Find f(g(x)] and g[f(x)]. f(x) = (x+1, g(x) = 12x² - 5

The value of h for which b in the plane spanned by a1 and a2 is 11.

A vector b is in the plane spanned by two vectors a1 and a2 if it can be written as a linear combination of a1 and a2. This means that there exist scalars x and y such that:

b = xa1 + ya2

[5, 4, h] = x[1, 4, -1] + y[-6, -20, 2]

Solving for x and y, we have:

5 = x - 6y

4 = 4x - 20y

h = -x + 2y

Using the first two equations, we can solve for x and y:

x = 5 + 6y

20y + 4 = 4x = 4(5 + 6y)

20y + 4 = 20 + 24y

4y = -16

y = -16/4 = -4

Substituting this value of y back into the first equation:

x = 5 + 6y

= 5 + 6 * -4

= 5 - 24

= -19

Finally, substituting x and y into the third equation:

h = -x + 2y

= -(-19) + 2 * (-4)

= 19 - 8

= 11

So for h = 11, the vector b is in the plane spanned by a1 and a2.

--The question is incomplete, answering to the question below--

"Let a1 = [1 4 -1], a2 = [-6 -20 2], and b = [5 4 h]. For what value(s) of h is b in the plane spanned by a1 and a2?"

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Answer:

6cm^2

Step-by-step explanation:

right triangle equation:

bh/2

so

3*4=12/2=6

Answer:

12 Square Units

Step-by-step explanation:

the right triangle: 4 x 3 = 12 12/2 = 6

the left triangle: 4 x 3 = 12  12/2 = 6

Altogether: 6 + 6 = 12

Answer:

(x+6)(x-2)

Step-by-step explanation:

using the x method, the only two numbers that multiply to get -12 and add to get 4 are 6 and -2

Answer:

(x+6)(x-2) A P E X :)

The rate of change in the given graph is 21/4.

The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:

Rate of change = Δy / Δx

To calculate the rate of change of the given graph, we need to identify 2 points first. We take:

(0, 0)

(4, 21)

Rate of change = Δy / Δx

Rate of change = y₂ - y₁

                             x₂ - x₁

Rate of change = 21 - 0

                               4 - 0

Rate of change = 21/4

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Answer:

A

Step-by-step explanation:

The displacement of the cyclist is 40.3 km west. To find the displacement of the cyclist, we need to consider the net effect of the individual displacements in each direction.

The cyclist rides 8.4 km east, then 63 km west, and finally 14.3 km east. The displacement is the vector sum of these individual displacements.

The total displacement in the east direction is 8.4 km + 14.3 km = 22.7 km.

The total displacement in the west direction is 63 km.

To find the net displacement, we subtract the west displacement from the east displacement:

Net displacement = 22.7 km - 63 km = -40.3 km (west)

Therefore, the displacement of the cyclist is 40.3 km west.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The length of the credit card is either l = 8.5 or l = -5.5. Since length can't be negative, we know that: l = 8.5

First, we need to use the given information to set up an equation for the length and width of the credit card. We know that the width w is 3 centimeters shorter than the length l, so we can write:

w = l - 3

We also know that the area of the credit card is 46.75 square centimeters, which can be expressed as:

A = lw = 46.75

Now we can use these equations to solve for the length and width. Substituting the first equation into the second equation, we get:

(l - 3)l = 46.75

Expanding the left side, we get:

l^2 - 3l = 46.75

Rearranging and factoring, we get:

(l - 8.5)(l + 5.5) = 0

So the length of the credit card is either l = 8.5 or l = -5.5. Since length can't be negative, we know that:

l = 8.5

Using the first equation, we can then find the width:

w = l - 3 = 8.5 - 3 = 5.5

Now we can find the perimeter by adding up the four sides of the credit card:

P = 2l + 2w = 2(8.5) + 2(5.5) = 17 + 11 = 28

So the perimeter is 28 centimeters.

To solve this problem, we'll first use the given information to find the width (w) and length (l) of the credit card. Then, we'll calculate the perimeter using the formula: Perimeter = 2 * (length + width).

Given that the width (w) is 3 centimeters shorter than the length (l), we can express this as:

w = l - 3

We are also given the area of the credit card, which is 46.75 square centimeters. The area can be calculated as:

Area = length * width
46.75 = l * (l - 3)

Now, let's solve for l:

46.75 = l^2 - 3l
l^2 - 3l - 46.75 = 0

Solving this quadratic equation, we get:

l ≈ 7.25 cm

Now that we have the length, we can find the width:

w = l - 3
w = 7.25 - 3
w ≈ 4.25 cm

Finally, we can calculate the perimeter using the formula:

Perimeter = 2 * (length + width)
Perimeter = 2 * (7.25 + 4.25)
Perimeter ≈ 23 cm

So, the perimeter of the credit card is approximately 23 centimeters.

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Answer:

A. x=4

Step-by-step explanation:

The y-axis is a vertical line at x=0, so for a line to be parallel to x=0, x must equal another constant. Option A is the only option that has a constant.

The values of the sides are 47 and 17

It is important to note that opposite sides of a parallelogram are equal or congruent.

From the diagram shown, we can see that;

Line BC and Line AD are opposite.

Then.

BC = AD

substitute the values

37 -2x = 8x - 33

collect the like terms

37 + 33 = 8x + 2x

add the values

10x = 70

Make 'x' the subject

x = 7

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Answer:

For every gallon of gas added to the tank, the buyer is charged $2.35

The constant of proportionality of the given equation y = 2.35x will be 2.35.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Let's x ∝ y

Then x = ky where k will be constant of proportional.

k = x/y which means when two variables are divided which were in proportion it will create a constant proportional.

So,

y /x = 2.35 will be constant of propotional.

Hence "The constant of proportionality of the given equation y = 2.35x will be 2.35".

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Answer:

\( x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5} \)   or   \( x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5} \)

Step-by-step explanation:

\( 5x^2 - 2 = 4x \)

\( 5x^2 - 4x - 2 = 0 \)

\( x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

\( x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(5)(-2)}}{2(5)} \)

\( x = \dfrac{4 \pm \sqrt{16 + 40}}{10} \)

\( x = \dfrac{4 \pm 2\sqrt{14}}{10} \)

\( x = \dfrac{2 \pm \sqrt{14}}{5} \)

\( x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5} \)   or   \( x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5} \)

Answer:

Answer:

x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5}x=

5

2

+

5

14

or x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5}x=

5

2

−

5

14

Step-by-step explanation:

5x^2 - 2 = 4x5x

2

−2=4x

5x^2 - 4x - 2 = 05x

2

−4x−2=0

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=

2a

−b±

b

2

−4ac

x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(5)(-2)}}{2(5)}x=

2(5)

−(−4)±

(−4)

2

−4(5)(−2)

x = \dfrac{4 \pm \sqrt{16 + 40}}{10}x=

10

4±

16+40

x = \dfrac{4 \pm 2\sqrt{14}}{10}x=

10

4±2

14

x = \dfrac{2 \pm \sqrt{14}}{5}x=

5

2±

14

x = \dfrac{2}{5} + \dfrac{\sqrt{14}}{5}x=

5

2

+

5

14

or x = \dfrac{2}{5} - \dfrac{\sqrt{14}}{5}x=

5

2

−

5

14

To show that angles are equal to each other using properties of equality, you can apply the following properties: Reflexive Property, Symmetric Property, Transitive Property, Substitution Property.

1. Reflexive Property: An angle is equal to itself. For example, ∠ABC = ∠ABC.

2. Symmetric Property: If ∠ABC = ∠DEF, then ∠DEF = ∠ABC. The order of the angles can be switched without changing their equality.

3. Transitive Property: If ∠ABC = ∠DEF and ∠DEF = ∠XYZ, then ∠ABC = ∠XYZ. If two angles are equal to a common angle, then they are equal to each other.

4. Substitution Property: If ∠ABC = ∠DEF and ∠DEF = ∠XYZ, then ∠ABC = ∠XYZ. You can substitute equal angles into other equations or properties.

By using these properties, you can establish the equality of angles by showing the necessary relationships between them.

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Present value, also known as discounted value, refers to the current worth of a future sum of money or a stream of cash flows, after accounting for the time value of money

Given function is f(t) = 1500t - 100t²

The rate of flow of money is given as f(t) = 1500t - 100t² dollars per year.

Let's calculate the present value and accumulated amount of money flow at T = 10.

(a) Present value is given by PV = A / (1 + r)tn

Where, A = future value

f(10) = 1500(10) - 100(10)²

r = annual interest rate = 5% = 0.05

t = time period = 10 years

PV = A / (1 + r)tn = (15000 - 10000) / (1 + 0.05)¹⁰

= 2,227.87 (approx)

(b) Accumulated amount of money flow at T = 10 is given by

A = Pe^(rt)

Where,P = initial principal = PV = 2,227.87

r = annual interest rate = 5% = 0.05

t = time period = 10 years

A = Pe^(rt) = 2,227.87 * e^(0.05 * 10)

= 3,752.23 (approx).

Therefore, the present value is $2,227.87 and the accumulated amount of money flow at T=10 is $3,752.23 (rounded to the nearest cent as needed).

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Answer:

D

Step-by-step explanation:

x -91

Answer:

The answer is B. X /91

Step-by-step explanation:

All the other answers indicate the number is/will end up being bigger than 91

In most situations, it would be reasonable to use a level .01 test with a sample size of 40,000 as it provides a high level of statistical power to detect smaller effects and reduce the likelihood of Type I error.

In most situations, it would be reasonable to use a level .01 test in conjunction with a sample size of 40,000. This is because a larger sample size provides more statistical power, meaning the test is more likely to detect a significant difference if one exists.

Additionally, a level .01 test is more conservative than a level .05 test, which reduces the risk of a type I error (rejecting the null hypothesis when it is actually true).

However, it is important to consider the context and specific research question being addressed, as well as potential confounding variables, to determine the appropriate statistical test and significance level for a given study.

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An electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

The circuit underneath is composed of:

A battery as a supply of direct modern-day which materials electricity within side the circuit for modern-day to go with the drift. Direct modern-day affords uni-directional modern-day. Here it has cells. Here 4 cells are linked in collection for the battery.

Two bulbs A and B linked in parallel connection. Each bulb has been parallel connected with a voltmeter.

A voltmeter measures the voltage throughout the element that it's miles linked with. It is continually linked in parallel with the additives.

Main circuit has an ammeter in collection with the battery and connection of bulb.

An ammeter measures the modern-day flowing within side the circuit. It is continually linked in collection.

Therefore, an electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

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Answer:

x=5.45

Step-by-step explanation:

Answer:

answer

Step-by-step explanation:

Exact form: 60/11

Decimal form: 5.45

Mixed form: 5 5/11

Hope it answers your question

To find the number of teaspoons of raisins per bar in 1 batch, we need to first calculate the total number of teaspoons of raisins used in 1 batch, and then divide that by the total number of bars in 1 batch.

The recipe calls for 2 cups of raisins per batch of dough, and 1 cup is equal to 48 teaspoons. Therefore, 2 cups of raisins is equal to:

2 cups * 48 teaspoons/cup = 96 teaspoons

One batch of dough makes 5 dozen bars, or 5 x 12 = 60 bars.

So, the number of teaspoons of raisins per bar in 1 batch is:

96 teaspoons / 60 bars = 1.6 teaspoons/bar

Therefore, the correct calculation to use is:

96 teaspoons / 60 bars = 1.6 teaspoons/bar

We have shown that cos 2R = (s² - r²) / t² using the cosine identity for double angles and the Pythagorean theorem in a right triangle.

A right triangle is a triangle that has one angle measuring 90 degrees, which is referred to as a right angle. In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are known as the legs.

In summary, a right triangle is a triangle with a 90-degree angle, and it exhibits unique properties and relationships between its sides and angles, which can be determined using the Pythagorean theorem and trigonometric ratios.

To prove the equation cos 2R = (s² - r²) / t², where ΔRST is a right triangle with a right angle at T, we can use the cosine identity for double angles, which states:

cos 2θ = 2 cos² θ - 1

Let's apply this identity to our equation:

cos 2R = 2 cos² R - 1

Now, we need to express cos² R in terms of the side lengths of the triangle.

In a right triangle, we can use the Pythagorean theorem:

s² = r² + t²

Rearranging the equation, we have:

s² - r² = t²

Substituting this into our equation, we get:

cos 2R = 2 (s² - r²) / t² - 1

Simplifying further:

cos 2R = (2s² - 2r²) / t² - 1

Now, let's simplify the numerator:

2s² - 2r² = 2(s² - r²)

Substituting back into the equation:

cos 2R = 2(s² - r²) / t² - 1

Therefore, we have shown that cos 2R = (s² - r²) / t² using the cosine identity for double angles and the Pythagorean theorem in a right triangle.

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Graph the solution of the inequality 4.5k>18 is equal to  k > 4 ( see image), by using the inequality equation.

Based on the given conditions,

4.5k>18

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

a ≠ b says that a is not equal to b

a < b says that a is less than b

a > b says that a is greater than b

(those two are known as strict inequality)

a ≤ b means that a is less than or equal to b

a ≥ b means that a is greater than or equal to b.

To solve given graph,

We can write,

4.5k>18

4.5k - 18 > 0

4.5k > 18

k > 18/4.5

We can get the division,

k > 4   (We can see image)

Therefore,

4.5k>18 Graph the solution of the inequality is k > 4 ( see image ), by using inequality equation.

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To solve problems concerning number lines, you have to note the following;

- Greater than (>) is represented by a small circle (not shaded) with an arrow pointing to the right.

- less than (<) is represented by a small circle (not shaded) with an arrow pointing to the left.

- less than or equal to (=) is represented by a small circle ( shaded) with an arrow pointing to the left.

- greater than or equal to (>/=) is represented by a small circle ( shaded) with an arrow pointing to the right.

Using the above rule to solve the problem;

You need to first of all locate 0 on the number line.

Then since the sign between them is greater than (>), the according to the given rule, It will be represented by a small circle (not shaded) on 0 with an arrow pointing to the right.

So, we have;

Answer:

3/13 which is 0.23 as a decimal

Step-by-step explanation:

We simply replace values for x and get values for y, these pairs of values can be ordered as points and then plotted in the cartesian plane.

For example, when we replace x = 0 in the expression, we obtain y = -4, so one point is (0, -4).

When we replace x = 1, we obtain y = -6, so another point is (1, -6) and so on.

After we have enough points, we "draw" a line connection such points [The points should be determined in order] giving as result the graph of the expression:

The given function is f(x) = sin³²x, where a is a real number. lim f(x)=sin³²a.  lim f(x) as x approaches 20 is  sin³²(20). lim f(x) as x approaches Ka is sin³²(Ka). f(a) = sin³²a

(a) lim f(x):

To calculate the limit of f(x) as x approaches a certain value, we substitute the value into the function and evaluate it. In this case, the function is f(x) = sin³²x. Since the function does not depend on a specific value of x, the limit is simply sin³²a.

(b) lim f(x) as x approaches 20:

Similarly, we substitute the value x = 20 into the function and evaluate. The limit becomes sin³²(20).

(c) lim f(x) as x approaches Ka:

In this case, we have a variable Ka instead of a specific value. Since the function does not depend on the specific value of Ka, the limit is sin³²(Ka).

(d) f(a):

To evaluate f(a), we substitute the value a into the function. In this case, f(a) becomes sin³²a.

Please note that the calculations provided above assume the standard trigonometric function notation. The superscript "³²" represents the power of sin(x), and "a" represents a real number.

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