Use a special right triangle to write tan 60° as a fraction

Answers

Answer 1

Answer: tan 60° = the square root of 3 over 1

Hope this helps!

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Solve the following three variable system. 2x + 3y + 4z = 9
-x + 2y - z = 0
-2x + 4y + z = 3

Answers

$1)\ \ \ 2x + 3y + 4z = 9\n2)\ \ \ -x + 2y - z = 0\n3)\ \ \ -2x + 4y + z = 3\n===================================\n3)\ \ \ -2x + 4y + z = 3\ \ \ \Rightarrow\ \ \ z=2x-4y+3\n\n1)\ \ \ 2x + 3y + 4z = 9\ \ \ \Rightarrow\ \ \ 2x + 3y + 4(2x-4y+3) = 9\n2x+3y+8x-16y+12=9\n10x-13y=-3\n\n2)\ \ \ -x + 2y - z = 0\ \ \ \Rightarrow\ \ \ -x+2y-(2x-4y+3)=0\n-x+2y-2x+4y-3=0\n-3x+6y=3\ /:(-3)\nx-2y=-1\ \ \ \Rightarrow\ \ \ x=2y-1\n\n$

$1)\ \ \ 10x-13y=-3 \ \ \ \Rightarrow\ \ \ 10(2y-1)-13y=-3\n20y-10-13y=-3\n7y=7\ /:7\ \ \ \Rightarrow\ \ \ y=1\n\n2)\ \ \ x=2y-1\ \ \ \Rightarrow\ \ \ x=2\cdot2-1=1\n\n3)\ \ \ z=2x-4y+3\ \ \ \Rightarrow\ \ \ z=2\cdot1-4\cdot1+3=2-4+3=1\n\nAns.\ x=y=z=1$

If there are 8520 bacteria present after 15minutes find K and round to the nearest thousandth (picture below)

Answers

Answer:

Choice A

Step-by-step explanation:

The scenario presented relates to exponential growth models; the population of bacteria is growing at an exponential rate given by the equation;

$B=1000e^(kt)$

In this case B represents the population of the bacteria, t the time in minutes, k the growth constant and 1000 represents the initial population at time 0.

After 15 minutes, the population of bacteria grows to 8520. This implies that B is 8520 while t is 15. We substitute this values into the given equation and solve for k, the growth constant;

$8520=1000e^(15k)$

Divide both sides by 1000;

$8.52=e^(15k)$

The next step is to introduce natural logs on both sides of the equation;

$ln8.52=ln(e^(15k))\nln8.52=15k\nk=(ln8.52)/(15)=0.143$

Which equation is true for x = –6 and x = 2?2x2 – 16x + 12 = 0
2x2 + 8x – 24 = 0
3x2 – 4x – 12 = 0
3x2 + 12x + 36 = 0

Answers

we know that

using a graph tool

let's proceed to graph each case to determine the roots

case 1) $2x^(2) - 16x + 12 = 0$

the roots are

$x1=0.8\ x2=7.2$ ------> is not the solution

see the attached figure N $1$

case 2) $2x^(2) +8x -24 = 0$

the roots are

$x1=-6\ x2=2$

see the attached figure N $2$ --------> is the solution

case 3) $3x^(2) - 4x - 12 = 0$

the roots are

$x1=-1.4\ x2=2.8$ ------> is not the solution

see the attached figure N $3$

case 4) $3x^(2) +12x +36 = 0$

the graph does not have x-intercepts

see the attached figure N $4$ ------> is not the solution

therefore

the answer is

the solution is

$2x^(2) +8x -24 = 0$

Second statement 2x2 + 8x – 24 = 0 Is true for the given conditions. When x = -6 2x2 + 8x – 24 = 0 Becomes 2(-6)2 + 8(-6) – 24 = 0 2(36) - 48 - 24 = 0 72 - 48 - 24 = 0 0 = 0 Which is true. When x = 2 2x2 + 8x – 24 = 0 Becomes 2(2)2 + 8(2) – 24 = 0 2(4) + 16 - 24 = 0 8 + 16 - 24 = 0 0 = 0 Which is true. So 2x2 + 8x – 24 = 0 will be answer.

When h has the value 12 calculate 5h - 2

Answers

58
(5x12) = 60
60 - 2 = 58

5(12)-2 distribution
60-2 subtraction
58 answer

The area of a rectangular painting is 4275cm². if the length of the painting is 75cm, what is its width?

Answers

Answer:

Width = 57cm

Step-by-step explanation:

The area of a rectangle can be found by using the formula:

Area = Length * Width

Since we know that the area is 4275cm² and the length of the painting is 75cm, we can plug these into the above equation to solve for the width.

Area = Length * Width

4275cm² = 75cm * Width

To find the width, we can simply divide both sides by 75 so that the width measurement is isolated:

Width = 57cm

To verify this, we can multiply the length and width to see if the area equals 4275cm²:

75cm * 57cm = 4275cm²

The front view of a podium is shown. Bryan wants to paint the front of the podium blue. He decomposed the shape into two triangles and a rectangle to find the area.

Answers

Complete Question

The front of a podium is in the shape of a trapezoid with base lengths 4 and 8.5 feet. the height is 2 feet. a gallon of paint covers about 350 square feet. Bryan wants to paint the front of the podium blue. He decomposed the shape into two triangles and a rectangle to find the area.

How many front frames of a podium can Bryant paint with 2 gallons of paint?

Answer:

56 front podiums

Step-by-step explanation:

A proper look at the image attached will provide the explanations

Answer:

Step-by-step explanation:

Given:

Base length:

A = 8.5 m

B = 4 m

Height, h = 2 ft

1 gallon = 350 ft^2

Area of trapezoid = 1/2 × (A + B) × h

= 1/2 × (8.5 + 4) × 2

= 12.5 ft^2

1 gallon = 350 ft^2

2 gallons = 700 ft^2

1 podium = 12.5 ft^2

= 700/12.5 podium

= 56 podiums will be painted with 2 gallons of paint.

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What is the zero function of f(x)=x+10

Simplification - 31/4 × 12/91 - 60/7 × 7/4 × 8/3 =