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?

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:

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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!

Answer:

3x^2+2x+1

Step-by-step explanation:

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

Easy.

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.

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]

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 :

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]

Answer:

4f-5+6g

Step-by-step explanation:

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

Answer:

11,390

Step-by-step explanation:

67,000 x 17%= 11,390

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:

Answer:

2.5*10^4

I hope this helps

Answer:

2.5 x 10^4

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

Answer:

good luck

Step-by-step explanation:

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:

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

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

Answer:

903

Step-by-step explanation:

Answer:

129 x 6=774

774+1=775

Step-by-step explanation:

Hope this helps

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

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

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

Answer:

The answer to this is agree . Hope it helps.

Answer:

x=6(given)

-5x+1

-5*6+1

-30+1

-29

hope this answer helps u

pls mark it as brainliest

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:

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

Answer:

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

Answer:

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

Step-by-step explanation:

Answer:

x – 4.9 = 0.3 and x – 4.9 = –0.3

Answer:

d

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

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.

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.