why can two prime numbers only have one common factor?

Given:

The three exterior angles of a pentagon measures 60,80 and 90.

To find:

The measure of other two exterior angle, assuming them equally.

Solution:

Let x be the measure of two other exterior angles of the pentagon.

We know that the sum of all exterior angles of a pentagon is 360 degrees.

[tex]60^\circ+80^\circ+90^\circ+x+x=360^\circ[/tex]

[tex]230^\circ+2x=360^\circ[/tex]

[tex]2x=360^\circ-230^\circ[/tex]

[tex]2x=130^\circ[/tex]

Divide both sides by 2.

[tex]\dfrac{2x}{2}=\dfrac{130^\circ}{2}[/tex]

[tex]x=65^\circ[/tex]

Therefore, the measures of both exterior angles are 65 degrees.

Answer:

shift

Step-by-step explanation:

shift

Answer:

Step-by-step explanation:

1.

7 > 0.7 > 0.07 > 0.007

2.

5h - 15hg

taking 5h common

5h (1 - 3g)

3.

5(2x- 1) = 35

dividing both sides by 5

2x - 1 = 7

2x = 7 + 1

2x = 8

x = 4

4.

if x is an odd number x + 2 will also be odd.

for example

11 is an odd number

on adding 2 we get 13 which is also an odd number.

Answer:

C

Step-by-step explanation:

AB + BC = AC , that is

5x + 4 + 4x - 8 = 23

9x - 4 = 23 ( add 4 to both sides )

9x = 27 ( divide both sides by 9 )

x = 3

Then

AB = 5x + 4 = 5(3) + 4 = 15 + 4 = 19 → C

Answer:

9x

Step-by-step explanation:

(x² + 2x) - (x² - 7x) ← distribute parenthesis

= x² + 2x - x² + 7x ← collect like terms

= 9x

Answer:

9x

Step-by-step explanation:

( x ² + 2 x ) - ( x² - 7 x )

Simply the expression

Remove unnecessary parantheses

combine like terms

Answer:

_-3__ + (-9) = -12

Step-by-step explanation:

___ + (-9) = -12

-9 is being added to the blank. You want the blank alone (isolated) on the left side. The opposite operation to adding a -9 is to add a positive 9.

You must do the same operation to both sides of an equation.

Add 9 to both sides.

___ + (-9) + 9 = -12 + 9

___ + 0 = -3

___ = -3

Answer: -3

Answer:

-3

Step-by-step explanation:

Hi there!

___ + (-9) = -12

Adding a negative number is the same as subtracting

___ - 9 = -12

To isolate the blank, we can add 9 to both sides of the equal sign so there won't be a -9 on the left side

___ - 9 + 9 = -12 + 9

___ = -12 + 9

___ = -3

Therefore, the number is -3.

I hope this helps!

Answer:

3x + 5 = 23

Step-by-step explanation:

Let x represents the number of persons in her group.

Since she brings 3 markers for each person, then number of markers brought for persons in her group = 3x.

She brings 5 extra markers for each person to share.

Thus, total markers she brought is now;

3x + 5

She brought 23 markers in all.

Thus, equation that represents the information is;

3x + 5 = 23

Answer:

1) Less than

2) greater than

Step-by-step explanation:

Equation of the first line:

(y+7)/(-13+7) = x/-1

(y+7))/-6 = -x

y+7 = 6x

y= 6x - 7

Equation of the second line:

A (4/3,0) ; B (0,8)

y/8 = (x-4/3)/-4/3

y/8 = (x-4/3) * -3/4

y/8 = -3/4x + 1

y = -6x + 8

Answer:

8

Step-by-step explanation:

Find 1/3 of 24, which is 8.

Answer:

Sam gave 8 balls to Rita.

Step-by-step explanation:

24 / 3 = 8

1/3 of 24 is 8, therefore Sam gave 8 balls to Rita.

Answer:

x = 3

Step-by-step explanation:

Hi there!

1) Prove similarity

The two triangles are similar due to angle-angle similarity. They both have an angle measured 90 degrees and the angles of the two corners that touch are equal, because opposite angles are equal.

2) Solve for x

Now, we can set up a proportion to solve for x:

[tex]\frac{x}{4} =\frac{4.5}{6} \\x=\frac{4.5}{6} *4\\x=3[/tex]

Therefore, x is 3 units long.

I hope this helps!

Answer:

B. (negative infinity, -1)

The values that complete the table are -14, -8, -2 and 4

Given the function y = 3x - 8, we are to complete the given table.

If x = -2

y = 3(-2) - 8

y = -14

If x = 0

y = 3(0) - 8

y = -8

If x = 2

y = 3(2) - 8

y = -2

If x = 4

y = 3(4) - 8

y = 4

Hence the values that complete the table are -14, -8, -2 and 4

Learn more on table of functions here: https://brainly.com/question/3632175

Answer:

hope this will help you more

Step-by-step explanation:

hope it is helpful to you

stay safe healthy and happy

Answer:

80in 2

Step-by-step explanation:

Answer:

a=(d1×d2)÷2

(20×12)÷2

240/2

120

x Almost-equals 2.2, y Almost-equals 2.4

Answer:

Its B

Step-by-step explanation:

correct on edge

the answer is in the picture above

Answer:

y = –|x - 1| + 3

Step-by-step explanation:

The "vertex" is (1 , 3)

y = –|x - 1| + 3

Answer:

From left to right, fill in 3.5 and 6.5

Step-by-step explanation:

Use the given formula to calculate y for the given values of x.

When x = 0.5, y = 3(0.5) + 1/0.5

y = 1.5 + 2

y = 3.5 if x = 0.5

When x = 2, y = 3(2) + 1/2

y = 6 + 0.5

y = 6.5 if x = 2

Answer:

Step-by-step explanation:

3===o===2=======1========0========-1=======x-2

I know this is backwards, but the question makes the choice of which direction is plus. o represents where anna lives.

Ben should be right at -2 where the x is.

Answer:

{2,6,14}

Step-by-step explanation:

The range are the f(x) values

the domain are the x values

So we have it that;

f(-1) = 4(-1) + 6 = 2

f(0) = 4(0) + 6 = 6

f(2) = 4(2) + 6 = 14

so we have the range as;

{2,6,14}

Answer:

5.18

Step-by-step explanation:

This is a chemistry question. However the solution to the problem is given below:

We'll begin by calculating the pOH of the solution. This can be obtained as follow:

Concentration of Hydroxide ion [OH¯] = 1.5×10¯⁹ M

pOH =?

pOH = –Log [OH¯]

pOH = –Log 1.5×10¯⁹

pOH = 8.82

Finally, we shall determine the pH of the solution. This can be obtained as follow;

pOH = 8.82

pH =?

pH + pOH = 14

pH + 8.82 = 14

Collect like terms

pH = 14 – 8.82

pH = 5.18

Therefore, the pH of the solution is 5.18

Answer:

5.18

Step-by-step explanation:

I took the test and got it right!

Răspuns:

8052

Explicație pas cu pas:

Al treilea termen al unei progresii aritmetice:

T (n) = a + (n - 1) d

Unde ;

a = primul termen; d = diferență comună = 4; n = al treilea termen (numărul termenului)

Al treilea (3) termen:

T (3) = a + (3-1) 4

T (3) = 12

12 = a + 2 (4)

12 = a + 8

12 - 8 = a

4 = a

Prin urmare, primul termen = a

Al 2013-lea mandat;

T (2013) = a + (2013-1) d

T (2013) = 4 + (2012) 4

T (2013) = 4 + 8048

= 8052

Answer:

The fraction of cup filled with water is 3/4.

Step-by-step explanation:

Antonia has a mug with a capacity of 2/3L of water. What fraction of that mug will she fill with 1/2L of water?

Capacity =  2/3 L

Amount of water = 1/2 L

Fraction of amount of water to the capacity of mug is

[tex]\frac{1}{2}\div \frac{2}{3}\\\\\frac{3}{4}[/tex]

Answer:

7.5         30

45         180

Step-by-step explanation:

The given line has x = 1.25 and y = 5.

y/x = 5/1.25 = 4

x is multiplied by 4 to get y since 1.25 * 4 = 5.

That means the equation is

y = 4x

For a proportional function, every value of x must be multiplied by 4 to get y.

x = 7.5

y = 4x = 4(7.5) = 30

7.5          30

We need to find the values for the last line.

11 * 4 = 44

There is no 44

13.75 * 4 = 55

There is no 55.

17.5 * 4 = 70

There is no 70

30 * 4 = 120

There is no 120.

45 * 4 = 180

There is a 180.

45         180

Answer:

7.5         30

45         180

Answer:

Units

Step-by-step explanation:

From the value above 478.92

4 represents hundreds

7 represents tens

8 represents units

Hence the answer is units

Answer:

z = - .5

Step-by-step explanation:

z = (x - μ)/ σ

z = 56 - 60/8 = -.5

Step-by-step explanation:

hi friend I can help you in this geometry work via Wazapp

Answer:

8(X^2+1)

Step-by-step explanation:

(X²+3)²-(X²-1)

(X²+3)(X²+3)-(X²-1)(X²-1)

X⁴+3X²+3X²+9-(X⁴-X²-X²+1)

X⁴+6X²+9-(X⁴-2X²+1)

X⁴+6X²+9-X⁴+2X²-1

8X²+8

Answer:

Procedure:

1) Form a system of 3 linear equations based on the two zeroes and a point.

2) Solve the resulting system by analytical methods.

3) Substitute all coefficients.

Step-by-step explanation:

A quadratic function is a polynomial of the form:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.

A value of [tex]x[/tex] is a zero of the quadratic function if and only if [tex]y = 0[/tex]. By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: [tex]A(x,y) = (r_{1}, 0)[/tex], [tex]B(x,y) = (r_{2},0)[/tex] and [tex]C(x,y) = (x,y)[/tex]

Based on such information, we form the following system of linear equations:

[tex]a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0[/tex] (2)

[tex]a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0[/tex] (3)

[tex]a\cdot x^{2} + b\cdot x + c = y[/tex] (4)

There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:

[tex]a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

And finally we obtain the equation of the quadratic function given two zeroes and a point.

Answer:

x = 10

Step-by-step explanation:

Mathematically, the sum of the interior angles of a triangle is 180

Thus, we have it that;

55 + 45 + (5x + 30) = 180

100 + 5x + 30 = 180

5x = 180-30-100

5x = 50

x = 50/5

x = 10