Solve the equation using the square root property:*

3x2 - 30 = 0

Answer:

The Pythagorean theorem states that, for all 90-degree triangles, the relationship between the lengths of the sides is given by the formula a^2 + b^2 = c^2.

DISTANCE FORMULA

The study of geometry in a graphical environment is called co-ordinate geometry.

In co-ordinate geometry, the standard formula for calculating the distance between 2 points is called the distance formula.

Step-by-step explanation:

Answer:

Short answer: They are essentially the same thing.

The distance formula is derived from the Pythagorean Theorem

We have distance formula:

[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Pythagorean Theorem:

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

The shortest distance between two points if a line. If you draw a line in the cartesian plane both points will have an x-coordinate and y-coordinate. Note that it forms a right triangle! Therefore, the distance between those points is the hypotenuse.

We can have a point [tex]a=(x_{1}, y_{1})[/tex] and point [tex]b=(x_{2}, y_{2})[/tex]

But once [tex]a[/tex] and [tex]b[/tex] can be positive or negative:

[tex]c = \sqrt{a^2+b^2}= D = \sqrt{(\pm a)^2+(\pm b)^2}[/tex]

The answer is f(x)=1/2x+25

Answer:

7/8 < 15/16

Step-by-step explanation:

Get a common denominator of 16

7/8 *2/2

14/16

14/16 < 15/16

so 7/8 < 15/16

Answer:

Look at the attachment

Answer:

The answer is 108.

Step-by-step explanation:

This can be solved with a simple proportion. 5/12 = 45/1. For 5 to become 45, you need to multiply by 9. You do the same to the denominator. 12 times 9 is 108.

Answer: z = 28 degrees

Step-by-step explanation:

Since this is an isosceles triangle, two of the angles are congruent.

180 - 124 = 56

56/2 = 28

To list out the range, you list the y coordinate values of each point of the function. Each point is of the form (x,y). Any duplicate values are tossed out when we talk about a set. All we care about are the unique values. It's common practice to sort the values of the set from smallest to largest.

Side note: Choice A is listing the x values of each point, which is the domain.

-3x-4= +12

X negative 3 and 4 then add +12 to it.

Answer:

x = 27

Step-by-step explanation:

4(x−9)=4(9+1/3x).

Divide each side by 4

(x−9)=(9+1/3x)

Subtract 1/3 x from each side

x - 1/3x -9 = 9+1/3x -1/3x

2/3x -9 = 9

Add 9 to each side

2/3x -9+9 = 9+9

2/3x = 18

Multiply each side by 3/2

3/2 * 2/3x = 18*3/2

x = 27

Answer:

27

Step-by-step explanation:

4(x−9)=4(9+1/3x)

4x-36=36+(4/3)*x

(12/3)*x-36=36+(4/3)*x

(8/3)*x=72

8x=216

x=27

Your answer would be approximately 30.93

Volume of a sphere is V=4 /3πr^3

3(x-1)-8=4(1+x)+5  

One solution was found :

                  x = -20

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*(x-1)-8-(4*(1+x)+5)=0  

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((3•(x-1))-8)-(4•(x+1)+5)  = 0  

Step  2  :

Equation at the end of step  2  :

 (3 • (x - 1) -  8) -  (4x + 9)  = 0  

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  -x - 20  =   -1 • (x + 20)  

Equation at the end of step  4  :

 -x - 20  = 0  

Step  5  :

Solving a Single Variable Equation :

5.1      Solve  :    -x-20 = 0  

Add  20  to both sides of the equation :  

                     -x = 20

Multiply both sides of the equation by (-1) :  x = -20

One solution was found :

                  x = -20

hope this is wht u wanted

Answer:  y = 0x+3 or y = 3

The slope is 0 and the y intercept is 3. So m = 0 and b = 3.

Plug those into y = mx+b to get y = 0x+3, and that simplifies to y = 3.

This graphs out a horizontal line that passes through the two points (0,3) and (1,3).

Answer: 2/8, 4/8, 4/4, 8,8

Step-by-step explanation:

They all have the denominator of 8.

Answer:

see below

Step-by-step explanation:

Since the initial value is 5 and it increases by 3 every time x goes up the equation is y = 5 * 3^x.

Answer:

The equation for this function in point slope form: y = -3x+47

Step-by-step explanation:

We are given that a swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour.

Slope is the rate of change per unit represented by m

So, m = -3

General equation : y = mx+c ----1

y represents the depth of water

t represents the time

The depth of the water after 5 hours is 32 inches.

So, y =32 and x =5

Substitute the values in the equation

So,32=-3(5)+c

32=-15+c

32+15=c

47=c

Substitute the value of c and m in 1

So, The equation for this function in point slope form: y = -3x+47

Answer:

C

Step-by-step explanation:

x-intercept occurs when y=0.

2x -3y= 8

When y=0,

2x -3(0)= 8

2x= 8

x= 8 ÷2

x= 4

Thus the coordinates is (4,0).

Answer:

Wrote it in the explanation :)

Step-by-step explanation:

Expression One: c + 25% = price of gas in august

Expression Two: c + 0.25 = price of gas in august

Expression Two would be easier to use if we knew "c" because the numbers are already in decimal form. If it were in percentage form, it would cause us an extra step to  convert it into a decimal.

Please tell me if you have any further questions...

Hope this helped!!

Answer:

a = -7

b = 0

c = 4

Step-by-step explanation:

Answer:

5x⁵4x³+2x²+5x+3

Polynomials will be closed under an operation if the operation produces another polynomial. (2x2 + 3x + 4) + (x2 - 5x - 3) = 3x2 - 2x + 1

Step-by-step explanation:

Answer:

$535.78

Step-by-step explanation:

First find out the annual earnings. So multiply 3.4% by 445

0.034 x 445 = 15.13

That's what the account earns every year. Now multiply it by 6 to know what it'll get in 6 years.

15.13 x 6 = 90.78

Now add that to the initial value.

90.78 + 445 = 535.78

That's the balance in the account after 6 years...

$535.78

Answer:

10 ft^3

Step-by-step explanation:

if a cube is 1/3ft then 3 cubes = 1ft

then 30 cubes = 10ft^3

Answer:

a and b are similarity i think that's what your looking 4 idk

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

This problem can be solved using concept of Pythagoras theorem.

Pythagoras theorem states that in a right angled triangle, if "a" and "b" are sides containing the right angle and h is hypotenuse then the relation between them is [tex]a^2 + b^2 = h^2[/tex]

_________________________________________

Given in the problem

a = 24

b = x

h = x+12

applying Pythagoras theorem

[tex]24^2 + x^2 = (x+12)^2\\=> 576 + x^2 = x^2 + 24x + 144\\=>576 = x^2 + 24x + 144 - x^2\\=> 576 = 24x + 144 \\=> 576 - 144= 24x\\=> 432 = 24x\\=> x = 432/24 = 18[/tex]

for (x+12)^2 we have used formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]

Thus, value of x is 18.

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Given:

[tex]\bold{f(x)= (\frac{3}{2})^x}\\\\\bold{g(x)= (\frac{2}{3})^x}\\[/tex]

Following are the graph attachment to this question:

The second function, that is [tex]g(x)= (\frac{2}{3})^x[/tex] is not even a function.

Remember that g(x) function is the inverted f(x) function. And when you see this pattern, a reflection on the Y-axis expects you.

Reflection in the axis.

In x-axis:

Increase the function performance by -1 to represent an exponential curve around the x-axis.

In y-axis:

Increase the input of the function by -1 to represent the exponential function around the y-axis.

We want to compare the graphs of the two given functions. We will see that the graph of g(x) is the graph of f(x) reflected across the line y = x.

The given functions are:

f(x) = (3/2)*x

g(x) = (2/3)*x

Note that each point on the line f(x) is written as:

(x, (3/2)*x)

And each point on the line g(x) is written as:

(x, (2/3)*x)

Now, if we multiply both sides of the above point by (3/2) we will get:

((3/2)*x, x)

Now, remember that for a general point (x, y), if we apply reflection across the line y = x, we get.

(y, x)

So the order of the values changes, exactly as we can see for f(x) and g(x).

Then we can conclude that g(x) is obtained by reflection f(x) across the line y = x.

Then the graph of g(x) is the graph of f(x) reflected across the line y = x.

If you want to learn more, you can read:

https://brainly.com/question/14536884

Answer:

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

 Step-by-step explanation:

Step(i):-

Given h(x) = - 16 x² + 48 x +6   ...(i)

Differentiating equation (i) with respective to 'x'

[tex]h ^{l} (x) = - 16 (2 x) +48 (1)[/tex]   ...(ii)

Equating Zero

- 3 2 x + 4 8 = 0

- 32 x = - 48

    x = 1.5

step(ii):-

The maximum height of the ball 'x' = 1.5

Again Differentiating equation (ii) with respective to 'x'

[tex]h ^{ll} (x) = - 16 (2 x) < 0[/tex]

The maximum height 'x' = 1.5

h(x) = - 16 x² + 48 x +6  

h(1.5) = - 16 (1.5)² +4 8 (1.5) +6

         =   42

The maximum height at x = 1.5 is  = 42

Final answer:-

i) The maximum height  of the ball 'x' = 1.5 seconds

ii)   The maximum height  = 42

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

[tex]-3x-8+6=7[/tex]

[tex]-3x-2=7[/tex]

[tex]-3x-2+2=7+2[/tex]

[tex]-3x=9[/tex]

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

[tex]-x=3[/tex]

[tex]x=-3[/tex]

Answer:

Since the first number after the decimal is lower than 5, you would need to round down.  So the answer would be 17(not 18).

Step-by-step explanation:

Answer:

y=(x+2)²-3

Step-by-step explanation:

when y=x² shifted 3 units down

its eq. is y=x²-3

when it is also shifted 2 units left then its eq. is

y=(x+2)²-3

Answer:

7x3 + 5x2 + 5

x2

= 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sum =6

Product =5

Factors = 5 , 1

x² + 6x + 5 = x² + x + 5x + 5*1

                  = x(x + 1) + 5(x+1)

                 = (x+1) (x +5)

[tex]\frac{x+5}{x^{2}+6x+5}=\frac{x+5}{(x + 1)(x+5)}\\\\=\frac{1}{x+1}[/tex]