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3 years ago

Unit 4 homework 3 Gina Wilson pls help w homework!

Mathematics

1 answer:

Llana [10]3 years ago

7 0

Answer/Step-by-step explanation:

1. An isosceles ∆ has two equal sides. The base angles of an isosceles ∆ are also equal.

Therefore:

m<U = 54° (base angle of isosceles ∆)

m<T = 180 - (54 + 54) (sum of ∆)

m<T = 72°

2. ∆LMN is an isosceles ∆, therefore:

m<M = ½*(180 - 28) = 76°

m<N = m<M (base angle of isosceles)

m<N = 76°

3. ∆FEG is an isosceles ∆, because it has two equal base angles.

Therefore:

EF = FG

EF = 18 in

m<F = 180 - (23 + 23) = 134°

4. ∆PQR is an equilateral ∆. All sides and angles of an equilateral ∆ are equal.

Therefore:

m<P = 60°

m<Q = 60°

m<R = 60°

5. 4x + 23 = 10x - 1 (2 asides of an isosceles ∆ are equal)

Collect like terms

4x - 10x = -23 - 1

-6x = -24

Divide both sides by -6

x = 4

6. 2*(9x - 25) = 180 - 104 (base angles of isosceles ∆)

18x - 50 = 76

Add 50 to both sides

18x = 76 + 50

18x = 126

Divide both sides by 18

x = 7

7. 5x - 7 = 8x - 55 (base angles of an isosceles)

Collect like terms

5x - 8x = 7 - 55

-3x = -48

Divide both sides by -3

x = 16

8. 4x + 8 = 60° (angle of an equilateral ∆)

Subtract 8 from each side

4x = 60 - 8

4x = 52

Divide both sides by 4

x = 13

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Hector needs 84 feet of fencing to enclose his rectangular gardenThe length of his garden is 12 feet less than twice its widthWh

mihalych1998 [28]

Answer:

The width of his garden is 18 feet.

Step-by-step explanation:

Let the length of Hector's rectangular garden is a feet and width is b feet.

So, by the given condition, we can write that

2(a + b) = 84

⇒ a + b = 42 ............ (1)

Again, the length of his garden is 12 feet less than twice its width.

So, a = 2b - 12 .............. (2)

Now, solving equations (1) and (2) we get,

(2b - 12) + b = 42

⇒ 3b = 54

⇒ b = 18 feet.

Now, from equation (1) we get,

a = 42 - b = 42 - 18 = 24 feet.

Therefore, the width of his garden is 18 feet. (Answer)

8 0

3 years ago

A sand box has an area of 45 ft. The length is 4 feet longer than the width. What are the dimensions of the sand box? Solve by c

erica [24]

So,

The sand box's area is 45 ft.

The length is 4 feet longer than the width.

We can solve by translating these sentences into mathematical form.

Let l represent length and w represent width.

First equation: lw = 45

Second equation: l = 4 + w

Substitute 4 + w for l in the first equation.
(4 + w)w = 45

Distribute
$w^{2} + 4w = 45$

Subtract 45 from both sides
$w^{2} + 4w - 45$

Factor
$(w + 9)(w -5) = w^{2} + 4w - 45$

Set both factors equal to zero.
w + 9 = 0
w - 5 = 0

Subtract 9 from both sides
w = -9

Add 5 to both sides
w = 5

We have to cross out -9 for the width, because, logically, it is impossible to have a negative width.

Substitute 5 for w in the second original equation.
l = 4 + (5)
l = 9

Check
5 * 9 = 45
45 = 45 This checks.

9 = 4 + 5
9 = 9 This also checks.

The length is 9 ft. and the width is 4 ft.

6 0

3 years ago

Write an equation for the translation of <img src="https://tex.z-dn.net/?f=y%5Cfrac%7B3%7D%7Bx%7D" id="TexFormula1" title="y\fra

lisov135 [29]

<h2><u>Answer:</u></h2><h2> $\boxed{\boxed{y=\frac{3}{x-6}-6}}$ </h2><h2 /><h2><u>Solution Steps:</u></h2>

______________________________

<h3>1.) Substitute x, y, and general form using the formulas:</h3>

Formula for x: $x=d=6$

Formula for y: $y=k=-6$

Formula for general form y: $y=\frac{a}{x-d}+k=y=\frac{3}{x-6}+(-6)$

Note:

<em> - When doing problems like this, it's best to list out each formula and do the drag down method, and replace methods rather than doing it the entire mathematical way, as doing it that way takes a long time and it's more confusing than it should be.</em>

<u>Equation at the end of Step 1:</u>

$y=\frac{3}{x-6}+(-6)$

<h3>2.) Simplify the d and k forms:</h3>

$y=\frac{3}{x-6}+(-6)=y=\frac{3}{x-6}-6$

<em> - The x(d) stays the same since the 6 was positive and we plugged it in making it negative, so it doesn't need to be changed. (Another way to know if you need to change it is if the original </em> $(d)$ <em> or </em> $(k)$ <em> when plugged in, you had to put them in parenthesis then most likely it needs to be changed. </em>

<em> - The y(k) changes from </em> $+(-6)$ <em> to </em> $-6$ <em> because when a </em> $(+)$ <em> and </em> $(-)$ <em> are next to each other, the rule is </em> $+$ <em>. The Minus always wins in this type of problem situation.</em>

So the answer is c, $\bold{y=\frac{3}{x-6}-6}$ .

______________________________

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3 years ago

HELP PLEASE!!!!! THESE ARE MY LAST POINTS HELP!!

Aleks04 [339]

9514 1404 393

Answer:

x ≈ 10.6

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relationship between trig functions and side of a right triangle. In particular, when the opposite side and hypotenuse are involved, the desired relation is ...

Sin = Opposite/Hypotenuse

For your triangle, this is ...

sin(62°) = x/12

x = 12·sin(62°)

x ≈ 10.6

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3 years ago

there are between 24 to 40 students in a class. the ratio of boys to girls is 4:7. how many students are in the class.

ZanzabumX [31]

Answer:

8 students

Step-by-step explanation:

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3 years ago

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