Find the equation of a line that passes through the point (0,4) and has a gradient of 2.
Leave your answer in the form
y
=
m
x
+
c

Edit, my calc is broken, sorry for the inconvenience, please disregard.

The number decreased by 14%  is found as the 133.7.

A percentage is defined as a relative value that represents the hundredth part of any quantity. Each percent (symbolized 1%) is one hundredth portion; thus, 100 percent symbolizes the entire amount and 200 percent defines twice the given amount.

Let the original number be 'x'.

number decreased by 14%

That means of x = 460.

Then,

86% of x = 1115

86x/100 = 115

x = 11500/86

x = 133.7

The original number be 133.7.

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Answer:

Step-by-step explanation:

As we do not know what your lesson is, It seems unlikely that we will be able to describe how this is different

a - ab = c

a(1 - b) = c

        a = c / (1 - b)

Answer:

10.84

Step-by-step explanation:

1.025*5+1.143*5=10.84

The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

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Let the length of the shorter leg is x.

The length of the the longer leg will be (x+3) m.

The length of the hypotenuse will be (x+6) m.

Applying the pythagorus theorem,

Neglecting the negative value of x.

Length of the shorter leg: 9 cm

Length of the longer leg: 9+3 cm=12 cm

Length of hypotenuse: 9+6 cm= 15 cm.

The center of mass for the system (x, y) is \(\left(\frac{a m+b M}{m+M}, 0\right)\).

What is center of mass?

The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.

The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.

Centre of mass is

\(x=\frac{m a+M b}{m+M}\)

and y=0

\((x, y)=\left(\frac{a m+b M}{m+M}, 0\right)\)

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The statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

In relation to the original function f, the inverse function is denoted by the symbol f⁻¹, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.

We know that inverse of function is NOT the reciprocal of f. The composition of the function f and the reciprocal function f inverse gives the domain value of x.

Hence, the statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

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Answer:

  D.  f(x) = (9x)² +2

Step-by-step explanation:

The function transformations we usually study include horizontal and vertical expansion (or compression), and horizontal and vertical translation. These can be summarized in the equation ...

  g(x) = v·f((x -a)/h) +b

where v and h are vertical and horizontal expansion factors, respectively, and (a, b) is the (right, up) translation.

__

The graph of F(x) has had its vertex moved 2 units upward (b=2), It is distinctly narrower than G(x), which could be the result of vertical expansion (v>1), or horizontal compression (h<1). Since the graph of F(x) has been compressed horizontally, the value of h must be less than 1.

__

There are two answer choices with b=2.

Choice B has h=3, a widening of the graph. Choice D has h=1/9, a narrowing of the graph.

The equation of the graph could be F(x) = (9x)² +2. The attachment shows this is an appropriate choice.

_____

Additional comment

You will notice that in this function, the vertical expansion factor is the reciprocal of the square of the horizontal expansion factor. In this case, h=1/9 is equivalent to v=81, a vertical expansion by a factor of 81.

  F(x) = (x/(1/9))² +2 = 81x² +2

The given graphs are not detailed enough to be able to judge either of these factors directly. We can estimate that h=1/9 is approximately correct by looking at the values of x where the graph has its upper boundary. At those points, x≈3 on the G(x) graph, and x<1/2 on the F(x) graph, consistent with a value of about x=1/3. The "expansion" factor is then (1/3)/3 = 1/9.

The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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Step-by-step explanation:

I hope this answer is helpful ):

The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

Herein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:

dy / dt = 3 · y · (1 - y / 14)

dy / [3 · y · (1 - y / 14)] = dt

dy / [- (3  / 14) · y · (y - 14)] = dt

By partial fractions we find the following expression:

- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt

- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.

y = 14 / [1 - C · tⁿ], where n = - 14² / 3.

If y(0) = 10, then the particular solution is:

y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

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Answer: 283.3333333% (283.3%)

Step-by-step explanation:

First, lets turn 2 5/6 into and improper fraction. It becomes 17/6.

Now, we divide 17/6

17/6 = 2.833333333

Now, to turn it into a percent, we multiply it by 100, or move the decimal point 2 places to the right. That gives us 283.3333333% (283.3%)

Hope this helps!

Answer:

The slope of the line that models this relationship is 0.50 US dollars per soda.

Step-by-step explanation:

At first we suppose the existence of a linear relationship between total cost (\(y\)), measured in US dollars, and the number of sodas (\(x\)), measured in sodas, that is:

\(y = m\cdot x\) (1)

If we know that \(x = 1\,soda\) and \(y = \$\,0.50\), then the slop of the line is:

\(m = \frac{y}{x}\)

\(m = \frac{\$\,0.50}{1\,soda}\)

\(m = 0.50\,\frac{USD}{soda}\)

The slope of the line that models this relationship is 0.50 US dollars per soda.

b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)

Answer:

0.35 I don't know how to explain it I looked it up lol

Answer:

the relationship between a prism and a pyramid with equal bases and heights is the volume of the prism is three times the volume of the pyramid.

Step-by-step explanation:

Hello there!

Answer:

16

Step-by-step explanation:

\( |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0\)

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

Answer:

6d + 49.8

Step-by-step explanation:

Step 1: Write out expression

-6(-4d - 8.3 + 3d)

Step 2: Parenthesis

-6(-d - 8.3)

Step 3: Distribute

6d + 49.8

Answer:

6

Step-by-step explanation:

c(2)=(-9/2)*(-4/3)^(2-1)=(-9/2)*(-4/3)=6

Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

Answer:

Denote the scale factor is k.

=> The ratio between the volume of two rectangular pyramids: k^3

=> k^3 = 11000/5632

=> k^3 = 1.95

=> k = ~1.25

Hope this helps!

:)

\( \sf Q) {[ {2}^{ - \frac { 1}{2} } . {7}^{ \frac{1}{3} }] }^{6} = {?} \)

\(\sf \implies {( {2}^{ \frac { \frac{1}{1} }{2} } . {7}^{ \frac{1}{3} }) }^{6} \)

\( \sf \implies {( \frac{ {7}^{ \frac{1}{3} } }{ {2}^{ \frac{1}{2} } } )}^{6} \)

\( \sf \implies \frac{ {7}^{2} }{ {2}^{3} } \)

\( \sf \implies \frac{49}{8} \) is the required answer.

Answer:

1

Step-by-step explanation:

Because each is just being multiplied by the same number.

Answer:

1

Step-by-step explanation:

anything times 1 is 1