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3 years ago

Translate "Three is less than thirty-seven" into a mathematical expression.

Mathematics

2 answers:

Scorpion4ik [409]3 years ago

8 0

Answer:

$3$

Step-by-step explanation:

We have been given a sentence and we are asked to translate our given sentence into an algebraic expression.

Sentence: "Three is less than thirty-seven".

We know that less than sign is .

We need to write three on left side of less than sign and 37 on the right side of less than sign as:

$3$

Therefore, our required mathematical expression would be $3$ .

scoray [572]3 years ago

5 0

$3 < 37$
Hope it will help you

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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

qwelly [4]

Answer:

$\displaystyle \frac{dy}{dt}=-\frac{33}{8}$

$\displaystyle \frac{dx}{dt}=\frac{3}{2}$

Step-by-step explanation:

x and y are differentiable functions of t, and we are given the equation:

$xy=6$

First, let's differentiate both sides of the equation with respect to t. So:

$\displaystyle \frac{d}{dt}\left[xy\right]=\frac{d}{dt}[6]$

By the Product Rule and rewriting:

$\displaystyle \frac{d}{dt}[x(t)]y+x\frac{d}{dt}[y(t)]=0$

Therefore:

$\displaystyle y\frac{dx}{dt}+x\frac{dy}{dt}=0$

We want to find dy/dt when x = 4 and dx/dt = 11.

Using our original equation, find y when x = 4:

$\displaystyle (4)y=6\Rightarrow y=\frac{3}{2}$

Therefore:

$\displaystyle \frac{3}{2}\left(11\right)+(4)\frac{dy}{dt}=0$

Solve for dy/dt:

$\displaystyle \frac{dy}{dt}=-\frac{33}{8}$

We want to find dx/dt when x = 1 and dy/dt = -9.

Again, using our original equation, find y when x = 1:

$(1)y=6\Rightarrow y=6$

Therefore:

$\displaystyle (6)\frac{dx}{dt}+(1)\left(-9)=0$

Solve for dx/dt:

$\displaystyle \frac{dx}{dt}=\frac{3}{2}$

5 0

3 years ago

Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at the

scZoUnD [109]

Answer:

$\frac{y}{x+y}$

Step-by-step explanation:

The required answer is the rate at which Machine A works when the two machines are combined.

Note: the rate of doing work is express as

$rate=\frac{1}{time taken} \\$

Hence we can conclude that Machine A working rate is

$machine A=\frac{1}{x} \\$ and machine B working rate is

$machine B=\frac{1}{y} \\$

When the two machine works together, the effective working rate is

$\frac{1}{x}+\frac{1}{y}\\\frac{xy}{x+y}\\$

The fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A

Hence the fraction of work done by A is expressed as

$\frac{1}{x}*combine working rate$

$\frac{1}{x}*\frac{xy}{x+y}\\\frac{y}{x+y} \\$

Hence the fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A is $\frac{y}{x+y} \\$

6 0

3 years ago

I need a. Correct answer I will mark brainliest

Otrada [13]

Answer:

Option (A)

Step-by-step explanation:

By satisfying the equation of a function 'f' by each coordinates given in the options we can get the point which lies on the graph of f(x) = $2\times (5)^x$

Option (A). (1, 10)

f(1) = $2\times (5)^1$

10 = 10

True.

Therefore, point (1, 10) lies on the graph.

Option (B). (0, 10)

f(0) = $2\times 5^0$

10 = 2

Not true.

Therefore, point (0, 10) doesn't lie on the graph.

Option (C). (10, 1)

f(10) = $2\times 5^{10}$

1 = 19531250

Not true.

Therefore, point (10, 1) doesn't lie on the graph.

Option (D). (0, 0)

f(0) = $2\times 5^0$

0 = 2

Not True.

Point (0, 0) doesn't lie on the graph.

Option (A) will be the answer.

4 0

4 years ago

X^2+14x-15=0 solve by completing square

Softa [21]

Answer:

${x}^{2} + 14x - 15 = 0 \\ {x}^{2} - x + 15x -15 = 0 \\ x(x - 1) + 15(x - 1) = 0 \\ (x - 1)(x + 15) = 0 \\ \boxed{x = 1} \\ \boxed{x = - 15}$

<h3>x=1 and x=-15 is the right answer.</h3>

7 0

3 years ago

Which function is the verse of f(x)=2x+3?

Hatshy [7]

Answer:

Option B is correct

Step-by-step explanation:

A function has form of f(x) = 2x + 3, or y = 2x + 3

To find the inverse of f(x), we are going to represent x in form of y.

To do this, we try to send all components containing x to one side of expression and send the other components to the other side of expression.

Now, let's do it.

y = 2x + 3

We firstly send 3 to the right, change the sign of 3 from + to -, we have:

y - 3 = 2x

We then rearrange both sides to get a standard form:

2x = y - 3

We now divide both sides by 2 to get the expression of x:

(2/2)x = (y - 3)/2

We simplify both sides of expression to obtain final result:

x = (1/2)y - 3/2

=> Inverse of f(x) is x = (1/2)y - 3/2

=> Option B is correct

5 0

3 years ago