All categories

3 years ago

#11 and #13 geometry help please help need work shown as well !!

Mathematics

1 answer:

Trava [24]3 years ago

4 0

Answer: In diagram (11) X = 30 degrees and Y = 60 degrees

In diagram (13) X = 20.55 degrees and Y = 69.45 degrees

Step-by-step explanation: What we have are two right angled triangles with two sides given in each case, therefore we can calculate the two unknown angles (since the third angle equals 90 degrees).

For the second triangle (number 13) we shall use Y as the reference angle. That means we have an opposite (the side facing the reference angle) which is 24 and we have an adjacent (the side that lies between the right angle and the reference angle) which is 9. Hence,

Tan Y = opposite/adjacent

Tan Y = 24/9

Tan Y = 2.6667

Checking with your calculator or table of values, 2.6667 = 69.45

Having two angles, which are 90 and 69.45, the third angle X can be computed as

X = 180 - (90 + 69.45)

Sum of angles in a triangle equals 180

X = 180 - 159.45

X = 20.55 and Y = 69.45

For the first triangle (number 11) we shall use X as the reference angle. We have two sides, the opposite (the side facing the reference angle) which is 3, and the hypotenuse (side facing the right angle) which is 6. Hence,

Sin X = opposite/hypotenuse

Sin X = 3/6

Sin X = 0.5000

Checking with your calculator or table of values,

X = 30 degrees.

Also, now that we have two angles we can easily compute the third angle as follows

Y = 180 - (90 + 30)

Sum of angles in a triangle equals 180

Y = 180 - 120

Y = 60

X = 30 and Y = 60

You might be interested in

HELP ME PLEASE ASAP

lakkis [162]

So I have the same problem with you

8 0

3 years ago

Factor Completely: 25x2 - 64 A) 5(x - 8)(x + 8) B) 5(x - 8)(x - 8) C) (5x - 8)(5x + 8) D) (25x - 1)(x + 64)

ZanzabumX [31]

Rewrite it in the form a^2 - b^2, where a = 5x and b = 8

(5x)^2 - 8^2

Use the Difference of Squares; a^2 - b^2 = (a + b)(a - b)

4 0

3 years ago

The sum of a number and forty-six

ad-work [718]

$\textsf{Hey there!}$

$\mathsf{\star \ The\ sum\ of\ a\ number\ \&\ forty-six}$

$\frak{Let's\ lable\ the\ keypoints\ so\ it\ can\ be\ easier\ to\ solve}$

$\bullet \ \textsf{The word \bf{\underline{SUM}}}\textsf{\ means\ add/addition}}$

$\bullet\textsf{ \underline{"A number"} is an unknown number so we can lable it as \bf{x}}$

$\bullet\textsf{ \underline{forty-six} is 46}$

$\textsf{The sum (+) does in the middle while \underline{x} \& \underline{46} will either be on left/right}$

$- \ \textsf{We can say that x is on your left}$

$-\ \textsf{ + can be in your middle}$

$- \ \textsf{\& lastly 46 can be on your right}$

$\boxed{\textsf{Thus, your answer SHOULD LOOK like: \boxed{\huge\text{\bf{x + 46}}}}}\checkmark$

$\textsf{Good luck on your assignment and enjoy your day!}$

~ $\frak{LoveYourselfFirst:)}$

4 0

3 years ago

On a number line, point D is at -3, and point E is at 6. The point F lies on DE. The ratio of DF to FE is 2:3. Where does point

expeople1 [14]

Answer: point F is at <u> 0.6 </u> on the number line

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

Explanation:

The ratio 2:3 scales up to 2x:3x for some positive real number x.

This means the distance from D to F is 2x units, and the distance from F to E is 3x units. Combine those two smaller distances to get 2x+3x = 5x to represent the full distance from D to E.

D is at -3 and E is at 6. This is a distance of 9 units since |-3-6| = |-9| = 9

Set this equal to the 5x from earlier and solve

5x = 9

x = 9/5

x = 1.8

This leads to 2x = 2*1.8 = 3.6

Therefore, we'll move 3.6 units from -3 to -3+3.6 = 0.6 which is the location of point F on the number line.

Notice that from 0.6 to 6 is 5.4 units and that 3x = 3*1.8 = 5.4 matches up to help confirm the answer.

5 0

3 years ago

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

Anastaziya [24]

(m+2)(m+3)= (m+2)(m-2)
⇒ m^2+ 3m+ 2m+ 6= m^2 -4
⇒ 5m+ 6= -4 (m^2 on both sides cancels out)
⇒ 5m= -4-6
⇒ 5m= -10
⇒ m= -10/5
⇒ m= -2

The final answer is m=-2~

6 0

3 years ago