All categories

3 years ago

Name all of the possible values for x in the triangle below. show your work.

Mathematics

1 answer:

salantis [7]3 years ago

7 0

Answer:

3 < x < 17

Step-by-step explanation:

As per triangle inequality theorem, sum of the lengths of any two sides must be greater than the length of the third side.

x < 10 + 7 ⇒ x < 17
7 < x + 10 ⇒ x > -3
10 < x + 7 ⇒ x > 3

<u>Combination of the inequalities above:</u>

3 < x < 17

The value of x must be between 3 and 17 units

You might be interested in

Its on the picture, plz go fast

Naily [24]

Answer:

Elimination

Step-by-step explanation:

You would not do substitution since it would not work so you do elimination since the 4y and -4y eliminate then you just solve for it.

7 0

2 years ago

Write an equation for (-1,-2),(-3,-4)

Marina86 [1]

Answer:

y=x+1

Step-by-step explanation:

First find the slope by subtracting the y values from both points and dividing it by the subtraction of the x values from both points:

-4--2/ -3--1= -2/-2= 1

so the slope is 1

Now find the y-intercept by plugging in the x and y from one of the points into the equation y=x+b

-3=-4+b

1=b

now plug the slope and y intercept in:

y=x+1

hope this helps :D

7 0

3 years ago

Find the equation of the axis of symmetry and the coordinates of vertex of the functions =2x^2+4x-3

SVEN [57.7K]

Hello,

Find the equation of the axis of symmetry is like find the maximum or minimum point of this function.

$f(x)=2x^2+4x-3\\\\\alpha=-\dfrac{b}{2a}=-\dfrac{4}{4}=-1\\\\$

The equation of the axis of symmetry is then : $x=-1$

$\beta=f(\alpha)=2(-1)^2+4(-1)-3=2-4-3=-5$

Coordinates of vertex : $(\alpha,\beta)=(-1;-5)$

8 0

4 years ago

A dog chases a squirrel. The dog is originally 200 feet away from the squirrel. The dog's speed is 150 feet per minute. The squi

Dafna11 [192]

Answer:

15 seconds

Step-by-step explanation:

If you make a table of values for the dog and the squirrel using d = rt, then the rates are easy: the dog's rate is 150 and the squirrel's is 100. The t is what we are looking for, so that's our unknown, and the distance is a bit tricky, but let's look at what we know: the dog is 200 feet behind the squirrel, so when the dog catches up to the squirrel, he has run some distance d plus the 200 feet to catch up. Since we don't know what d is, we will just call it d! Now it seems as though we have 2 unknowns which is a problem. However, if we solve both equations (the one for the dog and the one for the squirrel) for t, we can set them equal to each other. Here's the dog's equation:

d = rt

d+200 = 150t

And the squirrel's:

d = 100t

If we solve both for t and set them equal to each other we have:

$\frac{150}{d+200} =\frac{100}{d}$

Now we can cross multiply to solve for d:

150d = 100d + 20,000 and

50d = 20,000

d = 400

But we're not looking for the distance the squirrel traveled before the dog caught it, we are looking for how long it took. So sub that d value back into one of the equations we have solved for t and do the math:

$t=\frac{100}{d}=\frac{100}{400} =\frac{1}{4}$