Three strands of wire have a total length of
120 meters. One strand is twice the length of
the shortest strand, and the other strand is
three times the length of the shortest strand.
What is the length of the longest strand of
wire?

The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].

We need the knowledge of three distinct points to determine all coefficients of the vertical parabola based on the following general formula:

[tex]x^{2} + y^{2} + D\cdot x + E\cdot y + F = 0[/tex] (1)

If we know that [tex](x_{1}, y_{1}) = (-2, -18)[/tex], [tex](x_{2}, y_{2}) = (3,-13)[/tex] and [tex](x_{3}, y_{3}) = (5,-39)[/tex], then we have the following system of linear equations:

[tex]-2\cdot D -18\cdot E + F = -328[/tex] (2)

[tex]3\cdot D -13\cdot y + F = -178[/tex] (3)

[tex]5\cdot D -39\cdot E + F = -1546[/tex] (4)

The solution of the system of equations is: [tex]D = -21[/tex], [tex]E = 51[/tex], [tex]F = 548[/tex].

The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].

We kindly invite to check this question on parabolae: https://brainly.com/question/4074088

Answer:

2inch=1 foot

Step-by-step explanation:

so 2 to 1       2:1

Answer:

x = 7x^2

Step-by-step explanation:

4x-14=-3x^2

x-14=3x^2

x= 7x^2

Answer:

3x²+4x-14=0

Step-by-step explanation:

Standard form of a quadratic equation is ax²+bx+c=0. To do that, simply move -3x² over to the other side by adding it. That leaves you with the answer.

Step-by-step explanation:

I know but I m feeling bore

Answer:

-43x - 5

Step-by-step explanation:

−3x + 5 (−8x −1)

First, distribute 5 into the parenthesis:

= −3x + 5 (−8x −1)

= -3x - 40x -5

Combine like terms:

= -43x - 5

Answer:

-43x - 5

Step-by-step explanation:

I took the K12 test

Answer:

7.083

Step-by-step explanation:

Answer:

7.083 im pretty sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² + 5x - 5 =  (-6)² + 5*(-6) - 5

                 = 36 - 30 - 5  

                 = 36 - 35

                 = 1

Answer:

1

Step-by-step explanation:

-6^(2)+5(-6)-5

36 + 5(-6) -5

36- 30- 5

6 - 5

1

Answer:

the third one is the correct answer

Answer:1/10

Step-by-step explanation:so easy

The probability that the students she selects are both boys is 1/10.

Given is that a math class has 4 girls and 1 boy in the seventh grade and 5 girls and 5 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition.

The probability that the students she selects are both boys -

P{E} = P{1} x P{2}

P{1} : randomly selecting a seventh grader as a boy.

P{2} : randomly selecting a eight grader as a boy.

We can write -

P{1} = n{f}/n{s} = 1/5

P{2} = n{f}/n{s} = 5/10 = 1/2

P{E} = P{1} x P{2}

P{E} = 1/5 x 1/2

P{E} = 1/10

Therefore, the probability that the students she selects are both boys is 1/10.

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Answer:

-9/5

Step-by-step explanation:

(-3, 3) & ( 2, -4) -9/5 rise over run and negative because its in negative axis

Answer:

D

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = \frac{1}{3} x + 2[/tex]

And we want to find its inverse h.

To find the inverse of a function, we can switch the y and x variables and solve for the new y. This will be our inverse.

We begin with:

[tex]\displaystyle f(x) = y = \frac{1}{3} x+ 2[/tex]

Switching the variables yield:

[tex]\displaystyle x = \frac{1}{3}y + 2[/tex]

And solving for y yields that:

[tex]\displaystyle y = h(x) = 3x - 6[/tex]

In conclusion, the inverse function to f is 3x - 6. Our answer is D.

To understand why we switch the variables, recall that by the definition of inverse functions, if f(a) = b, then f⁻¹(b) = a. So, by switching the variables, we are essentially solving for f⁻¹(x).

Answer:

41

Step-by-step explanation:

i know skxkdkckxokdkakd

Answer:

I don't know sorry.....

Answer:

8.61

Step-by-step explanation:

Answer:

8.61 I think try that okay

You should first recognize the shape of the curve - it's an exponential function, so its equation takes the form [tex]y(x)=a\cdot b^{cx}[/tex] for some constants a, b, and c.

The curve lies above the x-axis, so a must be positive.

The curve is defined everywhere (there are no discontinuities), so b must be positive.

As you move left to right, the function is increasing, so c must also be positive. But to make things simpler, let's assume c = 1.

When x = 0, the curve passes through the point (0, 1). In our equation, we have

[tex]y(0) = a\cdot b^0 = a[/tex]

so it follows that a = 1.

When x = 1, the curve approximately passes through the point (1, 4); so

[tex]y(1) = b^1 = 4[/tex]

so b = 4.

Then the equation of the curve might be [tex]\boxed{y = 4^x}[/tex].

Answer:

3.98%

Step-by-step explanation:

R = $17,300/$435,000 = .0398, or 3.98%

===================================================

Explanation:

Let's say this population had 1000 people. You can pick any number you want, but I'm going for some nice big round number to work with.

The proportion of smokers is 0.3, which means 0.3*1000 = 300 people in this population are smokers and 1000-300 = 700 are nonsmokers.

Of the 300 people who do smoke, 40% of them lie on the application. This means 0.40*300 = 120 people lied. These 120 people say they don't smoke, but in fact they do smoke.

So if we were to survey this population, then 700+120 = 820 people would say they don't smoke

Only considering the people who write "don't smoke" on the survey, which is that 820 figure, 700 of them are true nonsmokers. Therefore, the probability we want is 700/820 = 0.8537 approximately

Answer:

[tex]y = a{x}^{2} + bx + c \\ 6 = a{2}^{2} + 2b + c \\ 6 = 4a+ 2b + c...(1) \\ 16 = 9a+ 3b + c...(2) \\ \frac{dy}{dx} = 7 = 4a + b...(3) \\ (2) - (1) \\ 10= 5a + b...(4) \\ (4) - (3) \\ 5a - 4a = 10 - 7 \\ \boxed{a = 3 }\\ sub \: a \: im \: (4) \\ 10 = 15 + b \\ \boxed{b = - 5} \\ sub \: a \: b \: in \: (1) \\ 6 = 4(3) + 2( - 5) + c \\\boxed{c = 4}[/tex]

Answer:

$437.58

Step-by-step explanation:

15% + 28%

= 43%

43/100 × 306

= $131.58

$131.58 + $306

= $437.58

Answer:

B. False

Step-by-step explanation:

To check if its a right angle triangle, you need to check if pythagoras' theorem works:

a² + b² = c²

(√17)² × (√17)² = 289 which is not equal to (√34)²

Answer:

[tex]y=-3x-7[/tex]

Answer:

horizontally shrink by factoring of 2, shift 3/2 units to the right, shift 2 units upward

Step-by-step explanation:

#1

(56,7) is the co-ordinate of point B.

#2

(56,7)

It means that the ball has travelled 56yards .it is at the height of 7ft.

Answer:

(56,7) is the answer of this questions

Answer:

$ 80,000

Step-by-step explanation:

2/5 + 1/3 = (6 + 5)/15 = 11/15

15/15 - 11/15 = 4/15

4/15 of 300,000

4/15 x 300,000 = 1,200,000/15 = 80,000

1)true

2)true

3)false

4)true

5)true

6) false

7))true

8)true

9)false

10)false.

11)false

12)true

Answer:

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

13.6 - x = -64.2

Step-by-step explanation:

x = 77.8

13.6 - 77.8 = -64.2 True!

Answer:

x=77.8

Step-by-step explanation:

13.6-x=-64.2

-13.6. -13.6

---------------------

since there is already -x it wouldn't be -77.8 bc that would cancel it out

d/dx cot(x) = -csc²(x)

d/dx sin(x) = cos(x)

So, if f(x) = 4 cot(x) + 10 sin(x), then

f '(x) = -4 csc²(x) + 10 cos(x)