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3 years ago

HELP PLEASE!! ASAP If triangles ABC and DEF are similar, what is y? Show your work.

Mathematics

2 answers:

rjkz [21]3 years ago

8 0

If both triangles are similar then ratio of sides will be same.

$\\ \sf\longmapsto \dfrac{12}{14}=\dfrac{y}{21}$

$\\ \sf\longmapsto 12(21)=14y$

$\\ \sf\longmapsto 14y=252$

$\\ \sf\longmapsto y=\dfrac{252}{14}$

$\\ \sf\longmapsto y=18$

Ivenika [448]3 years ago

3 0

Answer:

y = 18

Step-by-step explanation:

Since the triangles are similar, the corresponding sides are in proportion, that is

$\frac{BC}{EF}$ = $\frac{AC}{DF}$ , substitute values

$\frac{y}{12}$ = $\frac{21}{14}$ ( cross- multiply )

14y = 252 ( divide both sides by 14 )

y = 18

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If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her a

RSB [31]

Answer:

14 years old

Step-by-step explanation:

Define the variable

Let x be the actual age of Zeba (in years).

Create an equation using the give information and the variable x:

$(x - 5)^2=5x+11$

To find Zeba's age now, solve the equation for x.

Expand the brackets:

$\implies x^2-10x+25=5x+11$

Subtract 5x from both sides:

$\implies x^2-10x+25-5x=5x+11-5x$

$\implies x^2-15x+25=11$

Subtract 11 from both sides:

$\implies x^2-15x+25-11=11-11$

$\implies x^2-15x+14=0$

Factor the found quadratic

To factor a quadratic in the form $ax^2+bx+c$ , find two numbers that multiply to $ac$ and sum to $b$ , then rewrite $b$ as the sum of these two numbers:

$\implies x^2-14x-x+14=0$

Factor the first two terms and the last two terms separately:

$\implies x(x-14)-1(x-14)=0$

Factor out the common term (x - 14):

$\implies (x-1)(x-14)=0$

Apply the zero product property:

$\implies (x-1)=0 \implies x=1$

$\implies (x-14)=0 \implies x=14$

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

Check

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9

The square of 9 is: 9² = 81.

5 times her actual age: 5 × 14 = 70

81 is 11 more than 70, hence verifying that her actual age is 14 years old.

Learn more about quadratic equations here:

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5 0

9 months ago

Read 2 more answers

Estimate each sum or difference 9,245-4,033

Mars2501 [29]

Answer:

Sum 9,200 + 4,000 = 13,200

Difference 9,200 - 4,000 = 5,200

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A blue die and a red die are thrown. B is the event that the blue comes up with a 6. E is the event that both dice come up even.

iVinArrow [24]

Answer:

Size of |E n B| = 2

Size of |B| = 1

Step-by-step explanation:

I'll assume both die are 6 sides

Given

Blue die and Red Die

Required

Sizes of sets

- $|E\ n\ B|$

- $|B|$

The question stated the following;

B = Event that blue die comes up with 6

E = Event that both dice come even

So first; we'll list out the sample space of both events

$B = \{6\}$

$E = \{2,4,6\}$

Calculating the size of |E n B|

$|E n B| = \{2,4,6\}\ n\ \{6\}$

$|E n B| = \{2,4,6\}$

The size = 3 because it contains 3 possible outcomes

Calculating the size of |B|

$B = \{6\}$

The size = 1 because it contains 1 possible outcome

8 0

2 years ago

9(4b-1)=2(b+3) Slove for b plz answer as quick as u can please

Jobisdone [24]

$36b - 9 = 2b + 6 \\ 34b = 15 \\ b = \frac{15}{34}$

3 0

3 years ago

A. B. C. D. Help me please

scZoUnD [109]

Answer:

Step-by-step explanation:

An event that is not affected by other events. Example: tossing a coin. Heads or tails is not affected by previous tosses.

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2 years ago