1. What is the binomial expansion of (x + 3)5? ​

Answers

Answer 1

Answer:

5x + 15

Step-by-step explanation:

To expand the binomial, you need to multiply each term inside the parentheses by 5.

(x + 3)5

= (x * 5) + (3 * 5)

= 5x + 15


Related Questions

Find the quotient.



2^3 ÷ 5^2

Answers

Answer:

0.32

Step-by-step explanation:

2^3 = 2*2*2 = 8

5^2 = 5*5 = 25

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

8/25 = 0.32

The answer is because if you see it is 7

Help please.. z zzz z Z z z z z z z z z z z z z zz

Answers

Answer:

B

Step-by-step explanation:

look at the graph, it is really easy with such basic numbers involved :

the red dotted line is

y = 2

since the line is dotted (= the points on the line are not included in the solution), the colored area is below the line is

y < 2

the blue line is clearly just a 45° basic line through the origin (0,0), and that means for every point in that line x is equal to y.

y = x

and the line is solid, so the points are included in the solution. the shaded area is above the line, so, we need to use the ">" relation :

y >= x

the required solution is the combination of both, and therefore, B is correct.

Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?

There are 16 cups in a gallon.

Answers

Answer:

D

Hope this helps!

At a pizza restaurant it costs $4 to make a small pizza that sells for $12, and it costs $6 to make a large pizza that
sells for $15. In one week, the restaurant spent a total of $1100 to make pizzas and sold all of them for $2910. How
many small pizzas were sold?
small pizzas were sold?

Answers

simply just divide there total investment for pizza with the cost for one small pizza 1100/4=275

275 Small pizzas were sold

What's the length of an arc with a central angle of 120and a radius of 5 inches?

Answers

Answer:

(10/3)π units

Step-by-step explanation:Mark if it is correct

Answer:

[tex]\frac{10\pi }{3}[/tex] inches

≈ 10.5 inches

Step-by-step explanation:

The formula for arc length is as follows:
Arc length = [tex]\frac{\theta}{360} * 2\pi[/tex]

[tex]\frac{120}{360} * 10\pi \\= \frac{1}{3} * 10\pi \\= \frac{10\pi}{3}[/tex]

Hope this helps and feel free to mark this as brainliest!

Solve For x

[tex] \large \frak{5x + 15 = 30}[/tex]

Tysm!:)​

Answers

ans : x = 3

5x + 15 = 30
minus 15 on both sides, 5x = 15
then divide both sides by 5 so, x = 3

[tex]\boldsymbol{5x+15=30}[/tex]

Subtract 15 from both sides.

[tex]\boldsymbol{5x=30-15 }[/tex]

Subtract 15 from 30 to get 15.

[tex]\boldsymbol{5x=15 }[/tex]

Divide both sides by 5.

[tex]\boldsymbol{x=\dfrac{15}{5} }[/tex]

Divide 15 by 5 to get 3.

[tex]\boldsymbol{x=3 \ \ \to \ \ \ Answer}[/tex]

Verification

Let x=3.

[tex]\bf{5\times3+15=30 \ \ \to \ \ \ Multiply }[/tex][tex]\bf{15+15=30 \ \ \to \ \ \ Add}[/tex][tex]\bf{30=30 \to \ The \ equality \ is \ fulfilled.}[/tex]

Checked ✅

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

6.
(06.01 LC)

Choose the correct classification of 4x4 − 4x3 + 10x6. (1 point)

4th degree trinomial

12th degree trinomial

3rd degree trinomial

6th degree trinomial

Answers

the correct classification would be 16

3. a 12 inch apple pie is sliced into 9 slices. what is the area of one slice of pie?

Answers

Answer:

4 pi     ( = 12.566  in^2 )

Step-by-step explanation:

TOTAL area =   pi r^2    =    pi (6)^2 = 36 pi   in^2

  divide into 9 pieces    36 pi  / 9 = 4 pi   in ^2

The area of the square is 36 square cm. Find its side.

Answers

Answer:

s = 6 cm

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 36 , then

s² = 36 ( take square root of both sides )

s = [tex]\sqrt{36}[/tex] = 6

6x6 makes 36 meaning it’s sides are each 6 cm

HELPPPPP ITS AN EMERGENCY ITS MY FINAL GRADEEEEE

click on the photo

Answers

Answer:

D

Step-by-step explanation:

2 units right 1 unit down

Good luck

Answer:

(x-2, y+1)

Step-by-step explanation:

G(0, 4) -> G'(-2, 5)

H(2, 4) -> H'(0, 5,)

E(0, 2) -> E'(-2, 3)

F(-1, 2) -> F'(-3, 3)

Calculate the lenth of AC to 1 decimal place in the trapezium below.

Answers

Answer:

18.1cm

Step-by-step explanation:

Please refer to the attached photo for a better understanding. Apologies for the terrible drawing.

First we will find the length of BE by using pythagoras' Theorem.

[tex]c^{2} =a^{2} +b^{2} \\AB^{2} =BE^{2} +EA^{2} \\16^{2} =BE^{2} +7^{2} \\256=BE^{2} +49\\BE^{2} =256-49\\BE=\sqrt{207} cm[/tex]

We will leave BE as it is as it is not the final answer.

Since we know CD = BE,

CD = [tex]\sqrt{207} cm[/tex]

Now from the photo, draw a line from C to A or A to C, you will see another triangle.

Now we will use Pythagora's Theorem again to find AC.

[tex]AC^{2} =AD^{2} +DC^{2} \\AC^{2} =11^{2} +(\sqrt{207}) ^{2} \\AC^{2} = 121+207\\AC^{2} =328\\AC=\sqrt{328} \\=18.1cm (1dp)[/tex]

please helpp (15 points)

Answers

We have:

vertex = (-1, 16)vertical intercept =  (0, 14)x-intercepts = (-3,83, 0), (.1,83, 0).

How to find the vertex of the parabola?

For a parabola like:

[tex]y = a*x^2 + b*x + c[/tex]

The vertex is at:

[tex]x = -b/2a[/tex]

In this case, we have:

[tex]y = -2x^2 -4x + 14[/tex]

So the vertex is at:

[tex]x = 4/2*(-2) = -1[/tex]

To get the y-value, we need to evaluate in x = -1.

[tex]y = -2*(-1)^2 - 4*(-1) + 14 = -2 + 4 + 14 = 16[/tex]

So the vertex is (-1, 16)

How to find the y-intercept?

To do that we just evaluate in x = 0.

[tex]y = -2*0^2 -4*0 + 14 = 14[/tex]

The vertical intercept is (0, 14).

How to get the x-intercepts?

Using Bhaskara's formula we get:

[tex]x = \frac{4 \pm \sqrt{(-4)^2 - 4*(-2)*14} }{2*-2} \\\\x = \frac{4 \pm 11.31 }{-4}[/tex]

So the two roots are:

x = (4 + 11.31)/(-4) = -3.83

x = (4 - 11.31)/(-4) = 1.83

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can someone please help mee (20 points and i will give brainliest!!!)

Answers

Answer:

a. y-intercept:(0,  -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

a:

 So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes [tex]y=(0)^2-0-6[/tex] which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]. In this case a=1, b=-1, c=-6. So plugging those values in you get [tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}[/tex], which simplifies to [tex]x=\frac{1\pm5}{2}[/tex]. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of [tex]y=(x-h)^2+k[/tex] where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

[tex]y+6=x^2-x[/tex]

Complete the square by adding (b/2)^2

[tex]y+6+0.25 = x^2-x+0.25[/tex]

Rewrite as square binomial

[tex]y+6.25 = (x-0.5)^2[/tex]

Isolate y

[tex]y=(x-0.50)^2-6.25[/tex]

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation [tex]y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}[/tex]. which simplifies to [tex]x=\frac{-1\pm5}{-2}[/tex] which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

[tex]y=-(x^2-x-6)[/tex]

Add 6 to both sides (on the left side add -6 since -1 was factored out).

[tex]y-6=-(x^2-x)[/tex]

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

[tex]y-6-0.25 = -(x^2-x+0.25)[/tex]

Rewrite as square binomial

[tex]y-6.25=-(x-0.5)^2[/tex]

Add 6.25 to both sides

[tex]y=(x-0.50)^2+6.25[/tex]

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

Answer:

a) y-intercept (0,  -6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, -6.25)

b) y-intercept (0, 6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, 6.25)

Step-by-step explanation:

What is the measure of the unknown angle?

image of a two hundred ninety seven degree angle and an unknown angle

60°
63°
64°
70°

Answers

Answer:

63

Step-by-step explanation:

A circle is 360 degrees

So, subtracting 297 from 360, we'd get 63 degrees

63 degrees

The circle will be 360 degrees so
360-297= 63 so that’s our answer

Solve the following quadratic by
completing the square.
y = x2 - 6x +2

Answers

Answer:

Roots of the equation are  (−3−√7) , (−3+√7)

Step-by-step explanation:

For solving a quadratic equation using completing the square method:

set the value of 'y' = 0add and subtract the square of half of the coefficient of x.solve the obtained equation for 'x'

given equation:

y = x^2 - 6x +2

0 = x^2 - 6x + 2

0 = x^2 - 3^2 + 3^2 -6x +2

0 = (x-3)^2 -7

7 =  (x-3)^2

±[tex]\sqrt{7}[/tex] = x-3

±[tex]\sqrt{7}[/tex] + 3 = x

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Triangle A B C is cut by line segment S T. Line segment S T goes from side A B to side C B. Lines S T and A C are parallel. The length of S B is 10 feet, the length of B T is 9 feet, and the length of C T is 2.7 feet.
What is the length of Line segment S A?

1.89 ft
2.43 ft
3 ft
7 ft

Answers

In the triangle ABC, the length of the line segment SA=3 ft ( 3rd option).

In triangle ABC,

SB=10ftBT=9ftCT=2.7ft &ST|| AB

According to the triangle proportionality theory, we know that if a triangle has a line segment parallel to one of its sides, the line segment splits the other sides correspondingly.

Hence,

SA/SB=CT/BT

⇒SA/10=2.7/9

⇒SA=(2.7*10)/9

⇒SA=3

So, the length of SA is 3 ft.

Therefore the 3rd option is correct.

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Graph the inequality -1 < y +5x<11

Answers

Answer:

b

Step-by-step explanation:

could i get help with this equation?

Answers

Answer:

10

Step-by-step explanation:

use PEMDAS

PEMDAS order is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

2[32 — (4 − 1)³] =

2[32 — (3)³] =

2[32 — 27] =

2[5] =

10

khanacademy

In the number line below, JK is 5, LM is 6, and KL is 4. What is the length of the line segment formed by the midpoint of JK and midpoint of LM?

Answers

Answer:

By splitting the line segments into equal parts, we find that the length of the line segment formed by joining the mid-points is 5.5 units.

Step-by-step explanation:

Given lengths show that the length of JK is 5 units, KL is 4 units and LM is 6 units. Let the midpoint of JK be A. This means JK is splited into two equal parts JA and AK. Since the lengths of both the segments are same, it will be 5/2 = 2.5 units.

Now, let the midpoint of LM be B. So, we have two equal line segments LB and BM of length 6/2 = 3 units.

So, the length of the line segment formed by joining A and B will be 2.5 + 3 = 5.5 units

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Which algebraic expression represents the phrase “two times the quantity of a number minus 12”?

Answers

Answer:

The algebraic expression which represents the phrase “two times the quantity of a number minus 12” is : 2x- 12

Step-by-step explanation:

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

for example :-

3x + 4y – 7,  4x – 10, etc.

These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign

let the quantity mentioned in the question be 'x'

therefore according to the statement the algebraic expression which represents the phrase “two times the quantity of a number minus 12” is : 2x- 12 is

⇒2x - 12 (answer)

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Unit 2 Show Your Work, BYU Geometry Part 1

Answers

The true statements about ∠MJK and ∠MJL are

The sum of the two angles is 180 degreesJK and JL are opposite raysJK and JL form a straight line

How to determine the true statements?

The statement is given as:

∠MJK and ∠MJL are a linear pair of angles and the angles are also supplementary

As a general rule, linear pair angles are adjacent angles that add up to 180 degrees. This means that:

They are supplementary anglesThey have a sum of 180 degreesThe angles may or may not be congruentThey have opposite rays i.e. straight line

The above means that, the following options are true:

(e), (f) and (h)

Also, the converse of the statement is:

∠MJK and ∠MJL are supplementary angles and the angles are also  linear pair of angles

This is false because not all supplementary angles are  linear pair angles

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Rewrite each expression as a function of a single angle.
sqrt[(1 - cos 170°) / 2]

Answers

By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.

How to simplify a trigonometric expression

In this question we must apply trigonometric rules to simplify a given number, in which case we can take advantage of this expression:

[tex]\sin \frac{\theta}{2} = \sqrt{\frac{1 - \cos \theta}{2} }[/tex]

If we know that [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex], then the rewritten expression is:

x = sin 85°

By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.

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What is the difference of the polynomials?
(x² + x³ + x² + x) - (x²-x³+x²-x)
© 2x2
O 2x³+2x
O x6 +x²
O 2x5+2x²

Answers

Answer:

2x³ + 2x

Step-by-step explanation:

(x² + x³ + x² + x) - (x² - x³ + x² - x)

= x² + x³ + x² + x - x² + x³ - x² + x

Gathering like terms...

x³ + x³ +x² + x² -x² - x² + x + x

= 2x³ + 2x

The difference of the polynomials is 2(x³+x).

What is a polynomial?

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given are two polynomials (x² + x³ + x² + x) and (x²-x³+x²-x), we need to find the difference,

So,

(x² + x³ + x² + x) - (x²-x³+x²-x)

= x² + x³ + x² + x - x²+x³-x²+x

= 2x²-2x²+x³+x³+x+x

= 2x³+2x

= 2(x³+x)

Hence the difference of the polynomials is 2(x³+x).

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find the linear measure of arc vw on circle p, where pv = 32 inches and angle vpw = 84. use 3.14 for pie and estimate your answer to two decimal places.

Answers

The linear measure of arc vw as described in the task content is; 46.89in.

What is the linear measure of the arc vw?

It follows from the task content that the radius of the circle with center p is given as pv = 32in. and the angle subtended by the arc is; 84.

On this note, the measure of arc vw is;

= (84/360) × 2 × 3.14 × 32

= 46.89 inches.

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dawn simplified a power correctly and came up with a value of 64. which could have been the original exponential form of the expression dawn simplified? check all that apply.

Answers

Answer:

below

Step-by-step explanation:

the second option is the only expression that came up with the value of 64

(2^6)

Answer:2,⁶     (–8)²    and  (–2)⁶   hope I helped.        : )

Step-by-step explanation:                                                                                                                                              

hi :)

A(n)______ is a number sentence that shows how two or more expressions are not equal

Answers

Answer:

Inequality is the answer

Answer: Inequality ✅

Step-by-step explanation:

Hii, do you need to know the answer to your question? No problem!

The answer to your question is "inequality".

An inequality is a number sentence that shows how two or more expressions are not equal.

An example of that is [tex]\sf 4x+4\geqslant3x-5[/tex].

So 4x+4 is greater than or equal to 3x-5, but they're not 100% equal (such is the case in equations).

--

Hope that this helped! Best wishes.

--

What is the area of this trapezoid?

340 cm²

427.5 cm²

440 cm²

487.5 cm²

Answers

Answer:

440cm²

Step-by-step explanation:

*Area= (a+b)/2×h

(19+25)/2*20

= _ * 440cm². *_

Answer:

440cm²

Step-by-step explanation:

I believe its right

Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
-3/4m - 1/2 = 2 + 1/4m
2
3
4
5

Answers

Multiply by 4 on both sides

If a polygon has an area of 25cm and is dilated by a factor of 3, what will be the area of the dilated polygon?

Answers

Answer:

225 cm²

Step-by-step explanation:

dilatation factor = 3 , then

area factor = 3² = 9

the area of the dilated polygon is then 9 times the area of the original so

area of dilated polygon = 9 × 25 = 225 cm²

sin 30°-cos 30°÷ sin 60°

Answers

Answer:

-1/2

Step-by-step explanation:

sin(30 degrees) = sin (pi/6) = 1/2

cos(30 degrees) = cos (pi/6) = [sqrt(3)]/2]

sin (60 degrees) = sin(pi/3) = [sqrt(3)]/2]

1/2 - [sqrt(3)/2] / [sqrt(3)/2] = -1/2

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