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tamaranim1 [39]
2 years ago
13

Which is best represent the area of a triangle of a height of x+7 and a base of 2x+12

Mathematics
1 answer:
Archy [21]2 years ago
8 0

\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ h=x+7\\ b=2x+12 \end{cases}\implies A=\cfrac{1}{2}(2x+12)(x+7) \\\\\\ A=\cfrac{1}{2}\underset{\stackrel{\uparrow \qquad }{\textit{common factoring}}}{2(x+6)(x+7)}\implies A=(x+6)(x+7)\implies A=\stackrel{\mathbb{F~O~I~L}}{x^2+13x+42}

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Latoya, Milan, and Hong served a total of 154 orders Monday at the school cafeteria. Latoya served 10 more orders than Milan, Ho
Tems11 [23]

Orders served by Latoya, Milan and Hong are 34, 24, 96 respectively.

<u>Solution:</u>

Given, Latoya, Milan, and Hong served a total of 154 orders Monday at the school cafeteria.  

Let orders served by Latoya ne a, orders served by Milan be b and orders served by hong be c.

Then, a + b + c = 154 ⇒ (1)

Latoya served 10 more orders than Milan, ⇒ a = b + 10

Hong served 4 times as many orders as Milan. ⇒ c = 4b

We have to find how many orders did they each serve?

Now, substitute a and c values in (1)

(b + 10) + b + 4b = 154

b + b + 4b = 154 – 10

6b = 144

b = 24

Then, a = 24 + 10 = 34 and c = 4 x 24 = 96.

Hence, orders served by Latoya, Milan and Hong are 34, 24, 96 respectively.

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3 years ago
I WILL GIVE BARINLEST WHO HELP ME<br><br>3
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Answer:

whats the question

Step-by-step explanation:

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3 years ago
Read 2 more answers
\frac{5}{9}+\frac{y}{3}<br> Welp
Sergeeva-Olga [200]
The answer is 3y+5/9.
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3 years ago
Difference of Squares gives which complex factors for the expression x2 +3?
Andreas93 [3]

Step-by-step explanation:

Shortest way to solve this question is to find the factors of the given expression.

The given expression is (x² + 13).

Now we have to factorize it.

(x² + 13) = x² + (√13)²

            = x² + [-(i)²√(13)²]  [Since i = √(-1)]

            = x² - (i√13)²

            = (x - i√3)(x + i√3) [Since (a² - b²) = (a + b)(a - b)]-by-

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3 years ago
Consider the diagram below. which of the following represents the values x,y and z?
Gemiola [76]

Answer:

x=4\sqrt{6}\ units

y=4\sqrt{2}\ units

z=4\sqrt{3}\ units

Step-by-step explanation:

The picture of the question in the attached figure

step 1

In the right triangle ABD

Applying the Pythagorean Theorem

x^2=y^2+(12-4)^2

x^2=y^2+64

y^2=x^2-64 ----> equation A

step 2

In the right triangle BDC

Applying the Pythagorean Theorem

z^2=y^2+4^2

z^2=y^2+16

y^2=z^2-16 ----> equation B

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

12^2=x^2+z^2

144=x^2+z^2 ----> equation C

step 4

Equate equation A and equation B

x^2-64=z^2-16

x^2=z^2+48 -----> equation D

step 5

substitute equation D in equation C

144=z^2+48+z^2

solve for z

2z^2=144-48

2z^2=96

z^2=48

z=\sqrt{48}\ units

simplify

z=4\sqrt{3}\ units

Find the value of x

x^2=z^2+48

x^2=48+48=96

x=\sqrt{96}\ units

x=4\sqrt{6}\ units

Find the value of y

y^2=z^2-16

y^2=48-16

y^2=32

y=\sqrt{32}\ units

y=4\sqrt{2}\ units

3 0
3 years ago
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