Solve for c

21 = 5/6c - 9

Answer:

\(Slope = \frac{31}{29}\)

Step-by-step explanation:

Step 1:  Define the slope formula

\(Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Step 2:  Find the slope

\(Slope = \frac{71-9}{32-(-26)}\)

\(Slope = \frac{62}{58}\)

\(Slope = \frac{31}{29}\)

Answer:  \(Slope = \frac{31}{29}\)

Answer:

Solution,

Length(l)=7.2 cm

Breadth(b)=3.1 cm

Height(h)=4.8 cm

Now,

\(surface \: area \: of \: cuboid \\ = 2(l \times b + b \times h + h \times l) \\ = 2(7.2 \times 3.1 + 3.1 \times 4.8 + 4.8 \times 7.2) \\ = 2(22.32 + 14.88 + 34.56) \\ = 2(71.76) \\ = 143.52 \: {cm}^{2} \)

hope this helps...

Good luck on your assignment..

The surface area of cuboid is 143.52 square centimeters whose length is 7.2cm, width is 3.1 cm and height is 4.8 cm.

The formula for surface area of cuboid:

Surface area =  2(l×w + w×h + h×l).

Where l is length,

w is width,

h is height,

l=7.2 cm, w = 3.1cm and h=4.8 cm.

Plug in these values in above formula:

Surface area = 2(7.2×3.1 + 3.1×4.8 + 4.8×7.2)

=2(22.32 + 14.88 + 34.56)

=2(71.76)

=143.52

Hence, the surface area of cuboid is 143.52 square centimeters.

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a + b > 12---- equation 1

a > - 3----- equation 2

from equation 1

b > 12 - a

from equation 2, the values of a is greater

Given the expression:

3x² + x - 10

We can rewrite it as:

3x² + 6x - 5x - 10

Which can be factoriced as:

3x(x + 2) - 5(x + 2) =

(x + 2)(3x - 5)

Answer:

Step-by-step explanation: To find out what grade Sally needs to earn on her fifth and last math test to achieve a 90 average, we  use the following steps:

Step 1: Add the total points Sally has received: 80 + 82 + 92 + 98 = 352.

Sally has taken 4 tests so far.

Step 2: Find the total marks required for a 90 average on 5 tests: 90 x 5 = 450.

Step 3: Find the score Sally needs to achieve on her fifth test by subtracting the points earned  from the total required points: 450 - 352 = 98.

Therefore, Sally needs to earn a grade of 98 on her 5th and last test to achieve a 90 average on all five tests this semester.

Answer: 12 ft

Step-by-step explanation:

Answer:

\(\huge\boxed{12 \ \text{ft}}\)

Step-by-step explanation:

We can see that the yard stick and the tree are forming triangles with the ground.

We also given that these are similar figures. Therefore, the ratio between both their corresponding sides will be the same for every side.

AKA:

Since the yardstick has a 6ft leg, but the tree has a 24ft leg, the tree will be equally proportional to the yardstick.

What's the scale factor that we use to get from the yardstick to the tree?

We have 24 to 6.

\(24 \div 6 = 4\)

So the scale factor is 4.

Therefore, if we multiply the yardstick height by 4, we will get the height of the tree.

\(3 \cdot 4 = 12\)

So the tree is 12 feet tall.

Hope this helped!

Answer:

is finding the square root

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number.

When a number is squared, it is multiplied by itself. For example, squaring the number 4 gives 4^2 = 16.

The inverse operation undoes the effect of squaring and returns you to the original number. In this case, finding the square root of a number is the inverse operation of squaring.

The square root of a number "x" is a value that, when squared, gives the original number. It is denoted by the symbol √x.

For example, if you have the number 25 and you want to find its square root, you calculate:

√25 = 5

5 is the square root of 25 because when you square 5 (5^2), you get 25.

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number. The concept of square root and squaring are inverse operations that are used in various mathematical calculations and problem-solving.

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The value of x, given the parallel lines and the angles involved, can be found to be 12. 3 .

The angles on the parallel lines are drawn such that 11 x and 45 degrees are supplementary angles .

This means that they add up to 180 degrees .

The value of x can therefore be found to be :

11 x + 45 = 180

11 x = 180 - 45

11 x = 135

x = 135 / 11

x = 12. 3

In conclusion, the value of x is 12. 3 .

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Answer:

Please check the explanation.

Step-by-step explanation:

Given the equation

\(x^2\:-16x\:+\:39\:=\:0\)

Subtract 39 from both sides

\(x^2-16x+39-39=0-39\)

Simplify

\(x^2-16x=-39\)

Rewrite in the form x² + 2ax + a²

solve for a, 2ax = -16x

2ax = -16x

divide both sides by 2a

2ax/2x = -16x/2x

a = -8

Add a² = (-8)² to both sides

\(x^2-16x+\left(-8\right)^2=-39+\left(-8\right)^2\)

simplify

\(x^2-16x+\left(-8\right)^2=25\)

Apply perfect square formula:  (a-b)² = a² - 2ab + b²

\(\left(x-8\right)^2=25\)           ∵ \(x^2-16x+\left(-8\right)^2=\left(x-8\right)^2\)

Thus,

\(\left(x-8\right)^2=25\)

BONUS! EXTENDED SOLUTION!

We can further solve for x such as

\(\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}\)

solve

\(x-8=\sqrt{25}\)

\(x-8=\sqrt{5^2}\)

\(x-8=5\)        

\(x=13\)

similarly,

\(x-8=-\sqrt{25}\)

\(x-8=-5\)

\(x=3\)

Therefore,

\(x=13,\:x=3\)

Answer:The boat is traveling at a rate of 3 ft/s.

Step-by-step explanation:

18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

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Answer:

agree

Step-by-step explanation:

Answer:

n = 100

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

given A = 40π , then

πr² × \(\frac{n}{360}\) = 40π

π × 12² × \(\frac{n}{360}\) = 40π

144π × \(\frac{n}{360}\) = 40π ( divide both sides by π )

144 × \(\frac{n}{360}\) = 40 ( multiply both sides by 360 to clear the fraction )

144n = 14400 ( divide both sides by 144 )

n = 100

Answer:

Step-by-step explanation:

Volume = length x width x height

Answer:119.7

Step-by-step explanation:60 divided by 15%

Answer:

its C

Step-by-step explanation:

The midpoint of AB is M(4,1), If the coordinates of A are (2,8), then the coordinates of B are (6,-6).

The midpoint formula states that the midpoint of a line segment in a coordinate plane is given by the average of the x-coordinates and the average of the y-coordinates.

The midpoint of AB is M(4,1) and the coordinates of A are (2,8).

Therefore, we can write the following equation: x-coordinate of the midpoint = (x-coordinate of A + x-coordinate of B) / 2y-coordinate of the midpoint = (y-coordinate of A + y-coordinate of B) / 2

Substituting the given values into the above equation, we get:4 = (2 + x-coordinate of B) / 2 1 = (8 + y-coordinate of B) / 2

Simplifying the equations above, we get: x-coordinate of B = 6 y-coordinate of B = -6

Therefore, the coordinates of B are (6,-6).

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Answer

28 cm³ water entered the tank between 2 and 8 minutes;

Explanation

Rate of flow of water r(t) = dV/dt = 3√(t/2);

Flow of water between 2 and 8 minutes;

\(\int\limits dV = \int\limits^8_2 {3\sqrt{t/2} } \, dx\)

\(V = 3/\sqrt{2} \int\limits^8_2 {\sqrt{t} } \, dt\\\)

\(\\V = 2/\sqrt{2} (8^{3/2}- 2^{3/2} )\\\)

V = 28 cm³

The flow rate of a liquid is how a whole lot fluid passes through a place in a specific time. float fee can be articulated in either in terms of velocity and cross-sectional place, or time and quantity. As liquids are incompressible, the price of circulate an area must be equal to the rate of waft out of an area.

How do I calculate flow rate?

Rate is the flow rate or speed of the water, using the unit “meters per second. “ For example: The object travels a 5 meter length of stream in 8 seconds. Divide 5 (length traveled) by 8 (time it took to travel the distance) for an answer of .

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Answer: you didn’t even say please

explanation: why don’t you ask your mother you make me sad

Hello, This is the answer.

Please check the attached image.

By Benjemin ☺️

The distance (d) between two points is computed as follows:

where (x1, y1) and (x2, y2) are the points of interest. In this case, the points are (7, 8) and (-1, 0). Replacing into the equation:

To write the matrix Q[R1, ..., Rp] as a product of two matrices, where R1, ..., Rp are vectors in ℝn and Q is an m×n matrix, we can use matrix multiplication.

Let's denote Q[R1, ..., Rp] as M. Then, M is an m×n matrix.

M = Q[R1, ..., Rp]

To express M as a product of two matrices, we can write it as:

M = AB

where A is an m×k matrix and B is a k×n matrix, with k being a suitable intermediate dimension.

To find the values of A and B, we can use the following steps:

Calculate the matrix Q[R1, ..., Rp]:

M = [QR1, ..., QRp]

Here, Q*R1 represents the product of the matrix Q and vector R1, and so on for R2, ..., Rp.

Determine the dimensions of A and B:

Since M is an m×n matrix, A should have dimensions m×k, and B should have dimensions k×n.

Rearrange the matrix multiplication:

We can express M as a product of two matrices by rearranging the matrix multiplication:

M = Q[R1, ..., Rp] = [QR1, ..., QRp] = [QR1; ...; QRp]

Here, [QR1; ...; QRp] represents the vertical concatenation of the matrices QR1, ..., QRp.

Assign A and B:

A = [QR1; ...; QRp]

B = In

Here, In is the n×n identity matrix.

By following these steps, we express the matrix Q[R1, ..., Rp] as a product of two matrices, A and B, where A is an m×k matrix and B is a k×n matrix. Note that neither A nor B is an identity matrix.

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The highest value assumed by the loop counter in this case is 70.

In a correct for loop statement with the header

for (i = 7; i <= 72; i += 7)`, the highest value assumed by the loop counter is 70.

The loop in the question has the header `for (i = 7; i <= 72; i += 7)`.

This means that the loop counter `i` starts at 7 and will increase by 7 each time the loop runs.

The loop will continue to run as long as the loop counter `i` is less than or equal to 72.

So, the loop will execute for `72-7 / 7 + 1 = 10` times.

The loop counter will take the values: 7, 14, 21, 28, 35, 42, 49, 56, 63, and 70.

Therefore, the highest value assumed by the loop counter in this case is 70.

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Answer:

19.55m

Step-by-step explanation:

We solve the above question using the formula for Arc Length

The formula of Arc length when central angle is given in degrees = Length of AB

= θ/360 × 2πr

Central angle = θ = 140°

Radius = r = 8m

Hence,

Length AB = 140/360 × 2 × π × 8

= 19.547687622 m

Approximately to the nearest hundredth, the length of AB = 19.55m

Answer:

11 = x

Step-by-step explanation:

Concentration = \(9.17*10^{-4}\) moles/liter.

To find the pH of the solution with a \(H_{3}O^{+}\) concentration of \(9.17*10^{-4}\) moles/liter, we need to use the formula for pH: pH = -log [H+]. In this case, [H+] = \(H_{3}O^{+}\) concentration = \(9.17*10^{-4}\) moles/liter.
Substituting this value in the formula, we get pH = -log [9.17*10^-4] = 3.04. Therefore, the pH of the solution is 3.04.
pH is a measure of the acidity or basicity of a solution and is defined as the negative logarithm of the hydrogen ion concentration ([H+]). A lower pH indicates a higher acidity, while a higher pH indicates a higher basicity. A pH of 7 is considered neutral, while values less than 7 are acidic and values greater than 7 are basic. It is important to measure and control the pH of a solution in various industries such as food and beverage, pharmaceuticals, and environmental monitoring.

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Answer:

yes that's the answer because the volume of a cylinder= πr²h and the volume of a cone =1/3πr²h

Yes, Rolle's Theorem can be applied to f on the closed interval [0, 5].

To find the values of c in the open interval (0, 5) where f'(c) = 0, we first need to find f'(x):

f(x) = -x^2 + 5x
f'(x) = -2x + 5

Next, we need to find any values of c where f'(c) = 0:

-2c + 5 = 0
c = 5/2

Therefore, the only value of c in the open interval (0, 5) where f'(c) = 0 is c = 5/2.
Yes, Rolle's Theorem can be applied.

To apply Rolle's Theorem, the function f(x) must satisfy the following conditions:
1. f(x) is continuous on the closed interval [a, b].
2. f(x) is differentiable in the open interval (a, b).
3. f(a) = f(b).

Given f(x) = -x^2 + 5x on the interval [0, 5], let's check these conditions:

1. The function is a polynomial, so it is continuous on the entire real line, including the interval [0, 5].
2. Polynomials are also differentiable everywhere, so f(x) is differentiable in the open interval (0, 5).
3. f(0) = -(0)^2 + 5(0) = 0 and f(5) = -(5)^2 + 5(5) = -25 + 25 = 0. So, f(a) = f(b).

All conditions are met, so Rolle's Theorem can be applied.

Now, we need to find all values of c in the open interval (0, 5) such that f'(c) = 0.

First, find f'(x) by differentiating f(x): f'(x) = -2x + 5.

Next, set f'(x) equal to 0 and solve for x: 0 = -2x + 5, which gives x = 5/2.

Thus, there is one value of c in the open interval (0, 5) where f'(c) = 0: c = 5/2.

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