(trigonometry) solve for x

The bottom of the ladder is now 96 feet closer to the house compared to its initial position.

To solve this problem, we can use the concept of similar triangles. Let's denote the distance between the bottom of the ladder and the base of the wall as x (in feet). We are given the following information:

Initial ladder position:

Top of the ladder is 16 feet above the ground.

Bottom of the ladder is 12 feet away from the base of the wall.

New ladder position:

Top of the ladder is 18 feet above the ground.

Since the triangles formed by the ladder, the ground, and the wall are similar, we can set up a proportion to find the new distance between the bottom of the ladder and the base of the wall.

Using the initial position of the ladder:

(16 ft) / (x + 12 ft) = (18 ft) / (x)

Cross-multiplying:

16 ft * x = 18 ft * (x + 12 ft)

Expanding:

16x = 18x + 216 ft

Moving the terms involving x to one side:

16x - 18x = 216 ft

Simplifying:

-2x = 216 ft

Dividing by -2:

x = -108 ft

Since distance cannot be negative, we discard the negative solution. The distance between the bottom of the ladder and the base of the wall is 108 ft.

Now, to find how much closer to the house the bottom of the ladder is, we can subtract the initial distance (12 ft) from the new distance (108 ft):

108 ft - 12 ft = 96 ft

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According to the property of proportions,

Product of means = Product of extremes

So, simply we did cross multiplication.

Step-by-step explanation:

56/3 is the answer. Refer to the attachment for the solution. :)

Answer:

40 %

Step-by-step explanation:

the difference between cost and selling price:

91 - 65 = 26

Find the percentage:

26/65 = 0.4 --> 40%

Markup = 40%

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

dependant clause I think so I don't know sorry

Answer:

5x² + 13x - 6

Step-by-step explanation:

F - First ( multiply the first terms from each bracket )

I - Inner ( multiple the last term of the first bracket and the first term of the second bracket )

O - Outter ( multiply the outer terms i.e the first term of the first bracket with the last term of the 2nd bracket )

L - Last ( multiply the last terms of the brackets i.e the last term in the second bracket and the last term in the second bracket )

dont forget to take sign convention into consideration .

Answer:

[tex]t \le 6[/tex] min

Step-by-step explanation:

The time to do 25 problems should take less than (or equal to) the 150 minutes available.

[tex]25t \le 150\\t \le 6[/tex]

Answer:

B. four less than three times a number

Answer:

x=9

Step-by-step explanation:

−4(2x+5)+5x−1= −48

-8x-20+5x-1=-48

-3x-21=-48

-3x=-27

x=-27/-3

x=9

Answer:

63/100

Step-by-step explanation:

Im Pretty sure this the correct answer

Answer:

The answer is B

Step-by-step explanation:

Answer:

x = 5/7

Step-by-step explanation:

Here, we want to get the value of x

Firstly, according to indices;

(a^m)^n = a^(m * n) = a^mn

Also;

a^m * a*n = a^(m + n)

a^0 = 1 (any number raised to zero as its power is 1)

And lastly;

a^m divided by a^n = a^(m-n)

So using these we can have;

7^4x = 7^( 2 + 3)/7^3x

7^4x = 7^5/7^3x

7^4x = 7^(5-3x)

Since we have the same bases, we have to equate the powers

4x = 5-3x

4x + 3x = 5

7x = 5

x = 5/7

Answer:

D

Step-by-step explanation:

The very first thing you have to realize is that the temperature goes further down the minus scale which means that only A and D can be correct. That's because time in this question is positive.

So if you just try the first value (x = 3), you will get

-3/2 * 3 = -9/2 which would mean that you would add -4 1/2 onto - 10 which is much larger than - 10

A: is not the answer.

-2/3 * 3 - 10 = -6/3 - 10 = -2 - 10 = - 12

That is the answer you should get. The answer is D.

Answer & Step-by-step explanation:

Simplify the expression.

Exact Form:

7/12

Decimal Form:

0.583

Hope this Helps!!! :)

If you have any questions contact me in the comment section below!

Answer:

a. y= f(x-1)

Step-by-step explanation:

___________

Answer:

-1.3+2 that is point A to find ir

Answer:

x = 10

Step-by-step explanation:

We know that in a parallelogram base angles are supplementary angle (add up to 180°)

Given that;

∠U = 9x + 15

∠V = 6x + 15

we can say that:

∠U + ∠V = 180°

(9x + 15) + (6x + 15) = 180

Combining like terms we get;

15x + 30 = 180°

15x = 180 - 30

15x = 150

x = 150/15

x = 10

Hope this helps!

[tex]\huge{ \mathfrak{  \underline{ Answer} \:  \:  ✓ }}[/tex]

Figure - 1 :

The given triangles are similar, so their corresponding sides will be proportional.

Let the missing side be x

_____________________________

Figure - 2 :

The given figure is a Cylinder :

[tex] \large \boxed{ \mathrm{volume = \pi {r}^{2}h }}[/tex]

_____________________________

[tex]\mathrm{☠ \: TeeNForeveR \: ☠}[/tex]

Answer:

D.17

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

To find the answer we want to find the volume of each rectangular prism

Which ever prism has an exact volume of 98 is the correct answer

( note that volume of a rectangular prism = length times width times height )

For the first answer choice

4 * 3.5 * 7 = 98

We get an outcome of 98, which means that the first one could possibly be the correct answer however lets find the volume of the rest of the prisms just to be safe.

For the second one

6.25 * 7 * 2 = 87.5

87.5 ≠ 98 therefore the second choice is not correct

For the third one

3 * 6.5 * 5 = 97.5

97.5 ≠ 98 therefore the third choice is not correct

For the fourth one

7.5 * 1 * 14 = 105

105 ≠ 98 therefore the fourth choice is not correct

So we can conclude that the first answer choice is correct

Answer:

14

Step-by-step explanation:

The equation to find slope is [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. You plug in the values to get [tex]\frac{8-(-20)}{5-3}[/tex]. This simplifies to [tex]\frac{28}{2}[/tex], which is 14.

The rate charged per hour by the first mechanic = $105,

And the rate charged per hour by the second mechanic = $110.

Use the concept of ratio defined as:

A ratio indicates how many times one number contains another number. The ratio of two numbers is written as x: y, which is equivalent to x/y.

Where x and y are individual amounts of two quantities.

And, the Total quantity gives after combining as x + y.

Given that,

Two mechanics worked on a car.

The first mechanic worked for 10 hours.

The second mechanic worked for 5 hours.

Together, they charged a total of $1600.

The sum of the two rates charged per hour is $215.

Assume that,

The rate charged per hour by the first mechanic is = x dollars,

The rate charged per hour by the second mechanic is = y dollars.

The first mechanic worked for 10 hours,

The total amount earned by the first mechanic would be 10 times their hourly rate = 10x dollars.

Similarly,

The second mechanic worked for 5 hours,

The total amount earned by the second mechanic would be 5 times their hourly rate =  5y dollars.

Set up two equations based on the given information:

The first equation is the sum of the two rates, which is,

x + y = 215  ......(i)

The second equation is the total amount earned by both mechanics,

10x + 5y = 1600  .....(ii)

Use substitution to find the values of x and y:

From the first equation, we can express x in terms of y as,

x = 215 - y

Substitute this value of x into the second equation:

10(215 - y) + 5y = 1600

Expanding the equation, we get,

2150 - 10y + 5y = 1600

Combining like terms, we have:

-5y = 1600 - 2150

-5y = -550

Dividing both sides of the equation by -5, we get:

y = 110

Now that we have the value of y,

Substitute it back into the first equation to find x:

x + 110 = 215

Subtract 110 from both sides, and we get:

x = 105

Hence,

The rate charged per hour by the first mechanic is $105, &  the rate charged per hour by the second mechanic is $110.

Learn more about the ratio visit:

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Answer:

$12

Step-by-step explanation:

At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter. F(d), models the fee (in dollars) for climbing d meters. F(d)=110+0.12d, What is the increase in price for every 100 meters climbed?

Given:

F(d) = 110 + 0.12d

Where,

F(d) = the fee (in dollars)

d = number of meters climbed

What is the increase in price for every 100 meters climbed?

F(d) = 110 + 0.12d

$110 is the fixed fee

0.12 is the increase in price per meter.

Increase in price per 100 meters climbed = 0.12d

= 0.12 × 100

= 12

Increase in price per 100 meters climbed = $12

Answer:

circumference of the circle=2πr

=2×3.14×17

=106.76cm

Answer:

2018

Step-by-step explanation:

Answer:

1 . x 3 +  3 x 2 y  +  3 x y 2  +  y 3

2. x 3 -  3 x 2  y  +  3 x y 2  -  y 3

3. a + b

4 . a - b

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

B)

Step-by-step explanation:

Answer:

Step-by-step explanation: