Draw graphs of the following inequalities.
a.) X>3​

6√5 + 3√6 = 6√5 + 3√6 [cannot be simplified]

; roots do not contain any perfect squares, and the roots are not similar.

6√5(3√6) = 18√30 [can be simplified]

; although roots do not contain any perfect squares, the product rule can be applied to create a singular expression.

Answer:

9

Step-by-step explanation:

Using the rules of logarithms

log[tex]x^{n}[/tex] = nlogx

[tex]log_{b}[/tex] b = 1

Then

[tex]log_{x}[/tex] [tex]x^{9}[/tex]

= 9[tex]log_{x}[/tex] x

= 9

Answer: (D) 7

Step-by-step explanation:

Answer:

a.) x=7 or x=-11

b.) x=−2 or x=−8

Step-by-step explanation:

a)  x² + 4x – 77 = 0

Step 1: Factor left side of equation.

(x−7)(x+11)=0

Step 2: Set factors equal to 0.

x−7=0 or x+11=0

x=7 or x=−11

b.) x(x + 4) = -2(3x + 8)

Step 1: Simplify both sides of the equation.

x^2+4x=−6x−16

Step 2: Subtract -6x-16 from both sides.

x^2+4x−(−6x−16)=−6x−16−(−6x−16)

x^2+10x+16=0

Step 3: Factor left side of equation.

(x+2)(x+8)=0

Step 4: Set factors equal to 0.

x+2=0 or x+8=0

x=−2 or x=−8

Answer:

a) {-11, 7}.

b) {-8, -2}

Step-by-step explanation:

a) x^2 + 4x - 77 = 0

To factor this we need 2 numbers whose product is -77 and sum is + 4.

They are + 11 and - 7, so:

( x + 11)(x - 7) = 0

x + 11 = 0 or x - 7 = 0

x = -11,  7.

b) x(x + 4) = -2(3x + 8)

x^2 + 4x = -6x - 16

x^2 + 4x + 6x + 16 = 0

x^2 + 10x + 16 = 0

(x + 2)(x + 8) = 0

x = -8, -2.

Answer:

B (x+7, y-6)

Step-by-step explanation:

It goes right 7 and down 6

Answer:

(x,y) --> (x+7, y-6)

Step-by-step explanation:

Good luck with your exam! :DD

Answer:

Step-by-step explanation:

The measures of the exterior angles of all polygons add up to 360. So all we have to do is subtract the given values from 360 and we will have the missing angle.

a. 55

b. 118

c. 122

d. 50

Answer: See explanation

Step-by-step explanation:

The perimeter of a pentagon is gotten through the summation of its five sides. Let the first side be represented by x. Since each side of a pentagon is 10 cm greater than the previous side, then the sides will be:

First side = x

Second side = x + 10

Third side = x + 10 + 10 = x + 20

Forth side = x + 30

Fifty side = x + 40

Therefore,

x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 500

5x + 100 = 500

5x = 500 - 100

5x = 400

x = 400/5

x = 80

Therefore, the lengths will be:

First side = x = 80cm

Second side = x + 10 = 80 + 10 = 90cm

Third side = x + 20 = 80 + 20 = 100cm

Forth side = x + 30 = 80 + 30 = 110cm

Fifty side = x + 40 = 80 + 40 = 120cm

Given:

An exam starts at 10:10 and lasts for 75 minutes.

To find:

The time when the exam end.

Solution:

We have,

Starting time = 10:10

Exam duration = 75 minutes

First we will divide the 75 minutes in two parts 50 minutes and 25 minutes.

We know that 50 minutes after 10:10 is 11:00 and 25 minutes after 11:00 is 11:25. So,

10:10 + 75 minutes = 10:10 + 50 minutes +25 minutes)

                               = (10:10 + 50 minutes) +25 minutes

                               = 11:00 +25 minutes

                               = 11:25

Therefore, the exam ends at 11:25.

Answer:

x = 12.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 71 = 36/x

x tan 71 = 36

x = 36/tan 71

x=12.39579

To the nearest tenth

x = 12.4

Answer:

x <= -4 or x >= 2

Step-by-step explanation:

so, it actually says

|x+1| >= 3

so, then, this is valid for all x >= 2 (then x+1 is 3 or higher), and for all x <= -4 (then x+1 is -3 or lower, and |x+1| is still 3 or higher)

The conversion rate US dollars to Euros is represented with the function:

E(n)=0.72n

n- number of dollars

E(n) - Euros as a function of US dollars

The conversion rate Euros to Dirhams is :

D(x)=5.10x

x- number of Euros

D(x)- Dirhams as a function of Euros

We are trying to find D(x) in terms of n.

D(x) = 5.10x

x can be rewritten as E(n)

D(x) = 5.10(E(n))

D(x) = 5.10(E(n))

D(x) = 5.10(0.72n)

D(x) = 3.672n

According to this the following statement is true:

A) (D x E)(n) = 5.10(0.72n)

Answer:

A

Step-by-step explanation:

Firstly x cannot be -5 because the expression on th left would be undefined so it's only between choices a and c.

Create a number line with makes the expression on left 0 and undefined...so at 6 and -5 this happens.

-------(-5)--------(6)---------

Let's test the 3 intervals by choosing a value from that interval to see if all numbers from that interval will make the expression on left less than 0.

Number before -5 is -6:

(-6-6)/(-6+5)=-12/-1=12 >0 so this interval is not a part of our solution.

Number between -5 and 6 is 0:

(0-6)/(0+5)=-6/5<0 so this interval is a part of our solution

Number after 6 like 7:

(7-6)/(7+5)=1/12>0 so this interval is not a part of our solution.

The winner is everything between-5 and 6 so answer is A.

Answer:

C

Step-by-step explanation:

tanB = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] → C

Answer:

Length = 4.88

Step-by-step explanation:

Given

[tex]MR = 6.8cm[/tex]

[tex]AS = 7cm[/tex]

First, we calculate the lengths of each side of the rhombus.

Diagonals of a rhombus are bisected at right-angled.

So, the lengths (x,y) of the right-angled triangle formed are:

[tex]x = \frac{1}{2}MR = \frac{1}{2} * 6.8 = 3.4[/tex]

[tex]y = \frac{1}{2}AS = \frac{1}{2} * 7 = 3.5[/tex]

The length of the sides (z) is calculated using:

[tex]z^2 = x^2 + y^2[/tex]

[tex]z^2 = 3.4^2 + 3.5^2[/tex]

[tex]z^2 = 11.56 + 12.25[/tex]

[tex]z^2 = 23.81[/tex]

Take square roots

[tex]z = \sqrt{23.81[/tex]

[tex]z = 4.88[/tex] --- approximated

Answer:

A or C

Is my best I got stuck A or C

Answer:

[tex]\text{C. about }72.05\:\mathrm{cm^2}[/tex]

Step-by-step explanation:

This is a very fun problem that requires the use of multiple concepts to solve.

Concepts/formulas used:

The measure of an inscribed angle is equal to half the measure of the arc it forms. In circle Z, [tex]\angle XVY[/tex] is an inscribed angle that forms arc XY. Since XY is 40 degrees, angle XVY must be [tex]40\div 2=20^{\circ}[/tex].

Similarly, [tex]\angle VYX[/tex] is also an inscribed angle and forms arc XV. Notice how arc XY and arc XV form arc VY, which is half the circumference of the circle, since segment VY is a diameter of the circle. Since there are 360 degrees in a circle, arc VY must be 180 degrees. Therefore, we have:

[tex]\widehat{XY}+\widehat{XV}=180^{\circ},\\\widehat{XV}+40^{\circ}=180^{\circ},\\\widehat{XV}=140^{\circ}[/tex]

Now we can find the measure of angle VYX, using our knowledge that the measure of an inscribed angle is half the measure of the arc it forms.

[tex]m\angle VYX=\frac{140}{2}=70^{\circ}[/tex]

Now, we have two angles of triangle VXY. Since the sum of the interior angles of a triangle add up to 180 degrees, the third angle, [tex]\angle VXY[/tex], can be found:

[tex]\angle VXY+\angle VYX+\angle XVY=180^{\circ},\\\angle VXY+20^{\circ}+70^{\circ}=180^{\circ},\\\angle VXY+90^{\circ}=180^{\circ},\\\angle VXY=90^{\circ}[/tex]

We can now use this angle and the Law of Sines to find the length of segment VY. The Law of Sines works for any triangle and is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex] (the ratio of any angle and its opposite side is maintained throughout all angles of the triangle).

Since angle VXY's opposite side is VY and angle VYX's opposite side is VX, we have the following proportion:

[tex]\frac{\sin 70^{\circ}}{9}=\frac{\sin 90^{\circ}}{VY}[/tex]

Recall that [tex]\sin 90^{\circ}=1[/tex]. Cross-multiply:

[tex]9\sin 90^{\circ}=VY\sin 70^{\circ},\\9=VY\sin 70^{\circ},\\VY=\frac{9}{\sin 70^{\circ}}[/tex]

This is the diameter of the circle. By definition, all radii are half the diameter. Therefore, the radius of the circle is [tex]\frac{9}{\sin 70^{\circ}}\cdot \frac{1}{2}=\frac{9}{2\sin 70^{\circ}}[/tex].

The area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]. Substitute [tex]r=\frac{9}{2\sin 70^{\circ}}[/tex] to get the area of circle Z:

[tex]A=(\frac{9}{2\sin 70^{\circ}})^2\pi,\\A\approx (4.78879997614)^2\pi,\\A\approx 22.9326052115\pi,\\A\approx \boxed{72.05\:\mathrm{cm^2}}[/tex]

Answer:

y² + 11y + 18

Step-by-step explanation:

y² + 9y + 2y + 18

y² + 11y + 18

Answer:

m = -1/3

Step-by-step explanation:

To get the slope of the line, we identify two points on the line and use the slope formula

We can have the points (-2,3) and (1,2)

We have the slope formula as;

m = (y2-y1)/(x2-x1)

m = (2-3)/(1 + 2) = -1/3

Answer:

20

Step-by-step explanation:

When two numbers vary inversely, they always multiply to the same product, in this case, it is 80, because it is 8 x 10(product of two known values of p and q). This means, for q = 4, we can write:

p * 4 = 80

This means that p is equal to 20.

The value of p is 20 when q=4

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called constant of proportionality.

When two numbers vary inversely, then the will always multiply to the same product,

Here it is 80, because it is 8 x 10

Then product of two known values of p and q).

This means, for q = 4, we can write:

p x 4 = 80

This means that p is 20.

Learn more about directly inversely proportional relationship variable here:

https://brainly.com/question/13082482

#SPJ2

Answer:

Height is equal = Y = 1.8 X + 3.1 = 2.3 X + 1.9

=> 2.3 X - 1.8 X = 3.1 - 1.9

=> 0.5 X = 1.2

=> x = 1.2/0.5 = 2.4

Time = 2.4 weeks

Step-by-step explanation:

Answer:

2.4

Step-by-step explanation:

Answer:

[tex]sec~y=\frac{q}{r}[/tex]

Step-by-step explanation:

[tex]tan ~y=\frac{7}{r} \\\\\frac{sin~y}{cos~y} =\frac{7}{r} \\\\sin~y=\frac{7}{r} cos~y\\sin ~y=\frac{7}{q} \\\frac{7}{q} =\frac{7}{r} cos~y\\sec~y=\frac{7}{r} \times \frac{q}{7} =\frac{q}{r}[/tex]

The tangent is equal to the product of the sine and secant. The value of sec y is q over r, then the correct option is A.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

If sin y = 7/q and tan y = 7/r.

Then the value of sec y will be

We know that the identity

[tex]\sec x =\dfrac{\tan x}{\sin x}[/tex]

Then we have

[tex]\rm \sec y = \dfrac{7/r}{7/q} \\\\\\\sec y = \dfrac{q}{r}[/tex]

The value of sec y is q over r.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

Answer:

-64

Step-by-step explanation:

8x^3

Let x = -2

8 (-2)^3

8 * -8

-64

Answer:

−4096

Step-by-step explanation:

desmos

Answer:

x=10

Step-by-step explanation:

I hope this will help you

Answer:

Option D

Step-by-step explanation:

-14 > x - 32

Add 32 to both sides;

18 > x OR x < 18

Answer:

it should be the second one I hope this help

Answer:

The choose (B)

[tex] \frac{4 {x}^{2} }{12 x^{2} - 4 } \\ \frac{4 {x}^{2} }{4(3 {x}^{2} - 1)} \\ \frac{ {x}^{2} }{3 {x}^{2} - 1} [/tex]

Answer:

Yes, its a rational number.

Step-by-step explanation:

Rational numbers can be whole numbers, fractions, and decimals, and in this case it is a decimal.

Hope this helped!

Answer: yes

Step-by-step explanation:

yes 1.86 is a rational number