please answer asap ------------------ ------------------ ------------------ ------------------

Answer:

5

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + 10^2 = (5 sqrt(5))^2

a^2 +100 = 25(5)

a^2 +100 = 125

a^2 = 125-100

a^2 = 25

Taking the square root of each side

sqrt(a^2) = sqrt(25)

a = 5

y - 1/z = 1   ==>   y = 1 + 1/z

z - 1/x = 1   ==>   z = 1 + 1/x

==>   y = 1 + 1/(1 + 1/x) = 1 + x/(x + 1) = (2x + 1)/(x + 1)

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

==>   2x ² - 1 = 2x + 1

==>   2x ² - 2x - 2 = 0

==>   x ² - x - 1 = 0

==>   x = (1 ± √5)/2

If you start solving for z, then for x, then for y, you would get the same equation as above (with y in place of x), and the same thing happens if you solve for x, then y, then z. So it turns out that x = y = z.

Answer:

D

Step-by-step explanation:

2ab*cos(C)=a^2+b^2-c^2

2ab*cos(C)=5^2+4^2-2^2=25+12=37

Answer:

The answer is 37

Step-by-step explanation:

Note that the  quadratic model for the data is  y = -0.008x² + 0.75x + 13.47.

Here are the steps on how to  find a quadratic model for the data.

Here is the output of the quadratic regression feature on my graphing calculator

y = -0.008x² + 0.75x + 13.47.

where  -

x is the speed in miles per hour

y is the fuel economy in miles per gallon.

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The sum of the interior angles in a triangle is 180 degrees.

72 + 35 + <1 = 180

107 + <1 = 180

<1 = 73 degrees

Hope this helps!

Answer:

<1 = 73

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

72+ 35+ <1 = 180

Combine like terms

107 + <1 =180

Subtract 107 from each side

<1 = 180-107

<1 = 73

Answer:

25

Step-by-step explanation:

f(5)=5(5-1)+5

f(5)=5(4)+5

f(5)=20+5

f(5)=25

Answer:

f(5) = 24

Step-by-step explanation:

f(1) = 4

f(n) = f(n − 1) + 5

Let n = 2

f(2) = f(2 − 1) + 5 = 4+5 = 9

Let n = 3

f(3) = f(3 − 1) + 5 = f(2)+5 = 9+5 = 14

Let n = 4

f(4) = f(4 − 1) + 5 = f(3)+5 = 14+5 = 19

Let n = 5

f(5) = f(5 − 1) + 5 = f(4)+5 = 19+5 = 24

Answer:

Hello,

Step-by-step explanation:

slope of the line=3/7

slope of the perpendicular = -7/3

equation of the perpendicular:

y-3=(x-3)*(-7/3)

or

y=-7/3*x +7+3

or

y=-7/3*x+10

Given:

The function is:

[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]

To find:

The roots of the given equation.

Solution:

We have,

[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]

For roots, [tex]f(x)=0[/tex].

[tex]4x^5-8x^4+8x^2-4x=0[/tex]

[tex]4x(x^4-2x^3+2x-1)=0[/tex]

[tex]4x((x^4-1)+(-2x^3+2x))=0[/tex]

[tex]4x((x^2+1)(x^2-1)-2x(x^2-1))=0[/tex]

On further simplification, we get

[tex]4x(x^2+1-2x)(x^2-1)=0[/tex]

[tex]4x(x-1)^2(x+1)(x-1)=0[/tex]

[tex]4x(x+1)(x-1)^3=0[/tex]

Using zero product property, we get

[tex]4x=0[/tex]

[tex]x=0[/tex]

Similarly,

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

And,

[tex](x-1)^3=0[/tex]

[tex]x=1[/tex]

Therefore, the zeroes of the given function are [tex]-1,0,1[/tex] and the factor form of the given function is [tex]f(x)=4x(x+1)(x-1)^3[/tex].

Answer:

A' (0,20)

B' (30,-20)

C' (-10,-40)

Answered by GAUTHMATH

Answer:

a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]

Step-by-step explanation:

[tex]a^{2} +b^{2} = 5 ^{2}[/tex]

a = b

[tex]2a^{2} = 5 ^{2}[/tex]

[tex]2a^{2} = 25\\[/tex]

[tex]a^{2} = \frac{25}{5}[/tex]

a = [tex]\frac{5}{\sqrt{5} }[/tex]

must rationalize...

a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]

Answer:

-6 and - 65

Step-by-step explanation:

X-12x-29, by completing the square we get (x-6)^2-65

Answer:

hope it helps

Step-by-step explanation:

Answer:

SEE THE IMAGE FOR SOLUTION..

Solution:-10

As <AGQ and <EQG are corresponding interior angles

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 60°+a=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow a=180-60[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow a=120}[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow b=75°}[/tex]

According to angle sum property

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow b+c+<PQR=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+75+60=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+135=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c=180-135[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow c=45°}[/tex]

Answer:

[tex]\displaystyle 4[/tex]

Explanation:

[tex]\displaystyle y = 3sin\:(\frac{\pi}{2}x + \frac{\pi}{2}) \\ y = 3cos\:\frac{\pi}{2}x[/tex]

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4} \hookrightarrow \frac{2}{\frac{\pi}{2}}\pi[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4} \hookrightarrow \frac{2}{\frac{\pi}{2}}\pi[/tex]

You will need the above information to help you interpret the graph. So, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-5, 0],[/tex] from there to [tex]\displaystyle [-1, 0],[/tex] they are obviously [tex]\displaystyle 4\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 4.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

E. 248

Step-by-step explanation:

1 to 500 in set A, 250 to 750 in set B

500 - 250 = 250

100 and 200 are divisible by 100.

250 - 2 = 248

Answer: D

Step-by-step explanation:

[tex]a=0,\ b=0,\ k=2\\equation\ of\ the\ parabola:\\\\y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\\\y=-\dfrac{x^2}{4}+1 \\\\x^2=-4(y-1)\\\\Answer\ D[/tex]

Step-by-step explanation:

Hello!

In order to graph this, a point would have to go through (-6, 1). Then, since it says it needs a slope of 5 (or, to make things a bit easer, we could see it as 5/1) we'd need the next point to be 5 up and 1 across.

One possible solution:

(-6, 1) -> (-5, 6)

===========================================

Explanation:

The two equations given to us are

Divide the second equation over the first equation and that would lead to b = 6

Notice how the 'a' terms divide to 1 and go away, i.e. cancel out.

The b terms divide to (b^2)/b = b

The right hand side values divide to 18/3 = 6

So that's how we end up with b = 6

-------------------------

Now if b = 6, then we can say,

ab = 3

a*6 = 3

a = 3/6

a = 1/2

Or we could say

ab^2 = 18

a*6^2 = 18

a*36 = 18

a = 18/36

a = 1/2

Here we want to find the expressions we need to use to see if the functions g(x) and h(x) are inverses of each other.

The correct option is the last one, counting from the top.

∛((x + 72)^3) - 72  and -(∛(-x) - 72 + 72)^3

Two functions f(x) and g(x) are inverses if:

f( g(x) ) = x

g( f(x) ) = x

In this case, we have the functions:

g(x) = ∛(-x) - 72

h(x) =  -(x + 72)^3

Then the expressions we need to check are:

g( h(x) ) = ∛(-h(x)) - 72 = ∛(+(x + 72)^3) - 72 = (x + 72) - 72 = x

h( g(x) ) = -(g(x) + 72)^3 = -(∛(-x) - 72 + 72)^3 = -(∛(-x) )^3 = x

So we found that the two expressions needed are:

∛((x + 72)^3) - 72  and -(∛(-x) - 72 + 72)^3

Then the correct option is the last one, counting from the top.

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Answer:

GUYS ITS C THAT IS THE ANSWER

Answer:

Hello,

answer:  -2 < k < 8

Step-by-step explanation:

As there are 2 roots: Δ>0

As there is a mininum, k-6 <0 ==> k<6,

minimum :y'=0 ==> (k-6)*2x-8=0 ==> x=4/(k-6)

[tex]\Delta=8^2-4*k*(k-6)\\=64-4k^2+24k\\=-4(k^2-6k+9)+36+64\\=100-4(k-3)^2\\=4(8-k)(k+2)\\\\\Delta\ is\ positive\ for\ -2 < k < 8[/tex]

175 m above the terrace + 80 m from terrace to ground + 8m from ground to basement:

175 + 80 + 8 = 263 meters

Answer:

Step-by-step explanation: Scale [tex]\frac{130}{100} = \frac{13}{10}[/tex]

New dimensions [tex]16 * 1.3 --- 24*1.3 =20.8 cm * 31.2 cm[/tex]

Step-by-step explanation:

sin and tan are the only ones with p positive valued

Answer:

Rs 2160

Step-by-step explanation:

1 dozen = 12 copies

2 dozen = 24 copies ( 2*12)

72÷12 = 6 dozen

72 copies = 6 dozen

1 dozen = Rs 720÷2

1 dozen Rs 360

6 dozen = 360*6

6 dozen = 72 copies = Rs 2160

Answer: 22,200 words per hour.

Step-by-step explanation:

You can set up a proportion for this: 370 words/per 1 min= x words/ per 60 mins. Cross multiply and you get 22,200=1x which basically equals to 22,200 words per hour or 60 mins.

3rd step

Solution:-

[tex]\\ \sf\longmapsto -2x+8-3x=7[/tex]

[tex]\\ \sf\longmapsto -2x-3x+8=7[/tex]

[tex]\\ \sf\longmapsto -5x+8=7[/tex]

[tex]\\ \sf\longmapsto -5x=7-8[/tex]

[tex]\\ \sf\longmapsto -5x=-1[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-1}{-5}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1}{5}[/tex]

Answer:

a) 4 packages

b) 7000 g or 7 kg

Step-by-step explanation:

x is the number of 250g packages and y is the number of 750g packages.

2x = y

3(x + 2 x (750 : 250)) = 5(y - 2)

3(x + 6) = 5(y - 2)

3(x + 6) = 5(2x - 2)

3(x + 6) = 5(2(x - 1))

3(x + 6) = 5 * 2 * (x - 1)

3(x + 6) = 10(x - 1)

3x + 18 = 10x - 10

(3x + 18) + 10 = (10x - 10) + 10

3x + 28 = 10x

28 = 10x - 3x

28 = 7x

x = 28/7

x = 4

y = 2 * 4 = 8

(250 * 4) + (750 * 8) = 7000 g