Use the numbers below to answer the following
question.
6^1, 3^2, 2^3, 1^7
Which shows the numbers ordered from least to
greatest?

Answers

Answer 1
Power with a natural exponent.

Definition:

[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]

also

[tex]a^1=a\\\\a^0=1[/tex]

[tex]6^1=6\\\\3^2=3\cdot3=9\\\\2^3=2\cdot2\cdot2=8\\\\1^7=1[/tex]

therefore

[tex]\huge\boxed{1^7 < 6^1 < 2^3 < 3^2}[/tex]

Related Questions


A triangle has the dimensions shown. The perimeter of the triangle would be represented by which type of expression?

linear expression
quadratic expression
exponential expression
rational expression

Answers

The third side is a linear expression , Option A is the right answer.

The missing diagram is attached with the figure.

What is a Triangle ?

A triangle is a polygon with three sides , three vertices , three angles .

It is given that the side of the triangle as 3x+1 , 5x-2 , y

Perimeter is given as 10x-1

Perimeter = 3x+1 +5x-2 + y  = 10x-1

8x -1 +y = 10x -1

y = 2x

which is a linear expression.

Therefore the third side is a linear expression , Option A is the right answer.

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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= 3m
B. m+3n=32
m=3n
C. m+n=32
m=3n
D. m+n=3
32m=n

Answers

Answer:

The correct set of equations is C.

Step-by-step explanation:

m + n = 32

m = 3n

We have 4n = 32, so n = 8 and m = 24.

What is the area of the figure?

Answers

Answer:

21.5

Step-by-step explanation:

break the shape down to make two shapes: a triangle and rectangle.
triangle = A=bxh/2

3x5=15/2=7.5

Rectangle = A=bxh

2x7=14

7.5+14= 21.5

Hope this helps :)

Answer:

21.5

Step-by-step explanation:

(all steps provided in image attached)

Graph the linear equation. Find three points that solve the equation, then plot on the graph.
-3x + 2y = 2

Answers

Step-by-step explanation:

I have done it go and check it once

what is the result of applying the square root property to the equality of the equation X plus B over two a squared equals -4 AC plus B2 over 4a two squared

Answers

After doing simplification, the result that we got is the quadratic formula

x = [-b ±√(b² - 4ac)] / 2a.

The given statement can be explained with the following equation:

[x + (b/2a)]² = (b² - 4ac) / 4a²

Now, we will take the root on both the sides:

x + (b/2a) = ±√[(b² - 4ac) / 4a²]

x = -(b/2a) ± √[(b² - 4ac) / 4a²]

x = [-b ±√(b² - 4ac)] / 2a

The final equation resembles the quadratic formula.

So, the result of applying the square root property to this equation is that we get the quadratic formula after simplification.

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The graph of quadratic function f has zeros of -8 and 4 and a maximum at (-2,18). What is the value of a in the function’s equation?

Answers

Quadratic Function Equations

To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:

[tex]y=a(x-r)(x-s)[/tex]

r and s = intercepts/zeros of the graph

Solving the Question

We're given:

Zeros: -8, 4Maximum: (-2, 18)

[tex]y=a(x-r)(x-s)[/tex]

⇒ Plug in the given information:

[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]

Answer

[tex]a=-\dfrac{1}{2}[/tex]

What is value of x? Enter your answer in the box.​

Answers

Answer:

x = 10

Step-by-step explanation:

the ray is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is

[tex]\frac{x+4}{2x +1}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2(2x + 1) = 3(x + 4) ← distribute parenthesis

4x + 2 = 3x + 12 ( subtract 3x from both sides )

x + 2 = 12 ( subtract 2 from both sides )

x = 10

What is -8/15 of 21/12

Answers

Answer:

-14/15

Step-by-step explanation:

"of" means multiply, thus:

-8/15 * 21/12

-8 * 21 / 15 * 12

-2 * 7 / 15

-14/15

Answer:

-14/15

Step-by-step explanation:

So first you need to get rid of the negative sign. Don't worry you will add it back later!

So, you will do

-8/15×21/12

Once you cross cancel, you will have

-2/5x7/3

That would be equivalent to

-14/15

That's your answer!

Hope this helped :)

In the Kite ABCD, AB = 5√2mm AP= 5mm, PD = 7mm, find the area to the nearest mm2.

Answers

The area of the kite ABCD will be 60 square millimeters.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

In the Kite ABCD, AB = 5√2mm = 7.07 mm, AP= 5mm, PD = 7mm

Then the area of the kite ABCD will be

Area = 2(area of triangle APB and area of triangle APD)

The side length of PB will be

AB² = AP² + PB²

PB² = AB² – AP²

PB² = 7.07² – 5²

PB² = 50 – 25

PB² = 25

 PB = 5 mm

Then the area will be

Area = 2[(1/2 × 7 × 5) + (1/2 × 5 × 5)]

Area = 60 square mm

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CD is the perpendicular bisector of both XY and ST, and CY = 16. Find TY.

Answers

The value of TY is 14

Given that CD is the perpendicular bisector of XY and ST and CY = 16

We need to find the value of TY

Here M is the midpoint of ST  and D is the midpoint of XY

As shown in the diagram we can say that

CT = CS =12

We can also say that ST║XY

So , ∠CST = ∠CSY

∠CTS = ∠CYX

ΔSCT = ΔXCY

SX = CS - CX

= CY - CX

We can say that MT = SM = 5

DY = DX = 7

TY = SX = 4

CY = CX = 16

ST = SM + MT

ST= 5+5

∴ ST= 10

XY = XD +DY

XY = 7+7

∴ XY = 14

Hence the value of XY is 14

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On a coordinate plane, a solid straight line has a negative slope and goes through (negative 2, 2) and (2, negative 8). Everything above and to the right of the line is shaded. The line has an equation of y greater-than-or-equal-to negative five-halves x minus 3.
Which linear equality will not have a shared solution set with the graphed linear inequality?

y > Two-fifthsx + 2
y < Negative five-halvesx – 7
y > Negative two-fifthsx – 5
y < Five-halvesx + 2

Answers

The linear inequality  [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality. the correct option is D.

What is inequality?

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

On a coordinate plane, a solid straight line has a negative slope and goes through (-2, 2) and (2, -8).

m = (-8 -2)/ (2 +2)

m = -10/ 4

m = -5/2

The line has an equation of y greater-than-or-equal-to negative five-halves x minus 3.

[tex]y \geq -5/2 (x-3)[/tex]

The linear inequality  [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality.

Thus, the correct option is D.

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Answer:

its b the guy above me is wrong

Step-by-step explanation:

If the zeros of a quadratic equation are
7 and 4, what would be the factors?

Answers

Answer:

The factors are (x-7) and (x-4)

Step-by-step explanation:

We are finding the factors of a function from the zeros

The zeros are 7 and 4

We can use the zero product property which is

(x-b)(x-c) = 0  where b and c are the zeros

(x-7) (x-4) =0

The factors are (x-7) and (x-4)

They should be (x-7) and ( x - 4 )

A(-5, 2)
-10-8-6-4-2
10
↑リ
8
64
2
2
4.
6
-8
-10
B(1,6)
2
4
6 8 10
D(3,-10)
C(9,-6)
What is the area of rectangle ABCD?
O 43 units²
52 units²
O104 units²
O208 units²

Answers

The area of ABCD is 104 units²

What is area of rectangle?

The area of rectangle is the product of its length to its breadth.

i.e., Area of rectangle= length * breadth

As, ABCD is in the shape of rectangle.

Using distance formula,

AB = √(1-(-5)² + (6-2)²

AB = √36+16

AB = √52

AB= 2√13

BC= √(9-1)² + (-6-6)²

BC= √64+144

BC =√208

BC= 4√13

Now, area of rectangle

=length *  breadth

= 2√13 * 4√13

= 8*13

=104  units²

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Solve |x| > -9.

1. no solution
2. all reals
3. {x | x < -9 or x > 9}

Answers

Answer:

2. All reals

Step-by-step explanation:

It covers everything as absolute value (distance from 0)

If you graph it you will see

Answer:  All reals

Reason:

Absolute value represents distance on a number line. Specifically it's the distance from x to 0.

For example, |-2| = 2 means -2 is 2 units away from 0.

Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.

Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")

Two positive integers have a product of 242. One integer iS twice the other. What are the integers?​

Answers

Answer:

11 and 22

Step-by-step explanation:

let one positive integer be n then the other is 2n , so

n × 2n = 242

2n² = 242 ( divide both sides by 2 )

n² = 121 ( take square root of both sides )

n = [tex]\sqrt{121}[/tex] = 11

2n = 2 × 11 = 22

the 2 integers are 11 and 22

sam and jose mowed 2/3 of the yard. jose mowed 3/4of that amount. whta part of the yard did jose mow?

Answers

Answer:

09

Step-by-step explanation:

34

If y varies inversely as x, and y = 58 when x = 9, find y when x = 261.

Answers

Answer:

y = 2

Step-by-step explanation:

Y varies indirectly with x (as x gets bigger, y gets smaller)

You have to find k, the constant of proportionality.

y = [tex]\frac{k}{x}[/tex]

Plus in the x & y values you are given

58 = [tex]\frac{k}{9}[/tex]  Multiply both sides by 9 to solve for k

k= 522

Now plug in the new value of x to solve for y

y = [tex]\frac{522}{261}[/tex]

y = 2

someone please help me with this question!! ​

Answers

The Answer is in simplest form:-

4/9

=0.4444444444

Answer:

4/9

Step-by-step explanation:

1) since we know that; when a fraction is raised to a negative power, we take reciprocal of the fraction and raise both the numerator and the denominator to a positive power,

(27/8)^-⅔

that's how we write it then

2) we take the reciprocal and multiply with positive power respectively

(8/27)⅔

that is by expanding

8^⅔/27^⅔

enter it in your calculator and you should get

4/9

hope that helps!

Please help solve for x..

Answers

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

[tex]x^{100}-4^x \cdot x^{98}-x^2+4^x=0[/tex]

Factor out -1:

[tex]\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0[/tex]

Divide both sides by -1:

[tex]\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0[/tex]

Rearrange the terms:

[tex]\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:[/tex]

[tex]\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0[/tex]

Factor out the common term [tex](x^{98}-1)[/tex] :

[tex]\implies (4^x-x^2)(x^{98}-1)=0[/tex]

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

[tex]\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}[/tex]

Therefore, the solutions to the given equation are: x = 1 or x = -1

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Put these types of angles in order, sta rting with the smallest angle size.
Smallest
Obtuse
Acute
Reflex
Right angle
Largest
<<<<
Update

Answers

Answer:

Acute, right angle, obtuse, reflex

Step-by-step explanation:

Answer:

Acute

right angle

obtuse

reflex angle

Step-by-step explanation:

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

Answers

The answer is -9 < x - 4 < 9

How do I solve the following system of inequalities graphically on the set of axes below?
y> x-3 y≥− 6/1 x+4

Answers

I don't know.

Thank you!!

3x squared + 6 x cube - 9x squared y when factorused​

Answers

[tex]3x ^{2} \: + \: {6x}^{3} \: - \: 9 {x}^{2} y[/tex]

Factor the expression with the common factor that is "3x²".

[tex] \boxed{ \bold{3 {x}^{2} \: \times \: (1 \: + \: 2x \: - \: 3y)}}[/tex]

MissSpanish

Answer:

[tex]\boxed{3x²(1 + 2x - 3y)}[/tex]

Step-by-step explanation:

3x squared + 6 x cube - 9x squared y

To factor

Solution:

A process when algebraic expression is expressed as a product of two or more expressions is factorisation.

ATP,

Square = a²

Cube = a³

3x² + 6x³ - 9x²y

We can see that 3x^2 is common in this expression.

So rewrite as:

[tex]3x²(1 + 2x - 3y)[/tex]

Done!

Write the fraction as a decimal.

six tenths

0.6
0.06
6.0
1.6

Answers

Answer:

[tex]\huge\boxed{\dfrac{6}{10}=0.6}[/tex]

Step-by-step explanation:

[tex]0.6=\dfrac{6}{10}[/tex]

one digit after the decimal point - one zero in the denominator

[tex]0.06=\dfrac{6}{100}[/tex]

two digits after the decimal point - two zeros in the denominator

[tex]6.0=6[/tex]

[tex]1.6=1\dfrac{6}{10}\ \text{or}\ 1.6=\dfrac{16}{10}[/tex]

six tenths would be written as 0.6

I WILL GIVE BRAINIEST PLS HELP

∠2 and ∠8 are _____________ because they are _______________________.

supplementary/consecutive angles

congruent/consecutive angles

congruent/alternate interior angles

supplementary/alternate interior angles

Answers

Answer:

congruent/alternate interior angles

Step-by-step explanation:

just took the quiz

the sum of twice the number x and 25 more than three times the number y

Answers

Answer:

Correct expression:

[tex]2x + 3y + 25[/tex]

A man 1.8 m tall observes the angle of elevation of a tree to be 26 degrees, if he is standing bf 16 m from the tree find the height of the tree

Answers

The height of the tree is the man's height plus x.

[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]

So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]

experimental verification​

Answers

See below for the verification of ∠ACD =  ∠ABC + ∠BAC

How to verify the angles?

The following proof works for both triangles.

The sum of angles in a triangle is 180 degrees.

So, we have:

∠ABC + ∠BAC + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ABC - ∠BAC

The sum of angles on a straight line is 180 degrees.

So, we have:

∠ACD + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ACD

Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC

180 - ∠ACD = 180 - ∠ABC - ∠BAC

Subtract 180 from both sides

- ∠ACD = - ∠ABC - ∠BAC

Multiply both sides by -1

∠ACD =  ∠ABC + ∠BAC

Hence, ∠ACD =  ∠ABC + ∠BAC has been verified

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Solve the system of equations by substitution.
x + y = A system of equations. StartFraction 3 over 8 EndFraction x plus StartFraction one-third EndFraction y equals StartFractions 17 over 24 EndFraction.
x + 7y = 8
(, )

Answers

A will have a value of 2. The value of A is found by the substitutional equation system.

What is the system of two equations?

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation 1: [tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24}[/tex]

Equation 2: [tex]x+7y=8[/tex]

Rearrange equation 2 as;

x=8-7y

Substitute the value of x;

[tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24} \\\\ \frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24} \\\\ \frac{-21}{8} y+\frac{1}{3} = \frac{17}{24}-3 \\\\ \frac{-63y+8y}{24}=\frac{17-72}{24}\\\\ \frac{-55 \ y}{24} = - \frac{55}{24}\\\\ y= 1[/tex]

Substitute the value of y in equation 2 as;

x+7y=8

x+7(1)+8

x=8-7

x=1

The system of equations by substitution obtained the value of A is;

x + y = A

1+1=A

A=2

Hence the value of A will be 2.

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4. Angles A and B are supplementary. If mA = 67, find mB

Answers

Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]

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