All categories

3 years ago

Can someone Help I’ve been stuck on this

Mathematics

2 answers:

N76 [4]3 years ago

6 0

Answer:

x = 5, y = 12

Step-by-step explanation:

I highly encourage you to follow along drawing the diagram and filling the measurements in as we go along for better understanding.

straight line angles add up to 180 degrees

x) 125 + 12x - 5 = 180

125 - 5 + 12x = 180

120 + 12x = 180

12x = 180 - 120

12x = 60

x = 5

y) vertically opposite angles are equal hence the lower parallel line will have 125 to the left of 12x - 5.

co-interior angles: - inside parallel lines

- same side of the transversal

- add up to 180

-the left of the transversal will have 125 at the bottom and 55 at the top

having that, 8y + 29 + 55 = 180

8y + 84 = 180

8y = 180 - 84

8y = 96

y = 12

EastWind [94]3 years ago

3 0

Answer:

x=5

y=12

Step-by-step explanation:

the equation is

12x-5+125=180

12x+120=180

12x=60

x=5

According to the question

8y+29=125

8y=96

y=12

You might be interested in

2x+9=2x-5 what is x in this situation

Alexxandr [17]

your answer would be x=4 i believe

7 0

1 year ago

Read 2 more answers

Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

Read 2 more answers

I need help with this

svp [43]

I’m not sure how to explain it but the answer is B

6 0

3 years ago

Figure ABCDE is similar to figure FGHIJ. What is the length of segment FG?

Viefleur [7K]

It must be 6 since the length sides r doubled and it's similar

7 0

3 years ago

LOTS OF POINTS!!! HELP WITH 7 ANd EXPLAIN!!

saveliy_v [14]

Answer:

w=4

Step-by-step explanation:

The surface area of a prism is SA= 2lw+2lh+2hw

We are trying to find out the width if the SA is 240 square inches, length is 12 inches, and the height is 5 inches. Let's plug these numbers into the equation.

240=(2*12*w)+(2*12*5)+(2*5*w)

24w+120+10w

240= 34w+120

-120 -120

120= 34w

120/34 = 34w/34

w is approximately equal to 3.5 which can be rounded to 4

w=4

Hope this is right! It was confusing at first but I understood it!

3 0

3 years ago