What is the solution to this system of equations?

Please help!!

Answer:

∠YDC measures 140°.

Step-by-step explanation:

We can consider using the Exterior Angle Theorem. According to the theorem, the exterior angle of a triangle is equal to the two opposite interior angles.

In other words:

[tex]\displaystyle m \angle YDC = m\angle DCB + m\angle CBD[/tex]

Substitute:

[tex]\displaystyle (15x + 5) = (80) + (6x+6)[/tex]

Solve for x. Combine like terms:

[tex]15x + 5 = 6x + 86[/tex]

Simplify:

[tex]9x = 81[/tex]

And divide. Hence, the value of x is:

[tex]x = 9[/tex]

∠YDC is given by:

[tex]\displaystyle m\angle YDC = 15x + 5[/tex]

Since we now know the value of x, substitute and evaluate:

[tex]\displaystyle \begin{aligned} m\angle YDC &= 15x + 5 \\ &= 15(9) + 5 \\ &= 135 + 5 \\ &= 140^\circ\end{aligned}[/tex]

In conclusion, ∠YDC measures 140°.

Distribute the figure into three rectangles, namely, A, B and C as shown in the picture.

We know that,

Area of a rectangle

= 2(l + b)

Now,

Consider rectangle A,

Length = 25in

Breadth = 15in

Hence,

Area = 2 (l + b)

= 2 (25 + 15)

= 2 (40)

= 80in²

Consider rectangle B,

Length = 25 - 7 = 18in

Breadth = 16in

Hence,

Area = 2 (l + b)

= 2 (18 + 16)

= 2 (34)

= 68in²

Consider rectangle C,

Length = 11in

Breadth = 24in

Hence,

Area = 2 (l + b)

= 2 (24 + 11)

= 2 (35)

= 70in²

Area of the figure

= Area of rectangle A + Area of rectangle B + Area of rectangle C

= 80in² + 68in² + 70in²

= 218in²

Answer:

gfxdg

Step-by-step explanation:

This value is approximate.

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

Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

107+42+C = 180

149+C = 180

C = 180-149

C = 31

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To sum things up so far, we have these known properties of triangle ABC

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

b/sin(B) = c/sin(C)

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

b = 31.1804803080182 which is approximate

b = 31.2 miles is the distance from the storm to station A

Make sure your calculator is in degree mode.

The weather station A is 31.2 miles from the storm

From the triangle shown:

m<B = 90° - 48°

m<B = 42°

m<A = 17° + 90°

m<A = 107°

m<A + m<B + m<C = 180° (Sum of angles in a triangle)

107° + 42° + m<C = 180°

m<C = 180° - 149°

m<C = 31°

The distance between the weather stations A and B = 24 miles

That is, AB = 24 miles

The storm is at point C

The length AC is found by using the rule of sines:

[tex]\frac{sinC}{AB}=\frac{sinB}{AC} \\\\\frac{sin31}{24}=\frac{sin42}{AC} \\\\\frac{0.515}{24} = \frac{0.669}{AC} \\\\0.02146=\frac{0.669}{AC}\\\\AC=\frac{0.669}{0.02146} \\\\AC=31.2 miles[/tex]

The weather station A is 31.2 miles from the storm

Learn more on sine rule here: https://brainly.com/question/4372174

393/1000. i think, sorry. :c

Answer:

C. 8/17

Step-by-step explanation:

PM = 16+14 = 30 cm

KP= LN = 16×tan45° = 16×1 = 16cm

by using pythagorean theorem, we find :

KM² = PM²+KP²

= 30²+16²

= 900+256

= 1156

=> KM =√1156 = 34cm

so, cos theta = KP/KM = 16/34 = 8/17

Answer:

The pattern is [tex]n^{4}[/tex].

Step-by-step explanation:

[tex]1^{4}[/tex] = 1, [tex]2^{4}[/tex] = 16, [tex]3^{4}[/tex] = 81, [tex]4^{4}[/tex] = 256

So the pattern is [tex]n^{4}[/tex].

Step-by-step explanation:

open the bracket

6={(1/5×4y) + 1/5×10}

6=4/5y+2

6-2=4/5y

4=4/5y

divide both sides by 4/5

y=1/5

The answer you are looking for is y=5.

Solution/Explanation:

Writing out the problem,

6=1/5(4y+10)

Using the Distributive Property,

6=4/5y+2

Subtracting 2 from both sides of the equation,

6-2=4/5y

4=4/5y

Multiplying both sides by 5, to transform the fraction into a whole number,

20=4y

Finally, dividing both sides by 4,

So, therefore the final answer is y=5.

Answer:  Choice A.

- 4.5 because it is the negative number with the greatest absolute value.

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

Explanation:

Stuff to the left is smaller than stuff on the right for any number line.

For example, we can say 2 < 5 since 2 is to the left of 5.

Another example: -7 < 4

To find the smallest item of your given list, we need to look at the value that is furthest to the left. That value would be -4.5 and this value is negative with the largest absolute value (i.e. it is furthest away from 0).

Check out the number line diagram below. It shows where all of the values are placed. We can see that -4.5 is the left-most item.

Answer:

yes their size is medium

Answer:

answer of 11

Step-by-step explanation:

given A=30°

R.H.S=2sinA cosA

=2 * sin30° * cos30°

[tex] 2 \times \frac{1}{2} \times \frac{ \sqrt{3} }{2} [/tex]

[tex] = \frac{ \sqrt{3} }{2} [/tex]

=sin60°

sin 2*30°

=sin2A

L.H.S=R.H.S

Answer:

7500 ( 1.023 ) ^(x)

Step-by-step explanation:

x is the number of years that go by

hope this helps some

Answer:

(0,4)

Step-by-step explanation:

The line AD is a median, because D is the midpoint of BC.

The centroid is the point of intersection of three medians of triangle, we don't need to depict any another median, because we know that centroid divide each median in ratio 2:1 from the vertices of a triangle from which a median was depicted. That's obvious that the median AD was depicted from A. Let the point of centroid be M. AM:MD is 2:1. So we should find the coordinates of D

xD= (xa*1+xd*2)/ (2+1)= ((-4)*1+2*2)/3=0

yd= (ya*1+yd*2)/ (2+1)= (2*1+ 5*2)/3=12/3=4

(0,4)

Answer:

Ah Here We Go Again :) After Five Years

Answer:

    8- 3x = 2 I think this is

Answer: The unknown number is 2.

Step-by-step explanation:

Let the number be x

8-3x = 2

or, -3x = -6

so, x = -6/-3

so, x = 2

Answer:

y - 27 = 0 (x - 21) or y = 27

Step-by-step explanation:

Answer:

a) Option A is correct.

b) Option B is correct.

Step-by-step explanation:

[tex]a) \: \: 5 \times a \\ = 5a[/tex]

[tex]b) \: \: b \times b \\ = {b}^{2} [/tex]

Answer:

width = 12 ft

Step-by-step explanation:

A = w * l

w = a/ 1 = 204/ 17 = 12 ft

Answer:

Are you in geometry?

For question 5:

To solve for x:

Triangle to the right with the 72 degrees in one angle.

All triangles add up to 180.

Subtact 72 from 180 = 108

Now we need to find the two other angles of that triangle.

We know that the two given eqations for that triangle is 6x-2 and 11x-9 (remeber the property creating the area of intersection, two congruent angles, so the equation 11x-9 applys for both triangles.)

So for the triangle to the right;

(6x-2) + (11x-9) = 108

lets add like terms next

17x - 11 = 108

add 11 to 108

17x = 119

divide 17 from both sides

x = 7

Now we need to find y.

On triangle to the right we have 30degrees. Lets subtract 30 degrees from 180. This equals 150.

We can plug in 7 to the equation 11x-9 which give us 68.

We now know to angles of the triangle. Lets subtract 68 from 150.

We get 82.

The last angle is 82, Which means lets find y.

5y - 8 = 82

add 8 to both sides

5y = 90

divide by 5 to both sides

y = 18

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try number 6. on your own to see if you get it know. If you don't, comment to me regarding what you don't understand.

Answer:

2,083.3

Step-by-step explanation:

Step-by-step explanation:

8. b1 = (2×401.94)/19.8 - 14.4

= 40.6 - 14.4 = 26.2 cm

9. h = (2×205)/(20+21)

= 410/41

= 10cm

[tex]\\ \rm\longmapsto <AEC+<CED+x=180[/tex]

[tex]\\ \rm\longmapsto 47+90+x=180[/tex]

[tex]\\ \rm\longmapsto 137+x=180[/tex]

[tex]\\ \rm\longmapsto x=180-137[/tex]

[tex]\\ \rm\longmapsto x=43[/tex]

Answer:

r = - 29

Step-by-step explanation:

Given

- 3r = 87 ( divide both sides by - 3 )

r = [tex]\frac{87}{-3}[/tex] = - 29

Answer:

r=87÷ -3

r= -29

The formula that gives us the cost, in dollars, to fill up the rest of the tank is,

Cost = (g - 2) × c

Given that;

The car currently has 2 gallons of gas and can hold a maximum of g gallons,

Hence, the amount of gas needed to fill the tank is,

(g - 2) gallons.

If the cost of gas is c dollars per gallon, the total cost to fill up the rest of the tank can be calculated by multiplying the number of gallons needed by the cost per gallon:

Cost = (g - 2) × c

Thus, the formula that gives us the cost, in dollars, to fill up the rest of the tank is,

Cost = (g - 2) × c

To learn more about the equation visit:

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