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3 years ago

Evaluate each expression. Click on undefined as needed

Mathematics

1 answer:

Brums [2.3K]3 years ago

4 0

If the 0 is in the numerator, the value is 0
if the 0 is in the denominator, the value is undefined

so 0/8 = 0
and 3/0 = undefined

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Write an equation of a line passing through point p(4, 0) that is parallel to the line -x+2y=12

dedylja [7]

Answer:

y = $\frac{1}{2}$ x - 2

Step-by-step explanation:

Given parameters:

Coordinates = p(4,0)

Equation of the line -x+2y=12

Solution:

A line parallel to the given line will have the same slope as it is;

-x+2y=12

2y = x + 12

y = $\frac{1}{2}$ x + $\frac{12}{2}$

Since this conforms to y = mx + c where;

x and y are the coordinates

m is the slope

c is the intercept

Our slope is $\frac{1}{2}$

The equation of the line is

y = mx + c

let us find c;

c = y - mx

c = 0 - ( $\frac{1}{2}$ x 4)

c = -2

Now the equation of the line parallel to the line given is;

y = $\frac{1}{2}$ x - 2

7 0

3 years ago

The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

3 years ago

Need help please and thank you

Juli2301 [7.4K]

It would be C because it’s asking you to multiple 3/4 by 3/4 sense there is a 2 exponent. And in order to multiply fractions you multiply across the top and bottom and then simplify. Sense c is already simplified that would be your answer. 3 x 3
4x4 9/16 or c

3 0

3 years ago

Samantha drew Triangle JKL with the coordinates (2,3), (4, 3) and (5,2). She reflected this image over the x-axis to create an i

zavuch27 [327]

Answer:

J'(2,-3), K'(4, -3) and L'(5,-2)

Step-by-step explanation:

The given triangle has vertices at J(2,3), K(4, 3) and L(5,2).

The transformation rule for a reflection in the x-axis is:

$(x,y)\to (x,-y)$

We substitute the points to obtain the coordinates of the image triangle J'K'L'

$J(2,3)\to J'(2,-3)$

$K(4,3)\to K'(4,-3)$

$L(5,2)\to L'(5,-2)$

In other words, we negate the y-coordinates of triangle JKL to obtain the coordinates of J'K'L'

See attachment for graph.

3 0

3 years ago

What function is an example of exponential growth

Artist 52 [7]

Exponential growth functions are the functions that normally take the form
y=ab^x
where:
a=initial value
b=growth rate
x=time
An example of situation that takes this form is the population growth of a particular group say and organism.

5 0

3 years ago