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3 years ago

If triangle ABC = DEF AB = 8 , BC = 19 , AC = 14 , EF = 4x - 1 and DE=y-6, what are the values of x,y, and z

Mathematics

1 answer:

OleMash [197]3 years ago

6 0

Answer:

x = 5 and y = 14

Step-by-step explanation:

Given $\triangle$ ABC $\cong \triangle$ DEF.

Congruent triangles have congruent corresponding parts, so

$AB\cong DE\\ \\AC\cong DF\\ \\BC\cong EF$

Since

$AB=8\\ \\BC=19\\ \\AC=14\\ \\EF=4x-1\\ \\DE=y-6,$

then

$4x-1=19\\ \\4x=19+1\\ \\4x=20\\ \\x=5$

and

$y-6=8\\ \\y=8+6\\ \\y=14$

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Aleksandr-060686 [28]

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= 8/3 cups of oatmeal used

Therefore cups of oats left = 13/4 - 8/3

= 39/12 - 32/12

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Total she will have now = 19/12-7/4

= 19/12 - 21/12

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3 years ago

Which decimal is equivalent to -3 1/8<br><br> Please i need help quick

aalyn [17]

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The expression 8x2 − 144x 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represent

Rzqust [24]

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Given expression 8x² − 144x + 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998.

<h3>What is a quadratic equation?</h3>

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given expression is 8x² − 144x + 864

Let y = 8x² − 144x + 864

also, y - 864 = 8x² - 144x

by Extracting common factor 8 on the right side

y - 864 = 8(x² - 18x)

Add (18/2)² on both sides, we get

y - 864 + 8(18/2)² = 8 (x² - 18x + 81²)

y - 864 + 648 = 8 (x² - 8x + 9)

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y = 8(x - 9)² + 216

therefore, y = 8 (x - 9)² + 216

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

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2 years ago

In the exercise, X is a binomial variable with n = 5 and p = 0.2. Compute the given probability. Check your answer using technol

Ronch [10]

Answer:

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Step-by-step explanation:

We are told in the question that X isa Binomial variable. Hence we solve this question, using the formula for Binomial probability.

The formula for Binomial Probability = P(x) = (n!/(n - x) x!) × p^x × q ^n - x

In the above question,

x = 3

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q = probability for failures = 1 - 0.2 = 0.8

P(x) = (n!/(n - x) x!) × p^x × q ^n - x

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P(3) =( 5!/2! × 3!) × 0.2³ × 0.8²

P(3) = 10 × 0.008 × 0.64

P(3) = 0.0512

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3 years ago