What is the slope of the line represented by the equation y = -1/2x + 1/4

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:

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:

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]

Hello There!

I Provided Steps In The Image Attached.

Have A Great Day!

The form of linear equation that describes line is:

[tex]y=sx+n[/tex]

First we must calculate the slope.

[tex]s=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]

Now it looks a bit more like this:

[tex]y=\dfrac{5}{2}x+n[/tex]

All we need now is to put in y and x from one point doesn't matter which. I'll pick A.

The equation now looks like this:

[tex]-3=\dfrac{5}{2}\cdot2+n[/tex]

Solve for n.

[tex]

-3=5+n \\

n=-8

[/tex]

And finally write the equation.

[tex]f(x)=\dfrac{5}{2}x-8[/tex]

Hope this helps.

r3t40

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:

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

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:

x = -35/72

Step-by-step explanation:

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

x = -3/8 - 1/9

x = -35/72

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]

Answer:

see explanation

Step-by-step explanation:

Given

3x - y = 2

Substitute y = x - 1 into the equation

3x - (x - 1) = 2

3x - x + 1 = 2 ← simplify left side

2x + 1 = 2 ← required equation after substitution

Given.

3x - y = 2

Substitute x - 1 for variable y.

3x - x - 1 = 2 ← Resulting equation

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:

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]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:

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: There are 5 sig figs in 1.0025

Step-by-step explanation:

With significant figures, any number other then 0 is a significant figure. The two zeros are significant because they are followed by more numbers. If the number was 1.000, there would only be one sig fig.

Hope this helps!

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:

[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:

-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:

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:

(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)

[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).

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:

[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:

(2x^2)(y^16)

Step-by-step explanation:

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:

$1424.10

Step-by-step explanation:

APEX is obnoxious, I understand.

Answer:1424.10

Step-by-step explanation:

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:

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]