Marco needs to climb up to the roof of his house. He placed his ladder so that the bottom of
the ladder was 4 feet away from the wall. If his ladder was 13 feet long, how high up was the
top of the ladder against the wall of the house? Round your answer to the nearest tenth.

Step-by-step explanation: 6dsdsnds

Answer:

x = ±3 sqrt(2)

Step-by-step explanation:

x^2 = 18

Take the square root of each side

sqrt(x^2) = sqrt(18)

x = ± sqrt(18)

x =±sqrt(9*2)

x = ±sqrt(9) sqrt(2)

x = ±3 sqrt(2)

Answer:

The percentage discount for the cost of the guitar is 45%.

Step-by-step explanation:

First let's find the difference between the original price and the new price.

80 - 44 = 36

So the actual discount got the price down by $36.

To find the percentage discount we need to ask ourselves the question

36 is what percent of 80?

36 = X percent of 80

In math, of means multiply.

36 = X percent * 80

So to get the "X percent" part alone we divide by 80 on both sides.

36 divided by 80 = 0.45

36 is 45 percent of 80.

The percentage discount for the cost of the guitar is 45%.

Answer:

Yes, the card is a right triangle.

Step-by-step explanation:

The card is a right triangle, specifically a 3-4-5 right triangle.

A 3-4-5 right triangle is any right triangle that has side lengths in the ratio of 3:4:5.

The 3-4-5 rule says that any triangle with a side length ratio of 3:4:5 is a right triangle.

So, the card is a right triangle.

Answer:

(13+30c)/10

Step-by-step explanation:

Given the expression;

1/2 + 3c + 4/5

Find the LCM

= 5(1)+10(3c)+2(4)/10

=  (5+30c+8)/10

= (13+30c)/10

Hence the required sum is (13+30c)/10

Answer:

The 8th term of the sequence is 255

Step-by-step explanation:

To find the 8th term of the sequence, we have to use the given sequence formula

All we have to do here is to make a substitution

We simply have to substitute the value 8 for n as follows;

a8 = 2^8 - 1

a8 =256-1

a8 = 255

Answer:

26

Step-by-step explanation:

Perimeter= width+height+width+height

               = 5 + 8 + 5 + 8

               = 26 cm

Hope this helps!

Answer:  Choice C.  [tex]3\sqrt{17}[/tex]

================================================

Work Shown:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(12-15)^2 + (-21-(-9))^2}\\\\d = \sqrt{(12-15)^2 + (-21+9)^2}\\\\d = \sqrt{(-3)^2 + (-12)^2}\\\\d = \sqrt{9 + 144}\\\\d = \sqrt{153}\\\\d = \sqrt{9*17}\\\\d = \sqrt{9}*\sqrt{17}\\\\d = 3\sqrt{17}\\\\d \approx 12.3693169\\\\[/tex]

I used the distance formula for those steps above.

The two points were (x1,y1) = (12,-21)  and (x2,y2) = (15,-9) but you could swap the order.

As an alternative route, you can plot the two points on the same xy grid. Then form a right triangle such that the hypotenuse is between the two points mentioned. The pythagorean theorem should lead you to the same answer as above. In fact, the distance formula is basically a modified version of the pythagorean theorem.

Answer:

101 + 102 + 103 + ... + 998 + 999 + 1000

Step-by-step explanation:

=====================================================

Explanation:

This series is arithmetic since the common difference is 1. In other words, we're adding 1 to each term to get the next one.

The quickest way to find the sum is to use the formula below

S = (n/2)*(a+b)

where n is the number of terms, 'a' is the first term, and b is the last (or nth) term. This formula only works for arithmetic series.

We can see that n = 100, a = 1 and b = 100, so....

S = (n/2)*(a+b)

S = (100/2)*(1+100)

S = 50*101

S = 5050

-----------

This can be confirmed by noticing that we have 100/2 = 50 pairs of terms. Pair up the terms such that 1 goes with 100, 2 goes with 99, 3 goes with 98, and so on.

We have these fifty sums

1+100 = 101

2+99 = 101

3+98 = 101

....

48+53 = 101

49+52 = 101

50+51 = 101

We have 50 copies of 101 being added, which leads to 50*101 = 5050

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

The slowest and most tedious way to confirm this is to type 1+2+3+...+98+99+100 into your calculator. The result should say 5050. Using a spreadsheet would be a better option instead of using a handheld calculator. I don't recommend this unless you need more proof that we end up with 5050 as the final answer.

Answer:

Circumference of a circle

Step-by-step explanation:

The circumference of a circle is longer than its radius of the circle.

Answer:

180

Step-by-step explanation:

to work out all possibilities you multiple the amount of options.

4x5x9=180

Answer:

Step-by-step explanation:

[tex]One \ million = 1, 000, 000\\\\Two \ hundred \ and \ fifty \ thousand = 250, 000[/tex]

Difference between one million and two hundred and fifty thousand

[tex]1,000,000[/tex]  [tex]- \ 250,000[/tex] [tex]= 750000[/tex]

International  Number System,750,000: Seven Hundred  and Fifty Thousand

Nepalis Number System,7, 50,000 : Seven Lakh Fifty Thousand

you are driving onajor highway 94 mp

Answer:

10x is equal to 100 so 100+6=106

then

Step-by-step explanation:

4x is equal to 8 so 4+18=22

so it's 128

Answer:

B. (2, 6)

Step-by-step explanation:

Xp = 1 + (1/6 × (7-1)) = 1 + (1/6×6) = 1+1 = 2

Yp = 8 + (1/6 × (-4-8)) = 8+(1/6×(-12))

= 8+(-2) = 6

the coordinate => (2, 6)

Answer:

x = 20

Step-by-step explanation:

90 = 60 + (x + 10)

90 - 60 = x + 10

30 = x + 10

30 - 10 = x

20 = x

Answer:

x = 20

Step-by-step explanation:

From the diagram we see that ∠60° and ∠(x + 10)° are supplementary, therefore we know that the following is true...

60° + (x + 10)° = 90°

Now we just solve the equation and get the following...

60° + (x + 10)° = 90°

x° + 10° = 30°

x° = 20°

x = 20

Answer:

C. There are two solutions: 2 and –2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

we have

we know that

The solution of the function is equivalent to solve the following system of equations

 ------> equation A

 ------> equation B

The x-coordinate of the intersection point both graphs is the solution of the given function

Using a graphing tool

see the attached figure

The intersection points are  and  

therefore

The solution of the given function are

Solve x2 + 2 = 6 by graphing the related function. x^2 + 2 is a parabola with a vertex at the point (0, 2). When x = -1 or x = 1, then x^2 + 2 = 3, so we should put the points (-1,3) and (1,3) on the graph. When x = -2 or x = 2, then x^2 + 2 = 6, so we should put the points (-2,6) and (2,6) on the graph. We could continue adding points to the graph if we want, but we already have our two solutions. x^2 + 2 = 6 when x = -2 or x = 2. Therefore, x = -2, and x = 2 are the two solutions to this equation.

Answer: option C.

Step-by-step explanation:

Given  a quadratic function of the form , if the coefficient a is less than zero, then the function is opened upward.

The options A is not opened upwards, then it is not the answer.

Then the given equation  can be written as:

This function is equal to the parent function, shifted 4 units down.

Therefore, the graph that you are looking for must be a parabola that is opened upwards and has its vertex in the point (0,-4).

Then, the correct option is C. And the solution is:

Answer:

A = 6π

Step-by-step explanation:

Expression for the area of a sector is given by,

A = [tex]\frac{\theta}{360}(\pi r^{2} )[/tex]

For θ = 240° and r = 3,

By substituting these values in the given expression,

A = [tex]\frac{240}{360}(\pi) (3)^{2}[/tex]

   = [tex]\frac{240\times 9}{360}\pi[/tex]

   = 6π

Therefore, A = 6π is the answer.

Answer:

Step-by-step explanation:

1400×0.35

490+450

940

Answer:

The domain is thus [0, 1400].

The range is thus [$450, $940]

Step-by-step explanation:

A suitable function is P(N) = ($450) + ($0.35 / item)*N, where $450 is the base pay per week and N is the number of items sold.

In this case the salesman has only 1400 items available to sell each week.  Therefore N begins at 0 (no items to sell) and ends at 1400 (the max number of items available to sell).  The domain is thus [0, 1400].

The smallest amount the salesman could receive would be when he has not sold any items:  $450.  

The max amount is then $450 + ($0.35/item)(1400 items), or

                                         $450 + $490, or

                                          $940

The range is thus [$450, $940]

Answer:

< B = 180-30-65=85°

< E = 85°

< D = 30°

< C = 65°

BC = 20/35 × 28 = 16

Answer:

$45

Step-by-step explanation:

[tex]180 \times 25\%[/tex]

[tex]180 \times \frac{25}{100} [/tex]

[tex] \frac{18 \times 25}{10} [/tex]

[tex] \frac{450}{10} [/tex]

[tex]45[/tex]

Answer:

El pastel se debe dividir en 6 partes iguales, de las cuales Santiago debe tomar 3 y Alba debe tomar 2.

Step-by-step explanation:

Dado que Santiago quiere comer la mitad de un pastel y Alba quiere un tercio del mismo pastel, para repartirlo bien se deben reducir las fracciones a su común denominador. Así, para determinar en cuántas partes iguales deben dividir el pastel y cuántas partes debe tomar cada uno se deben realizar los siguientes cálculos:

Santiago = 1/2

Alba = 1/3

2 x 3 = 6

Santiago = 1/2 = 3/6

Alba = 1/3 = 2/6

Por lo tanto, el pastel se debe dividir en 6 partes iguales, de las cuales Santiago debe tomar 3 y Alba debe tomar 2.

Answer:

The value of x is 4.

Step-by-step explanation:

The perimeter of the triangle is the sum of the lengths of all its sides.

The perimeter of the rectangle is twice the sum of the length and the width.

base of triangle = x

two equal sides = x + 5

length of rectangle = x - 1

width of rectangle = x + 4

According to the question,

Perimeter of triangle = perimeter of rectangle

x + x + 5 + x + 5 = 2 ( x - 1 + x + 4)

3 x + 10 = 2 (2 x + 3 )

3 x + 10 = 4 x + 6

4 x - 3 x = 10 - 6

x = 4

Answer:14 m

Step-by-step explanation:

Dada

larga [tex]l=20\ m[/tex]

superficie [tex]A=280\ m^2[/tex]

Suponga que el ancho es w

La superficie está dada por el producto de la longitud y la anchura.

[tex]\therefore A=lw\\\Rightarrow 280=20\times w\\\Rightarrow w=14\ m[/tex]

Por lo tanto, el ancho es de 14 m.

Given:

The figure of a right angle triangle.

A line segment intersect the two sides and parallel to third side of the triangle

To find:

The value of x.

Solution:

According to basic proportionality theorem, if a line segment intersect the two sides and parallel to third side of the triangle, then it divides the two sides proportionally.

Using basic proportionality theorem, we get

[tex]\dfrac{8}{20-8}=\dfrac{6}{x}[/tex]

[tex]\dfrac{8}{12}=\dfrac{6}{x}[/tex]

[tex]\dfrac{2}{3}=\dfrac{6}{x}[/tex]

On cross multiplication, we get

[tex]2\times x=6\times 3[/tex]

[tex]2x=18[/tex]

[tex]x=\dfrac{18}{2}[/tex]

[tex]x=9[/tex]

Therefore, the value of x is 9.