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valentinak56 [21]
2 years ago
6

Teresa runs each lap in 5 minutes. She will run less than

Mathematics
1 answer:
horrorfan [7]2 years ago
5 0

Answer:

11 laps i think

Step-by-step explanation:

mark brainliest and have a great day!

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If f(x) = -5x – 4 and g(x) = -3x - 2, find (f+ g)(x).
Andrej [43]

Answer: See below

Step-by-step explanation:

(f+g)(x) is another way for saying f(x)+g(x). Since we know f(x) and g(x), we can add them together.

-5x-4+(-3x-2)                  [distribute the 1 to (-3x-2)]

-5x-4-3x-2                      [combine like terms]

-8x-6

(f+g)(x) is -8x-6. You can also factor this.

1. Factoring

-2(4x+3)

4 0
3 years ago
Find the y intercepts of 3x^2+24x-51. quadratic formula
julia-pushkina [17]
  • Quadratic Formula: x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} , with a = x^2 coefficient, b = x coefficient, and c = constant.

Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:

y=3*0^2+24*0-51\\y=0+0-51\\y=-51

<u>Your y-intercept is (0,-51).</u>

Next, using our equation plug the appropriate values into the quadratic formula:

x=\frac{-24\pm \sqrt{24^2-4*3*(-54)}}{2*3}

Next, solve the multiplications and exponent:

x=\frac{-24\pm \sqrt{576-(-648)}}{6}\\\\x=\frac{-24\pm \sqrt{576+648}}{6}

Next, solve the addition:

x=\frac{-24\pm \sqrt{1224}}{6}

Now, simplify the radical using the product rule of radicals as such:

  • Product Rule of Radicals: √ab = √a × √b

√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34

x=\frac{-24\pm 6\sqrt{34}}{6}

Next, divide:

x=-4\pm \sqrt{34}

<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>

Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

x=-4+ \sqrt{34},-4- \sqrt{34}\\x\approx 1.83, -9.83

<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>

5 0
3 years ago
Which pair of ratios form a proportion?
boyakko [2]
5:8 and 20:32 would be a proportion.

Easy way to find this:
Set up the proportion as a fraction.
Use the cross product property. Multiply the diagonals and if the products of the diagonals are the same, then they are proportional.
3 0
3 years ago
Read 2 more answers
What are the coordinates of the point that is of the way from A to B?
Leokris [45]

Answer:

The coordinates are 3,1

Step-by-step explanation:

i did the assignment and it js correct

8 0
1 year ago
A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require
Aleksandr-060686 [28]

Answer:

r\approx 1.084\ feet

h\approx 1.084\ feet

\displaystyle A=11.07\ ft^2

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

  •  Produce a function which depends on only one variable
  •  Compute the first derivative and set it equal to 0
  •  Find the values for the variable, called critical points
  •  Compute the second derivative
  •  Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 ft^3. The volume of a cylinder is given by

\displaystyle V=\pi r^2h

Equating it to 4

\displaystyle \pi r^2h=4

Let's solve for h

\displaystyle h=\frac{4}{\pi r^2}

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

\displaystyle A=\pi r^2+2\pi rh

Replacing the formula of h

\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )

Simplifying

\displaystyle A=\pi r^2+\frac{8}{r}

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

\displaystyle A'=2\pi r-\frac{8}{r^2}=0

Rearranging

\displaystyle 2\pi r=\frac{8}{r^2}

Solving for r

\displaystyle r^3=\frac{4}{\pi }

\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet

Computing h

\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

\displaystyle A''=2\pi+\frac{16}{r^3}

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}

\boxed{ A=11.07\ ft^2}

8 0
2 years ago
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