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Yakvenalex [24]
2 years ago
7

A 21 foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground if 14 f

oot from the base of the building. How high up the wall does the ladder reach
Mathematics
1 answer:
Evgesh-ka [11]2 years ago
5 0

Answer:

15.65 foot

Step-by-step explanation:

Pythagoras theorem can be used

a² + b² = c²

a being 14
b being unknown ( x )
c being 21

hence,

14² + x² = 21²
196 + x² = 441

x = √245  

  = 15.65 foot (answer)

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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20" id="TexFormula1" title=" \fra
beks73 [17]

Here is you're answer:

In order to get the answer you have to find the common denominator then add.

  • \frac{1}{2} + \frac{1}{3}
  • Find common denominator:
  • CD = 6
  • Add:
  • 1 + 1 = 2
  • = \frac{2}{6}
  • Simplify:
  • \frac{2}{6} \div 2 = \frac{1}{3}
  • = \frac{1}{3}

Therefore you're answer is "1/3."

Hope this helps!

3 0
3 years ago
The amount of protein a person needs each day is proportional to his or her weight. Rod weighs 165 pounds and needs 60 grams of
lukranit [14]
The equation for this would be: \frac{60}{165}=  \frac{x}{220}. first you want to multiply 60 by 220, then divide the product by 165.  60 times 220 is 13,200.  Now divide 13,200 by 165.  This will give you 80.  Todd has to eat 80 grams of protein each day to stay healthy.
6 0
3 years ago
What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79
Julli [10]

Answer:

Tn = Tn-1 + 2(n-1) + 5

Kindly note that Tn-1 means T subscript n-1

Step-by-step explanation:

Here, we want an expression for the nth term.

First term is 7

Then first common difference is 7

second common difference is 7 + 2

Third common difference is 9 + 2

So within the common differences, the nth term is 7 + (n-1) 2

Now, the nth term of the series would be;

Tn = Tn-1 + 7 + 2(n-1)

Tn = Tn-1 + 7 + 2n -2

Tn = Tn-1 + 2n + 5

Now there is a fix to this,

n for the term is not the same n for the common difference.

the 7th term works with the 6th common. difference, while the 8th term work for the 7th common difference.

So we might need to rewrite the final expression as follows;

Tn = Tn-1 + 2(n-1) + 5

6 0
3 years ago
Each interior angle of a regular hexagon is 4x+24°. What is x?
Oduvanchick [21]
Each interior angle of a regular hexagon is 120°.
.. 4x +24° = 120°
.. 4x = 96° . . . . . . . subtract 24°
.. x = 24° . . . . . . . . divide by 4
7 0
3 years ago
Find the polynomial of minimum degree, with real coefficients, zeros at
drek231 [11]

Answer:

\huge\boxed{p(x)=4x^3-20x^2+4x+300}

Step-by-step explanation:

\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has  a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)

\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300

7 0
3 years ago
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