Which of the following does NOT represent a straight line?

1. What is the difference of 6.394 and 3.2?

insens350 [35]

You do 6.394-3.200 which =
3.194

5 0

4 years ago

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T(r+4)=28 solve for t pls help

Reptile [31]

Answer: 28/r+4

Step-by-step explanation: Divide each term by r + 4 and simplify

3 0

3 years ago

50 points + brainliest

xxTIMURxx [149]

Solving this problem involves repeated application of the distance formula. In order to figure out which vertices we need to connect to another vertex, we should first plot the points on the coordinate plane to get an idea of what the polygon looks like. To form the sides of this polygon (which is, in our case, a pentagon), we'll need to connect the points in the following pairs:

(-2, -2) and (3, -3)
(3, -3) and (4, -6)
(4, -6) and (1, -6)
(1, -6) and (-2, -4)
(-2, -4) and (-2, -2)

In case you forgot, the distance formula is simply an application of the Pythagorean Theorem that treats the x-distance and y-distance between two points as the "legs" of a right triangle, and the shortest distance between them as the "hypotenuse."

If a and b are the legs of a right triangle, and c is the hypotenuse, the Pythagorean Theorem can be written as:

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

Or, if we're just looking for the value of c:

$c=\sqrt{a^2+b^2}$

Since the hypotenuse in our case represents distance, it's more descriptive to rename that variable d. Also, the "legs" a and b in this problem represent the distances between the x and y components of the two points. If we take any two points $(x_1,y_1)$ and $(x_2,y_2)$ , the distance between the x components of those points would be their difference, $x_2-x_1$ , and the distance between the y components would be $y_2-y_1$ . Substituting that all in, the distance formula becomes:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

All that's left to do now is substitute our specific points into the formula for each side of the polygon:

(-2, -2) and (3, -3):
$d=\sqrt{(3-(-2))^2+(-3-(-2))^2}\\ d=\sqrt{(3+2)^2+(-3+2)^2}\\ d=\sqrt{5^2+(-1)^2}\\ d=\sqrt{25+1}\\ d=\sqrt{26}\\ d\approx5.1$

(3, -3) and (4, -6)
$d=\sqrt{(4-3)^2+(-6-(-3))^2}\\ d=\sqrt{1^2+(-6+3)^2}\\ d=\sqrt{1+(-3)^2}\\d=\sqrt{1+9}\\ d=\sqrt{10}\\ d\approx3.2$

(4, -6) and (1, -6)
$d= \sqrt{(1-4)^2+(-6-(-6))^2} \\ d= \sqrt{(-3)^2+0^2} \\ d= \sqrt{9} \\ d=3$

(1, -6) and (2, -4)
$d= \sqrt{(2-1)^2+(-4-(-6))^2}\\ d= \sqrt{1^2+(-4+6)^2}\\ d= \sqrt{1+2^2}\\ d= \sqrt{1+4} \\ d= \sqrt{5}\\ d\approx2.2$

(2, -4) and (-2, -2)
$d= \sqrt{(-2-2)^2+(-2-(-4))^2}\\ d= \sqrt{(-4)^2+(-2+4)^2} \\ d= \sqrt{16+2^2}\\ d= \sqrt{16+4}\\ d= \sqrt{20} \\ d\approx4.5$

Rounding beforehand and adding up all of the distances gives us a perimeter of 18 units, which is remarkably close to the more precise approximation of 17.96 units. Given your options, 17.9 units would be the closest to the result we obtained here.

6 0

4 years ago

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The drawing below represents a 22-foot ladder with its base placed 10 feet from the bottom of a vertical wall.

Nesterboy [21]

Answer:

63°

Step-by-step explanation:

To get the value of x we will use the Pythagoras theorem

hyp² = opp²+adj²

Given

hyp is the length of the ladder = 22ft

Adjacent is the distance from the base of the ladder to the wall = 10ft

Angle of elevation = x

Using the SOH CAH TOA identity

Cos theta = adjacent/hypotenuse

Cos x = 10/22

Cos x = 5/11

x = arccos(5/11)

x = arccos(0.4545)

x = 62.96°

Hence the best estimate of x is 63°

4 0

3 years ago

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem.

Molodets [167]

Answer:

See verification below

Step-by-step explanation:

Remember that the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M.

Now, to apply the theorem, we have that f(0)=0²+0-1=-1, f(5)=5²+5-1=29, then f(0)=-1<11<29=f(5). Additionally, f is continous since it is a polynomial. Then the IVT applies, and such c exists.

To find, c, solve the quadratic equation f(c)=11. This equation is c²+c-1=11. Rearranging, c²+c-12=0. Factor the expression to get (c+4)(c-3)=0. Then c=-4 or c=3. -4 is not in the interval, then we take c=3. Indeed, f(3)=3²+3-1=9+3-1=11.

5 0

4 years ago