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3 years ago

The area of the triangle below is __ sq units. A.80 B.21 C.42 D.40

Mathematics

2 answers:

hammer [34]3 years ago

6 0

Hi there!

• Base, b = 16
• Altitude, a = 5

Area of triangle = $\dfrac{1}{2}$ × b × a = $\dfrac{1}{2}$ × 16 × 5 = 40 sq. units.

Hence,
Option D. 40 sq. units is Correct

~ Hope it helps!

lorasvet [3.4K]3 years ago

3 0

Answer
40

The formula to determine the area of the right triangle is a*b/2

First, let’s input the numbers into the formula.

16*5/2

Now we need to solve.

16*5= 80
80/2= 40

Therefore, the answer would be 40.

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3 years ago

SIMPLIFY 1/4 × 1/3 - 1/5× 1/4 + 1/4 × 1/6

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Answer:

3/40

Step-by-step explanation:

1/4 x 1/3 - 1/5 x 1/4 +1/4 x 1/6

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3[-x + (2 x + 1)] = x - 1<br><br><br> what is x

Nataly_w [17]

The answer you are looking for is x=-2.

Solution/Explanation:

Writing out the equation

3[-x+(2x+1)]=x-1

Simplifying inside of the brackets first

Combining like terms, since -x+2x=x

3(x+1)=x-1

*You can remove the parenthesis, if preferred.

Using the Distributive Property on the left side of the equation

3x+3=x-1

Now, subtracting the "x" variable from both sides

3x+3-x=x-x-1

"x-x" cancels out to 0.

3x+3-x=-1

Combining like terms and simplifying

3x-x+3=-1

2x+3=-1

Subtracting 3 from both sides of the equation

2x+3-3=-1-3

"3-3" cancels out to zero.

2x+0=-1-3

2x=-1-3

Simplifying the right side of the equation

2x=-4

Finally, dividing both sides by 2

2x/2=-4/2

Simplifying the final part of the problem

Since 2x/2=x and -4/2=-2

x=-2

So, therefore, the final answer is x=-2.

Hope that this has helped you. Good day to you.

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2 years ago

Find the solutions to x⁴-5x²-36=0 and the x-intercepts of the graph of y=x⁴-5x²-36.

disa [49]

Answer:

The solutions $x^4-5x^2-36=0$ are $x=3,\:x=-3,\:x=2i,\:x=-2i$ and the x-intercepts of $y=x^4-5x^2-36$ are $x=3,\:x=-3$

Step-by-step explanation:

Finding the solutions to $x^4-5x^2-36$ means finding the roots, a root is where the function is equal to zero.

The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero.

To find the roots you need to:

Rewrite the equation with $u=x^2$ and $u^2=x^4$

$u^2-5u-36=0$

Solve by factoring

$\mathrm{Break\:the\:expression\:into\:groups}\\u^2-5u-36=\left(u^2+4u\right)+\left(-9u-36\right)$

$\mathrm{Factor\:out\:}u\mathrm{\:from\:}u^2+4u=u\left(u+4\right)$

$\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9u-36=-9\left(u+4\right)$

$u^2-5u-36=u\left(u+4\right)-9\left(u+4\right)$

$\mathrm{Factor\:out\:common\:term\:}u+4\\\left(u+4\right)\left(u-9\right)$

$u^2-5u-36=\left(u+4\right)\left(u-9\right)=0$

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions to the quadratic equation are:

$\:u=-4,\:u=9$

Substitute back $u=x^2$ , solve for x

$x^4-5x^2-36=(u-9)(u+4)=(x^2-9)(x^2+4)$

Apply the difference of squares formula

$x^4-5x^2-36=(x^2-9)(x^2+4)=(x-3)(x+3)(x^2+4)$

$(x-3)(x+3)(x^2+4)=0$

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions are:

$\:x=3,\:x=-3,\:x=2i,\:x=-2i$

Because two of the solutions are complex roots the only x-intercepts are $x=3,\:x=-3$

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3 years ago