On which number line are -3 and its opposite shown?

hypotenuse = 8

unknown leg = b

known leg = 4

Pythagorean theorem:

[tex]c=\sqrt{{a}^{2}+{b}^{2}}[/tex]

The answer is

[tex]8=\sqrt{{b}^{2}+{4}^{2}} [/tex]

Answer:

[tex]20x^{11}[/tex]

Step-by-step explanation:

An expression in algebra that contains one term is called a monomial.

These include numbers, whole numbers and variables that are multiplied together.

Any number, a whole number without variables can also be monomial, like 32, 5236 etc.

So, here the monomial is [tex]20x^{11}[/tex].

Option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

As we know in the monomial there will be only one term.

Option (C) and Option (D) contains two terms so they are not monomial.

Option (B) contain fractional term.

Thus, option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.

Learn more about Polynomial here:

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Answer:

The radius of the circle is 14 inches.

Step-by-step explanation:

How is the circumference of a circle related to its radius?

[tex]\displaystyle \text{Circumference} = \pi\times \text{Diameter} = \pi\;(2\times \text{Radius})[/tex].

In brief,

[tex]\text{Circumference} = 2\pi\times \text{Radius}[/tex].

For this question,

Divide both sides of the equation by [tex]2\pi[/tex]:

[tex]\displaystyle \frac{\text{Circumference}}{2\pi} = \text{Radius}[/tex].

[tex]\displaystyle \text{Radius} = \frac{\text{Circumference}}{2\pi} = \frac{28\pi}{2\pi} = 14[/tex].

In other words, the radius of this circle is 14 inches.

[tex]A'=(2-5,-1+3)=(-3,2)[/tex]

Answer:

1. 5

2. 13

3. 25

4. 7

Step-by-step explanation:

|-5|=5

|13|=13

|25|=25

|7|=7

Answer:

its A :(

Step-by-step explanation:

By using the concept of slope of a Straight line,we arrive to the conclusion that the equation of line through (2,-4) and having slope off 3/5 is  y = - (1/2)x - 26/5.

The slope of this Straight line is given as=3/5

Thus,the equation of the straight line becomes y=(3/5)x [tex]+[/tex]c.

Now,if substituting the Slope of the line in the equation of this line.

y=(3/5)x [tex]+[/tex]c.

In the point(2,-4):

-4=(3/5)(2) [tex]+[/tex] c

-4=(6/5) [tex]+[/tex] c

c=-4-(6/5)

  = - 26/5

Therefore, the final equation is y= - (1/2)x - 26/5

To learn more about Straight line,

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Answer:

180+69=249

I got 180 from the ABC, that is half the circle then + the 69

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Slope = change in y ÷ change in x

The line passes through (3,7) and (-1,4)

Slope = [tex]\frac{7 - 4}{3 - -1}[/tex] = [tex]\frac{3}{4}[/tex]

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

According to the data we have the following points:

[tex](x_ {1}, y_ {1}): (- 1,4)\\(x_ {2}, y_ {2}) :( 3,7)[/tex]

Substituting we have:

[tex]m = \frac {7-4} {3 - (- 1)} = \frac {3} {3 + 1} = \frac {3} {4}[/tex]

Thus, the slope of the line is [tex]\frac {3} {4}[/tex]

Answer:

[tex]\frac {3} {4}[/tex]

Answer: 1) x⁴ + 5x² + 12x - 31

              2) 3x³  -  x²  + 2

              3) 8x³ + x² + 3

Step-by-step explanation:

1) Line up like terms and add the coefficients of each term

 -5x⁴ + 6x²          - 43

+ 6x⁴ -  1x² + 12x + 12

    x⁴ + 5x² + 12x - 31

2) Line up like terms and add the coefficients of each term

   1x³ - 2x² + 4

+ 2x³ + 1x²  - 2

  3x³  -  x²  + 2

3) Line up like terms and add the coefficients of each term

   7x³  - 1x² + 1

+ 1x³ + 2x² + 2

   8x³ + x² + 3

Answer:

The solutions are x=0, x=1

Step-by-step explanation:

we know that

The solution of the equation f(x)=g(x)

are the values of x when the value of f(x) is equal to the value of g(x)

Observing the table

For x=0

f(0)=1  and g(0)=1

so

For x=0 ------> f(x)=g(x)

For x=1

f(1)=1/2  and g(1)=1/2

so

For x=1 ------> f(x)=g(x)

therefore

The solutions are x=0, x=1

Answer:

29.74 degrees.

Step-by-step explanation:

Tan(theta) = opposite / adjcent.

opposite = 8

adjacent = 14

Tan(theta) = 8/14

Tan(theta) = 0.5714

theta = tan^-1(0.5714)

theta = 29.74 degrees

Answer:

A) 32y³ + 24y² - 12y - 9

Step-by-step explanation:

(-8y² + 3)(-4y - 3) = (-8y² x -4y) + (-8y² x -3) + (3 x -4y) + (3 x -3)

                           = 32y³ + 24y² - 12y - 9

The product of [tex]-8y^2+3[/tex] and [tex]-4y-3[/tex] is:

               [tex]32y^3+24y^2-12y-9[/tex]

We are asked to find the product of the two expressions which are given by:

[tex]-8y^2+3[/tex] and [tex]-4y-3[/tex]

i.e.

we are asked to find the product of a quadratic and a linear polynomial.

We are asked to find the result of:

[tex](-8y^2+3)\cdot (-4y-3)[/tex]

Hence, on using the distributive property we have:

[tex]-8y^2(-4y-3)+3(-4y-3)\\\\=-8y^2\times -4y-8y^2\times (-3)+3\times (-4y)+3\times (-3)\\\\i.e.\\\\=32y^3+24y^2-12y-9[/tex]

The correct answer is: Option: A

Answer:

x = 8

Step-by-step explanation:

Step 1: Write an equation

2x - 9 = 7

Step 2: Use the Addition Property of Equality

2x = 16

Step 3: Use the Division Property of Equality

x = 8

Answer:

number = 8

Step-by-step explanation:

Let "number" = x. Set the equation.

"product of 2 and number" = 2(x)

"nine less" = -9

"equal to 7" = "= 7"

2x - 9 = 7

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 9 to both sides.

2x - 9 (+9) = 7 (+9)

2x = 7 (+9)

2x = 16

Divide 2 from both sides.

(2x)/2 = (16)/2

x = 16/2

x = 8

8 is your answer.

~

Answer:

7 billion

Step-by-step explanation:

Rounding decreqases when number is under 5 and if its above (Ex, 7,685,000,000) it is rounded to 8 billion. But here, it is under 5 so it is 7 billion.

Answer:

7,000,000,000

Step-by-step explanation:

Note the Billions place value. 7 is in the billions place value. To find out if you round up or down, look at the place value directly to the right of the one you are trying to find, in this case, being the hundred million place value. The value inside the hundred million place value is a 1.

Note that the number has to be 5 or greater to round up, or else you round down. Because 1 < 5, you round down.

7,125,000,000 rounded to the nearest billion is 7,000,000,000.

~

Answer:

8

Step-by-step explanation:

to find the number of sides when you are given an exterior angle you divide 360 (because that's what all exterior angles equal) by the one exterior angle you were given. in this case 360/45=8

Answer:

8 sides

Step-by-step explanation:

because you use the formula for exterior angles; [tex]\frac{360}{n}[/tex], you plug in the number of sides in the denominator and then divide 360 by n

Answer:

√61

Step-by-step explanation:

Distance between 2 points (x1, y1) and (x2,y2) is given by

Distance = √ [ (x2-x1)² + (y2-y1)² ]

in our case, x1 = 0, y1 = 6, x2 = 5, y2 = 12

Distance

= √ [ (5-0)² + (12-6)² ]

= √ [ (5)² + (6)² ]

= √ 61

Answer:

√61

Step-by-step explanation:

The distance between two points is given by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (5-0)^2 + (12-6)^2)

  =sqrt( 5^2 + 6^2)

 = sqrt(25+36)

 = sqrt(61)

Answer:

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

Look at the picture.

We have

center at (3, 5) → h = 3 anf k = 5

radius r = 8

Substitute:

[tex](x-3)^2+(y-5)^2=8^2\\\\(x-3)^2+(y-5)^2=64[/tex]

Answer:

∠2 = 18°

Step-by-step explanation:

∠WXZ = ∠1 + ∠2 ← substitute ∠1 = 3∠2

∠WXZ = 3∠2 + ∠2, that is

72 = 4∠2 ( divide both sides by 4 )

18 = ∠2, that is

∠2 = 18°

Answer:

21.16

Step-by-step explanation:

First find the tax

16.40 * 9%

16.40 *.09 = 1.476 = 1.48

Then we need to find the tip

16.40 *20%

16.40 *.20 = 3.28

The total is the bill  plus tax plus tip

16.40 + 1.48 + 3.28

21.16

Answer:

1372

Step-by-step explanation:

y=4(7)^3

You multiply 7x7x7 which gives you 343

Now you plug that in.

y=4(343)

Multiply it and you get

y=1372

Answer:

(a)(b²)√a

Step-by-step explanation:

√(a³b⁴)

Root both variables. Note that pairs of the same variables can be brought out of the root.

√(a³) = √(a * a * a) = a√a

√(b⁴) = √(b * b * b * b) = b²

(a)(b²)√a is your answer.

Answer:

United Kingdom , France,  Soviet Union , and China  

Step-by-step explanation:

United Kingdom , France,  Soviet Union , and China  was an ally of the United States durning World War II.

Answer: option b

Step-by-step explanation:

It is important to know that, by definition, the rule for 180 degrees counterclockwise rotation is:

[tex](x,y)[/tex]→[tex](-x,-y)[/tex]

Therefore, given the point (1, -6) we can find the image obtained for  for a 180° counterclockwise rotation about the origin by applying the rule mentioned before.

Then, the image is:

 [tex](1,-6)[/tex]→[tex](-(1),-(-6))=(-1,6)[/tex]

Answer:

The correct answer option is b. ( -1, 6).

Step-by-step explanation:

We are given a point which is rotated 180 degrees counterclockwise about the origin (0, 0). We are to find the coordinates of the image of this point after the rotation.

The rule for rotating a point 180 degrees counterclockwise is:

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

So for the given point, the coordinates of the image will be:

(1, -6) ---> (-1, -(-6)) ---> (-1, 6)

If you look at the graph, the line crosses the y axis at (0,3).

That means you can eliminate the inequality that shows the y intercept as -3 (which is the 3rd option)

Also the inequality has to have y ≤ ....     so that the correct part of the graph is shaded. This elimates all of the inequalities that has y ≥ ... ( which is the 2nd and 4th option)

This leaves you with only the first inequality left:

y ≤ 2x² - 8x + 3

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

Answer

y ≤ 2x² - 8x + 3

Answer:

Yes,a similar formula is used to find all the products

Step-by-step explanation:

The formula applied in this case is;

(a+b)²=   (a+b) (a+b)= a(a+b)+b(a+b) = a²+ab+ab+b²= a²+2ab+b²

In the first one;

[tex](x+3)^2= (x+3) (x+3) = x(x+3)+3(x+3) = x^2 +3x+3x+9  = x^2 +6x +9[/tex]

In the second one;

[tex](x+4)^2 = (x+4) (x+4) = x(x+4)+ 4(x+4) = x^2 +4x+4x+16 = x^2 +8x+16[/tex]

⇒This is the same for the third and fourth product.

Answer:

3rd option is right

Step-by-step explanation:

[tex]77500[/tex]

In this case, the digit in the hundredths place is a [tex]5[/tex].  We need to take a look at the next digit to the right, which is a [tex]4[/tex].

Since it is [tex]4[/tex] or less, we can simply replace the [tex]4[/tex] and the rest of the digits to the right with [tex]0[/tex]s to round it.

If the [tex]4[/tex] was [tex]5[/tex] or more, we would round the [tex]5[/tex] up to [tex]6[/tex] and replace the remaining digits to the right with [tex]0[/tex]s.

Answer:

77500

Step-by-step explanation:

To round something to the nearest hundred, we first look to the 10s digit. It is 4. Since 4 is less than 5, then we keep the same hundreds place. So we get 77500.

Answer:

see below

m = males = 50

e = females = 25

a = adults = 7

Step-by-step explanation:

Givens

Let the adults = a

let the males students = m

lef the female students = e

Equations

a + m + e = 82                                  

m = 7*a + 1

e = 1/2 * (7a + 1)

Solution

a + 7a + 1 + 1/2(7a + 1) = 82                 Remove the brackets on the left.

a + 7a + 1 + 3.5*a + 1/2 = 82                Combine the like terms on the left.

11.5a + 1.5 = 82                                    Subtract 1.5 from both sides.

11.5a + 1.5 - 1.5 = 82 - 1.5                     Combine

11.5a = 80.5                                          Divide by 11.5

a = 80.5/11.5

a = 7                  

The number of adults = 7

===============================

m = 7a + 1

m = 7*7 + 1

m = 50

===============================

e = 1/2 m

e = 1/2 * 50

e = 25

Answer:

= 135 m²

Step-by-step explanation:

First we divide the kite into 2  isosceles triangles

The bigger triangle has base angles = 45°

We can use these angle as follows to find the common base of the two triangles.

Cos 45=adjacent/9√2

Adj=9√2×cos 45

=9

common base =9×2=18

We can use the angle 45° above to find the height of the bigger triangle.

Tan 45°=opposite/adjacent

Opposite = adjacent×Tan 45

=9 tan 45=9

Area =1/2BH+1/2Bh where B is the common base H is the height of the big triangle, h represents the height of the smaller triangle.

A=1//2× 18 × 9 +1/2× 18 × 6

= 135 m²

Answer:

1) binomial

2) monomial

Step-by-step explanation:

mono-think one

bi-think two

tri-think thee

poly-1 or more

So 1 goes with binomial

and 2 goes with monomial

See if you can figure out 3 and 4

I can check them.