \tan( {30}^{o} ) = \cfrac{b}{a} [/tex]

[tex] \bf \cfrac{1}{ \sqrt{3} } = \cfrac{b}{2 \sqrt{3} } [/tex]

[tex]\bf b = 2[/tex]______________________

What is the length of the hypotenuse? If necessary, round to the nearest tenth.

Answers

Greeting to you! My name is Cecille and I’m here to answer that question

For more explanation, please see the attachment

Answer:

75 mm

Step-by-step explanation:

Pythagorean theorem:

 To find the hypotenuse, use Pythagorean theorem

Hypotenuse² = base² + altitude²

                  c² = 21² + 72²

                      = 441 + 5184

                      = 5625

                 [tex]\sf c = \sqrt{5625}[/tex]

                    [tex]= \sqrt{75*75}\\\\\boxed{\bf c = 75 \ mm}[/tex]

i need a little help -

Answers

The answer is 8 trust me

Given f(x) = (x - 1)(x + 2)(x − 3), what are the zeros and end behavior of the function?

Answers

A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x) = (x - 1)(x + 2)(x − 3), therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.

Hence, the zeroes of the functions are -2, 1, and 3.

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Answer:

−1, 2, −3; continues downward to the left and upward to the right

Step-by-step explanation:

11. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

Answers

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Answer:  [tex]\textsf{x}^2\textsf{ - 14x + 24}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{x = 12 and x = 2}[/tex]

Find: [tex]\textsf{Determine the quadratic equation}[/tex]

Solution:  In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.

Move the integers

Solution #1[tex]\textsf{x - 12 = 12 - 12}[/tex][tex]\textsf{x - 12 = 0}[/tex]

Solution #2[tex]\textsf{x - 2 = 2 - 2}[/tex][tex]\textsf{x - 2 = 0}[/tex]

Create and expression and distribute

[tex]\textsf{(x - 12)(x - 2) = 0}[/tex][tex]\textsf{(x * x) + (x * -2) + (-12 * x) + (-12 * -2) = 0}[/tex][tex]\textsf{x}^2\textsf{ - 2x - 12x + 24 = 0}[/tex][tex]\textsf{x}^2\textsf{ - 14x + 24 = 0}[/tex]

Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.

A square with side lengths 12 feet. 4 2 feet by 2 feet squares are cut out of each corner of the square.
Tariq designed the pool shown. The owner of the pool has one square cover to use. Find the area of the space that needs to be covered. (The four corners are squares.)

The area that needs to be covered is

ft2.

Answers

••••••••••••••••••••••••••••••••••••••••••••••••[tex] \mathbb{PROBLEM:} [/tex]

A square with side lengths 12 feet. 4 2 feet by 2 feet squares are cut out of each corner of the square.

Find the Area of the Space.

[tex] \mathbb{SOLUTION:} [/tex]

[tex] \bold{A = Length \: x \: Width} [/tex]

[tex] \bold{A = 12 \: ft \: x \: 4.2 \: ft } [/tex]

[tex] \blue{\bold{A = 50.4 \: ft} }[/tex]

[tex] \bold{ A\red{ = 50.4 } \: x \: 2 \: ft} [/tex]

[tex] \boxed{ \bold{ A = 100.80 ft²}}[/tex]

"If the 2 is quantity use multiply it again"

••••••••••••••••••••••••••••••••••••••••••••••••

NOTE:The way to solve a square area is by measuring the length and width of your area then multiplying those two numbers together to get the area in feet squared (ft2).

"Problem has been solve"

(ノ^_^)ノ

[tex]\large\bold{SOLUTION} \\ [/tex]

GIVEN :-

A square with side lengths 12 feet.4.2 feet by 2 feet squares are cut out of each corner of the square .

FIND :-

Find the area of the space that needs to be covered .

By finding the area of the space that needs to be covered we must use multiplication and multiply the given measurements .

[tex] \bold{Formula:}[/tex]

[tex] \qquad \boxed{ \bold{ \: \: Area = Length \times Width \: \: }}[/tex]

Now let's start solving :-

[tex] \quad \sf \implies{Area = Length \times Width} \\ [/tex]

[tex] \quad \sf \implies{Area = 12ft \times 4.2ft} \\ [/tex]

[tex] \quad \sf \implies{Area = 12feet \times 4.2ft = \pmb{50.4 ft}} \\ [/tex]

[tex] \quad \sf \implies{Area = 50.4ft \times 2ft = \pmb{100.80ft^2}} \\ [/tex]

Therefore, the area of the space that needs to be covered is 100.80ft² .

[tex] \underline{ \rule{185pt}{3pt}}[/tex]

A sign on a roadway at the top of a mountain indicates that for the next 4 miles, the grade is 10.5°. Find the change in elevation over that distance for a car descending the mountain. Round to the nearest hundredth.

Answers

the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

How to find the change in elevation?

To do this, we can think on the situation as a right triangle, where the hypotenuse is 4 miles, the angle that we look at measures 10.5°, and the change in elevation (let's call it x) will be the opposite cathetus to that angle.

Then we can use the relation:

Sin(a) = (opposite cathetus)/(hypotenuse)

Replacing what we know, we get:

sin(10.5°) = x/4mi

x = sin(10.5°)*4mi = 0.73mi

So the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

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Need help finding the one complete period of a non transformed contangent function

Answers

One complete period of a non-transformed cotangent function is π.

The period of the function is defined as the interval after which the function value repeats itself.

For example, f(T+x)=f(x)

where T is the period of the function.

Here given that there is a non-transformed function cotangent function.

We have to find the period of the function in which interval the value of the function will repeat.

So for the function y=f(x)=cot x

the period of the function is π. means after π the value of the cotangent repeats.

cot(π+x)=cot x

Then one cycle of the cotangent graph lies between 0 and π.

Therefore One complete period of a non-transformed cotangent function is π.

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What are the zeros of this function?

Answers

If you need the y zero, you would take the 2 points on the graph of (3, 0) and (6, 0) so the 2 zero’s are 3, and 6.

HI PLEASE ANSWER THIS QUESTION THANK YOU SO MUCH!

Mr. Avanzado has an underground in his house. What unit ofmeasure will he use to find its volume?

A. mm3
B. cm3
C. dm3
D. m3
2.What is the best unit of measure to use in finding the volumeof a rectangular pencil case?

A. mm3
B. cm3
C. dm3
D. m3
3.What is the formula to be used in finding the volume of a cube?

A. V = s x s or s2
B. V = s x s x s or s3
C. V = l x w x h
D. V = s + s + s
(NO TROLLS PLEASE)

Answers

1.  

2. cm³

3.

What is Unit?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

1. Volume is measure in

2.  volume of a rectangular pencil case in cm³

3. V = s x s x s or s³

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How to subtract negative number from 1

Answers

when you subtract a negative number from any platitude number the equation changes to addition so you would add the value of the negative number to 1.

To subtract a negative number from one you will need to set it up like this

1- (-x) x equals the negative number you're talking about

so we use the method KCC (keep change change)

So we KEEP the positive one, CHANGE the subtraction sign in to a plus sign "+" then CHANGE the negative number to a positive

lets say the negative number is 2

1-(-2)

1+ (+2)

1+2 = 3

Juanita’s boss told her that once she has worked with the company for 10 years, her salary will be increased to 3 times what she makes now plus $2,000. If s represents her original salary, which expression represents what her salary will be after 10 years at the company?
One-third s + 2,000
StartFraction 3 Over s EndFraction + 2,000
3 s + 2,000
2,000 minus 3 s

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Juanita’s salary once she completes 10 years, her salary will be increased to 3 times what she makes now plus $2,000. Now, if her salary is represented by s, then the expression that would represent her salary after 10 years is,

Salary after 10 years = 3s + 2000

Hence, the correct option is C.

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Answer:

C

Step-by-step explanation:

A mapping diagram showing a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 9), (2, negative 6), (negative 5, 4), (1, 2), (6, 0).
What is the domain of the function shown in the mapping?

Answers

Answer:

{-3, 2, -5, 1, 6}

Step-by-step explanation:

The domain is the set of input values.

Triangle ABC is a right triangle with CD | AB. Angle C is a right angle.​

(BC)²+(AC)² = (AB)(BD + AD). Using
gives Blank space for answering Question.
(BC)²+(AC)=(AB) (AB), which simplifies to (BC)2 + (AC)2 = (AB)2

Possible answers
CPCTC
Side-Angle-Side Similarity Postulate
congruent
Side-Side-Side Similarity Postulate
segment addition postulate
proportional

Answers

First blank: Side-Angle-Side similarity postulate

Second blank: proportional

help please fast grade 5 math help extra points to thooese who explain marking brainliest

Answers

7/12 x 4= 28/12 and good luck again
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anyone? got an answer Write the fraction as a decimal.six tenths 0.6 0.06 6.0 1.6 Consumers experience ______ marginal utility the more they consume of a particular good or service. The government raises money on the federal level through which taxes? check all that apply. Which inequality is equivalent to |x-4| less than 9? 9 > x 4 < 9 9 < x 4 < 9 x 4 < 9 or x 4 < 9 x 4 > 9 or x 4 < 9 Read the excerpt from The Dark Game.Montgomery quickly fetched Admiral Hall. The head of Room 40, nicknamed "Blinker" for the uncontrollable twitching in his eyes, hurried into the room and stood in front of de Grey's desk. Without saying a word, de Grey stood and handed the message to the small, ruddy-faced man, Hall's eyes took in what Montgomery and de Grey had discovered. His eye twitches became more pronounced as he tried to assess the impact of what he was reading.Based on information in the excerpt, the reader can infer that the information in the 1.wireless message was2.extraordinarily important.3.impossible to decipher.4.of little significance.5.already known. A(-5, 2)-10-8-6-4-210864224.6-8-10B(1,6)246 8 10D(3,-10)C(9,-6)What is the area of rectangle ABCD?O 43 units52 unitsO104 unitsO208 units Is Ponyboy a reliable or unreliable narrator. Include reasons to support your answer. Which approach allows us to understand how the decisions of the different eras have longlasting implications or impact on present-day? What are examples of volatile liquid anaesthetics? How many yards are in 1 mile 60 feet? -34, -2 3/4, ____, -1.5, 0, 2.5, 10, 25 1/5what number is missing yo what extent is the lynn white argument percipient to the cause of ecological crisis in malawi? what determines the velocity of an object I WILL GIVE BRAINLIESTWhich is true of dependent events?ANSWER CHOICES: The probability of all dependent events can be calculated using the OR formula P(A+B) =P(A) +P(B)-P(A and B) .You can use a two-way frequency table to calculate the conditional probability of events that are dependent.You can find the AND probability of dependent events using the formula P(A or B)= P(A) times P(B) .The outcome of one event has no effect on the outcome of a second event. 5) "The emotionally charged word deficit conjures images of impending economic meltdown. While a five hundred billion dollar trade deficit sounds dreadful, upon close examination, it is hardly a deficit in the normal sense of the word." The tone of the passage above allows the reader to understand that the essay's purpose is to: a) explore the connotations of different word choices b) redefine the term "deficit" c) convince the government to reduce its deficit d) explain what leads to economic meltdown Most of the text below should have been written in the past tense. Read it carefully and then correct the 3 verbs that are in the wrong tense.We located the object on radar and then we moved to the telescope. I take a bearing and Andy swivel the barrel around. Putting his eye to the eyepiece, he saw a glowing, yellow-red orb floating in mid-air. It hovered for about 30 seconds before it shoot off upwards at high speed. We couldn't believe our eyes! What is the only u. S. National park to bid for the winter olympics?. the sum of m and n is 32, and the value of m is three times the value of n. what is the value of m and n?A. m+n=32 n= 3mB. m+3n=32 m=3nC. m+n=32 m=3nD. m+n=3 32m=n what is 4/5+40/75+100%=