f(x)=x+3
g(x) = 2x² - 4
Find (f. g)(x).

The common difference based on the sequence given is 15.

It should be noted that the sequence given Isa arithmetic sequence.

The common difference will be the second term minus the first term. This will be:

= 101 - 86

= 15

In conclusion, the difference is 15.

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The story that the fraction given represents is that A. A whiteboard is 2/5 Meyer long and has na area of 1/3 square meter. How wide is the whiteboard?

From the information given, it should be noted that the fraction given is 1/2 ÷ 2/5.

Therefore, this is represented by the story that a whiteboard is 2/5 Meyer long and has na area of 1/3 square meter. How wide is the whiteboard?

In conclusion, the correct option is A.

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The story problem that this division problem represent 1/2 ÷ 2/5 is a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the white board and is denoted as option A.

This is a description which represents a part of a whole.

The area of a rectangular shape of length L and width W is:

A = L×W

W=A/L

Only option A uses 1/2 as the area of the whiteboard and 2/5 is the other side of the board.

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The equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

Simple harmonic motion can be defined as a periodic motion of a point in a straight line, such that its acceleration is towards a fixed point and is proportional to its distance from that point to the line.

It is derived from the projection to the axis of a circle of a point in constant speed on the circumference

Displacement is represented thus;

d ( t ) = A sin⁡ ( 2 π f t )

T = 1/f

Where,

Note that there is no phase shift

d (t) = 7 sin ( 2π × 1/ 6 t)

d (t) = 7 sin ( 2π/6 t)

d (t) = 7 sin ( 3π t)

Thus, the equation modeling the displacement 'd' as a function of time  is d (t) = 7 sin ( 3π t)

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The coordinates of the edges of the mini-solar cooker are (x₁, y₁) = (0, - 60) and (x₂, y₂) = (0, 60).

The distance between the two edges is 120 centimeters.

The equation for the parabolic mirror is x + 32 = (2/225) · y².

Herein we must understand the geometry of the design of the mini-solar cooker to determine all needed information. The y-coordinates of the edges of the cooker are determined by Pythagorean theorem:

[tex]y = \pm \sqrt{(68\,cm)^{2}-(32\,cm)^{2}}[/tex]

y = ± 60

The coordinates of the edges of the mini-solar cooker are (x₁, y₁) = (0, - 60) and (x₂, y₂) = (0, 60). The distance between the two edges is 120 centimeters.

Lastly, the equation of the parabolic mirror can be determined based on the equation of the parabola in vertex form:

x - h = C · (y - k)²     (1)

Where:

h, k - Coordinates of the vertex

C - Vertex constant

If we know that (h, k) = (- 32, 0) and (x, y) = (0, 60), then the vertex constant of the equation of the parabola is:

0 + 32 = C · 60²

C = 2/225

Then, the equation for the parabolic mirror is x + 32 = (2/225) · y².

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The curve will be dotted and upper portion of the graph will be shaded.

Inequality are expressions not separated by an equal sign Given the following inequality

y−x>−x2−1

Equate to zero

y > x^2 + x -1

Since the inequality sign in the given expression is a less than sign, hence the curve will be dotted.

Also, since the inequality sign is a "greater than", hence upper portion of the graph will be shaded.

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The constant of proportionality of our given tables is; 5.

We are given that x and y are proportional, and this means that:

y = r*x

where;

r is the constant of proportionality.

We are given the table;

x    y

7    35

12   60

20   100

Now, we can replace those values in our equation and get, for the first pair: 35 = r*7

r = 35/7 = 5

For the second pair:

60 = r*12

60/12 = r

r = 5

Thus, we can conclude that the constant of proportionality is 5.

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Answer: 3

Step-by-step explanation:

Hope that helps...........................

Answer:

  True

Step-by-step explanation:

Lines in three dimensions can be one of ...

Lines are coplanar when a plane can be defined that includes the entirety of both of them. In the attached image, lines m₁ and n intersect and both lie in the gray plane. They are coplanar.

Lines m and m₁ are parallel, and both are contained in the turquoise plane. They are coplanar. A plane can always be drawn that will contain a pair of parallel lines. That is, any two parallel lines must be coplanar.

The lines m and n in the figure are skew, non-intersecting and non-parallel. They cannot be contained in a single plane.

__

Additional comment

Three or more parallel lines may not be coplanar. They will only definitely be coplanar when considered in pairs.

Answer:

connect the dots (0, -5) and (5, -10).

Answer:

[tex]-\frac{4}{3}[/tex](Your answer choices were really confusing, so I just put the plain answer)

Step-by-step explanation:

To find the slope of a line with just two points, we can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. In this case, [tex]\frac{5-(-3)}{2-8}[/tex]. This is [tex]\frac{8}{-6}[/tex]. This reduces to [tex]-\frac{4}{3}[/tex]

The number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways

From the given information, we should use the formula for permutation without repetition.

The formula is given as;

Permutation = [tex]\frac{n!}{n -r !}[/tex]

Where n = number of set = 9

r = 4, this is so because, the sides of a square a four

Permutation = [tex]\frac{9!}{9 - 4!}[/tex]

Permutation = [tex]\frac{9!}{5!}[/tex]

Permutation = [tex]\frac{362, 880}{120}[/tex]

Permutation = 3, 024 ways

Thus, the number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways

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The measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two lines that are parallel to each other or p ll q

The angle made by transversal t is 136 degrees

The measure of the other angle = 180 - 136 = 44 degrees

Draw a line parallel to p and q and passes through the intersection point of line t and v

The angle made by the transversal and the line drawn is the same as 44 degrees.

The measure of the other angle = 121 - 44 = 77 degrees

Thus, the measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

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The distance between the coordinate point (3, 2) and line y = ¹/₄x - 9 is; 10.25 units

We want to find the distance between the coordinate point (3, 2) and line y = ¹/₄x - 9.

Thus, we will plug in 3 for x in the line equation given to get;

y = ¹/₄(3) - 9

y = 0.75 - 9

y = -8.25

Thus, we can say that point on the line is (3, -8.25)

The difference in y-values would give us the required distance;

Required distance = -8.25 - 2

Required distance = -10.25

However distance cannot be negative and so we will take the absolute value as 10.25 units.

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Answer:

19.50

Step-by-step explanation:

32m = 624

m = 19.50

need more words

Answer:

Step-by-step explanation:

Therefore, the values of

a

1

and r are 2 and -1, respectively.

The values of a₁ and r of the geometric series are 2 and -1 respectively.

Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.

We have the series 2, -2, 2, -2, ......

Here, The first term is 2.

and, the Common Ratio = -2 / 2

                                        = 2/(-2)

                                         = -1

So, the first term is 2 and r is -1.

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Answer:

D. 4

Step-by-step explanation:

[tex]\sqrt{2-\left( 4\right)^{2} } =\sqrt{2-16} =\sqrt{-12}[/tex]

since ,√(-12) is not a real number

Then

The function f is not defined for x = 4

Answer:

D. 4

Step-by-step explanation:

thank you for your help 4 was the correct answer took the test and got it right

The change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

It is important to note that the maximum height is the peak altitude the balloon reached

To find the difference, we use the formula

Change = Maximum height - recovery height

Maximum height = 5000 meters

Recovery height = 3700 meters

Substitute the values

Change = 5000 - 3700

Change = 1300 meters

Thus, the change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

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The mean distance increased by a factor of 2^(²/₃)

The given equation for the relationship between a planet's orbital period, T and the planet's mean distance from the sun, A is;

T² = A³.

Let the orbital period of planet X = T(X).

Let the orbital period of planet Y = T(Y).

Let the mean distance of planet X from the sun = A(X).

Let the mean distance of planet Y = A(Y).

Thus;

A(Y) = 2A(X)

Therefore;

[T(Y)]² = [A(Y)]³ = [2A(X)]^3

However, [T(X)]² = [A(X)]³

Thus;

[T(Y)]² = 2³[T(X)]² * [T(Y)]²/[T(X)]² = 2³T(Y)/T(X) = 2^(³/₂)

That's for orbital period but the mean distance will increase by 2^(²/₃)

Thus we conclude that, the mean distance increased by a factor of 2^(²/₃)

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Answer:

2 Superscript three-halves

Step-by-step explanation:

Edge

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{-\dfrac{3}{12}}[/tex]

[tex]\huge\textbf{Simplify:}[/tex]

[tex]\mathsf{-\dfrac{3}{12}}[/tex]

[tex]\mathsf{= \dfrac{-3\div 3}{-12\div3}}[/tex]

[tex]\mathsf{= -\dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{- \dfrac{1}{4}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Levada borrows $30,900 from her bank to open a florist shop at rate of 0.98% per month.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

It is given that Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%.

P = $30,900

T = 18 months

Interest  = 5.5%

Interest rate =  P×R×T

5.5 = 30,900 × R × 18

R = 0.000988

Or, R = 0.98% per month.

The complete question is

"a) How much must she pay the bank in 18 months?"

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The negative solution is -2.21 and positive solution is 12.21

Given the quadratic equation expressed as:

x^2-10x-27 = 0

Find the solution using the general formula

x^2-10x-27 = 0

x = 10±√(10)²-4(1)(-27)/2

x =  10±√100+108/2

x =  10±√208/2

x = 10±14.422/2

Simplify

x = 10+14.422/2 and x = 10-14.422/2

x = 24.422/2 and -4.422/2

x = 12.21 and -2.21

Hence the negative solution is -2.21 and positive solution is 12.21

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The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

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Hence, the missing internal angle is [tex]15[/tex].

What is the angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays.

Angles are also formed by the intersection of two planes. These are called dihedral angles.

Here given that,

[tex]Q = 87 + 40Q = 127X + 127 + 38 = 180X = 180 - 127 - 38X = 15[/tex]

Hence, the missing internal angle is [tex]15[/tex].

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Mrs Kingsley cut the ribbon into a length of 12.75 inches each.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Length of each ribbon = 102 / 8 = 12.75 inches

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It is to be noted that the determination of whether or not there is a significant difference between the two groups will be done using a t test.

A t-test is a statistical test that juxtaposes two samples' means. It is used in hypothesis testing, using a null hypothesis that the variance in group means is zero and an alternative hypothesis that the difference is not zero.

The conditions to use the t test are:

The degrees of freedom (k) to be utilized for this text will be derived using the conservative method given below:

df = [(s₁²/n₁) + (s₂²/n²)/[((s₁²/n₁)²/((n₁-1)) + (s₂²/n₂)²/((n₂-1))]

= [(3.0952/15) + (6.4095/15)]² / [((3.0952/15)²/14) + ((6.4095/15)²/14)]

= 24.965

Hence,

df ≈ 24 (if approximated to the floor)

Recall the the standard deviation of the population are unequal and unknown. This thus requires that we utilize the two-sample unpooled t-test.

Here, H₀ is given as;

[tex]t = \frac{\bar{x_{1} -\bar{x_{2}}}}{\sqrt{\frac{s_{1}^{2} }{n_{1} } + \frac{S_{2}^{2} }{n_{2}} } } \sim t_{df}[/tex]

t = [(3.33333 - 4.13333)]/√[(3.0952/15) + (6.4095/15)]

= - 0.8/√0.6337

t = - 1.005

The 95% confidence interval is computed using the following formula:

[tex](\bar x_{2} - \bar x_{1}) \pm t_\alpha_/_2_,_df \left({\sqrt{\frac{S_{1}^{2} }{n_{1} } + \frac{S_{2}^{2} }{n_{2}} } } \right)[/tex]

= - 0.8 ± t₀.₀₂₅,₂₄ (√0.6337)

= - 0.8 ± 2.064 (√0.6337)

= -2.4429, 0.8429

To derive the 90% interval, we state:

[tex](\bar x_{2} - \bar x_{1}) \pm t_\alpha_/_2_,_df \left({\sqrt{\frac{S_{1}^{2} }{n_{1} } + \frac{S_{2}^{2} }{n_{2}} } } \right)[/tex]

= - 0.8 ± t₀.₀₅₀,₂₄ (√0.6337)

= - 0.8 ± 0.685 (√0.6337)

= -2.162, 0.562

From the intervals computed, we must fail to reject H₀

H₀ : μ₁ = μ₂

It is clear from the above intervals computed from that the differences between the mean of both groups is significant. This is because, zero is included on the two intervals.

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The value of the limit of the function given when the value of x tends to zero is 0

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular inputs.

Given the function limit below;

lim x→0 [1 − cos(2x) /x]

Substitute the value of x into the expression to have;

f(0) = 1-cos2(0)/0
f(0) = 1-1/0

f(0) = 0/0 (ind)

Apply the L'hospital rule to have:

lim x→0 [ − (-2sin2x)) /1]

Substitute the value of x into the result

f(0) = 2sin2(0)/1

f(0) = 2(0)

f(0) = 0

Hence the value of the limit of the function given when the value of x tends to zero is 0

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The maximum amount of water that can be used by each house on a daily basis is 100 liters.

4,500 = 500 + 40x

4,500 - 500 = 40x

4,000 = 40x

x = 4,000 / 40

x = 100 liters

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Answer:

y = 3x + 1

Step-by-step explanation:

The formula for equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

Now, since we have coordinates, we will get the equation as;

(y - y1)/(x - x1) = m

(y - 1)/(x - 0) = 3

y - 1 = 3x

y = 3x + 1