10
6
What is the length of the missing side?

Answer:

59.04°

58.31 inches

Step-by-step explanation:

The solution triangle is attached below :

Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;

Let the angle = θ

Tanθ = opposite / Adjacent

Tanθ = 50/30

θ = tan^-1(50/30)

θ = 59.036°

θ = 59.04°

The length of ladder can be obtained using Pythagoras :

Length of ladder is the hypotenus :

Hence,

Hypotenus = √(adjacent² + opposite²)

Hypotenus = √(50² + 30²)

Hypotenus = √(2500 + 900)

Hypotenus = 58.309

Length of ladder = 58.31 inches

Answer:

59°

58.3 inches

Step-by-step explanation:

Here is the full question :

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Please check the attached image for a diagram explaining this question

The angle the ladder makes with the ground is labelled x in the diagram

To find the value of x given the opposite and adjacent lengths, use tan

tan⁻¹ (opposite / adjacent)

tan⁻¹  (50 / 30)

tan⁻¹ 1.667

= 59°

the length of the ladder can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√(50² + 30²)

√(2500 + 900)

√3400

= 58.3 inches

[tex]\boxed{\sf 1-sin^2\theta=cos^2theta}[/tex]

[tex]\boxed{\sf cos^2\theta=\dfrac{1}{sec^2\theta}}[/tex]

Solution:-

Let's do

[tex]\\ \sf\longmapsto k=sec^2\theta(1+sin\theta)(1-sin\theta)[/tex]

[tex]\\ \sf\longmapsto k=sec^2\theta(1-sin^2\theta)[/tex]

[tex]\\ \sf\longmapsto k= sec^2\theta(cos^2\theta)[/tex]

[tex]\\ \sf\longmapsto k=sec^2\theta\times \dfrac{1}{sec^2\theta}[/tex]

[tex]\\ \sf\longmapsto k=1[/tex]

[tex]\color{lime}\boxed{\colorbox{black}{Answer : - }}[/tex]

[tex] \sec^{2} θ(1 + \sinθ)(1 - \sinθ) = k[/tex]

[tex] \sec^{2} θ \: (1 - { \sin}^{2} θ) = k[/tex]

[tex] { \sec }^{2} θ \cos^{2} θ = k[/tex]

[tex] \sec ^{2} θ. \frac{1}{ {sec}^{2}θ } = k[/tex]

[tex]1 = k[/tex]

Therefore:

[tex] \color{red}k = 1[/tex]

Answer:

we have to add (-b) to get (a)

Step-by-step explanation:

a+b+(-b)=a

a+b-b=a

a=a

Hence verified.

Hope this helps you. Have a nice day^_^

The most common denominator for them is the LCM which is 21

Now

2/7 = 2/7×3/3

= 6/21

Therefore 6/21 and 10/21

Must click thanks and mark brainliest

Answer:

96 dollars and 50 cents

Step-by-step explanation:

Step-by-step explanation:

Hi there!

Given;

Point Q is located at (-4, 6). Point R is located at (8, 6).

Note: Use distance formula.

Now;

[tex](d) = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

Keep all values;

[tex](d) = \sqrt{ {(8 + 4)}^{2} + ( {6 - 6)}^{2} } [/tex]

Simplify;

[tex](d) = \sqrt{( {12)}^{2} } [/tex]

Therefore, the distance is 12 units.

Hope it helps!

Answer:

D

Step-by-step explanation:

Sector of Area=(theta/360)*pi*r^2

Sector of area=(135/360)*pi*19^2=(1083)/8 pi

Answer:

Nicholas can order up to 3 toppings.

Step-by-step explanation:

Solve for the tip:

15% of the total cost = 15% × $7.50

Convert percentage into a decimal:

0.15 × 7.50 = 1.125

Variable x = number of toppings

Set up an equation:

7.50 + 1.125 + 1.25x = 13

Combine like terms:

8.625 + 1.25x = 13

1.25x = 4.375

x = 3.5

Since it is impossible to order "half" of a topping (0.5), Nicholas can only order up to 3 toppings.

Answer:

The second one....

Less than "3" and Greater than "2"

Step-by-step explanation:

Step-by-step explanation:

Claim: There's 14 Goats and 9 Chickens!!

Data:

Working with the Provided Information.

Let the Number of goats be x

let the Number of Chickens be y

x + y = 23..... (i)

Since the goat Possesses Two Pair of Legs... Which is a Total of 4 Legs... We say Let its Contribution be 4x.

The Chicken has Only a Pair Of Legs...Which is a total of 2 legs.... We say let its contribution be 2y

4x + 2y = 74 .....(ii)

BRINGING BOTH EQUATIONS TOGETHER.

x + y = 23

4x + 2y = 74

From Eqn i

x= 23 - y

Substitute into eqn ii

4(23 - y ) + 2y = 74

92 - 4y + 2y = 74

92 - 2y = 74

2y = 92 - 74

2y = 18

y= 9.

Substitute y into any of the eqns to get x

x + y = 23

x + 9=23

x = 23 - 9

x = 14

This simply proves that there are 14 Goats and 9 Chickens!!!.

HAVE A GREAT DAY!

Answer:

40

Step-by-step explanation:

Answer:10/5

Step-by-step explanation:

Answer:B

Step-by-step explanation:

From calculating the equations below, we find that all sections have m equal to negative three.

According to the second option, it is most likely because six is added.

Answer:

[tex]m=\frac{15}{8}[/tex]

Step-by-step explanation:

[tex]-6\left(1-m\right)=9-2m[/tex]

[tex]-6(1-m)=-6+6m[/tex]

[tex]-6+6m=9-2m[/tex]

Add 6 to both sides:-

[tex]-6+6m+6=9-2m+6[/tex]

[tex]6m=-2m+15[/tex]

Now, add 2m to both sides:-

[tex]6m+2m=-2m+15+2m[/tex]

Divide both sides by 8:-

[tex]\frac{8m}{8}=\frac{15}{8}[/tex]

[tex]m=\frac{15}{8}[/tex]

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

OAmalOHopeO

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

Answer:

your answer is m=15/8

Answer:

Who is at the trail start at 9:00 a.m.? : Andy

Who runs fastest? : Caedin

When do Andy and Berta cross paths? : 9:08 am

Who is closest to the 1.5 mile mark after 6 minutes? : Berta

Step-by-step explanation:

assignment

Answer:

The measure of the angle is greater than 360°.

Answer:that s math

Step-by-step explanation:

Answer:

the choices for answers are technically incorrect...

the "correct" answer is [tex]m^6n^4[/tex]

the answer that matches that (which is not simplified) is:

"A":    [tex]\frac{m^{7} n^{3} n}{m}[/tex]

Step-by-step explanation:

Answer:

Both are TRUE.

Step-by-step explanation:

The sum of 2 rational numbers is always rational.

The sum of 2 irrational numbers is always irrational.

The sum of two rational numbers is always rational the sum of two irrational numbers is always irrational.

Rational number are real numbers that can be expressed as a ratio of two integers.

Irrational number are real numbers that cannot be expressed as a ratio of two integers.

Now, to prove that,

The sum of two rational numbers is always rational.

Let us take an example,

Suppose two rational numbers sqrt(16) and sqrt(36),

So, there sum is given as,

sqrt(16) + sqrt(36) = 4 + 6

sqrt(16) + sqrt(36) = 9

which is rational.

Hence, the sum of two rational numbers is always rational.

The sum of two irrational numbers is always irrational

Let us take an example,

Suppose two irrational numbers sqrt(7) and pi,

So, there sum is given as,

sqrt(7) + pi = 5.7857...

This cannot be reduced to any kind of fraction

So, we will get an irrational number.

Thus, the sum of two irrational numbers is always irrational.

Hence, the sum of two rational numbers is always rational the sum of two irrational numbers is always irrational.

To learn more about rational and irrational numbers :

https://brainly.com/question/15267867

#SPJ2

Answer:

1267f335677632157853

Answer:

a) (x + 2)(3x + 1) = x^2 + 7x + 2

b) (2x - 3)(2x + 4) = 4x^2 + 2x - 12

c) (x + 2)(avg. length of base, x + 6) = x^2 + 8x + 12

d) Is the radius 4x + 12? If so: (4x + 12)(4x + 12) = (16x^2 + 96x + 144) x pi

Step-by-step explanation:

Brainliest, please!

We have to find 2℅of the amount

[tex]\\ \sf\longmapsto 4.3\times \dfrac{2}{100}[/tex]

[tex]\\ \sf\longmapsto \dfrac{8.6}{100}[/tex]

[tex]\\ \sf\longmapsto 0.086[/tex]

It will spend $0.086Trillion

Answer:

160

Step-by-step explanation:

20 dollars per hour * 8 hours per day

160 dollars per day

Answer:

Alex makes $ 160 per day

Step-by-step explanation:

If she earns $20 per hour and works for 8 hours

8 × 20 = 160

Answer:

1.5

Step-by-step explanation:

y=2x - 3

0 = 2x - 3

-2x = - 3 /÷(-2)

x = 3 ÷ 2

x = 1.5 3/2

Answer:

24 days

total units = 120* 30 = 3600

used after 10 days =  120*10 = 1200

remaining units after 10 days = 3600-1200 = 2400

2400/100 people = 24 days that the provisions will last

Step-by-step explanation:

Answer:

x = 17.51

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 35 = x/25

25 tan 35 =x

x=17.50518

Answer:

universal set is the right answer

Answer:

0.47 yes, 0.1666... yes, 0.5473 no, 0.541 yes

Step-by-step explanation:

0.47 yes: is a repeating decimal

0.1666... yes: is a repeating decimal

0.5473 no: is neither terminating or repeating

0.541 yes: is terminating

Hi, I'm happy to help!

To simplify this expression, we need to first use the order of operations (Parenthesis, Exponents, Multiplication or Division (Left to Right), and Addition or Subtraction (Left to Right)), then combine like terms. (80,40,57, or 6t, 8t, 98t, or 2t²,7t²,83t²)

When a number is next to parenthesis with no sign, it means we are using multiplication. We can change this expression to look like this, by changing all the numbers next to the parenthesis with no sign, to one with a multiplication sign.

8(5+t) - 2(t+1) 8(5 + t) - 2(t+1)=

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

We start with parenthesis and solve everything inside of those, but, because everything inside the parenthesis are unlike terms, we cannot combine them.

Next, We look for any exponents (x²). There are none in this equation.

We then look for multiplication or division. There is a lot of multiplication, so we start solving that from left to right.

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

Now, before we do anything else, we need to recheck the parenthesis, now that they have changed. We can further simplify the middle parenthesis by adding together like terms.

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - ((80t+16t)+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

Now, we look for addition or subtraction of like terms. We can now remove the parenthesis, since everything inside of the last two parenthesis is negative, we turn it negative, as long as we only combine the like terms.

40+8t - 96t-16t²-80 - 2t-2=

Once we find like terms, we can rearrange the expression.

(40-80-2)+8t - 96t+16t² - 2t

(-42)+8t - 96t-16t² - 2t

(-42)+8t - 96t-16t² - 2t

(-42)+(8t-96t-2t)-16t²

(-42)+(-90t)-16t²

(-42)+(-90t)-16t²

This doesn't have any like terms, so we don't alter it.

(122)+(-90t)-16t²

We can now remove the parenthesis.

122-90t-16t²

Since there are no more like terms this is the furthest we can simplify. We can then rearrange the expression to be arranged completely correct.

-16t²-90t-42

I hope this was helpful, keep learning! :D

Answer:

B

Step-by-step explanation:

The angle in a semicircle is 90° , then

x = 180° - (90 + 47) = 180° - 137° = 43° → B

Answer:

B. 43

Step-by-step explanation:

ignore the other triangle with the y angle. it is just there to confuse us.

the main information is given already by the main triangle with the angles x and 47 degrees.

because it's baseline is the diameter of a circle, and its top point is also on the circumference of the same circle.

all triangles that can be inscribed into a circle that way are by definition right-angled triangles.

so, the angle at the top point is actually 90 degrees.

and as we know, the sum of all angles in a triangle is always 180 degrees, we can simply calculate :

180 = 90 + 47 + x = 137 + x

x = 43 degrees

that's it.

Answer:

3 : 1

Step-by-step explanation:

volume = length * width * height

The volume of the solid as it is shown is:

volume = 10 m * 6 m * 10 m = 600 m^3

old volume = 600 m^3

Now we triple the length.

The length becomes 3 * 10 m = 30 m

The new volume is:

volume = length * width * height

volume = 30 m * 6 m * 10 m = 1800 m^3

new volume = 1800 m^3

ratio of new volume to old volume = 1800 m^3 : 600 m^3

Divide both sides of the ratio by 600 m^3.

Ratio = 3 : 1

Answer:     3 : 1