using special right triangles, solve for x.

Answer:

x = 7.3

Step-by-step explanation:

We're going to use the formula for the area of a triangle:

Area = 1/2 x base x height

We can see that the height of the triangle is 10, but we don't know what the base length is.

We know that one of the angles is 54 °, so we're going to use SOH CAH TOA to work out the length of the base.

We're using the height and the base, which are the opposite (O) and adjacent  (A) sides relative to our angle. According to SOH CAH TOA we'll use tan (T).

The equation is tan(Ф°) = O/A, where Ф is our angle (54°), O is our opposite side (10), and A is our adjacent side. Since we don't know what A is we'll use x.

tan (54°) = 10/x

Multiply both sides of the equation by x.

x tan (54°) = 10

Divide both sides of the equation by tan(54°).

x = 10/tan(54°)

Use your calculator to solve for x.

x = 7.265

To the nearest tenth, x = 7.3

Answer = 42.8

Step-by-step explanation:

All right triangles have one right (90-degree) angle, and the hypotenuse is the side that is opposite or the right angle, or the longest side of the right triangle.[1] The hypotenuse is the longest side of the triangle, and it’s also very easy to find using a couple of different methods. This article will teach you how to find the length of the hypotenuse using the Pythagorean theorem when you know the length of the other two sides of the triangle. It will then teach you to recognize the hypotenuse of some special right triangles that often appear on tests. It will finally teach you to find the length of the hypotenuse using the Law of Sines when you only know the length of one side and the measure of one additional angle

Answer:

a1 = 0.5; common ratio = 5

Step-by-step explanation:

Let the common ratio = r

a2 = 2.5

a3 = 2.5r

a4 = 2.5r * r = 2.5r^2

We are told a4 = 62.5, so

2.5r^2 = 62.5

Divide both sides by 2.5

r^2 = 25

r = 5

a2 = a1 * r

a1 = a2/r = 2.5/5 = 0.5

Answer: a1 = 0.5; common ratio = 5

Answer:

J - Age of Jan

G - Age of George

J + G = 65

J+10 = 4(G+10)

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

because what is 24 meters- 24meters=0

Answer:

He weighs 172 pounds

Step-by-step explanation:

you can look up conversions like this on google and it will give you the exact weight and everything!

After converting Lucas's weight of 78 kg is 171.192 pounds

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 minutes

1 km = 1000 m

We have,

78 kg

Now,

1 kg = 2.204 pounds

Multiply 78 on both sides.

78 kg = 78 x 2.204 pounds

78 kg = 171.912 pounds

Thus,

78 kg is 171.912 pounds

Learn more about unit conversion here:

https://brainly.com/question/13899873

#SPJ2

Answer:

see below

Step-by-step explanation:

From Netgames

175≥ 99 + 8x

Subtract 99 from each side

175-99 ≥ 99-99 + 8x

76≥  8x

Divide each side by 8

76/8 ≥  8x/8

9.5≥  x

He can get up to 9 months along with the equipment

From Anytime

175≥ 19 + 19x

Subtract 19from each side

175-19 ≥ 19-19 + 19x

156≥  19x

Divide each side by 19

156/19 ≥  19x/19

8.210526316≥  x

He can get up to 8 months along with the equipment

Since he can get more months from Netgames, he should rent from netgames

Answer:

The center should rent from Net games

Step-by-step explanation:

1. Net games:

175 ≥ 99 + 8x

175 - 99 ≥ 8x

76 ≥  8x

9.5 ≥  x

It can rent games for 9 and a half months

2. anytime games:

175 ≥ 19 + 19x

156 ≥  19x

8.2 ≥  x

It can rent games for 8 months

3. Since the center can rent games for a longer period of time with Net games (9.5 months compared to anytime's 8 months), it should rent from there.

Hope this helps, and please mark me brainliest if it does!

Answer:

7

Step-by-step explanation:

10-3=7

Answer:

y

Step-by-step explanation:

The variable in 8y^3 is y because a variable is a number that we don't know yet, and that is the only one.

Answer:

Percent of error = 4.80% (Approx)

Step-by-step explanation:

Given:

Mass of sample = 109 gram

Actual mass of sample = 104 gram

Find:

Percent of error.

Computation:

Error = Mass of sample - Actual mass of sample

Error = 109 gram - 104 gram

Error =5 gram

Percent of error = (Error / Actual mass of sample)100

Percent of error = (5 / 104)100

Percent of error = 4.80% (Approx)

Answer:

see explanation

Step-by-step explanation:

15

The x- coordinate of E is the same as the vertex F

The y- coordinate of E is the same as the vertex G

E = (b, c )

The x- coordinate of D is the same as vertex G

The y- coordinate of D is the same as vertex F

D = (a, 0 )

16

The x - axis is an axis of symmetry in the rhombus , thus

D is a reflection of B so D = (0, b )

The y- axis is an axis of symmetry in the rhombus, thus

E is a reflection of C so E = (a, 0 )

Answer:

x = 4 , 2

Step-by-step explanation:

x² - 6x + 8=0

(x -2)(x + 4)=0

x= 4,2

Therefore the zeros of f(x) are 4 and 2.

Hope this helps.

Answer: a

Step-by-step explanation:

Answer:

121

Step-by-step explanation:

The exterior angle  measurement is equal to the sum of the opposite interior angles

34+ 87 = z

121 = z

Answer:

work is shown and pictured

Answer:

(4x + 5)(4x + 5)

Step-by-step explanation:

Took test.

Want a more in-depth explanation? Try visiting the Math Nation site.

Answer:

180 degrees rotation

Step-by-step explanation:

you take the. values of the object and multiply by -1 to obtain the values of the image

________________________________

5y-3y+12

=2y+12

So the new expression becomes 2y+12

hope it helps

Good luck on your assignment

________________________________

Answer:

2y+12

Step-by-step explanation:

Answer:

The correct option is (B)

(B) x-y = 6 , 3x+4y = 4

Step-by-step explanation:

As we can see in the graph given below, both lines intersect at (4, -2), which should be the solution of given equations:

Find the values of x and y for (B);

x - y = 6 ⇒ (i)

3x + 4y = 4 ⇒ (ii)

Lets consider equation (i)

x - y = 6

x = 6 + y

Substitute in equation (ii)

3(6+y) + 4y = 4

18 + 3y + 4y = 4

7y = -14

y = -2

Substitute in equation (i)

x - (-2) = 6

x + 2 = 6

x = 6 - 2

x = 4

As solution of part C is also (4, -2), it represents the graph

You can also find the (x, y) for other options the similar way, which will show you they don't have the same value

Answer:

its  B

Step-by-step explanation:

Answer:

15:2; there are 2 counselors to every 15 campers

Step-by-step explanation:

Answer:

C 6 yd by 7 yb

Step-by-step explanation:

Answer: De ansa is A m African sista.

Step-by-step explanation:

Answer:

(2, -2)

Step-by-step explanation:

Go along the x line to under point B (2) and then go up the y line to across form point B (2) then reflect it so (2, -2)

Answer:

(2,-2)

Step-by-step explanation:

when you reflect from b you two down to the x axis and the do it again. you will get your coordinates

Answer:

Step-by-step explanation:

Given sin α = –4∕5 and sin β = 1∕2

To get α from sin α = –4∕5,

α = arcsin(-4/5)

α = arcsin (-0.8)

α = -53.13°

If angle α is in quadrant III, then α = 180+53.13 = 233.13° (sin is negative in the 3rd quadrant)

Similarly for sin β = 1∕2

β = arcsin(1/2)

β = arcsin(0.5)

β = 30°

Since  β is in quadrant II,  β = 180-30 = 150°

To find  cos (α + β). where α = 233.13° and  β = 30°

cos (α + β)= cos (233.13 + 150)

= cos 383.13°

cos (α + β) = 0.9196

Answer:

x = 3 will be the answer.

Step-by-step explanation:

From right triangle ABC,

By applying Sine rule,

Sin45° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{BC}{AC}[/tex]

    [tex]\frac{1}{\sqrt{2}}[/tex]  = [tex]\frac{BC}{6\sqrt{2}}[/tex]

BC = 6 units

Now from right triangle BCD,

By applying Cosine rule,

Cos60° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{BD}{BC}[/tex]

[tex]\frac{1}{2}=\frac{x}{6}[/tex]

x = [tex]\frac{6}{2}[/tex]

x = 3

Answer:

X=42

Step-by-step explanation:

AB and BC make a right angle

So, 24°+x+24° =90°

48°+x=90°

X=90°-48°

X=42

______________________________

a. 42 degree.

b.i. q=135 degree( being vertically opposite angles)

j=135 degree( being corresponding angles)

b.ii. 225

a. 24+X+24=90[ sum of complementary angles]

or, 48+X=90

or,X= 90-48

X=42 degree

b.i. q=135 degree( being vertically opposite angles)

Vertically angles are always equal to each other.

j=135 degree( being corresponding angles)

Corresponding angles are always equal to each other.

b.ii. p+135=180[ sum of angle in straight line]

or,p= 180-135

p=45 degree.

q= 135 degree[ being vertically opposite angles]

r=p[being vertically opposite angles]

r=45 degree

Now,

p+q+r

= 45+135+45

=225 degree

Hope it helps

Good luck on your assignment

__________________________________

Answer:

[tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex].

Step-by-step explanation:

If a line passing through two points, then the equation of line is

[tex](y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It is given that the passing through (1,3) and (-9,-2).  So, equation of line in point slope form is

[tex]\Rightarrow (y-3)=\dfrac{-2-3}{-9-1}(x-1)[/tex]

[tex]\Rightarrow (y-3)=\dfrac{1}{2}(x-1)[/tex]

Slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

Now,

[tex](y-3)=\dfrac{1}{2}(x-1)[/tex]

[tex]\Rightarrow (y-3)=\dfrac{1}{2}(x}-\dfrac{1}{2}(1)[/tex]

[tex]\Rightarrow y=\dfrac{1}{2}(x}-\dfrac{1}{2}+3[/tex]

[tex]\Rightarrow y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex]

Therefore, the required equation is [tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex].

Answer:

The Answer is C

Step-by-step explanation:

i think This is correct

Answer:

B. y=(2x-3)/(x-4)

Step-by-step explanation:

Find the asymptotes.

Vertical Asymptotes:  

x  =  4

Horizontal Asymptotes:  

y  =  2

No Oblique Asymptotes.

The graph.

Answer:

44

Step-by-step explanation:

First you have to make sure that you move everything from one side to the other and set the equation equal to zero. Then you have to simplify the equation as much as you can so you get:

x/14

7 * (x/14)

eventually you get

(x-22)/2 =0

from there you can solve for 44

Step-by-step explanation:

You could do this in your head, but I'm going to type out everything.

Also, you're going to have to just test these out, there is no short cut for this sort of problem.

[tex]2(-2)-4(-3)=2\\-4+12=2\\8\neq 2\\\\2(-3)-4(-2)=2\\-6+8=2\\2=2[/tex]

I didn't do the last ordered pair because we already found one that fit the equation. Also, it wouldn't be a 1:1 equation if that last one was true, so you can rule it out once you see that (-3,-2) is the correct answer.

Answer:

(-3,-2)