914−456 whta's the answer

The constant of variation of the given problem is calculated as; 240 miles

A constant of variation (k) is defined as a ratio that represents the relationship between the independent variable (x) and the dependent variable (y).

Now, we are told that average speed, s, in miles per hour is inversely proportional to the time, t, the trip takes in hours. Thus;

s ∝ 1/t

Thus;

s = k(1/t)

where k is the constant of proportionality

we are told that If the train takes 2 hours, and the average speed is 120 mph. Thus;

120 = k(1/2)

Multiply both sides by 2 to get;

240 miles = k

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Answer:

Area of the metal sheet required = 364 square inches

Step-by-step explanation:

Area of the metal sheet required = Surface area of the lateral sides of the vent transition

Since, lateral sides of the vent is in the shape of a trapezoid,

Therefore, surface area of the vent = 4(Surface area of one lateral side)

                                                           = \(4[\frac{1}{2}(b_1+b_2)h]\)

Here, \(b_1\) and \(b_2\) are two parallel sides and \(h\) is the distance between these parallel sides.

Surface area of the vent = \(4[\frac{1}{2}(8+5)14]\)

                                         = 364 square inches

Therefore, area of the metal sheet required = 364 square inches

Answer:

(5 + 16)=7 + (4 x 7)

Step by step - explanation:

Solve:

Add the numbers

(5 + 16)= 21.

(4 x 7) = 28 + 7 = 35.

So the result is 21 = 35.

Hope that helps. x

Answer:

Step-by-step explanation:

(5+16)=7+(4.7)

(21)=7+(4.7)

21=7+(4.7)

21=7+(28)

21=7+28

21=35

Answer: 21=35

Answer:

= 1 × 10^-7

(scientific notation)

= 1e-7

(scientific e notation)

= 100 × 10^-9

(engineering notation)

(billionth; prefix nano- (n))

= 0.0000001

(real number)

Step-by-step explanation:

10^7 = 10000000

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\(\large\text{4(6x + 11)}\)

\(\large\text{Distribute}\)

\(\large\text{4(6x) + 4(11)}\)

\(\large\text{4(6x) = 24x}\)

\(\large\text{4(11) = 44}\)

\(\large\text{= 24x + 44}\)

\(\boxed{\boxed{\large\text{Answer: \bf{24x + 44}}}}\huge\checkmark\) ☑️

\(\text{Good luck on your assignment and enjoy your day!}\)

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Answer:

In order to obtain the graphs of the functions f(x) = √(x) - 3 and g(x) = √(x - 3), we start with the parent function f(x) = √(x).

For the function f(x) = √(x) - 3:

Therefore, the graph of f(x) = √(x) - 3 is obtained by shifting the parent function √(x) three units to the right and three units downward.

For the function g(x) = √(x - 3):

Therefore, the graph of g(x) = √(x - 3) is obtained by shifting the parent function √(x) three units to the right, without any vertical shift.

The question is incomplete. The complete question is:

Find an equation of the tangent line to the curve y = \(\sqrt{x}\) at the given point (16,4). To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16,4) we know that (16,4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula m tan = lim x↔a f(x) - f(a)/ x - a.

Answer: y = \(\frac{x}{8} + 2\)

Step-by-step explanation: The tangent line is a line that intercepts a curve in only one point. The point-slope formula for a line is \(y-y_{0} = m(x-x_{0})\), where m is the slope of the line and can be calculated by the first derivative of the given curve. For this case:

y = \(\sqrt{x}\)

f'(x) = \(\frac{dy}{dx} = \sqrt{x}\)

f'(x) = \(\frac{1}{2\sqrt{x} }\)

At point (16,4), the slope will be:

m = f'(16) = \(\frac{1}{2.\sqrt{16} }\)

m = \(\frac{1}{8}\)

With slope and a point, the line function will be:

\(y-y_{0} = m(x-x_{0})\)

y - 4 = \(\frac{1}{8}\)(x - 16)

y = \(\frac{x}{8}\) - 2 + 4

y = \(\frac{x}{8}\) + 2

The tangent line to the curve is y = x/8 + 2

The slope of the line, given the point on the line and the y - intercept, is - 5. 33

The slope of a line tells us the relationship between the dependent variable and the independent variable. In other words, it tells us what a change in the independent variable leads to in the dependent variable.

The slope can be found in the slope - intercept formula form of :

y = mx + b

m is the slope

b is the y - intercept

We have the y - intercept and a y and x value in ( -3, 6 ) so the slope is:

6 = - 3 ( m ) + ( - 10 )

6 = - 3m - 10

- 3m = 6 + 10

- 3 m = 16

m = 16 / - 3

m = - 5. 33

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Actually Welcome to the Concept of the Logarithms,

so we get as,

t = 2

Answer:

See Explanation

Step-by-step explanation:

Given

\(\begin{array}{cc}{Class} & {Frequency} & A\ 39-44 & 1 & B\ 45-50 & 3 & C\ 51-56 & 8 & D\ 57-62 & 6 & E\ 63-68 & 8 & F\ 69-74 & 3 & G\ 75-80 &2 \ \end{array}\)

Solving (a): The histogram

To do this, we simply plot each data on each class on the x-axis and the frequency on the y-axis.

(See attachment for histogram)

Solving (b): The type of distribution

The histogram appears to have a bell shape. This means that the distribution is approximately normal.

Answer:

A. -5< x≤10

Step-by-step explanation:

7x>-35 and -5x ≥ -50

7x>-35

x>-5

-5x ≥ -50

x≤ 10

so, the result is:

-5< x ≤10

Hold down the Shift and press F3 . When you hold Shift and press F3, the text toggles from sentence case (first letter uppercase and the rest lowercase), to all uppercase (all capital letters), and then all lowercase.

Answer:

The most possible answer is B- an uppercase letter because a point is pointed towards the highest elevation and back to the lowest elevation making the highest elevation an uppercase and the lowest elevation an uppercase. For example, lowest elevation would be B whilst highest elevation is H. That would make it (A,H). Unless you were doing a negative point but nobody uses those these days.

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want to finish filling the given 2-way table.

Any single missing value in a row or column will be the value that makes the total correct for that row or column. Filling the single missing values will fill enough of a row or column with two or more missing values so that the remaining missing values can be filled the same way.

It is basically a series of subtraction problems.

For example, the upper left cell is filled with 20 -4 = 16, so the total on that row is 16+4=20.

Answer:11/4

Step-by-step explanation: First you put the points in m=x1-x2/y1-y2

m=15-4/3+1=15

Answer:

{xl x > 5)

Hope This Helps!

Answer: 69 and 420

Step-by-step explanation:

Option B: \(4+x+7x^6-3x^2\) represents a sixth-degree polynomial with a leading coefficient of seven and a constant term of four.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. A function that can be expressed as a polynomial is referred to as a polynomial function. A polynomial equation's definition can be used to derive the definition. A polynomial is typically denoted by P. (x). The degree of the variable in P(x) is its maximum power. The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large. Whole real numbers make up a polynomial function's domain (R).

Option B: \(4+x+7x^6-3x^2\) represents a sixth-degree polynomial with a leading coefficient of seven and a constant term of four.

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Brian will receive £\(1.75\) from Sue buying \(500\) grams of berries.

The metric measure for a tiny amount of mass and weight is the gram (g). It weighs the same as one milliliter (or one cubic centimeter) of water. 1,000 grams make to one kilogram (kg). One liter liquid water weighs exactly one kilogram (kg).

Using a scale is the most accurate technique to measure in grams. Kitchen spoons and cups, for example, offer an approximate approximation. Moreover, always have a conversion tool or chart on available so you can estimate grams without a scale.

Brian paid a total of £\(15.75\) for \(4\frac{1}{2}\) kg of strawberries. To find out the price per gram, we can divide the total cost by the total weight:

Price per gram \(=\)Total cost / Total weight

Total weight of strawberries \(= 4.5 kg = 4500 grams\)

Price per gram \(=\) £\(15.75 / 4500\) grams

Price per gram \(=\) £\(0.0035\) per gram

So, Brian paid £\(0.0035\) for every gram of strawberries he picked.

Cost of \(500\) grams \(=\) \(500 grams *\) £\(0.0035/gram\)

Cost of \(500\) grams \(=\) £\(1.75\)

Therefore, Sue should pay Brian £\(1.75\) for \(500\) grams of strawberries.

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Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

The solution to the variables are x = 7 and y = 4

From the question, we have the following parameters that can be used in our computation:

Shape = Triangle

The marks on the triangles imply that

So, we have the following representation

3x - 5 = 5y - 4

3x - 5 = y + 12

Substitute 3x - 5 = y + 12 in 3x - 5 = 5y - 4

y + 12 = 5y - 4

Evaluate the like terms

4y = 16

So, we have

y = 4

Substitute y = 4 in 3x - 5 = y + 12

3x - 5 = 4 + 12

So, we have

3x = 21

This gives

x = 7

Hence, the values are x = 7 and y = 4

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9514 1404 393

Answer:

  D

Step-by-step explanation:

The given line's equation is in slope-intercept form:

  y = mx + b

where m = -4 is the slope, and b = -1 is the y-intercept.

The slope of the perpendicular line will be ...

  -1/m = -1/(-4) = 1/4

You want the point-slope equation for the line, which is ...

  y -k = m(x -h) . . . . line with slope m through point (h, k)

Your equation will have m=1/4, (h, k) = (-2, 7), so it will be ...

  y -7 = 1/4(x +2)

Answer:

Explanation:

Given the equation:

Answer:

(f - g)(x) = -x - 6

(f + g)(x) = 3x - 4

(f*g)(4) = -9

Step-by-step explanation:

These are your equations:

f(x) = x - 5

g(x) = 2x + 1

To find (f - g)(x), subtract g(x) from f(x).

(f - g)(x) = x - 5 - (2x + 1)

(f - g)(x) = x - 5 - 2x - 1

(f - g)(x) = -x - 5 - 1

(f - g)(x) = -x - 6

To find (f + g)(x), add f(x) with g(x).

(f + g)(x) = x - 5 + 2x + 1

(f + g)(x) = 3x - 5 + 1

(f + g)(x) = 3x - 4

To find (f*g)(4), you need to first find (f*g)(4).  You can do this by multiplying f(x) wih g(x).

(f*g)(x) = (x - 5)(2x + 1)

(f*g)(x) = 2x² - 9x - 5

Now that you have (f*g)(x), solve with x as 4.

(f*g)(4) = 2(4)² - 9(4) - 5

(f*g)(4) = 2(16) - 9(4) - 5

(f*g)(4) = 32 - 36 - 5

(f*g)(4) = -9

The required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
f(x)=x-5
g(x) = 2x+1

According to the question,
[f + g ](x) = x - 5 + 2x + 1 = 3x - 4

[f + g ](x) =  3x - 4

[f - g ](x) =  x - 5 - 2x - 1
[f - g ](x) = -x - 6

(f.g)(x) = (x - 5)(2x + 1)
(f.g)(x) = 2x² -4x -5

(f.g)(4) = 2[4]² - 4[4] - 5
         = 32 - 16 - 5
         = 11
(f.g)(4) = 11

Thus, the required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.

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The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

If you have the coordinates of two points, you can use the distance formula to find the length of the line segment between them. The distance formula is:

\(d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

where:

And to find a perimeter add all the sides as the perimeter is the sum of all sides of the shape or object.

Perimeter: Sum of all sides

Area : Length * breadth or base*height for rectangle

Step-by-step explanation:

The equation is v-1 = -3

Here is the graph :

1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

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Answer:

this is way to hard

Step-by-step explanation:

Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

\(x_1 = -4, x_2 = 5, x_3 = 12\)

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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