solve similar triangles (advanced)

Answer:

112

Step-by-step explanation:

the average weight of 4boys 39.6 is Wight

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Explanation:

I'll use the variable x in place of 'a'

The expression we need to factor is [tex]21x^2-57x+30[/tex] which is in the form [tex]ax^2+bx+c[/tex]

So,

We'll plug those three values into the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-57)\pm\sqrt{(-57)^2-4(21)(30)}}{2(21)}\\\\x = \frac{57\pm\sqrt{729}}{42}\\\\x = \frac{57\pm27}{42}\\\\x = \frac{57+27}{42} \ \text{ or } \ x = \frac{57-27}{42}\\\\x = \frac{84}{42} \ \text{ or } \ x = \frac{30}{42}\\\\x = 2 \ \text{ or } \ x = \frac{5}{7}\\\\[/tex]

The two roots of [tex]21x^2-57x+30 =0[/tex] are [tex]x = 2 \text{ and } x = \frac{5}{7}[/tex]

The root x = 2 leads to the factor (x-2) after subtracting 2 from both sides.

The root [tex]x = \frac{5}{7}[/tex] leads to the factor (7x-5) after first multiplying both sides by 7, and then subtract 5 from both sides.

So we have this set of steps:

[tex]x = \frac{5}{7}\\\\7x = 5\\\\7x-5=0\\\\[/tex]

The two factors are (x-2) and (7x-5).

This leads to (x-2)(7x-5)

The last step is to replace x with 'a' so that the variables match up.

We arrive at  (a-2)(7a-5)

However, as the next section shows, we have a bit of a problem. Don't worry, it can be easily fixed.

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Let's expand out that factored expression we found earlier.

[tex](a-2)(7a-5)\\\\b(7a-5)\ \text{ ..... let b = a-2}\\\\7ab - 5b\\\\7a(b) - 5(b)\\\\7a(a-2) - 5(a-2)\ \text{ ..... plug in b = a-2}\\\\7a^2-14a - 5a+10\\\\7a^2-19a+10\\\\[/tex]

That's not good. We should have arrived at the original expression [tex]21a^2-57a+30[/tex]. To fix this discrepancy, we can stick a 3 out front and then notice that:

[tex]3(a-2)(7a-5) = 3(7a^2-19a+10) = 21a^2-57a+30[/tex]

The error has been fixed.

We have the full factorization of 3(a-2)(7a-5)

The order of the factors doesn't matter, so we could have written the answer as 3(7a-5)(a-2). Usually the factor without any variables will be listed first.

Based on the screenshot you posted, if that '7' is locked in place, then the only possible answer is 3(7a-5)(a-2) since you'll have 3 in the first slot, then a ( in the next slot. The other slots are filled out in a similar manner. There are no spaces between any symbol or letter.

Answer:

y=3.7x + 120.3, 180

Step-by-step explanation:

Add them into a graphing calculator and you get y=3.7x + 120.3

Put 16 in for x:

3.7 (16) + 120.3

59.2 + 120.3 = 179.5, rounds to 180

Answer:

2/3

Step-by-step explanation:

I hope it's the answer. if it isn't tell me so that I can try it again bye.

it is letter C. 3.9

hope it helps

#Chloe919

#thanks for the points

#carry on learning

Answer:

5/72

Step-by-step explanation:

this is the answer hope it helps

Answer:

correct answer is 10

Step-by-step explanation:

5/6÷1/12

5/6×12/1

5×2

=10

Answer:

If it's not what You are looking for type in the equation solver your own ... is 12 percent of 912.6 - step by step solution || 2x-9=2x-9 || 2(x-3)=4(x+2) ...

Step-by-step explanation:

sorry if im wrong

Answer:

∠BAC=70°

Step-by-step explanation:

If AB || CD and BC II DE that means the two triangles are congruent or the same, this means ∠BAC°=∠DCE°, ∠ABC°=∠EDC°, and ∠BCA°=∠DEC°. The three angles of a triagle add up to 180°. If ∠DEC=45° and ∠EDC=65°

Total°-(∠DEZ°+∠EDC°)=∠DCE° or ∠ECD°

180°-(65°+45°)=70°

∠BAC°=∠DCE°

Therefore ∠BAC=70°

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{3(7x - 6)}\\\large\rightarrow\textsf{3(7x) + 3(-6)}\\\large\rightarrow\textsf{21x - 18}\\\\\\\huge\text{Therefore, your answer is: \boxed{\textsf{21x - 18}}}\huge\checkmark[/tex]

[tex]\large\textbf{Note: All you had to do is DISTRIBUTE 3 the}\\\large\textbf{WITHIN PARENTHESES. }\large\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

y=(-1/4)x+(-6)

Step-by-step explanation:

slope is (-1/4) and the y intercept is (-6)

slope intercept form is

y=(-1/4)x+(-6)

Don't put parentheses in answer.

Step-by-step explanation:

(2m + 4) / 8 = w

2m + 4 = 8w

2m = 8w - 4

m = 4w - 2

Step-by-step explanation:

option A is correct.

hope this answer helps you dear! take care

Answer:

1100

Step-by-step explanation:

Answer:

A = 55.15

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos A = adj side / hypotenuse

cos A = 4/7

Taking the inverse cos of each side

cos ^-1 ( cos A) = cos ^-1( 4/7)

A =55.15009542

To the nearest hundredth

A = 55.15

Answer:

x=2

Step-by-step explanation:

6x+3+2x+1+4x=12x+4

5x+5x+3x+2=13x+2

12x+4=13x+2

4-2=13x-12x

2=x

Answer:

[tex]\huge\boxed{\sf |AB| = 8\ units}[/tex]

Step-by-step explanation:

Given the two co-ordinates:

A(x1,y1) = (-4,-8)

B(x2,y2) = (-4,0)

Putting them in the distance formula:

[tex]|AB| = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\|AB| = \sqrt{(-4-(-4))^2+(0-(-8))^2} \\\\|AB| = \sqrt{(-4+4)^2+(0+8)^2} \\\\|AB| = \sqrt{8^2} \\\\|AB| = 8\ units\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer: 1/8

Step-by-step explanation: 3-4 = -1

-3-5= -8

-1/-8=1/8

Answer:

Step-by-step explanation:

HOPE THIS HELPS :)

Answer:A standard form is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules. Representing very large or very small numbers concisely, the standard form is used. For example, 4.5 billion years is written as 4,500,000,000 years.

Step-by-step explanation:

Answer:

C 6,000,000

Step-by-step explanation:

Answer:

hi this should be your answer (-2,4),(0,0),(2,-4)

Step-by-step explanation:

hope this helps!

Answer: 125 hearts and 375 stars

Step-by-step explanation:

25% of 100 is 25. Take 100 and x it by 5. 100 x 5 is 500 making 25 x 5 125. That being said 125 hearts and 375 stars

Answer:

125 hearts and 375 stars

Step-by-step explanation:

Given the function f(x) = log 0.75x

The interval that contains all the x-values must be greater than 1.333

For the function to be positive, the expression 0.75x must be greater than and equal to 1 as shown:

Divide both sides by 0.75

0.75x/0.75 ≥ 1/0.75

x ≥ 1/0.75

x ≥ 1.333

Hence the interval that contains all the x-values must be greater than 1.333

Learn more on inequalities here: https://brainly.com/question/11613554

Answer:

Shifted to the right by 9 units, and down by 7 units

Step-by-step explanation:

y=x is the origin.

(x-9) shows that the graph has moved 9 units to the right, as what is inside the parentheses indicates the opposite direction

(you can be able to review why this is from online resources or you can ask your teacher)

the -7 shows that the graph moves 7 units down the graph, it's outside the parentheses, so it follows the same direction

let's sum up:

for this situation,

- what is inside the parentheses is the x

- what is outside the parentheses is the y

- the x-values direction shifts opposite from the sign (+/-)

- the y-values direction shifts like the sign (+/-)

So,

the vertex has been shifted to the right by 9 units, and down by 7 units compared to y=x.

Answer:

105t1

Step-by-step explanation:

por qué los sumas te da

Answer:

90,000

Step-by-step explanation:

3750ml/hr *24 hrs

Therefore, A leaking tap will waste 90000 ml in a day.

Hoped this helped

[tex]BrainiacUser1357[/tex]

Answer:

y = 5/6 x

Step-by-step explanation:

rise/run = slope

rise = 5

run = 6

so, 5/6 = slope

Answer:

v = 32

Step-by step explanation:

Step-1: Subtract 15 both sides

⇒ v/4 + 15 = 23

⇒ v/4 + 15 - 15 = 23 - 15

⇒ v/4 = 8

Step-2: Use cross multiplication

⇒ v/4 = 8

⇒ v = 8 × 4 = 32

Answer:

The answer is 15

Step-by-step explanation:

15*3=45-5=40