A 15 foot ladder leans against a building and reaches a window 12 feet above the ground. What is the measure of the angle, to the nearest degree, that the ladder forms with the ground?

The area of the triangle is 6 square units

The formula for calculating the area of a triangle is expressed as:

From the given triangle, the length of the diagonal of each square is expressed as:

[tex]l=\sqrt{1^2+1^2} \\l=\sqrt{2}[/tex]

Height of the triangle = √2 + √2 = 2√2

Base of the rectangle = √2 + √2 + √2= 3√2

Area of the triangle= 0.5 * 2√2 * 3√2  

Area of the triangle 3(2)

Area of the triangle = 6 square units

Hence the area of the triangle is 6 square units

Learn more on area of triangle here; https://brainly.com/question/17335144

Answer:

Step-by-step explanation:

C=25m plus 75

Answer:

[tex]x+\sqrt{x+3}=3+3\sqrt{1-x}[/tex]

[tex]Remove~ Square ~root[/tex]

[tex]-36x^3+252x^2-540x+324=[/tex]

[tex]x^4-32x^3+286x^2-480x+225[/tex]

[tex]Now ~\mathrm{Switch\:sides}[/tex]

[tex]x^2-6x\sqrt{-x+1}-15x+18\sqrt{-x+1}+18=x+3[/tex]

[tex]\mathrm{Subtract\:}x^2-15x\mathrm{\:from\:both\:sides}[/tex]

[tex]x^2-6x\sqrt{-x+1}-15x+18\sqrt{-x+1}+18-\left(x^2-15x\right)=[/tex]

[tex]x+3-\left(x^2-15x\right)[/tex]

[tex]New ~Simplify[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}+18=-x^2+16x+3[/tex]

[tex]Subtract ~18~ from ~ both~ sides[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}+18-18=-x^2+16x+3-18[/tex]

[tex]Simplify[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}=-x^2+16x-15[/tex]

[tex]Now~ factor:[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}(-x+3)[/tex]

[tex]6\sqrt{-x+1}\left(-x+3\right)=-x^2+16x-15[/tex]

[tex]Solve~~-36x^{3}+252x^{2} -540x+324=x^{4} -32x^{3} +286x^{2} -480x+225=[/tex]

[tex]x=1,\:x=-3[/tex]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of kids and y represent the number of adults that can be invited to the park.

Since the family has at most $190 to spend, hence:

8x + 4y ≤ 190    (1)

Also, the maximum number of invites is 35 people. This is represented by the equation:

x + y ≤ 35       (2)

Graphing equation 1 and equation 2 using geogebra online graphing

We have the solution as:

(0, 35), (23.75, 0) and (12.5, 22.5)

Since the number of people must be a whole number, the possible solutions are:

0 children and 35 adults or 23 children and 0 adults or 12 children and 22 adults

Answer:

C

Step-by-step explanation:

C => 7 is mapped into both 8 and 12, and in a function, this is not allowed

Answer: 2

Step-by-step explanation:

Given

The polynomial is [tex]x^4+x^3-2x^2+x+1[/tex] is divided by [tex]x-1[/tex]

According to the remainder theroem

[tex]\Rightarrow x-1=0\\\Rightarrow x=1[/tex]

Put [tex]x=1[/tex] in the polynomial to get the remainder

[tex]\Rightarrow 1+1-2+1+1\\\Rightarrow 2[/tex]

So, we get the remainder 2.

Answer:

Answer:

(6/5) π in^2 or 1.2 π in^2

Step-by-step explanation:

the area of a circle and the area of one circle sector are proportional.

Area of the circle = radius^2 * π = 3^2 π = 9π in^2

the hidden date is that the centre angle of a circumference is 360 degrees

we have now to use a proportion that has this meaning:

if the area is 9π in^2 when the angle is 360 degrees, what is the area when the angle is 48 degrees?

9π : 360 = x : 48

x = (48 *9π)/360 = (6/5) π in^2

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Explanation:

The ratio of A to B is 5:3

Multiply both parts by x to get 5x:3x

We need 5x parts of A and 3x parts of B

Adding those parts should get us 656 mL total

A+B = total

5x+3x = 656

8x = 656

x = 656/8

x = 82

Therefore, we need 5x = 5*82 = 410 mL of compound A

Also, we need 3x = 3*82 = 246 mL of compound B

In total, we have A+B = 410+246 = 656 mL which helps confirm the answer.

-----------

Side note: The ratio  410:246 reduces to 5:3 after dividing both parts by 82.

Answer:

y=-4x

Step-by-step explanation:

First, out it into y=mx+b. Then find the slope(m). insert slope and one set of coordinates into equation and solve for y-intercept (b). Then you have your answer.

Answer:

y = 1x + 10

Step-by-step explanation:

y2 - y1 / x2 - x1

2 - 8 / -8 - (-2)

-6/ -6

1

y = 1x + b

2 = 1(-8) + b

2 = -8 + b

10 = b

Answer:

It will be above the ground in C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Correct choice is D

It depends on what type of triangle you’re dealing with, and what is marked similar.

Answer:

Something that's in your budget.

Answer:

how many members are in the club??

Answer:

7. 1583.36 cm³

8. 13,627.18 m³

Step-by-step explanation:

Volume of space consumed by the paper = volume of outer cylinder - volume of center cylinder

✔️Volume of Outer Cylinder:

Volume = πr²h

r = ½(12) = 6 cm

h = 14 cm

Volume = π*6²*14

Volume = 1583.36 cm³

✔️Volume of center cylinder:

Volume = πr²h

r = ½(4) = 2 cm

h = 14 cm

Volume = π*2²*14

Volume = 175.93 cm³

✅Volume of space of the toilet paper = 1583.36 - 175.93 = 1583.36 cm³

8. Volume of the solid = volume of the cone + volume of the cylinder

✔️Volume of the cone = ⅓πr²h:

r = 13 m

h = 14 m

V = ⅓*π*13²*14

V = 2,477.67 m³

✔️Volume of the cylinder = πr²h

r = 13 m

h = 21 m

V = π*13²*21

V = 11,149.51 m³

✅Volume of the solid = 2,477.67 + 11,149.51 = 13,627.18 m³

Answer:

ans: option D

Step-by-step explanation:

exterior angle of triangle is equal to sum of opposite interior angle I.e

angle ACD= angle CAB + angle ABC

Answer:

d

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ACD is an exterior angle of the triangle, then

∠ ACD = 80° + 60° = 140° → d

Answer:

209.25 ft²

Step-by-step explanation:

2.7cm * 5 = 13.5 ft

3.1cm * 5 = 15.5 ft

Area

a = 13.5 * 15.5

a = 209.25 ft²

Answer:

8.37cm

Step-by-step explanation:

2.7cm×3.1cm=8.37cm

Area rectangle is length by width

Answer:

Sin < A is 4 / 5

Step-by-step explanation:

sin = Opposite side / Hypotenuse side

sin = 8 / 10

sin = 4 / 5

Answer:

30.

Step-by-step explanation:

The 120 degree has to be the vertex angle.

The other 2 angles in the triangle will be congruent as the triangle is isosceles.

These 2 are both = (180-120) / 2

= 60/2

= 30 degrees.

Answer:

Answer:

Adjacent: <ABC and <CBD

Vertical: <ABC and <EBD

Step-by-step explanation:

Adjacent angles: Angles that share one ray.

Vertical Angles: Opposite angles created by the intersection of two lines.

Hope this helps!!

Answer:

ASA

Step-by-step explanation:

In given triangle

Line BC = Line QR

Angle ABC = Angle PQR

Angle ACB = Angle PRQ

Computation:

Angle ABC = Angle PQR (Angle)

Line BC = Line QR (Side)

Angle ACB = Angle PRQ (Angle)

So,

ΔABC ≅ ΔPQR

By Angle Side Angle property

ASA

Answer:

B cause it same

Step-by-step explanation:

If am wrong correct me thanks

Answer:

orange :P

Step-by-step explanation:

volume = a x a x a = 15 x 15 x 15 =3375 cubic mm

Answer:

3375 cm (so the 3375 with the 3 in the corner)

DONT PUT THE ONE WITH THE 2 IN THE CORNER. Put the one with the 3 in the corner. I have made this mistake too many time lol.

Work:

Given, side of a cube =15 cm

Volume of a cube = Length x Width x Height

A cubes length, width, and height are the same.

15×15×15=3375 cm squared  

Answer:

[tex]x = \frac{ 5 \ + \ \sqrt{31}}{2} \ , \ x = \frac{ 5 \ - \ \sqrt{31}}{2}[/tex]

Step-by-step explanation:

[tex]2x^2 - 10x - 3 = 0 \\\\a = 2 \ , b = - 10 \ , \ c = - 3 \\\\x = \frac{-b^2\ \pm \ \sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{10 \ \pm \sqrt{(-10)^2 - ( 4 \times 2 \times -3)} }{2 \times 2}\\\\x = \frac{10 \ \pm \sqrt{(100 - ( -24 )} }{4}\\\\x = \frac{10 \ \pm \sqrt{(100 + 24 } }{4}\\\\x = \frac{ 10 \ \pm \sqrt{124}}{4}\\\\x = \frac{ 10 \ \pm \sqrt{4 \times 31}}{4}\\\\x = \frac{ 10 \ \pm \sqrt{2^2 \times 31}}{4}\\\\x = \frac{ 10 \ \pm2 \sqrt{31}}{4}\\\\x = \frac{ 5 \ \pm\sqrt{31}}{2}\\\\[/tex]

[tex]x = \frac{ 5 \ + \ \sqrt{31}}{2} \ , \ x = \frac{ 5 \ - \ \sqrt{31}}{2}[/tex]

Answer:

y=cx-b/a

Step-by-step explanation:

ay+b=cx

ay=cx-b

y=cx-b/a

Answer:

Step-by-step explanation:

A transversal is a line that passes through two lines in the same plane at two distinct points. 

Transversals play a role in establishing whether two or more other lines in the Euclidean plane are parallel.

Eight angles of a transversal.

Answer:

A. 0.4 , -6

Step-by-step explanation:

equate each of them to 0

5x - 2 =0 , x + 6 = 0

5x = 2 , x = 0 - 6

x = 2/5 , x = -6

x = 0.4 , x = -6

Answer:

y = 2/3x - 5

Step-by-step explanation:

If two lines are parallel, they have the same slope. This means the line we are looking for has a slope of 2/3. Since we are also given a point, we can start by writing the equation in point-slope form which is represented by

[tex]y-y_{1} =m(x-x_{1} )[/tex]

Where m is the slope and (x1, y1) is a point. We have both, so we can substitute the values and simplify:

y + 1 = 2/3 (x - 6)

y + 1 = 2/3x - 4

y = 2/3x - 5