The triangle below is isosceles. Find the length of side xx in simplest radical form with a rational denominator.

Answer:

Step-by-step explanation:

Explanation:

For any 30-60-90 triangle, the hypotenuse is always twice as long compared to the short leg. The short leg is always opposite the 30 degree angle.

The length of x is 6.

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given problem,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = [tex]\frac{perpendicular}{hypotenuse}[/tex]

∅ = 30°

⇒ sin30 = [tex]\frac{3}{x}[/tex]

⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{x}[/tex]  [ sin30 = [tex]\frac{1}{2}[/tex] ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ 6² = 3² + Base²

⇒ 6² - 3² = Base²

⇒ Base² = 25

⇒ Base = √25

⇒ Base = 5

Hence, we can conclude the value of x to be 6.

Learn more about right-angled triangle here:

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Answer:

7

Step-by-step explanation:

Exterior Angle Theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

In this case:

(4x + 7) + (97) = (17x + 13)

4x + 104 = 17x + 13

4x + 91 = 17x

91 = 13x

7 = x

Answer:

[tex]2y^2-7y+6=0[/tex]

Step-by-step explanation:

We are given that [tex]\alpha[/tex] and [tex]\beta[/tex] are the zeroes of the polynomial [tex]6y^2-7y+2[/tex]

[tex]y^2-\frac{7}{6}y+\frac{1}{3}[/tex]

We have to find a quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex].

General quadratic equation

[tex]x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes[/tex]

We get

[tex]\alpha+\beta=\frac{7}{6}[/tex]

[tex]\alpha \beta=\frac{1}{3}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2[/tex]

[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}[/tex]

[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3[/tex]

Substitute the values

[tex]y^2-(7/2)y+3=0[/tex]

[tex]2y^2-7y+6=0[/tex]

Hence, the quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex] is given by

[tex]2y^2-7y+6=0[/tex]

Answer:

1441.08 in^3

Step-by-step explanation:

Volume of rectangular prism = 15 * 9 * 9 = 1215 in^3

radius = 3 in

Volume of the cylinder = 3^2 * 3,14 * 8 = 226.08 in^3

Total volume = 1215 + 226.08 = 1441.08 in^3

Answer:

HJHJGHJHG

Step-by-step explanation:

JGHU45565677689789

Answer:

is it me or can I not see anything

Answer:

100 degrees

Step-by-step explanation:

You can tell by just looking at the picture :)

the way to do these recurring decimals is by firstly separating the repeating part or recurring part and then multiply it by some power of 10 so we move it to the left, lemme show

[tex]3.5\overline{41}\implies \cfrac{35.\overline{41}}{10}\qquad \stackrel{\textit{say that the repe}\textit{ating part is }~\hfill }{x = \overline{0.41}\qquad \qquad \textit{so that }35.\overline{41}=35+\overline{0.41}=35+x}[/tex]

now, let's multiply that repeating part by some power of 10 that moves the 41 to the left, well, we have two repeating decimals, 4 and 1, so let's use two zeros, namely 100 or 10², thus

[tex]100\cdot x = 41.\overline{41}\implies 100x - 41+\overline{0.41}\implies 100x = 41+x\implies 99x=41 \\\\\\ \boxed{x =\cfrac{41}{99}}\qquad \qquad \textit{so then we can say that}~~\cfrac{35.\overline{41}}{10}\implies \cfrac{35+\frac{41}{99}}{10} \\\\\\ \cfrac{~~\frac{3506}{99}~~}{10}\implies \cfrac{~~\frac{3506}{99}~~}{\frac{10}{1}}\implies \cfrac{3506}{99}\cdot \cfrac{1}{10}\implies \cfrac{3506}{990}\implies \blacktriangleright \stackrel{\textit{which simplifies to}}{\cfrac{1753}{495}} \blacktriangleleft[/tex]

The image of the 2 mile markers is missing as well as the options and so i have attached them.

Answer:

> 1.5 hours = 105 miles/speed

> Speed = 105 miles/1.5 hours

> 105 miles = 1.5 hours × speed

Step-by-step explanation:

From the image attached, the distance of the first mile marker is given as 50 miles while the distance of the second mile marker is given as 155 miles.

Thus, difference in distance between the two markers; d = 155 - 50 = 105 miles

Also, we see that the time of first marker is 3 pm while the second marker is 4:30 pm.

Thus, difference in time = 4:30 - 3 = 1 hour 30 minutes or 1.5 hours.

We know that;

Speed = distance/time

Thus;

Speed = 105/1.5

Speed = 70 mph

Thus, the 3 equations that represent this situation from the options are;

> 1.5 hours = 105 miles/speed

> Speed = 105 miles/1.5 hours

> 105 miles = 1.5 hours × speed

Answer:

1.5 hours = 105 miles/speed

Speed = 105 miles/1.5 hours

105 miles = 1.5 hours × speed

Step-by-step explanation:

Answer:

discounted price = original price ( 1 - discount rate)

Step-by-step explanation:

Answer:

So the answer is 30%

Step-by-step explanation:

1. For 50 = 15 increase euros

2. For 100 = 15/50 x 100 = 30 increase in euros

3. 30/100 = 30%

OR....

1. Ten percent of 50 is 5.

2. 5x3= 15(increase in euros)

3. 10 percent three times which is equal to 30%.

3.75 quarts

Brainly plz and thank you

Answer:

d

Step-by-step explanation:

ive had this exac problem before

Answer:

B. 1

Step-by-step explanation:

Since the sides are equal to each other, the equations will be equal.

4x + 7 = x + 10

      -7          -7

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

4x= x + 3

-x    -x

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

3x = 3

----   ---

3      3

x = 1

The answer is 1.

Answer:

Step-by-step explanation:

so they used  a total of  560  units

we are next told that if the units of usage are 360 or less use the 1st formula, but there is morn than 360 units in the given amount so use the 2nd formula

0.1(x-360+54)

0.1(560-360) + 54 = monthly bill

20+54 = monthly bill

74 = monthly bill

answer D looks good

Answer:

cost per serving can be used as a result of using your head to think

Answer:

4w-8

Step-by-step explanation:

4(w-2)

(4*w)-(4*2)

4w-8

Answer:

4w-8

Step-by-step explanation:

4(w - 2)

Distribute

4*w - 4*2

4w-8

Answer:

[tex]x=43[/tex]

Step-by-step explanation:

Corresponding angles are equal. It is implied that the two angles referred to in the triangles are equal, otherwise they should not be labelled as corresponding.

Therefore, we can set both equations equal to each other:

[tex]2x-5=81^{\circ}[/tex]

Add 5 to both sides:

[tex]2x=86[/tex]

Divide both sides by 2:

[tex]x=\frac{86}{2}=\boxed{43}[/tex]

Answer:

4.2+9.Write f (x)in the form:f(x)=x-2 4.3Draw

Answer:

x =-2

Step-by-step explanation:

5x+1=2x-5

Subtract 2x from each side

5x-2x+1=2x-2x-5

3x+1 = -5

Subtract 1 from each side

3x+1-1 = -5-1

3x=-6

Divide by 3

3x/3 = -6/3

x = -2

Answer: Choice C. 32,768

Explanation:

2.5 hours = 2.5*60 = 150 minutes

150/10 = 15

There are 15 periods that are 10 minutes each in a 2.5 hour timespan.

y = a*b^x

y = 1*2^15

y = 32,768

If you started with a = 1 bacterium, then it will double a total of 15 times to end up with 32,768 bacteria after the 2.5 hour period.

Answer:

-12+4y=x..............1

6(-12+4y)+4y=8

-72+24y+4y=8

28y=80

y=3.33

-12+4(3.33)=x

1.32=x

Answer:

ans is C................

Given:

The vertices of a triangle are D(1,5), O(7,-1) and G(3,-1).

To find:

The perpendicular bisector of line segment DO.

Solution:

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

The midpoint of DO is:

[tex]Midpoint=\left(\dfrac{1+7}{2},\dfrac{5+(-1)}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{8}{2},\dfrac{4}{2}\right)[/tex]

[tex]Midpoint=\left(4,2\right)[/tex]

Therefore, the midpoint of DO is (4,2).

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Slope of DO is:

[tex]m=\dfrac{-1-5}{7-1}[/tex]

[tex]m=\dfrac{-6}{6}[/tex]

[tex]m=-1[/tex]

Therefore, the slope of DO is -1.

We know that the product of slopes of two perpendicular line is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]m_1\times (-1)=-1[/tex]

[tex]m_1=1[/tex]

The slope of perpendicular bisector is 1 and it passes through the point (4,2). So, the equation of the perpendicular bisector of DO is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-2=1(x-4)[/tex]

[tex]y-2+2=x-4+2[/tex]

[tex]y=x-2[/tex]

Therefore, the equation of the perpendicular bisector of DO is [tex]y=x-2[/tex].

Answer:

Step-by-step explanation:

Answer:

In a problem where you

calculate the "solution" to a "system of equations"

one of three things will happen....

#1) you end up with x=3 , or y=7 .. or something like that

  if that happens then there is ONE SOLUTION

#2) you end up with  5=5, or 7=7 , or 0=0

   in this case the lines are the same and you have "all real numbers" as the solution (there are an infinite number of solutions, the lines are the same line)

#3) you end up with 1=2, 0=5, 2=7, etc. this is impossible, there are no solutions ... the lines are parallel

Step-by-step explanation:

Answer:

x + y = -12

Step-by-step explanation:

x - y = 2

2x – 3y = 11

-2x +2y = -4

2x – 3y = 11

-y = 7

y  = -7

x = -5

x + y = -12

Hello!

[tex]\large\boxed{x = 4}[/tex]

7(x + 9) + 5 = 96

Distribute:

7x + 63 + 5 = 96

Combine like terms:

7x + 68 = 96

Subtract 68 from both sides:

7x = 28

Divide both sides by 7:

x = 4

Answer:

[tex]\fbox{x = 7}[/tex]

Step-by-step explanation:

7(x + 9) + 5 = 96

Solve for x.

Step 1 :- Distribute 7.

Step 2:- Add 63 and 5.

Step 3 :- Move constant to the right-hand side and change their sign.

Step 4 :- Subtract 68 from 96.

Step 5 :- Divide both side by 7.