Find the distance between the points (6,5√5) and (4,3√2).
2, 2√2, 2√3

Answer:

-2

Step-by-step explanation:

Isolate the variable y. Note the equal sign, what you do to one side, you do to the other. Divide 3 from both sides:

(3y)/3 = (15 - 6x)/3

y = (15 - 6x)/3

y = 5 - 2x

Note the equation:

y = mx + b

m = slope

b = y-intercept

x & y = the point (x , y)

Note that the slope is directly next to x. -2 is your answer.

~

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]3y = 15-6x\\y = \frac {15} {3} - \frac {6x} {3}\\y = 5-2x\\y = -2x + 5[/tex]

So we have to:

[tex]m = -2[/tex]

Answer:

The slope is -2

Answer:

Step-by-step explanation:

[tex]9(2x+1)<9x-18\qquad\text{divide both sides by 9}\\\\2x+1<x-2\qquad\text{subtract 1 from both sides}\\\\2x<x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\x<-3\\\\-4<-3[/tex]

Answer:

[tex]x = 5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}[/tex]

Step-by-step explanation:

We need to solve the quadratic equation

6 = x^2 -10x

Rearranging we get,

x^2-10x-6=0

Using quadratic formula to solve the quadratic equation

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a= 1, b =-10 and c=6

Putting values in the quadratic formula

[tex]x=\frac{-(-10)\pm\sqrt{(-10)^2-4(1)(-6)}}{2(1)}\\x=\frac{10\pm\sqrt{100+24}}{2}\\x=\frac{10\pm\sqrt{124}}{2}\\x=\frac{10\pm\sqrt{2*2*31}}{2}\\x=\frac{10\pm\sqrt{2^2*31}}{2}\\x=\frac{10\pm2\sqrt{31}}{2}\\x = 5\pm\sqrt{31}[/tex]

So, [tex]x=5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}[/tex]

Answer:

The solutions are:

x1= 5 +√31

x2= 5 -√31

Step-by-step explanation:

We have 6=x^2-10x

Balance the equation by adding the same constant to each side

x^2-10x+25=6+25

x^2-10x+25=31

Rewrite as perfect square,

(x-25)^2=31

Taking square root at both sides

√(x-5)^2 = √31

x-5 = (+/-)√31

x1= 5 +√31

x2= 5 -√31

Therefore the solutions are x1= 5 +√31 , x2= 5 -√31

Answer:

B

Step-by-step explanation:

4x + 2y = 3

(send 2y to the right and 3 to the left)

4x - 3 = -2y

(divide everything by -2)

(4x)/(-2) - 3/(-2) = y

So now we have a function which is like

y = ax + c

c = the y value of intersection point of the equation and the y-axis

a = amount of increase in y values per x value

so in this example:

(4x/(-2)) = (4/(-2))x -> a = 4/(-2) = -2

and

c = -3/-2 = 3/2

So the graph that we're searching for is increasing (-2) y values (so decreasing 2 y values) per 1 x value and has an intersection with the y-axis where y = 3/2

Answer:

[tex](x-3)^{2}+(y+2)^{2}=49[/tex]

Step-by-step explanation:

The center-radius form of the equation of a circle is in the format;

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

with the center being at the point (h, k) and the radius being r units.

We simply plugin the values of the center and radius given in order to determine the equation of the circle;

The equation of the circle with center (3, -2) and radius 7 is;

[tex](x-3)^{2}+(y+2)^{2}=49[/tex]

Answer:

[tex](x-3)^2 + (y+2)^2 = 49[/tex]

Step-by-step explanation:

The general equation of a circle has the following form:

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

Where the point (h, k) represents the center of the circle and r represents the radius

In this case we know that the center is (3, -2) and the radius is 7.

Therefore:

[tex]h=3\\k = -2\\r=7[/tex]

Finally the equation of the circle is:

[tex](x-3)^2 + (y-(-2))^2 = 7^2[/tex]

[tex](x-3)^2 + (y+2)^2 = 49[/tex]

Answer:

34 degrees

Step-by-step explanation:

The measure of the angle ∠VXZ will be 34°. Then the correct option is C.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the angle ∠VXZ will be given as,

∠VXZ = 1/2(93 – 25)

∠VXZ = 1/2(68)

∠VXZ = 34°

Then the correct option is C.

More about the angled link is given below.

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Answer:

the number is -1

Step-by-step explanation:

Turn this into an equation. 4x = x-3

subtracting x from both sides gives

3x=-3

so x = -1

Hope this helps!

Answer:

(x - 7)(x - 8)

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the constant term (+ 56) which sum to give the coefficient of the x- term (- 15)

The factors are - 7 and - 8, since

- 7 × - 8 = + 56 and - 7 - 8 = - 15, hence

x² - 15x + 56 = (x - 7)(x - 8)

Answer:

LCM of 24, 36  = 72

Step-by-step explanation:

24 = 24, 48, 72, 96

36 = 36, 72, 109

Answer:

The LCM of 24 and 36 = 72

Step-by-step explanation:

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 24:

24, 48, (72), 96, 120

Multiples of 36:

36, (72), 108, 144

Hope this helped!

Answer:  B) F(x) = √x and G(x) = 3x + 2

Step-by-step explanation:

The composite function G(F(x)) is when you replace every x-value in the G(x) function with the F(x) function.

[tex]A)\ G(3x+2) = \sqrt{3x+2}\\\\B)\ G(\sqrt{x})=3(\sqrt{x})+2\quad =3\sqrt{x}+2\\\\C)\ G(\sqrt{x}+2) = 3\quad \text{there are no x-values in the G(x) function to replace}\\\\D) G(3\sqrt{x})=2\quad \text{there are no x-values in the G(x) function to replace}[/tex]

The only one that matches G(F(x)) = 3√x + 2 is OPTION B

Answer:  The correct option is (B) 7.

Step-by-step explanation:  Given that a karate studio charges $35 for the first course and $22.50 for each course after that, even if the student leaves the course early.

Cena paid $170 for her son to take courses.

We are to find the number of courses that he took.

Let x represents the number of courses that Cena took.

Then, according to the given information, we have

[tex]35+22.50\times (x-1)=170\\\\ \Rightarrow 22.50(x-1)=170-35\\\\ \Rightarrow 22.50(x-1)=135\\\\ \Rightarrow x-1=\dfrac{135}{22.50}\\\\\Rightarrow x-1=6\\\\ \Rightarrow x=7[/tex]

Thus, the required number of courses that Cena took is 7.

Option (B) is CORRECT.

Answer:

$1424.10

Step-by-step explanation:

APEX is obnoxious, I understand.

Answer:1424.10

Step-by-step explanation:

Answer:

3x^2-x-6

Step-by-step explanation:

f-g means you are going to do (3x^2-4)-(x+2)

3x^2-4-x-2

Combine like terms

3x^2-x-6

Answer:

[tex](f-g) (x) = 3x ^ 2- x - 6[/tex]

Step-by-step explanation:

We have the following functions

[tex]f (x) = 3x ^ 2-4[/tex]

[tex]g (x) = x + 2[/tex]

To find [tex](f-g) (x)[/tex] we must subtract the function f(x) with the function g (x)

Then we perform the following operation

[tex](f-g) (x) = 3x ^ 2-4- (x + 2)[/tex]

[tex](f-g) (x) = 3x ^ 2-4- x - 2[/tex]

[tex](f-g) (x) = 3x ^ 2- x - 2-4[/tex]

Finally we have that:

[tex](f-g) (x) = 3x ^ 2- x - 6[/tex]

To find the inverse of an equation just switch the places of the x and y, then solve for y like so...

(keep in mind that f(x) means the same thing as y)

original equation:

y = 4x + 8

switching x and y:

x = 4y + 8

x - 8 = 4y

[tex]\frac{1}{4}x[/tex] - 2 = y

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The shorter piece is 10 in. and the longer one is 50 in.

Step-by-step explanation:

First, let's set the shorter piece to be length x. Then the longer piece is 5x, or 5 times longer than the shorter piece.

Since both pieces combined equals to the length of the entire board, we can set these two lengths equal to it:

x + 5x = 60

And now solve for x:

6x = 60

x = 10 in (length of shorter piece)

Now let's find the length of the longer piece:

Longer = 5x = 5(10) = 50 in.

Answer:

2A/h = b

Step-by-step explanation:

A= (1/2)(b)(h)

Multiply each side by 2

2A = 2*1/2 *b*h

2A = bh

Divide each side by h

2A/h = bh/h

2A/h = b

Step-by-step explanation:

all work is pictured and shown

Answer:

25

Step-by-step explanation:

2x + 2 + 5x + 3 = 180      

2 lines that cross make consecutive angles supplementary.

Combine the left.

7x + 5 = 180        Subtract 5 from both sides.

7x +5-5=180-5    Combine

7x = 175               Divide by 7

7x/7=175/7          

x = 25

[tex]\tan(2\alpha)=\dfrac{2\tan \alpha }{1-\tan^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha}}{1-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha}{\cos^2\alpha}-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha-\sin^2 \alpha}{\cos^2\alpha}}[/tex]

[tex]\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha}{\cos\alpha} \cdot\dfrac{\cos^2\alpha}{\cos^2\alpha-\sin^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha\cos\alpha}{\cos^2\alpha-\sin^2 \alpha} \\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\sin(2\alpha)}{\cos(2\alpha)}[/tex]

Answer:

See below.

Step-by-step explanation:

tan 2A = sin 2A / cos 2A

= 2 sinA cosA / (cos^2A - sin^2A)

Now divide top and bottom of the fraction by cos^2 A:

2 sinA cosA               cos^2A         sin^2 A

-------------------      /     -----------   -   -------------

cos^2A                      cos^2 A        cos^2 A

= 2 tan A / 1 - tan^2A).

Answer:

B

Step-by-step explanation:

So, for this problem, it is only asking for vertex A, so you only have to apply the transformations to one point (unless you want to find out where the other points are at).

Vertex A is at (-4,2).

The triangle is first translated 2 units right and 5 units down.

So to find the coordinate of that you have to understand that is you translate something right or left, the x value will change. And if it's up or down, the y value will change. If you are going right or up, the amount it's moved will be added. And left or down will be subtracted.

-4+2=-2 (so the new x-value will be -2)

2-5=-3 (so the new y-value will be -3)

Thus vertex A' is (-2,-3).

Now for the next transformation.

(-2,-3) is moved 5 units right and 4 units up.

-2+5=3 (so x-value will be 3)

-3+4=1 (so the y-value will be 1)

SO, the new coordinate of vertex A" is...

(3,1)! aka B

(Also, you can just illustrate this on a graph but i'm showing it to you this way because when you get more advanced the amount it is being translated will be much higher.)

Answer: The answer is B

Answer:

9[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplify each radical before summing

[tex]\sqrt{8}[/tex] = [tex]\sqrt{4(2)}[/tex] = 2[tex]\sqrt{2}[/tex]

3[tex]\sqrt{2}[/tex] is in simplified form

[tex]\sqrt{32}[/tex] = [tex]\sqrt{16(2)}[/tex] = 4[tex]\sqrt{2}[/tex]

Hence

2[tex]\sqrt{2}[/tex] + 3[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{2}[/tex] = 9[tex]\sqrt{2}[/tex]

When point D in shape ABCDE is reflected over the x-axis, the y-coordinate changes its sign. If it is then translated 3 units to the left, the x-coordinate of D decreases by 3. Therefore, if the original coordinates of D are (d1, d2), after these transformations, its new coordinates will be (d1-3, -d2).

To answer this question, we need to understand how the reflection and translation transformations affect the coordinates of point D in the shape ABCDE.

First, when a point is reflected over the x-axis, the y-coordinate changes sign. For example, if the original coordinates of D are (d1, d2), after reflection over the x-axis, the new coordinates will be (d1, -d2).

Next, a translation of 3 units to the left (in the negative x direction), lowers the x coordinate by 3 units. Thus, after this translation, the final coordinates of point D will be (d1-3, -d2).

So, if you know the original coordinates of point D in the shape ABCDE, you can calculate its new position after these transformations in the described way.

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The new coordinates of point D after reflection over the x-axis and translation 3 units left is

The coordinates is solved by considering the sequence of transformation that took place

Reflection over the x-axis will result to

D (-3, -1) → D' (-3, 1)

Translation of 3 units left will result to

D' (-3, 1) → D"(-6, 1)

Learn more about Translation

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Answer:

[tex]2x^2 - 8x + 6[/tex]

Step-by-step explanation:

Use the FOIL method of multiplying binomials.

First term in each binomial: [tex]x * 2x = 2x^2[/tex]

Outside terms: [tex]x * -2 = -2x[/tex]

Inside terms: [tex]-3 * 2x = -6x[/tex]

Last term in each binomial: [tex]-3 * -2 = 6[/tex]

Now, add them all together.  [tex]2x^2 - 2x - 6x + 6[/tex]

Simplified, this equals [tex]2x^2 - 8x + 6[/tex], which is the answer.

Answer:

x = -35/72

Step-by-step explanation:

3x + 1/9 = 2x - 3/8

x = -3/8 - 1/9

x = -35/72

Answer:

yes you start solving whats in the parentheses

Step-by-step explanation:

In algebra you use the order of operations or PEMDAS

PEMDAS is a way to help you remember what you solve first

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

(2x^2)(y^16)

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

If the lines are parallel, the slopes are the same.

Since the green line has a slope of -2, the red line has a slope of -2

Answer:

5 sqrt(5) =c

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the hypotenuse

a^2 + b^2 = c^2 since this is a right triangle

5^2 + 10^2 = c^2

25+100 = c^2

125 = c^2

Take the square root of each side

sqrt(125) = sqrt(c^2)

sqrt(25*5) = c

sqrt(25) sqrt(5) = c

5 sqrt(5) =c

Alright, in a right-angled triangle, the lengths of the three sides are related by the Pythagorean Theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
This can be written as:
c² = a² + b²
In the question you provided, you've given that side a is 5 and side b is 10, and you'd like to find side c, the hypotenuse.
Following the Pythagorean Theorem :
c² = a² + b² = 5² + 10² = 25 + 100 = 125
Now we need to find the length of side c by taking the square root of c²:
c = √125
This can be further simplified by recognizing that 125 is equal to 25 * 5, and the square root of 25 is 5.
c = √(25 * 5) = √25 * √5 = 5√5
Therefore, the length of side c in its simplified radical form is:
c = 5√5
That would be the value of the hypotenuse of the right triangle with side lengths 5 and 10.

Answer:

[tex]s=4w+12[/tex]

Step-by-step explanation:

Let

s -----> the number of stamps

w ----> the number of weeks

we know that

The linear equation that represent this situation is

[tex]s=4w+12[/tex] ----> equation of the line into slope intercept form

where

the slope m is equal to [tex]m=4\ stamps/week[/tex]

the y-intercept b is equal to [tex]b=12\ stamps[/tex] ---> (the initial value)

Answer:

748 in^3.

Step-by-step explanation:

This consists of a triangular prism and a  rectangular cuboid .

Volume of the prism =  .1/2 * 8 *11 * 17 = 748 in^3

Volume of the cuboid =  5*8*17 = 680 in^3

Therefore the volume of the whole figure

= 680 + 748 =  1428 in^3.

Answer:

What is the volume of the composite figure?

748 cubic inches

Step-by-step explanation: