Please help me
The elevation of Kristianstad, Sweden, a city founded by King Christian IV of Denmark, is meters . Which of these describes the elevation of Kristianstad?

Answer:

Approximately 1.86 times smaller

Step-by-step explanation:

5×10-7 = (5×10=50) = 50-7 = 43

8.5×10-4 = (8.5×10=84) = 84- 4 = 80

80/43 = approximately 1.86

43×1.86 = approximately 80

80/1.86 = approximately 43

Answer:

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Step-by-step explanation:

red: green : total

7          2       7+2

7          2          9

When we use the ratios, the total is 9

We are given the total is 63

63 divided by 9 is 7

We need to multiply each number by 7

red: green : total

7*7      2*7       9*7

49       14             63

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Answer:

the answer is red apples 49 and green apples 14.

Answer:

Q3

Slope = 5

Standard= y=5X+15

Q5

Slop =-4

Standard= y=-4x+4

Step-by-step explanation:

m=-5-5/-4+2=-10/-2= 5

y-5=5(x+2)

y-5=5x+10

y=5x+15

Answer: [tex]\boxed{\sqrt{12x-1}}[/tex]

Step-by-step explanation:

[tex]\sqrt{2(6x-3)+5}\\ \\\sqrt{(12x-6)+5} \\\\\boxed{\sqrt{12x-1}} \\\\This\ is\ as\ far\ as\ you\ can\ simplify\ this[/tex]

Answer:

-7

Step-by-step explanation:

To add a positive number, 5, and a negative number, -12, take the absolute value of both numbers.

You get 5 and 12.

Subtract the smaller absolute value from the larger absolute value.

12 - 5 = 7

The sign of the answer is the same sign as the number that has the larger absolute value. The absolute of 5 is 5. The absolute value of -12 is 12. -12 has the larger absolute value, and -12 is negative, so the answer is negative.

5 + (-12) = -7

Answer:

631

Step-by-step explanation:

This problem can be expressed as:

0.05x + 15 = 21.55
0.05x + 15 - 15 = 21.55 - 15
0.05x = 6.55
0.05x/0.05 = 6.55/0.05
x = 131

We also know that:

0.05x + 15 = x + 500

If x = 131:

x + 500
131 + 500
631

For the time period of  the projectile at least 192 feet above the ground is between 2 second and 6 second

Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:

16t2-128t+192=0 or, simplified, 8t2-64t+96=0

or t2-8t+12=0

since it is now in quadratic form, we can solve using the quadratic formula:

t = 2 and 6

So the time period from approximately 2 second and 6 second has the projectile above 192 feet.

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The energy required is 30 watts second.

In order to accomplish work and to produce heat and light, energy must be transferred to a body or to a physical system. Energy is the quantitative attribute that does this. Energy is a preserved resource; according to the rule of conservation of energy, energy can only be transformed from one form to another and cannot be created or eliminated.

The voltage of a battery is 12 V and;

The charge is 2.5C.

Now, energy can be defined as the product of voltage and charge.

Therefore,

E = V × C

E = 12 × 2.5

E = 30 watt second

Hence, the energy needed by the 12 V battery to move 2.5 C through the electrical circuit is 30 watts second.

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If a pipe is leaking at a rate of 8 US fluid ounces per minute, then 3.75 US liquid gallons of the fluid will leak from the pipe in an hour.

As per the question statement, a pipe is leaking at a rate of 8 US fluid ounces per minute and we are required to calculate the amount of leak that will occur at the same rate of leakage, in an hour, in the units of US liquid gallons.

To solve this question, we need to know to know about two basic mathematical conversions, i.e.,

1 US Liquid Ounce = 0.00781 US Liquid Gallons, and

1 hour = 60 minutes.

Therefore, amount of leak that will occur at the rate of 8 US fluid ounces per minute, in an hour = [tex](8 * 60)=480[/tex] US fluid ounces.

And 480 US fluid ounces = [tex](0.00781 * 480)=3.75[/tex] US Liquid Gallons.

Hence, 3.75 US Liquid Gallons of fluid will leak from the pipe in an hour.

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Answer:

120

Step-by-step explanation:

60 gallons of 30% antifreeze means there are 18 gallons of antifreeze.

Let the number of gallons of 60% antifreeze be x. Then,

[tex]\frac{0.6x+18}{x+60}=\frac{1}{2} \\ \\ 1.2x+36=x+60 \\ \\ 0.2x=24 \\ \\ x=129[/tex]

What is that for?

??????????????????????????????????????????????????????????????????????

Answer:

Step-by-step explanation:

create the cartesian system, sign the points, because the new triangle is reflected, so we need to use the straight lines which points on its ends, perpendicular to the x-axis, then we get A(0,-6), B(3,0), C(4,-3)

Answer:

  E = mc²

Step-by-step explanation:

You want an example of a literal equation.

A literal equation is one that uses variable names to represent numerical values.

Any equation that has no numbers is a literal equation.

One of the more famous literal equations in the world is Einstein's relation between mass and energy:

  E = mc²

We use literal equations as formulas for length, area, volume, and relations between chemical and engineering properties.

  P = 2(L+W) . . . . perimeter of a rectangle with length L and width W

  V = I·R . . . . voltage in a circuit with current I and resistance R

  PV = nRT . . . . ideal gas law relating pressure, volume, temperature, and quantity of gas

The amount he would pay is $46.40.

Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.

The amount paid = list price of the first shirt + [list price of the second shirt x ( 1 - percentage discount)]

$29 + [$29 x (1 - 0.4)]

$29 + ($29 x 0.6) = $46.40

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m= 15

b= 45

y= 15x +45

Overall equation

The equation of a line in slope-intercept form is given by y= mx +b, where m is the slope and b is the y-intercept.

Slope, m

The slope is the measure of how steep the line is. It also defines how the y-axis changes with respect to the x-axis. The formula for finding slope is as shown below.

[tex]\boxed{\text{Slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

where [tex](x_1,y_1)[/tex] is the first coordinate and [tex](x_2,y_2)[/tex] is the second coordinate

y-intercept, b

This is the y-value in which the line cuts through the y-axis (vertical axis).

Slope, m

Let's identify two pairs of coordinates on the line.

2 square units on the y-axis represent $30. Thus, 1 unit on the y-axis represents $15.

The 2 points are: (0, 45) and (5, 120)

Substitute the 2 points into the slope formula:

Slope

= [tex]\frac{120-45}{5-0}[/tex]

= [tex]\frac{75}{5}[/tex]

= 15

Thus, m= 15.

y-intercept, b

From the graph, the line cuts through the y-axis at y= 45.

Thus, b= 45.

Overall equation

Substitute m= 15 & b= 45 into y= mx +b:

∴ The equation of the line is y= 15x +45.

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answer and steps to get it in the picture

The values of x and y are 25° and 33° respectively.

It is important to note the following;

From the information given, we have that

Angles 5x + 4 and 3x - 24 are supplementary.

This is represented as;

5x + 5 + 3x - 24 = 180

collect like terms

8x = 180 + 20

add lik terms

8x = 200

x = 200/8

x = 25°

Also,

2y and 114 are on a straight line

This is represented as;

2y + 114 = 180

collect like terms

2y = 180 - 114

2y = 66

Make 'y' the subject

y = 66/2

y = 33°

Thus, the values of x and y are 25° and 33° respectively.

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Answer:

Infinite Solutions

Step-by-step explanation:

3(4x + 6) = 2(6x + 9)

Distribute coefficients

12x + 18 = 12x +18

Same equations which means infinite solutions

The volume of the sphere when it is completely closed is 4508.58 cubic inches

The formula for calculating the volume of a sphere is expressed as:

V = 4/3πr³

where

r is the radius = 20.5/2

radius = 10.25 in

Substitute

V = 4/3 (3.14)*10.25³

V = 4/3(3.14)
V =4508.58 cubic inches

Hence the volume of the sphere when it is completely closed is 4508.58 cubic inches

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Answer:

formula for the derivative of x*lnx is equal to 1 + lnx.

Step-by-step explanation:

we need to find derivative of f(x) = x*lnx,

so we take the limiting value as x approaches x + h.

To simplify this, we set x = x + h,

and we want to take the limiting value as h approaches 0.

Now according to first derivative formula we have;

f'(x) = [tex]\lim_{h \to \zer0}[/tex]f(x+h) - f(x)]/[(x+h) - x]

[tex]\lim_{h \to \zer0}[/tex][ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = [tex]\lim_{h \to \zer0}[/tex][(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) + h ln(x+h) - xlnx]/h

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) - x lnx + h ln(x+h)]/h

= [tex]\lim_{h \to \zer0}\\[/tex][x(ln(x+h) - lnx) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln [(x+h)/x] + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln (1+h/x) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex] [x ln (1+h/x)]/h + limh→0 ln(x+h)

= [tex]\lim_{h \to \zer0}[/tex][ ln (1 + h/x) ] / (h/x) + limh→0 ln(x+h)

= 1 + lnx --- [Using limit formula [tex]\lim_{h \to \zer0}[/tex] [ ln (1 + x) ] / x = 1]

Hence, we have proved that the formula for the derivative of x*lnx is equal to 1 + lnx.

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Answer:

Step-by-step explanation:

In this section, we will determine the differentiate of xlnx using the first principle of derivatives, that is, the definition of limits. To derive the derivative of f(x) = xlnx, we take the limiting value as x approaches x + h. To simplify this, we set x = x + h, and we want to take the limiting value as h approaches 0. We will use the following formulas to prove the result:

f'(x) = limh→0[f(x+h) - f(x)]/[(x+h) - x]

limx→0 [ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = limh→0[(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= limh→0[x ln(x+h) + h ln(x+h) - xlnx]/h

= limh→0[x ln(x+h) - x lnx + h ln(x+h)]/h

= limh→0[x(ln(x+h) - lnx) + h ln(x+h)]/h

= limh→0[x ln [(x+h)/x] + h ln(x+h)]/h

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Answer:

a=A/8

Step-by-step explanation:

This MIGHT be the answer, I am 99% sure!

The equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4

The expression is given as:

4 − 3(x + 2) + 2(3 − 2x)

Open the brackets

4 − 3(x + 2) + 2(3 − 2x) = 4 - 3x - 6 + 6 - 4x

Collect the like terms

4 − 3(x + 2) + 2(3 − 2x) = - 3x - 4x + 4 - 6 + 6

Evaluate the like terms

4 − 3(x + 2) + 2(3 − 2x) = -7x + 4

Hence, the equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4

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Let the terms be a, ar, ar², ...

The sum to infinity being 27 means that:

[tex]\frac{a}{1-r}=27 \implies a=27(1-r)[/tex]

The sum of the first two terms being 15 means:

[tex]a+ar=15 \\ \\ (27-27r)+r(27-27r)=15 \\ \\ 27-27r+27r-27r^2 =15 \\ \\ 27r^2 -12=0 \\ \\ 27r^2 =12 \\ \\ r^2=\frac{12}{27}[/tex]

Since all the terms are positive, r>0.

[tex]\boxed{r=\frac{2}{3}} \\ \\ \implies a=27\left(1-\frac{2}{3} \right)=\boxed{9}[/tex]

Step-by-step explanation:

the constant k of proportionality is defined by

y = kx

or in our case

b = ka

so, let's see

14 = k×2

k = 14/2 = 7

this also works for the other data pairs :

7×5 = 35

7×9 = 63

7 × 1/3 = 7/3

perfect.

so, the constant of proportionality is 7.

[tex]{\sf{12 \times ( - 4) = -48}}[/tex]

Following the first term [tex]n[/tex], the [tex]k[/tex]-th term [tex]\left(k\in\{1,2,3,\ldots,n\}\right)[/tex] in [tex]f(n)[/tex] is given by

[tex]\dfrac{16k + (9-4k)n - 3n^2}{4kn + 3n^2}[/tex]

That is,

[tex]k=1 \implies \dfrac{16 + (9-4)n - 3n^2}{4n + 3n^2} = \dfrac{16 + 5n - 3n^2}{4n + 3n^2}[/tex]

[tex]k=2 \implies \dfrac{16\cdot2 + (9-8)n - 3n^2}{4\cdot2n + 3n^2} = \dfrac{32 + n - 3n^2}{8n + 3n^2}[/tex]

and so on, up to

[tex]k=n \implies \dfrac{16n + (9-4n)n - 3n^2}{4n^2 + 3n^2} = \dfrac{25n - 7n^2}{7n^2}[/tex]

We then have

[tex]\displaystyle f(n) = n + \sum_{k=1}^n \frac{16k + (9-4k)n - 3n^2}{4kn + 3n^2} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} - \frac1n \sum_{k=1}^n \frac{4kn + 3n^2}{4k + 3n} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}- \frac1n \sum_{k=1}^n n \\\\ ~~~~~~~ = \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}[/tex]

Now as [tex]n\to\infty[/tex], the right side converges to a definite integral.

[tex]\displaystyle \lim_{n\to\infty} f(n) = \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} \\\\ ~~~~~~~~~~~~~ \,= \int_0^1 \frac{16x + 9}{4x + 3} \, dx[/tex]

Wrap up by substituting [tex]x\mapsto\frac{x-3}4[/tex].

[tex]\displaystyle \lim_{n\to\infty} f(n) = \frac14 \int_0^1 \frac{16x + 9}{4x + 3} \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \frac{4x - 3}x \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \left(4 - \frac3x\right) \, dx \\\\ ~~~~~~~~~~~~~\, = \left. \frac14 (4x - 3\ln|x|) \right\vert_3^7\\\\ ~~~~~~~~~~~~~\, = \boxed{4 + \frac34 \ln\left(\frac37\right)}[/tex]

Answer: irrational

Step-by-step explanation:

because it still cant be turned into a fraction after adding 9 to pi