How do I work out 3t-7=5t

Answers

Answer 1

Answer: $3t-7=5t\ \ 3t-5t=7 \n\n-2t=7\ \ / :(-2)\n\nt=-(7)/(2)$

Answer 2

Answer: $3t-7=5t\n 2t=-7\n t=-(7)/(2)$

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19/20-3/20 in simplest form

Answers

The correct answer is 8

A certain species of tree grows an average of 3.1 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 400 centimeters tall.

Answers

Answer:

$y = 3.1x+400$ c

Step-by-step explanation:

Slope intercept form:

The equation of straight line is given by:

$y =mx+b$ ....[1]

where, m is the rate or slope and b is the initial value of y-intercept.

As per the statement:

A certain species of tree grows an average of 3.1 cm per week.

Let x be the number of week and y represents the weekly height of the tree.

then;

" tree grows an average of 3.1 cm per week." translated to 3.1 x

It is also given that:

the measurements begin when the tree is 400 centimeters tall.

⇒y(0) =b = 400 cm

Substitute the given values in [1] we have;

$y = 3.1x+400$

Therefore, an equation for the sequence that represents the weekly height of this tree in centimeters is, $y = 3.1x+400$

Y = 400 + 3.1x

X for the number of weeks
Y for total CM

Hope this helps...

Use the explicit formula an=a1 (n-1)d to find the 500th term of the sequence below.24,31,38,45,52,..

Answers

First off...the right formula is an=a₁+(n-1)d
an=nth term=500th term
a₁=first term=24
n=common difference=31-24=7
n=500
an=24+(500-1)7
=24+(499)7
=24+ 3493
=3517
The 500th term is 3517

Answer:

3517

Step-by-step explanation:

How do you turn a fraction into a decimal, and how do you turn a decimal into a fraction?

Answers

If = 123/100, then 1.23 = decimal
If = 8765432/9000000, then 0.8765432 = decimal

Answer:70/100

Step-By-Step:

Well you should simplify 70/100 which would be 7/10, so now that is a decimal and will move one step to the left which is 0.7 in decimal form

A russian igor carl faberge firebird egg costs 327,317.28 russian rubles. how much is that in united states dollars?

Answers

1 Russian ruble is equivalent to 0.01742 U.S. dollars.

Therefore, to find how much US dollars is equivalent to 327,317.28 Russian rubles, all you have to do is cross multiplication as follows:
amount = (327,317.28 * 0.01742) / 1
amount = 5701.867018 US dollars

The function y = -0.03(x - 14)^2 + 6 models the mump of a red kangaroo where x is the horizontal distance in meters and y is the vertical distance in meters for the height of the jump. What is the kangaroo's maximum height? How long is the kangaroo's jump?

Answers

From the vertex of the quadratic equation, we find that: The kangaroos maximum height is of 6 meters.

From the roots of the equation, we find that: The kangaroo's jump is 28.14 meters long.

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Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

$f(x) = ax^(2) + bx + c$

It's vertex is the point $(x_(v), y_(v))$

In which

$x_(v) = -(b)/(2a)$

$y_(v) = -(\Delta)/(4a)$

Where

$\Delta = b^2-4ac$

If a<0, the vertex is a maximum point, that is, the maximum value happens at $x_(v)$ , and it's value is $y_(v)$ .

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

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^(2) + bx + c, a\neq0$ .

This polynomial has roots $x_(1), x_(2)$ such that $ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))$ , given by the following formulas:

$x_(1) = (-b + √(\Delta))/(2*a)$

$x_(2) = (-b - √(\Delta))/(2*a)$

$\Delta = b^(2) - 4ac$

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

The quadratic equation is:

$y = -0.03(x - 14)^2 + 6$

Placing in standard form:

$y = -0.03(x^2 - 28x + 196) + 6$

$y = -0.03x^2 + 0.84x + 0.12$

Thus, it has coefficients $a = -0.03, b = 0.84, c = 0.12$

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

The kangaroo's maximum height is the y-value of the vertex, thus:

$\Delta = b^2 - 4ac = (0.84)^2 - 4(-0.03)(0.12) = 0.72$

$y_(v) = -(\Delta)/(4a) = -(0.72)/(4(-0.03)) = 6$

The kangaroos maximum height is of 6 meters.

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

The length of the kangaroo's jump is the positive root. The roots are found at the values of x for which y = 0, thus, the solutions of the quadratic equation.

$x_(1) = (-0.84 + √(0.72))/(2(-0.03)) = -0.14$