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3 years ago

Help me out PLEASE. begging.

Mathematics

1 answer:

spayn [35]3 years ago

5 0

The ladder will reach 122 ft up the building.

The 120 feet of the extended ladder, since it will be leaning against the building, will be the hypotenuse of the right triangle. x will be the height from the top of the fire truck to the point where the ladder hits the building. 75° is the angle the ladder will make with the fire truck.

We have an angle, the side opposite the angle, and the hypotenuse. Opposite/hypotenuse is the ratio for sine, so we set up our equation as such:

x/120 = sin 75

Multiply both sides by 120:
120(x/120) = 120*sin 75
x = 120*sin 75
x ≈116

However, this is just from the top of the fire truck to the point where the ladder hits the building. We still add the 6 feet from the top of the truck to the ground. 116+6 = 122.

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3 years ago

Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?

worty [1.4K]

Answer:

Step-by-step explanation:

$(x+y+z)(xy+xz+yz)=18$ Equation 1

$x^2(y+z)+y^2(x+z)+z^2(x+y)=6$ Equation 2

What is the value of $xyz$ where each variable represents a real number?

Let's expand equation 1:

$(x+y+z)(xy+xz+yz)=18$

$x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18$

Simplify each term if can:

$x^2y+x^2z+xyz+y^2x+xyz+y^2z+xyz+z^2x+z^2y=18$

See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have $x^2$ and if I factored $x^2$ from first two terms I would have $x^2(y+z)$ which is the first term of left hand side of equation 2.

So let's see what happens if we gather the terms together that have the same variable squared together.

$x^2y+x^2z+y^2x+y^2z+z^2y+z^2x+xyz+xyz+xyz=18$

Factor the variable squared terms out of each binomial pairing:

$x^2(y+z)+y^2(x+z)+z^2(y+x)+xyz+xyz+xyz=18$

Replace the sum of those first three terms with what it equals which is 6 from the equation 2:

$6+xyz+xyz+xyz=18$

Combine like terms:

$6+3xyz=18$

Subtract 6 on both sides:

$3xyz=12$

Divide both sides by 3:

$xyz=4$

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3 years ago

What is. C(3a+b) and what does it equal to

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4 years ago

I need help with number 2 ASAP!!!!! The pictures is number 2.

mars1129 [50]

Answer:

$a=22.5\ units$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

In this problem

If polygon RSUPE is similar to polygon KQUIC

then

$\frac{RS}{KQ}=\frac{RE}{KC}$

substitutes the values and solve for a

$\frac{a+2}{14}=\frac{17.5}{10}\\ \\10a+20=14*17.5\\ \\10a=245-20\\ \\a=225/10\\ \\a=22.5\ units$

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3 years ago

After spending $30 on a dress, Mary had 3/8 of her money left. How much money did she have at first?

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4 years ago

Read 2 more answers