Which side lengths cannot form a triangle? Select all that apply.

Write an equation in slope - intercept form for the line that satisfies each set of conditions

ivanzaharov [21]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(1)

Rearrange 3x + 2y = 1 into this form by subtracting 3x from both sides

2y = - 3x + 1 ( divide all terms by 2 )

y = - $\frac{3}{2}$ x + $\frac{1}{2}$ ← in slope- intercept form

with slope m = - $\frac{3}{2}$

Parallel lines have equal slopes, thus

y = - $\frac{3}{2}$ x + c ← is the partial equation

To find c substitute (- 6, 15) into the partial equation

15 = 9 + c ⇒ c = 15 - 9 = 6

y = - $\frac{3}{2}$ x + 6 ← equation of line

(2)

Rearrange x + 2y = 8 into slope- intercept form by subtracting x from both sides

2y = - x + 8 ( divide all terms by 2 )

y = - $\frac{1}{2}$ x + 4 ← in slope- intercept form

with slope m = - $\frac{1}{2}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{1}{2} }$ = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (5, - 2) into the partial equation

- 2 = 10 + c ⇒ c = - 2 - 10 = - 12

y = 2x - 12 ← equation of line

3 0

3 years ago

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find the present value of an investment that is worth $19,513.75 after earning 3percent simple interest for 5.5 years

Dahasolnce [82]

Answer:

present value = $16750

Step-by-step explanation:

The simple interest formula allows us to calculate A, which is the final amount. According to this formula, the amount is given by A = P (1 + r*t), where P is the principal, r is the annual interest rate in decimal form, and t is the loan period expressed in years

simple interest formula:

t: time

P: present value

A: amount

r : anual interest

A = P (1 + r*t)

P = A / (1 + r*t)

P = 19,513.75 / (1 + 3/100 * 5.5)

P = 19,513.75/ (1 + 0.165)

P = 19,513.75 / 1.165

P = 16750

present value = $16750

5 0

4 years ago

It was recently estimated that females outnumber males by about three or two. If there are 1770 people in a county, how many of

max2010maxim [7]

GIVEN

1) Females outnumber males by 3 to 2.

2) There are 1770 people in the city.

SOLUTION

Let the number of males be x and the number of females y. Therefore, the total number of people can be written to be:

$x+y=1770\text{ -----------(1)}$

If there are 3 females for every 2 males, we have that:

$\begin{gathered} \frac{y}{3}=\frac{x}{2} \\ \therefore \\ x=\frac{2y}{3}\text{ ----------(2)} \end{gathered}$

We can substitute equation (2) into equation (1) and solve for y:

$\begin{gathered} \frac{2}{3}y+y=1770 \\ \frac{2y+3y}{3}=1770 \\ 5y=1770\times3 \\ 5y=5310 \end{gathered}$

Dividing both sides by 5, we have

$y=1062$

There are 1062 females in the county.

3 0

1 year ago

Solve the system of equations -5x – 2y = 13 and 3x-y = 12 by combining the equations

Ne4ueva [31]

Answer:

x=1 y =15

Step-by-step explanation:

hopefully correct

-5x-2y=13 (i)

3x-y=12

-y=12-3x

y=-12+3x (ii)

substitute ii into i

-5x-2(-12+3x)=13

-5x +24-6x=13

-11x=-11

x=1

substitute x into ii

y=-12+3(1)

y=15

.

. . x=1 and y =15

4 0

3 years ago

Question and choices are in the photo please explain the answer

Natasha_Volkova [10]

Answer:

$\text{A) }68\:\mathrm{cm}$

Step-by-step explanation:

The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.

Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.

To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a $90^{\circ}$ , creating right triangles $\triangle TOP$ and $\triangle SOP$ .

The Pythagorean Theorem states that the following is true for any right triangle:

$a^2+b^2=c^2$ , where $c$ is the hypotenuse, or the longest side, of the triangle

Thus, we have:

$10^2+TP^2=26^2,\\TP^2=26^2-10^2,\\TP^2=\sqrt{576},\\TP=24$

Since both TP and SP are tangents of the circle and extend to the same point P, they will be equal.

What we know:

$TP=SP=24$
$TO=SO=10$

Thus, the perimeter of the quadrilateral PTOS is equal to $24+24+10+10=\boxed{\text{A) }68\:\mathrm{cm}}$

7 0

4 years ago

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