Geometry HW! PLS HELP

Please help me with this one question, and I'll upvote the brainliest answer

ra1l [238]

Answer: " x = 12 " .

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Step-by-step explanation:

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Note: If 2 (two) triangles are "similar" ; then their corresponding sides are "proportional".

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Since one of the sides [the "hypotenuse"] of one the triangles given ; shows the measurement containing an expression with a value of "x" — specifically; " 6x + 28 " ;

→ And since we want to solve for the value of "x" ; we use this "hypotenuse" of said particular triangle to set up a "proportion" with corresponding sides; so we can solve for "x" :

→ Set up proportions as a "ratio" ; or fraction:

→ 7:28::25:(6x + 28) ; Solve for "x" ;

Let us write this in the form of a "fraction" :

→ $\frac{7}{28} = \frac{25}{(6x+28)}$ ;

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Note:

→ Rewrite: " $\frac{7}{28}$ " ; by simplifying to:

" $\frac{1}{4}$ " ;

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→ Since: " $\frac{7}{28}$ " ;

= " (7÷7) / (28÷7) " ;

= " (1 /4) " ;

= " $\frac{1}{4}$ " .

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Now, rewrite the "proportion" ; as follows:

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$\frac{1}{4} = \frac{25}{(6x+28)}$ ;

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Now: "Cross multiply" ; that is:

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→ Given: " $\frac{a}{b} = \frac{c}{d}$ " ;

and: " b $\neq$ 0 " ; " d $\neq$ 0 " ;

→ Then: " a * d " = " b * c " .

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Likewise: " 1(6x + 28) = (4) * (25) " ;

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SImplify: " 6x + 28 = 100 " ; Solve for "x" ;

→ Subtract "28" from each side of the equation:

→ " 6x + 28 - 28 = 100 - 28 " ;

to get: → " 6x = 72 " ;

Now, divide each side of the equation by: " 6 " ;

to isolate "x" on one side of the equation; & to solve for "x" ; as follows:

→ " 6x = 72 " ;

→ 6x / 6 = 72 / 6 ;

to get:

→ " x = 12 " ;

→ which is the answer.

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Hope this helps!

Best wishes in your academic pursuits

— and within the "Brainly" community!

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5 0

2 years ago

For what value of c is the function defined below continuous on (-\infty,\infty)?

kozerog [31]

$f(x)= \left \{ {{x^2-c^2,x \ \textless \ 4} \atop {cx+20},x \geq 4} \right
$

It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
A function, f, is continuous at x = 4 if
 $\lim_{x \rightarrow 4} \ f(x) = f(4)$

In notation we write respectively
 $\lim_{x \rightarrow 4-} f(x) \ \ \ \text{ and } \ \ \ \lim_{x \rightarrow 4+} f(x)$

Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just 4c + 20.

On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
$\lim_{x \rightarrow 4-} f(x) = \lim_{x \rightarrow 4-} (x^2 - c^2) = 16 - c^2$

Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c²

$c^2+4c+4=0
\\(c+2)^2=0
\\c=-2$

That is to say, if c = -2, f(x) is continuous at x = 4.

Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers $(-\infty, +\infty)$

4 0

2 years ago

a farmer bought a number of pigs for $180. However, 3 of them died before he could sell the rest at a profit of 8 per pig. His t

Gre4nikov [31]

Answer:

He bought approximately 16 pigs.

Step-by-step explanation:

In order to find how many pigs the farmer had originally all you have to do is add three to amount of pigs he sold, since three of the died. In order to find how many he sold all you need to do is divide 109 by 8, since he made a profit of $8 per pig. 109 / 8 = 13.625, 13.625 + 3 = 16.625

4 0

3 years ago

Planes Q and R are parallel. Explain how you know lines a and b are skew.

gizmo_the_mogwai [7]

Answer:

We don't know that they skew but if Q and R are the same length then they aren't. But if Q and R are different lengths then they are skew. It would help to post a picture.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Who was regarded as the father of geomotry

zheka24 [161]

Answer:Euclid

Step-by-step explanation:

Euclid was an ancient Greek mathematician in Alexandria, Egypt. Due to his groundbreaking work in math, he is often referred to as the 'Father of Geometry'. Euclid's most well-known collection of works, called Elements, outlines some of the most fundamental principles of geometry.

4 0

1 year ago

Read 2 more answers