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3 years ago

Ej bisects def, m dej-5x+7, m JEF=8x-8. find x

Mathematics

1 answer:

Georgia [21]3 years ago

5 0

Answer:

$x = 5$

Step-by-step explanation:

Given that segment EJ bisects angle DEF, it implies that angle DEF is divided into two equal angles, namely, angle DEJ = 5x + 7, and angle JEF = 8x - 8.

To find the value of x, let's derive an equation by setting m<DEJ equal to m<JEF, since both are equal parts of angle DEF bisected by segment EJ.

Thus:

$5x + 7 = 8x - 8$

Solve for x

$5x + 7 - 8x = 8x - 8 - 8x$ (subtracting 8x from both sides)

$-3x + 7 = - 8$

$-3x + 7 - 7 = - 8 - 7$ (Subtracting 7 from both sides)

$-3x = -15$

$\frac{-3x}{-3} = \frac{-15}{-3}$ (dividing both sides by -3)

$x = 5$

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F(x)=x2-10 and g(x)=11-x find (f-g)(x)(f-g)(10) and (f/g)(x) if they exist

tester [92]

Answer:

$(f - g)(x) = x^2 + x-21$

$(f - g)(10) = 89$

$(f/g)(x) = \frac{x^2 - 10}{11 - x}$

Step-by-step explanation:

Given

$f(x) = x^2 - 10$

$g(x) = 11 - x$

Solving (1): (f-g)(x)

$(f - g)(x) = f(x) - g(x)$

Substitute values for f(x) and g(x)

$(f - g)(x) = x^2 - 10 - (11 - x)$

Open Bracket

$(f - g)(x) = x^2 - 10 - 11 + x$

$(f - g)(x) = x^2 -21 + x$

Reorder

$(f - g)(x) = x^2 + x-21$

Solving (2): (f-g)(10)

In (1)

$(f - g)(x) = x^2 + x-21$

So:

$(f - g)(10) = 10^2 + 10-21$

$(f - g)(10) = 100 + 10-21$

$(f - g)(10) = 89$

Solving (3): (f/g)(x)

$(f/g)(x) = \frac{f(x)}{g(x)}$

Substitute values for f(x) and g(x)

$(f/g)(x) = \frac{x^2 - 10}{11 - x}$

6 0

3 years ago

7' 7" − 4' 11"<br> (It's not easy)<br> I posted this twice

Hitman42 [59]

4 foot and 5 inches?

6 0

4 years ago

Jordyn bought some books that cost $6 each. She spent a total of $18. How many books, b did she buy?

Westkost [7]

2 because she spent a total of $18 and the books each cost 6 times two will equal 18

7 0

3 years ago

What is the volume of this prism?

marin [14]

Answer:

160 u^3

Step-by-step explanation:

For the sake of ease, I will split this prism into 2 prisms. One prism will be 2x4x5 while the second one will be 4x5x6. The volume of the prism will be the sum of the volume of both prisms.

Prism A: Volume would be lwh or 2*4*5=40

Prism B: Volume would also be lwh which is 4*5*6=120

40+120=160

The volume is 160 units^3

Hope this is correct and helps!

7 0

3 years ago

find the compound interest earned. round to the nearest cent. $600 at 5% compounded quarterly for 1 1/2 years

stepladder [879]

Answer:

$46.43

Step-by-step explanation:

First, let's use the compound amount equation,

A = P(1+r/n)^(nt), where P is the principal, r is the annual interest rate as a decimal fraction, n is the # of compounding periods per year, and t is the number of years.

Here,

A = $600(1 + 0.05/4)^(4*[1 1/2]). Let's evaluate this:

A = $600*(1.0125)^6

= $646.43.

This is the amount due after 1.5 years if $600 were the original principal borrowed.

If you want ONLY the compound interest, subtract $600 from $646.43:

Compound interest was $46.43.

6 0

4 years ago