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3 years ago

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Isosceles triangle DEF has base angles D and F. If DE = (4x + 10) and EF = (8x – 2), what is the value of x, and what is the val

ue of DE? Please show all work!

1 answer:

Vlada [557]3 years ago

5 0

Answer:

X=3

DE=22

Step-by-step explanation:

You might be interested in

Lucinda works as a tutor. She made $600 this week, working 12 hours. How much does she charge per hour for her tutoring?

Cerrena [4.2K]

Answer:

$7.14

Step-by-step explanation:

First we need to find out how many hours she worked during the whole week. WE multiply 12 by 7 and get 84. To find out how ,much she charges per hour, divide 600 by 84 and you get this amount.

5 0

3 years ago

The function y = f (x) is graphed below. What is the average rate of change of the function f(x) on the interval - 1 ≤ x ≤ 3?

jonny [76]

Answer:

$\displaystyle -2$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Average Rate of Change: $\displaystyle \frac{f(b) - f(a)}{b - a}$

Step-by-step explanation:

<u>Step 1: Define</u>

Interval -1 ≤ x ≤ 3

a = -1, b = 3

f(a) = f(-1) = 4

f(b) = f(3) = -4

<u>Step 2: Find Average</u>

Substitute in variables [ARC]: $\displaystyle \frac{f(3) - f(-1)}{3 + 1}$
Substitute: $\displaystyle \frac{-4 - 4}{3 + 1}$
[Fraction] Subtract/Add: $\displaystyle \frac{-8}{4}$
[Fraction] Divide: $\displaystyle -2$

4 0

3 years ago

Find the difference: (6y3 17y − 3) − (4y3 − 11y 9)

Natali [406]

If you would like to find the difference (6y^3 + 17y - 3) - (4y^3 - 11y + 9), you can do this using the following steps:

(6y^3 + 17y - 3) - (4y^3 - 11y + 9) = 6y^3 + 17y - 3 - 4y^3 + 11y - 9 = 2y^3 + 28y - 12

The correct result would be 2y^3 + 28y - 12.

8 0

3 years ago

Someone help again pls

xxMikexx [17]

Answer:

D

Step-by-step explanation:

First, compare the tens and ones places.

Bats 1 and 2 are each 27 point something ounces. 27 is less than 28 and 29, so we know the answer is either Bat 1 or 2.

Now let's look at the tenths place. Bat 1 is 27.1 oz, Bat 2 is 27.4. Since 1 is less than 4, we know that Bat 1 weighs the least!

5 0

3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago