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bogdanovich [222]
2 years ago
10

One side of triangle is 5 more than 3 times the shortest side. The third side is 24 feet more than the shortest side. The perime

ter is 114 . Find all three sides.
Mathematics
1 answer:
Feliz [49]2 years ago
3 0

Answer:

17, 56, 41,

Step-by-step explanation:

"third side is 24 more than shortest side"

Let a be the shortest side.

c = a+24

"perimeter is 114"

a+b+c = 114

a+b+(a+24) = 114

2a + b = 90

"one side is 5 more than 3 times the shortest side"

That side must be b; c is an extraneous solution.

b = 3a+5

2a+(3a+5) = 90

a = 17

b = 56

c = 41

(a,b,c) = (17,56,41)

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Write an equation in slope-intercept form for the line that passes through (4,-3) and is parallel to the line described by y=1/2
Marat540 [252]

Given:

The point, (4, -3)

The line,

y=\frac{1}{2}x+5

To find an equation in slope-intercept form for the line that passes through (4,-3) and is parallel to the given line:

The slope of the line is,

m=\frac{1}{2}

Since the given line is parallel to the new line, so the slope will be same for the both.

Using the point-slope formula,

y-y_1=m(x-x_1)

Substitute the point and slope we get,

\begin{gathered} y-(-3)=\frac{1}{2}(x-4) \\ y+3=\frac{1}{2}x-2 \\ y=\frac{1}{2}x-2-3 \\ y=\frac{1}{2}x-5 \end{gathered}

Hence, the equation in slope-intercept form for the line is,

y=\frac{1}{2}x-5

8 0
1 year ago
What is an equation of the line that passes through the points (2, -2) and (8, 4)?
WITCHER [35]

Answer:

HAVE YOU WATCHED OCTOPUS GAME

Step-by-step explanation:

5 0
2 years ago
Please help!
crimeas [40]

Answer:

The zeros are:

x =4, x=2, x = 5

  • The function has three distinct real zeros.

Hence, option (B) is true.

Step-by-step explanation:

Given the expression

h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)

Let us determine the zeros of the function by putting h(x) = 0 and solving the expression

0=\left(x-4\right)^2\left(x^2-7x+10\right)

switch sides

\left(x-4\right)^2\left(x^2-7x+10\right)=0

as

x^2-7x+\:10=\left(x-2\right)\left(x-5\right)

so

\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0

Using the zero factor principle

  • \mathrm{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)

so

x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0

x =4, x=2, x = 5

Thus, the zeros are:

x =4, x=2, x = 5

It is clear that there are three zeros and all the zeros are distinct real numbers.

Therefore,

  • The function has three distinct real zeros.

Hence, option (B) is true.

4 0
2 years ago
What are the solutions to x2 + x - 5≤0
Juliette [100K]

I have no idea what that x is doing, so imma take it out.

2+x-5≤0

-3+x≤0

+3     +3

x≤3

---

hope it helps

8 0
3 years ago
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