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3 years ago

If the perimeter of an isosceles triangle with integral sides is 2017, how many different lengths are possible for the legs

1 answer:

7 0

Because the perimeter is 2017, the side lengths must add to 2017;
a+b+c=2017
An isosceles triangle has two sides of the same length, so b=a. These two sides of the same length are the "legs".
a+a+c=2017
2a+c=2017
Integral means integer (assuming this is not a calculus problem). So, the smallest possible length for side c is 1.
2a+1=2017
2a=2016
a=1008
The legs can be up to 1008 units long apiece. Because the legs must be integer values, 1008 different lengths are possible for the legs.

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The total cost of a sweater and a pair of pants was $89.47. If the price of the sweater was $8.53 less than the pair of pants, w

Strike441 [17]

Answer:

Let S = price of sweater

Let P = price of pants

S + P = 89.47 because that was the total spent

S = P - 8.53 because the sweater is 8.53 less than pants

Substitute P-8.53 in place of S in the

1st equation and solve for P

P - 8.53 + P = 89.47

2P - 8.53 = 89.47 add 8.53 to both sides

2P = 89.47 + 8.53

2P = 98.00 divide both sides by 2

P = 98.00/2

P = $49.00

S = P - 8.53

S = 49.00-8.53

S = $40.47

A sweater costs $40.47 and the pants cost $49.00

5 0

2 years ago

A car travels 20 mph slower in a bad rain storm than in sunny weather. the car travels the same distance in 2 hrs in sunny weath

ycow [4]

You can create two equations.

"<span>A car travels 20 mph slower in a bad rain storm than in sunny weather."
</span>
$\sf x-20=y$

Where 'x' represents speed in sunny weather and 'y' represents speed in rainy weather.

"<span>The car travels the same distance in 2 hrs in sunny weather as it does in 3 hrs in rainy weather."

$\sf 2x=3y$

</span>Where 'x' represents speed in sunny weather and 'y' represents speed in rainy weather.

We want to find the speed of the car in sunny weather, or 'x'. Plug in the value for 'y' in the first equation into the second equation.

$\sf \boxed{\sf x-20}=y$
$\sf 2x=3y\rightarrow2x=3(x-20)$

Distribute:

$\sf 2x=3x-60$

Subtract 3x to both sides:

$\sf -x=-60$

Divide -1 to both sides:

$\sf x=60$

So the car goes 60 mph in sunny weather.

5 0

2 years ago

What is the correct value of x in the equation 2x + 3= 6

Brrunno [24]

Answer:

x=(3/2) OR 1.5

Step-by-step explanation:

2x+3=6

2x=6-3

2x=3

x=(3/2) OR 1.5

5 0

2 years ago

Read 2 more answers

The function f ( x ) = x ^3 + 2x^2− 5 x − 6 has a root at 2. Name all roots of this function.

Tomtit [17]

sub x=1 into f(x),

remainder= 1^3+2(1)^2-5(1)-6= -8

since remainder≠0, x=1 is not a root of the function

sub x=-1,

remainder = (-1)^3+2(-1)^2-5(-1)-6= 0

by remainder theorem,

x=-1 is a root of f(x)

hence, the correct ans is c

6 0

2 years ago

How does making a list help you find common factors

Flura [38]

Is the greatest factor that two or more numbers have in common. One way to find the GCF is to make lists of the factors for two numbers and then choose the greatest factor that the two factors have in common.

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3 years ago

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