Use the fact that
5x2 − y2 = c
is a one-parameter family of solutions of the differential equation
y
dy
dx
= 5x
to find an implicit solution of the initial-value problem
y
dy
dx
= 5x, y(3) = −8.

If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its  possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.

Percent error = 1%

Kilogram of iron ore = 500 kilograms

First step is to find the 1% of 500 kilograms

= .01 × 500 kilograms

= 5

Second step is to find the possible reading

Possible reading :

500 - 5

=495

500 + 5

= 505

Therefore we can conclude that  based on the above analysis the possible reading can be between 495 and 505.

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Answer:

a. 4.67 dollars per hour

b. 0.43 minutes per page

Explanation:

Part a.

To know the cost per hour of bike use, we need to divide the total cost by the number of hours, so:

So, the cost is 4.67 dollars per hour

Part b.

In the same way, the number of minutes per page can be calculated as the division of the number of minutes by the number of pages, so:

So, it takes 0.43 minutes per page.

Using Cramer's rule, the solution to the system of equations is given as follows:

x = -10, y = 9.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

There are multiple ways to solve a system of equations, and one of them is Cramer's Rule, in which we use the determinants of matrices to find the solutions.

In the context of this problem, the system is:

The matrix for the system is:

[tex]M = \left[\begin{array}{cc}1&2\\-3&-2\end{array}\right][/tex]

Hence it's determinant is:

|M| = 1(-2) - (-3)(2) = -2 + 6 = 4.

The matrix for x is given by:

[tex]M_x = \left[\begin{array}{cc}8&2\\12&-2\end{array}\right][/tex]

Hence it's determinant is:

|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.

The matrix for y is given by:

[tex]M_y = \left[\begin{array}{cc}1&8\\-3&12\end{array}\right][/tex]

Hence it's determinant is:

|My| =  12 - (-3)(8) = 12 + 24 = 36.

Then the solutions are given as follows:

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The simplified form for (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y) is (5x² + 0y² - 10x + 4y - 2xy).

At least one squared term must be present because a quadratic is a second-degree polynomial equation. It is also known as quadratic equations. The answers to the issue are the values of the x that satisfy the quadratic equation. These solutions are called the roots or zeros of the quadratic equations. The solutions to the given equation are any polynomial's roots. A polynomial equation with a maximum degree of two is known as a quadratic equation, or simply quadratics.

The equation can be made simpler by adding up all of the coefficients for the specified correspondent term through constructive addition or subtraction of terms, as suggested in the question.

Given, the equation is (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y)
Removing brackets and the adding we get,
3x² + 2x² + 2y² - 2y² + (- 5x) + (- 5x) + y + 3y + (- 2xy) = (5x² + 0y² - 10x + 4y - 2xy)

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So we need to solve the following equation for x:

We can apply a square root to both sides but it is important to remember the following property. For any given number a we have:

Which means that:

So for our case we have:

Then the solutions are 7 and -7.

Using transformations, the functions that could represent the one graphed are given as follows:

A transformation is when a function undergoes a change in it's definition. Depending on the type of the transformation, the function can keep the same orientation, same side lengths, and so on.

In the context of this problem, the function kept the same orientation, it just changed it's position, hence the type of transformation that the function underwent was a translation.

The possible translations are given as follows:

The domain of the graphed function is given by:

x ≥ 0.

Which is the same domain as the parent square root function, given as follows:

y = sqrt(x).

From the graph, the function was translated down a units, changing it's range, hence the function has the following format:

y = sqrt(x) - a.

Hence the first two options can be correct, either with a = 1 or with a = 3. The last two options change the range but not the domain, hence they are incorrect.

The image at the end of the answer gives the complete problem.

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The number of different committees that can be formed is 34,650.

First, we know that there are 11 teachers and the committee needs to have two teachers, so let's find the number of combinations here.

Remember that if we have a set of N elements and we need to select K of these, the number of different selections is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case we would have N = 11 and K = 2, so we get:

[tex]C(11, 2) = \frac{11!}{(11 - 2)!*2!} = \frac{11*10}{2} = 11*5 = 55[/tex]

There are 55 combinations.

For the students we do the same thing, here we have 36 students and we need to select two, so:

[tex]C(36, 2) = \frac{36!}{(36 - 2)!*2!} = \frac{36*35}{2} = 630[/tex]

So we have 55 combinations for the teachers and 630 for the students, then the total number of different committees is:

C = 630*55 = 34,650

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Answer: (0,3)

Step-by-step explanation:

The y-intercept for f(x)=x would be (0,0). Therefore, if we translate it up by three to get g(x), then the y coordinate would go up by 3, resulting in (0,3).

If Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

Here Nolan is dividing 2 by 11.

Division is one of  the basic arithmetic operation. Division is operation of splitting a specific number into equal parts

The quotient is the result from dividing a number from another number.

Divide the given terms and the result will be

2/11 = 0.1818...

The result will be a repeating quotient . Here the pattern is repeating endlessly

Hence, if Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

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The factorised form of the algebraic expression 16cd − 56c²d as given in the task content is; 8cd (2 - 7c).

It follows from the task content that the factorised form of the expression; 16cd − 56c²d as given is to be determined.

Since the given expression is;

16cd − 56c²d

First, each of the terms can be factored as follows;

16cd = 2 × 2 × 2 × 2 × c × d

56c²d = 2 × 2 × 2 × 2 × 7 × c × c × d

Therefore, since the factors which are common to both terms as follows; 2 × 2 × 2 × c × d = 8cd.

Therefore the factorised form of the expression is;

8cd (2 - 7c).

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Answer:

Step-by-step explanation:

[tex]2\frac{5}{8} =\frac{2 \times 8+5}{8} =\frac{21}{8} \\2\frac{1}{4} =\frac{2 \times 4+1}{4} =\frac{9}{4} \\2\frac{5}{8} / 2\frac{1}{4} \\=\frac{21}{8} /\frac{9}{4} \\=\frac{21}{8} \times \frac{4}{9} \\=\frac{7}{6} \\=1\frac{1}{6}[/tex]

Step-by-step explanation:

5 people went on the Carowinds trip.

6/18=×/36

solve for x

x=(6/18)36

x=6(36/18)

x=6(2)

x=12

The dimensions of the rectangular garden are 20 feet and 29 feet respectively.

It is vital to note that the formula for the area of a rectangle is expressed as;

Area = lw

Where;

From the information given, we have that;

Area =  580ft²

Length = 9 + width

L = 9 + w

Substitute the values into the formula, we have;

580 = (9 +w)(w)

expand the bracket

580 = 9w + w²

Make into quadratic equation

w² + 9w - 580 = 0

Factorize the equation

w² + 29w - 20w - 580 = 0

Factor the common terms

w( w + 29) - 20(w + 29) = 0

Then,

w + 29 = 0

w = -29

and w - 20 = 20 feet

We have the expression of length as l = 9 + w

Length, l = 9 + 20

Length, l = 29 feet

Thus, the values are 20 feet and 29 feet

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Using the formula for the area of a circle calculate the area for both deals.

for the 18-inch pizza

for the two 12-inch pizza

Ms. Lantz would need to finish in 50.28 minutes to be eligible for the Houston Marathon.

The relationship between a score and the mean over a set of scores is simply quantified by a Z-Score, which is a measurable statistic.

A Z-score can explain to a trader why a value is unusual or average for a given set of data.

A Z-score below 1.8 suggests that a company is on the verge of bankruptcy, while a score closer to 3 shows that the company is doing well financially.

Solution:

The z-score is calculated using the formula: 

z = (x - μ)/σ

μ = Sample's average

σ = Sample's standard deviation

The values are as follows:

μ equals 57 minutes.

σ = 8 minutes

Probability equals 20%, or 0.20.

Determine the z-score for 0.20 using the negative z-table.

Z score is -0.84.

To find x, enter the values into the z formula.

z = (x - μ)/σ

-0.84 = (x - 57)/8

Simplifying;

x = -6.72 + 57

x = 50.28 minutes

Thus, Ms. Lantz would need to complete the Rocket Run 5k in 50.28 minutes in order to be eligible for the Houston Marathon.

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The most appropriate choice for perimeter of rectangle will be given by-

Mr Smith must buy 61 m of fencing.

What is perimeter of rectangle?

It is equal to the total distance of the boundary of the rectangle.

If length of rectangle is l m and breadth of rectangle is b m, perimeter of rectangle is 2 x (l + b) [tex]m^2[/tex]

Here,

Length of yard = 61 ft

Breadth of yard = 39 ft

Perimeter of yard = 2 x (61 + 39)

                             = 2 x 100

                             = 200 ft

1 ft = 0.305 m

200 ft = 0.305 x 200 m

          = 61 m

Mr Smith must buy 61 m of fencing.

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Answer:

Step-by-step explanation:

All the identifiers that are included when identifying significant digits are-

Each of the digits of a number starting with the digit farthest to a left that is not zero as well as ending with the digit farthest to a right that is neither zero or is a zero but is considered exact.

For the given options.

Except option 1 every option is correct.

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The width of the rectangle DOGS is 119cm

To solve this, since is a ratio problem, we know that the two ratios must add to the total. This is, for a ratio of 5:7, 5 + 7 = 12 is the total "divisions" for the ratio.

This means that if 12 of 12 parts add to the perimeter (408cm):

12/12 represents the perimeter 408cm.

The, we can divide the perimeter by 12 and get:

Since the width is 7/12 of the perimeter:

But, we are taking the perimeter of a rectangle, which is twice the width plus twice the length, thus we need to divide this number by 2:

And we get the final answer of 119cm

Answer:

The percentage change is 15%

Step-by-step explanation:

Can I have brainliest?

Answer:

6 is the awnswer

Step-by-step explanation:

Given the fraction below

To simplify the above fraction, we will divide both the numerato

Answer:   The graph is below

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

Explanation:

If x = 0, then,

g(x) = -x+1

g(0) = -0+1

g(0) = 0+1

g(0) = 1

Therefore, x = 0 leads to y = 1. The point (0,1) is on the g(x) line.

Now try x = 1

g(x) = -x+1

g(1) = -1+1

g(1) = 0

The point (1,0) is also on the g(x) line.

Draw a line through the points (0,1) and (1,0)

Then erase the portion that is to the left of x = -4

This is because g(x) is only graphed when x > -4; i.e. we're only graphing stuff to the right of x = -4.

We'll have an open hole when x = -4 since we aren't including it as part of the graph.

See below.

Let's look at car A first.

As already solved, just after it is purchased its value decreases 20%.

Purchased at $30000, its value inmediatly decreases to $24000 ($30000 -

0.2*$30000 = $24000).

We know the yearly depreciation for car A os $2000.

Then, at the end of the first year, its value will decrease from $24000 to $24000 - $2000 = $22000.

Every year its value decreases $2000. Followint the same logic, at the end of the second year its value will decrease from $22000 to $22000 - $2000 = $20000 and so on. Now, we can build the table:

End of first year: $24000 - $2000 = $22000

End of second year: $22000 - $2000 = $20000

End of third year: $20000 - $2000 = $18000

End of fourth year: $18000 - $2000 = $16000

End of fifth year: $16000 - $2000 = $14000

Answer:

1/6 chance

Step-by-step explanation:

The answer to the given function is [tex]B(a)= a/6-9[/tex].

A trapezoid, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides. A trapezium's bases are its parallel sides, while its legs are its non-parallel sides.

Given :

[tex]A(b)= 12( b+9)/2[/tex]

where, A(b) is the trapezoid's area

and b is the other base value

On solving the above equation further we get ;

[tex]A= 6(b+9)[/tex]

[tex]A/6= b+9[/tex]

this implies we get;

b= [tex]A/6-9[/tex]

Now convert this into function notation we get

[tex]B(a)= a/6-9[/tex]

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Answer:

c. 250 miles

Step-by-step explanation:

[tex]d=(50)(5)=250[/tex]

Answer:

4826.166666km

Step-by-step explanation:

d=distance

  [tex]\frac{1259km}{1h} =\frac{d}{23/6h}[/tex]

= [tex]\frac{1259km}{1h}= \frac{6d}{23}[/tex]

= [tex]1259=\frac{6d}{23}[/tex]

= [tex]1259*23=6d[/tex]

= [tex]28,957=6d[/tex]

= [tex]\frac{28,957}{6}=d[/tex] ≈4826.166666