1.) A ladder is leaning against the side so that the distance on the ground between
the base and the house is 7 feet.
If the ladder is 15 feet long, then what is the angle at which the ladder is leaning?

Answers

Answer 1

Answer:

62.182°

Step-by-step explanation:

Using cos and sin you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.

Answer 2

The angle at which the ladder is leaning is 62.18°.

What is trigonometry?

Trigonometry is the branch of mathematics that deals with calculating the angles of triangles or the lengths of their sides. It mainly concerned on the properties of right angled triangle.

For the given situation,

The length of the ladder = 15 feet

The distance between the house and the ladder base = 7 feet

The angle at which the ladder is leaning can be found by using trigonometric ratio, cos θ.

we know that, [tex]cos[/tex] θ = [tex]\frac{Base}{Hypotenuse}[/tex]

The figure below shows the relationship between the sides.

⇒ [tex]cos[/tex] θ = [tex]\frac{7}{15}[/tex]

⇒ θ = [tex]cos^{-1}(\frac{7}{15} )[/tex]

⇒ θ = [tex]62.18[/tex]

Hence we can conclude that the angle at which the ladder is leaning is 62.18°.

Learn more about trigonometry here

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1.) A Ladder Is Leaning Against The Side So That The Distance On The Ground Betweenthe Base And The House

Related Questions

what is the decimal multiplier to increase by 2.5%

Answers

%100 x 2,5 is the answer

Solve this system:

2x+5y+z=3
x-3y+2z=2
-x+2y-3z=-7

Answers

Answer:

x= -3

y= 1

z= 4

Step-by-step explanation:

Please see the attached pictures for the full solution.

*I evaluated the determinants using Sarrus' rule (see last picture):

∆= aei +bfg +cdh -gec -hfa -idb

*The symbol '∆' (delta) is usually used to denote a determinant.

(0,0) is a solution to y> -3x + 4

Answers

Answer:

(0,0) is a solution.

Step-by-step explanation:

To see if this is true you can put (0,0) into the [tex]y[/tex] and [tex]x[/tex] variables like so: [tex]0>-3(0)+4[/tex]. When you solve this you get [tex]0>4[/tex] so this statement is true

2 2/3 as a improper fraction

Answers

Answer:

8/3

Step-by-step explanation:

Answer: 8/3

Step-by-step explanation: if you write 2 has a fraction with the denominator being 3 you will get 6/3 then you can add 6/3+2/3=8/3

Someone help me please

Answers

Answer:

good luck

Step-by-step explanation:

129 times 6+1 pronto fast

Answers

Answer:

903

Step-by-step explanation:

Answer:

129 x 6=774

774+1=775

Step-by-step explanation:

Hope this helps

X(x+5)+7(x+5)



Help please its for algebra class thanks for your support and your help thanks a lot

Answers

Answer:

x^2+12x+35

Step-by-step explanation:

Let's simplify step-by-step.

x(x+5)+7(x+5)

Distribute:

=(x)(x)+(x)(5)+(7)(x)+(7)(5)

=x^2+5x+7x+35

Combine Like Terms:

=x^2+5x+7x+35

=(x^2)+(5x+7x)+(35)

=x^2+12x+35

Answer:

=x^2+12x+35

X^2+12x+35
Pls mark brainliest

can someone please help me with this ​

Answers

Answer:

m<B=74°

Step-by-step explanation:

3x-23+2x-12=180

5x-35=180

5x=180+35

5x=215

x=215÷5

x=43

m<B=2x-12=2(43)-12=86-12=74

answer:

b= 10x i pretty sure

Step-by-step explanation:

Solve

3x + 8 = 2x + 21

Answers

Answer:

Step-by-step explanation:Simplifying

3x + 8 = 2x + -21

Reorder the terms:

8 + 3x = 2x + -21

Reorder the terms:

8 + 3x = -21 + 2x

Solving

8 + 3x = -21 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

8 + 3x + -2x = -21 + 2x + -2x

Combine like terms: 3x + -2x = 1x

8 + 1x = -21 + 2x + -2x

Combine like terms: 2x + -2x = 0

8 + 1x = -21 + 0

8 + 1x = -21

Add '-8' to each side of the equation.

8 + -8 + 1x = -21 + -8

Combine like terms: 8 + -8 = 0

0 + 1x = -21 + -8

1x = -21 + -8

Combine like terms: -21 + -8 = -29

1x = -29

Divide each side by '1'.

x = -29

Simplifying

x = -29

3x + 8 = 2x + 21

3x - 2x + 8 = 21

x + 8 = 21

x = 21 - 8

x = 13

Can someone do this for me ill give you brainliest

Answers

Answer:I think you make somthing like i think task one would be lets say (Av)task two would be like(Bx) and it would all end out like this C

Av+Bx=C

Step-by-step explanation:

Marcos is baking a cake. He has a recipe for a large cake that calls for 6 cups of flour, 2 cups of sugar, and 1 cup of butter. Marcos only has ½ cup of sugar, so he's going to make a smaller cake. How much flour and butter should he use in his recipe?

Answers

Answer:

3/2 cups of flour

1/4 cups of butter

Step-by-step explanation:

Cups of flour = 6

Cups of sugar = 2

Cup of butter = 1

Marcos only has ½ cup of sugar, so he's going to make a smaller cake.

Cups of sugar for big cake = 2

Cups of sugar for small cake = 1/2

Ratio of cups of sugar for big cake to small cake is

= 2 : 1/2

= 2 ÷ 1/2

= 2 × 2/1

= 4

This means to make smaller cake, all recipes should be divided by 4

Flour for small cake = flour for big cake / 4

= 6 / 4

= 3/2 cups of flour

= 1.33

Butter for small cake = Butter for big cake / 4

= 1 / 4 cups of butter

= 0.25

Pls help me with this question

Answers

Answer:

option C, x=1

Step-by-step explanation:

[tex]2^{9x-3} = 8^{3-x}[/tex]

[tex]2^{9x-3} = (2^3)^{3-x}[/tex]

[tex]2^{9x-3} = 2^{9-3x}[/tex]

cut 2 from LHS and RHS  you will get,

9x-3 = 9-3x

9x + 3x = 9 + 3

12x = 12

x = 12/12

x = 1

therefore, option C is the correct option

hope it helps you!

Answer:

[tex] \huge{ \boxed{ \bold{ \tt{x = 1}}}}[/tex]

Option C is correct.

Step-by-step explanation:

[tex] \text{First ,\: let's \: know \: about \: exponential \: equation} : [/tex]

Exponential Equation

An equation in which variables appears as an exponent of a base is known as exponential equation. The following axioms are useful while solving the exponential equations :

If [tex] \sf{ {a}^{x} = {a}^{b} }[/tex] , then x = bIf aˣ = 1 , then aˣ = a⁰ and x = 0

Thus , while solving an exponential equation, we should simplify the equation till the equation is obtained in the form [tex] \sf{ {a}^{x} = {a}^{b}} [/tex] or aˣ = 1 .

Now, let's start to solve :

[tex] \sf{ {2}^{(9x - 3)} = {8}^{( 3 - x)}} [/tex]

➸ [tex] \sf{ {2}^{9x - 3} = {2}^{3(3 - x)} }[/tex]

➸ [tex] \sf{ {2}^{9x - 3} = {2}^{9 - 3x}} [/tex]

➸ [tex] \sf{ \cancel{2} ^{ \: 9x - 3} = \cancel{2} ^{ \: 9 - 3x} }[/tex]

➸ [tex] \sf{9x - 3 = 9 - 3x}[/tex]

➸ [tex] \sf{9x + 3x = 9 + 3}[/tex]

➸ [tex] \sf{12x = 12}[/tex]

➸ [tex] \sf{ \frac{12x}{12} = \frac{12}{12}} [/tex]

➸ [tex] \boxed{ \sf{x = 1}}[/tex]

The value of x is 1 .

Hope I helped!

Best regards! :D

~[tex] \text{TheAnimeGirl}[/tex]

- (-6x + 6) + 3 = 3 + 4x
I need help

Answers

Answer:

x=3

Step-by-step explanation:

-1(-6x + 6) + 3 = 3 + 4x

6x - 6 + 3 = 3 + 4x

6x - 3 = 3 + 4x

2x - 3 = 3

2x=6

x=3

Answer:

x=3

Step-by-step explanation:

-(-6x+6)+3=3+4x

6x-6+3=3+4x

6x-3=3+4x

6x-4x=3+3

2x=6

x=6/2

x=3

final answer

thank you bro

Solve for a
3a +1=4. With a 7 under it

Answers

Answer:

a=9

Step-by-step explanation: 

(3a+1)/7=4

This deals with linear equations with one unknown.

Overview

Steps

Terms and topics

1 result(s) found

a=9

See steps

Step by Step Solution:

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (3*a+1)/7-(4)=0  

Step by step solution :

STEP

1

:

           3a + 1

Simplify   ——————

             7    

Equation at the end of step

1

:

 (3a + 1)    

 ———————— -  4  = 0  

    7        

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  7  as the denominator :

        4     4 • 7

   4 =  —  =  —————

        1       7  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(3a+1) - (4 • 7)     3a - 27

————————————————  =  ———————

       7                7    

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  3a - 27  =   3 • (a - 9)  

Equation at the end of step

3

:

 3 • (a - 9)

 ———————————  = 0  

      7      

STEP

4

:

When a fraction equals zero

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 3•(a-9)

 ——————— • 7 = 0 • 7

    7    

Now, on the left hand side, the  7  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  3  •  (a-9)  = 0

Equations which are never true:

4.2      Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3      Solve  :    a-9 = 0  

Add  9  to both sides of the equation :  

                     a = 9

One solution was found :

a = 9

Hope this helps! Please mark Brainliest!

subtract the 1 multiply by 7 on each side and divide by 3 a=7

Which conversions go from a smaller unit to a larger unit? Select all that apply.
centimeters to millimeters
decimeters to meters
hectograms to kilograms
liters to centiliters

Answers

Answer:

decimeters to meters

Step-by-step explanation:

There are 10 decimeters in a meter.

Answer:

decimeters to meters

hectograms to kilograms

Step-by-step explanation:

What is the Nature of Roots of x^2+9x+14=0?

Answers

Answer:

(x+7)(x+2)

Step-by-step explanation:

If we multiply it out we get:

x * x = x^2

7 * x = 7x

2 * x = 2x

7 * 2 = 14

Add it all, we get: x^2 +9x+14

Therefore these are the factors

Ryan earned a yearly income of $67,000, he needed to pay an income tax of 17% . What was the amount of income tax he paid

Answers

Answer:

11,390

Step-by-step explanation:

67,000 x 17%= 11,390

the empire state building weighs about 7.3X10 to the 8 power (pounds) the world trade center building weighs about 88,200,000 pounds. what’s is total weight, in pounds, of these two buildings? Expressing your answer in scientific notation in the form aX10 to the power of B, what are the values of A and B?

Answers

Answer:

which principle prevents a brach from abusing  its powerwhich principle prevents a brach from abusing  its power

Step-by-step explanation:

Does anyone know the answer to both of these questions??

Answers

The first one is m= -5 (D)
The second one is x= -3 (A)

Divide these polynomials.

(9x^3 + 9x^2 + 5x + 1) / (3x + 1)

Answers

Answer:

3x^2+2x+1

Step-by-step explanation:

Divide 9x^3+9x^2+5x+1 by 3x+1

Easy.

just a lil some some so please help me

Answers

Answer:

The answer to this is agree . Hope it helps.

The circumferences of earth is about 25,000 miles which is the circumference written in scientific notation

Answers

Answer:

2.5*10^4

I hope this helps

Answer:

2.5 x 10^4

this is a filler. I hope this helps though :)))))

solve the equation. -3x^2=12x+12
a.) no real solution
b.) x= -2
c.) x= 2
d.) x= -2 and x=2

Answers

3x^2+12x+12=0
=(3x+6)(x+2)
b) x=-2

At a pumpkin patch, if Armando guesses the weight of his pumpkin within 0.3 pounds, he gets to take the pumpkin home for free. If his pumpkin weighs 4.9 pounds, which two equations can be used to find the minimum and maximum weights he can guess in order to get his pumpkin for free?

x – 0.3 = 4.9 and x – 0.3 = –4.9
x + 0.3 = 4.9 and x + 0.3 = –4.9
x + 4.9 = 0.3 and x + 4.9 = –0.3
x – 4.9 = 0.3 and x – 4.9 = –0.3
Please Help <3

Answers

Answer:

x – 4.9 = 0.3 and x – 4.9 = –0.3

Answer:

d

Step-by-step explanation:

What is the value of x

Answers

Answer:

98 degrees

Step-by-step explanation:

First calculate the entire triangles angles:

180 - 53 - 45 = final angle of triangle

82 = final angle of triangle

Using the straight line rule for angles, x and the inner angle must equal to 180 degrees:

180 - 82 = x

98 = x

Angle x is 98 degrees.

the slopes of two lines are 2 and -2. because of this we can conclude these two lines are which of the following?

Answers

intersecting, as they would have one solution.

Answer:

they also can be considerd perpendicular because they interset and make a 90 degree/right angle

Step-by-step explanation:


A. y = 1x+2!
or
B. y = 1x - 21

Answers

Answer:

B.y=|x-2|

Step-by-step explanation:

y is equal to the modulus of x-2 two because in the graph the the line cut at -2


. Find the coefficient of x3 in the expansion of (3+2x+x2)6

Answers

Answer: 9180

Step-by-step explanation:

(3 + 2x + x^2)^6 = x^12 + 12x^11 + 78x^10 + 340x^9 + 1095x^8 + 2712x^7 + 5284x^6 + 8136x^5 + 9855x^4 + 9180x^3 + 6318x^2 + 2916x + 729

This can be found using Pascal's Triangle.

The coefficient of x^3 is 9180.

how do I write the expression (4f-3+2g)-(-4g+2) in standard form​

Answers

Answer:

4f-5+6g

Step-by-step explanation:

Given f (x) = -5x + 1, find f (6)

Answers

Answer:

x=6(given)

-5x+1

-5*6+1

-30+1

-29

hope this answer helps u

pls mark it as brainliest

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