find the missing side

Answer:

3.4657359...

Step-by-step explanation:

just put into your phone calculator 32 then hit In.

The value of ln 32 is 3.468 .

Logarithm is an inverse of Exponentiation , The power to which a number must be raised in order to obtain another number is known as a logarithm.

It is given that

ln 2 = 0.693

ln 32 = ?

32 = 2⁵

ln 32 = ln 2⁵

ln aⁿ = n ln a

ln 32 = 5 ln 2

ln 32 = 5 * 0.6936

ln 32 = 3.468

Therefore the value of ln 32 is 3.468 .

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ANSWER

[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]

EXPLANATION

The given function is

[tex] \frac{ - 12x}{ \sqrt{x} - 10 } [/tex]

In the denominator we have

[tex] \sqrt{x} - 10[/tex]

The conjugate of this surd is

[tex] \sqrt{x} + 10[/tex]

To rationalize this function, we multiply both the numerator and the denominator by the conjugate surd.

[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x} - 10)(\sqrt{x} + 1)} [/tex]

We apply the identity

[tex] (a + b)(a - b) = {a}^{2} - {b}^{2}[/tex]

in the denominator.

This implies that,

[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x})^{2} - {10}^{2} } [/tex]

[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]

Answer:

Step-by-step explanation:

In this question we will find the equation of the dotted line first.

Since this line passes through two pints (0, 2) and (-3, -7)

So slope of the line will be m = [tex]\frac{y-y'}{x-x'}[/tex]

                                                 = [tex]\frac{-7-2}{-3-0}[/tex]

                                                 = [tex]\frac{-9}{-3}[/tex]

                                                 = 3

y-intercept of the line is c = 2

Now we will put these values in the standard form of the equation

y = mx + c

y = 3x + 2

Now we will check the inequality shown by shaded region

we take a point from shaded region and plug in the value of x and y.

For point ( -2, 0) y = (-2)(2)+2

                              = -4 + 2 = -2 and 0>-2

So there should be the sign of greater than.

Therefore, inequality will be y > 3x + 2

Linear inequality represented by the graph is y > 3x +2 and this can be determine by using the slope intercept form.

Given :

Two points - (0 , 2) and (-3 , -7)

Slope of the line can be calculated as follows:

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-7-2}{-3-0}=3[/tex]

y intercept is 2.

Now we know that the slope intercept form is given by:

y = mx + c

y = 3x + 2 --- (1)

To check the inequality we take a point from the shaded region and plug in the value of x and y.

At Point (-3,0), equation (1) can be given by:

y = -9 + 2 = -7 < 0

Than inequality must be y > 3x + 2.

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Answer:

3(x-2)+x=4x+6

Step-by-step explanation:

case 1) we have

3(x-2)+x=4x-6

Solve for x

3x-6+x=4x-6

4x-6=4x-6

0=0 ----> is true for any value of x

therefore

The equation has infinite solutions

case 2) we have

3(x-2)+x=2x-6

3x-6+x=2x-6

4x-2x=-6+6

2x=0

x=0

case 3) we have

3(x-2)+x=3x-3

3x-6+x=3x-3

4x-3x=-3+6

x=3

case 4) we have

3(x-2)+x=4x+6

3x-6+x=4x+6

4x-4x=6+6

0=12 ------> is not true

therefore

The equation has no solution

Answer:

Step-by-step explanation:

The first equation is the one that doesn't have solution. Let's demonstrate this:

[tex]3(x-2)+x=4x+6\\3x-6+x=4x+6\\4x-6=4x+6\\4x-4x=6+6\\0=12[/tex]

As you can observe, the equation doesn't have any solutions, because it result in a false statement.

If we solve the other equations, we would have:

[tex]3(x-2)+x=2x-6\\3x-6+x=2x-6\\4x-6=2x-6\\4x-2x=-6+6\\2x=0\\x=0[/tex]

[tex]3(x-2)+x=3x-3\\3x-6+x=3x-3\\4x-3x=-3+6\\x=3[/tex]

[tex]3(x-2)+x=4x-6\\3x-6+x=4x-6\\4x-6=4x+6\\6=6[/tex]

The last equation has infinite solutions.

Therefore, the only one that doesn't have any solutions is

Answer:

-3

Step-by-step explanation:

First, solve what's inside the absolute value lines. -5+2=-3

Because it's in absolute value lines, the negative becomes a positive so |-3|=3

The result is -3 (because we still have that negative sign outside the absolute value lines.

Answer:

The travel time of the trip is 8.55 hours

Step-by-step explanation:

The average speed of an object is calculated using the following formula:

[tex]s=\frac{d_2 -d_1}{t}[/tex]

Where [tex]d_2 - d_1[/tex] is the total distance traveled by the object and t is the time it took the object to travel that distance.

So we know that:

[tex]d_2 - d_1=342\ miles[/tex]

[tex]s=40\ mph[/tex]

Therefore:

[tex]40=\frac{342}{t}[/tex]

[tex]t=\frac{342}{40}[/tex]

[tex]t=8.55\ hours[/tex]

Answer: 8 hours and 33 minutes

Step-by-step explanation:

you can set up a ratio, cross multiply, and divide.

Answer:

1. Simplify the inequality  5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4):

15.3+11.22x>-14.25-10.2x-24 10;15.3+11.22x>-10.2x-38.75.  

2. Separate terms with x and without x in different sides:

11.22x+10.2x>-38.75-15.3.

3. Add similar terms:

21.42x>-54.05.  

4. Divide by 21.42:

x>-54.05/21.42

x>-2.5

Step-by-step explanation:

i think this question already been solved:

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Answer:

degree 5

Step-by-step explanation:

(fg)(x) = f(x) × g(x)

f(x) × g(x) = 3x²(4x³ + 1) = 12[tex]x^{5}[/tex] + 3x²

The degree of the polynomial is determined by the value of the largest exponent, that is

12[tex]x^{5}[/tex] ← largest exponent of 5

Hence (fg)(x) is of degree 5

Answer:

30 sq. units

Step-by-step explanation:

Multiply the length of the two diagonals together and divide by two

[tex]\frac{d1 * d2}{2}[/tex]

10 * 6 = 60

60/2 = 30

The area of the kite is 30 sq. units

Answer: B

Step-by-step explanation:

How to get the area of a rhombus

( diagonal x the other diagonal )1/2

(6*10)1/2

60*1/2

30

Answer:

B; 18

Step-by-step explanation:

9/11 = 18/22

Answer:

the correct answer will be D) 9

Step-by-step explanation:

Answer:

20°

Step-by-step explanation:

One way of doing this is to find the constant of proportionality, k:

8k + 6k + 4k = 90°    Then 18k = 90°, and k turns out to be 90/18, or 5.

Then the angles are 8(5), 6(5) and 4(5).  The smallest of these angles is thus 20°

let's recall that the sum of all interior angles in a triangle is 180°.

we know the angles are in a 8:6:4 ratio, so we simply divide 180 by (8+6+4) and then distribute accordingly.

[tex]\bf 8:6:4\qquad \qquad \left( 8\cdot \cfrac{180}{8+6+4} \right) : \left( 6\cdot \cfrac{180}{8+6+4} \right) : \left( 4\cdot \cfrac{180}{8+6+4} \right) \\\\\\ (8\cdot 10):(6\cdot 10):(4\cdot 10)\implies 80~:~60~:~\stackrel{\textit{smallest}}{40}[/tex]

Answer:

No real solutions

Step-by-step explanation:

Using the quadratic formula, you will end up with a square root of a negative number in the numerator. Hence there is no real solution.

see attached.

The solution to the equation x^2 + 3x + 4 = 0 can't be computed using real numbers, because the formula we use (the quadratic formula) results in the square root of a negative number. Therefore, the solutions will be in the form of complex numbers.

The subject question falls under Mathematics, specifically algebra. The equation given is a standard form of a quadratic equation. The general form of a quadratic equation is ax2 + bx + c = 0.

To find the solution for the equation x2 + 3x + 4 = 0, we usually use the quadratic formula x = [-b ± sqrt(b2 - 4ac)] / 2a. Applying this formula, we can put a = 1, b = 3 and c = 4. However, when we compute b2 - 4ac, which is 9 - 16, we receive a negative result (-7). This implies that the equation has no real solutions, because square roots of negative numbers are not real numbers, they are complex numbers.

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Answer:

The measures of two complementary angles are 63° ,  27°

Step-by-step explanation:

The measures of two complementary angles are 6y + 3 and 4y - 13.

Sum of complementary angles = 90°

6y + 3  + 4y - 13 =  90°

10y - 10 =  90°

10y = 90 + 10 = 100

10 y = 100

y    = 100/10 = 10

One angle = 6y + 3 = 6 * 10 + 3 = 60 + 3 = 63

other angle = 4y - 13 = 4 * 10 - 13 = 40 - 13 = 27

The angles are 63° ,  27°

Answer:

Option D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Step-by-step explanation:

step 1

we know that

The SSS Similarity Theorem , states that If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar

In this problem

[tex]\frac{HG}{JK}=\frac{GF}{JL}=\frac{HF}{KL}[/tex]

Verify

substitute the values

[tex]\frac{48}{12}=\frac{32}{8}=\frac{36}{9}[/tex]

[tex]4=4=4[/tex] ---> is true

therefore

The triangles are similar by SSS similarity theorem

step 2

we know that

The SAS Similarity Theorem , states that two triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

In this problem

Two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

therefore

The triangles are similar by SAS similarity theorem

Answer:

D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Step-by-step explanation:

Edge 2020 (2021)

Answer:

lcm = 352

Step-by-step explanation:

32 = 2 × 2 × 2 × 2 × 2 = [tex]2^{5}[/tex] ← product of prime factors

44 = 2 × 2 × 11 = 2² × 11 ← product of prime factors

lowest common multiple (lcm) = [tex]2^{5}[/tex] × 11 = 352

32 = 2*2*2*2*2 = 2^5

44 = 2*2*11 = 2^2*11

We take common and non-common numbers with the highest exponent and we multiply them.

2^5*11 = 32*11 = 352.

Answer:

-1/5x +1/2

ghiybifvcodtgy78

Answer:

b.[tex]y=-\frac{1}{5}x+\frac{1}{2}[/tex]

Step-by-step explanation:

We have to find the linear which has same slope  as the slope represented by the table.

Slope formula :m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

By using the formula and substitute [tex]y_1=\frac{1}{5},y_2=\frac{7}{50},x_1=-\frac{1}{2},x_2=-\frac{1}{5}[/tex]

Slope=[tex]\frac{\frac{7}{50}-\frac{1}{5}}{-\frac{1}{5}+\frac{1}{2}}[/tex]

Slope=[tex]\frac{-\frac{3}{50}}{\frac{3}{10}}[/tex]

Slope=[tex]-\frac{3}{50}\times \frac{10}{3}[/tex]

Slope=[tex]-\frac{1}{5}[/tex]

a.[tex]y=-\frac{1}{2}x+\frac{1}{10}[/tex]

Compare with

[tex]y=mx+b[/tex]

we get m=[tex]-\frac{1}{2}[/tex]

Slope=[tex]-\frac{1}{2}[/tex]

Hence, option A is false.

b.[tex]y=-\frac{1}{5}x+\frac{1}{2}[/tex]

Slope of given function=[tex]-\frac{1}{5}[/tex]

It is true.

c.[tex]y=\frac{1}{5}x-\frac{1}{2}[/tex]

Slope of given function=[tex]\frac{1}{5}[/tex]

Hence, option is false.

d.[tex]y=\frac{1}{2}x-\frac{1}{10}[/tex]

Slope of given function=[tex]\frac{1}{2}[/tex]

Hence, option is false.

Answer:

3x - 6 < 12

3x < 18

x < 6

X could be numbers that's less than 6

[tex]3 x - 6 < 12 \\3x<18\\x<6[/tex]

Change f(x) to y , switch x and y , and solve for y.

                   [tex]f^{-1}x=\dfrac{\ln (x+4)}{2}[/tex]

We know that while finding the inverse of a function the following steps are to be followed:

We are given a function f(x) by:

[tex]f(x)=e^{2x}-4[/tex]

Now, we put

[tex]f(x)=y[/tex]

i.e.

[tex]e^{2x}-4=y[/tex]

Now, we interchange x and y as follows:

[tex]e^{2y}-4=x[/tex]

and finally we solve for y

i.e.

[tex]e^{2y}=x+4[/tex]

Taking logarithmic function both the side of the equation we get:

[tex]2y=\ln (x+4)\\\\i.e.\\\\y=\dfrac{\ln (x+4)}{2}[/tex]

i.e.

[tex]f^{-1}x=\dfrac{\ln (x+4)}{2}[/tex]

Answer: the rectangular

Step-by-step explanation:

All the sides are equal for a regular polygon

Answer:

The Rectangle Is Not A Regular Polygon, Option 2

Step-by-step explanation:

For a polygon to be regular all sides and angles have to be the same! A square is an example of a regular polygon, since all sides and angles are even, a rectangle is not.

Answer:

[tex]\large\boxed{x=0\ \vee\ x=1}[/tex]

Step-by-step explanation:

[tex]Domain:\\\\x-2\neq0\ \wedge\ x+1\neq0\\\\x\neq2\ \wedge\ x\neq-1\\\\\boxed{D:\ x\in\mathbb{R}-\{-1,\ 2\}}\\\\=============================[/tex]

[tex]\dfrac{x}{x-2}+\dfrac{x-1}{x+1}=-1\qquad\text{subtract}\ \dfrac{x-1}{x+1}\ \text{from both sides}\\\\\dfrac{x}{x-2}=-1-\dfrac{x-1}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-(x+1)}{x+1}+\dfrac{-(x-1)}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-(x+1)-(x-1)}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-x-1-x+1}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-2x}{x+1}\qquad\text{cross multiply}[/tex]

[tex]x(x+1)=-2x(x-2)\qquad\text{use the distributive property}\\\\(x)(x)+(x)(1)=(-2x)(x)+(-2x)(-2)\\\\x^2+x=-2x^2+4x\qquad\text{add}\ 2x^2\ \text{to both sides}\\\\3x^2+x=4x\qquad\text{subtract 4x from both sides}\\\\3x^2-3x=0\qquad\text{distributive}\\\\3x(x-1)=0\iff 3x=0\ \vee\ x-1=0\\\\x=0\in D\ \vee\ x=1\in D[/tex]

Answer:

Step-by-step explanation:

I'm taking this to mean

x/(x-2) + (x-1)/(x+1)  =  -1

Multiply through by (x - 2)*(x + 1) to get rid of the denominator on the left.

x(x + 1) + (x - 1)(x - 2) = -1 * (x - 2)(x + 1)

Remove the brackets on the left and right.

Be careful about the right side. Do it in two steps (or three)

x^2 + x + x^2 - 3x + 2 = - (x^2 - 2x + x - 2)  

2x^2 - 2x + 2 = - (x^2 - x - 2)

2x^2 - 2x + 2 = - x^2 + x + 2

Bring the right side to the left

2x^2 - 2x + 2 + x^2 - x - 2 = 0

3x^2 - 3x = 0

Factor this

x*(3x - 3) =0

x = 0

3x - 3 = 0

Add 3 to both sides.

3x = 3

Divide by 3

x = 3/3

So either x = 0

or

x = 1

Just to confirm that that is correct, a graph is included which shows the x roots are 0 and 1

Answer:

Should be 5, hopes this helps

Step-by-step explanation:

That's it.

Final answer:

To find the original number, we use the equation 2x + 1 = 11; solving for x gives us the number 5.

Explanation:

To find the number that when doubled and added to 1 gives 11, we can set up a simple algebraic equation to solve for the unknown number. Let's call the unknown number x. According to the problem, if we double the number (2x) and then add 1, the result is 11. So, our equation is 2x + 1 = 11.

Next, we can solve for x by subtracting 1 from both sides of the equation, giving us 2x = 10. Finally, we divide both sides by 2 to isolate x, resulting in x = 5. Thus, the number we're looking for is 5.

To see if 8 is the solution to the equation,  3 (x - 2) + 4 = 22, you must replace x with 8 and solve using the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction) REMEMBER: IF NOT APPLICABLE TO THE EQUATION YOU MAY SKIP THAT STEP IN PEMDAS . If the sides are equal to each other then 8 IS a solution.

3(8 - 2) + 4 = 22

Parentheses...

3(8 - 2) + 4 = 22

8 - 2 <<<In the parentheses so you must solve first

6

so...

3(6) + 4 = 22

Multiplication...

3(6) + 4 = 22

3 * 6

18

so..

18 + 4 = 22

Addition...

18 + 4 = 22

18 + 4

22

so...

22 = 22

Are they equal to each other? YES!!!

8 is a solution to the equation 3 (x - 2) + 4 = 22

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

200 more on Friday than thursday

you can't solve this nor find the value of y because its not a full equation

Answer:

You cant solve for y without knowing the end number.

Step-by-step explanation:

maybe your equation y + 30 = 32 then we would know y is = to 2

Answer:

5x - 8

Step-by-step explanation:

(2x - 7) + (3x - 1)

We would first solve for whatever is in the parenthesis, but there is a variable with both expressions, so we need to remove it to simplify:

2x - 7 + 3x - 1

Now combine like terms and simplify:

2x + 3x - 7 - 1

So the answer is 5x - 8

Final answer:

To add the expressions (2x-7) and (3x - 1), simply combine the like terms, resulting in 5x - 8.

Explanation:

When you are tasked with adding the expressions (2x-7) and (3x - 1), you combine like terms. This means you add the coefficients of the same powers of x together and combine the constants. To demonstrate:

(2x-7) + (3x - 1) = (2x + 3x) + (-7 - 1)

You combine the x terms:

2x + 3x = 5x

And then combine the constants:

-7 - 1 = -8

Thus, the sum of the expressions is:

5x - 8

Answer:

f(2) = -6

Step-by-step explanation:

f(x) = 3x - 12

Plug in 2 for x & solve:

f(2) = 3(2) - 12

Remember to follow PEMDAS. First multiply, then subtract:

f(2) = 3(2) - 12

f(2) = 6 - 12

f(2) = -6

f(2) = -6 is your answer.

~

Answer:

[tex]r=180-\frac{7\pi }{12}[/tex]

Step-by-step explanation:

To find the reference angle of a given angle, first of all, the quadrant of the given angle is determined.

So for 7pi/12

The quadrant is 2nd.

For the angle belonging to 2nd quadrant the equation for reference angle will be:

r=180 - theeta

[tex]r=180-\frac{7\pi }{12}[/tex]

Answer:

B hope I helped.

Step-by-step explanation: