Determine a if x - 2 is a factor of f(x) = 4x^4 - 7x^3 + 3x^2 - ax + 18. ​

The simplified exponential notation of the given expression is [tex](2\sqrt{3}.a - 3\sqrt{3}b )^2[/tex].

The given expression is: [tex]12a^{2} -36ab + 27b^{2}[/tex]

An expression in the form of [tex]x^{a} .y^{b}. z^{r}[/tex] is called exponential expression.

We can write the above expression as:

[tex]12a^{2} -36ab + 27b^{2}[/tex]

We know that

[tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]

So,  [tex]12a^{2} -36ab + 27b^{2}[/tex] can be written in the form of [tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]

[tex]12a^{2} -36ab + 27b^{2} = (2\sqrt{3}a )^{2} - 2.2\sqrt{3} .3\sqrt{3} +({3\sqrt{3} } b) ^{2}[/tex]

[tex]12a^{2} -36ab + 27b^{2} = (2\sqrt{3}.a - 3\sqrt{3}b )^2[/tex]

Hence, the simplified exponential notation of the given expression is .

[tex](2\sqrt{3}.a - 3\sqrt{3}b )^2[/tex]

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Answer:

 [tex]x=-\frac{3}{2}\\[/tex]

Step-by-step explanation:

We must isolate x in this equation. To do that, we can multiply both sides by [tex]\frac{3}{2}[/tex].

[tex](\frac{3}{2})(\frac{2}{3})x=-1(\frac{3}{2})[/tex]

[tex]x=-\frac{3}{2}[/tex]

There were 10 different combinations to the multiple choice questions.

Combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

It is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

[tex]C_{n,r} = \frac{n!}{(n-r)! r!}[/tex]

where n = 5

r = 3

[tex]C_{5,3} = \frac{5!}{(5-3)!3!} \\= \frac{5!}{2!3!}[/tex]

= [tex]\frac{5(4)(3!)}{2!3!}[/tex]

= 20/2

= 10 ways

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Observing the geometry and the properties of sides and angles provided in the figure, We can conclude that option 2 is the correct answer. GJ is less than HJ.

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry. A field of mathematics known as geometry is described as "concerning the measurement, characteristics, and relationships of points, lines, angles, surfaces, and solids." Geometry is a branch of mathematics that deals with points, lines, forms, and surfaces, to put it another way.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

angle GFJ = 60

angle JFH = 62

We know larger angle corresponds to larger sides, So, The side opposite to 62 is larger than of 60.

So, GJ is smaller than HJ.

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so we know the area if 44 cm², and we also know the "L" is 3 more than twice "W", hmmm what's twice W anyway?  well, just 2W, and 3 more than that?  well 2W + 3, hmmm so

[tex]A=LW ~~ \begin{cases} L=length\\ W=width\\[-0.5em] \hrulefill\\ A=44 \end{cases}\implies 44=LW\hspace{5em}\stackrel{\textit{3 more than twice W}}{L=2W+3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{44=(\underset{L}{2W+3})W}\implies 44=2W^2+3W \\\\\\ 0=2W^2+3W-44 \implies 0=(2W+11)(W-4) \\\\[-0.35em] ~\dotfill\\\\ 0=2W+11\implies -11=2W\implies \cfrac{-11}{2}=W ~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ 0=W-4\implies 4=W ~~ \textit{\LARGE \checkmark}[/tex]

now, the negative value is a valid value for W, however for this case, the width cannot be a negative number, it must be positive, thus we do away with it, and since L = 2W+3, that means L = 2(4)+3 = 11.

Statistics prove that motorcyclists are B: 35 times as likely as a passenger car occupant to die in a motor vehicle accident.

Compared to the occupants of motor vehicles, motorcycles provide their riders with very little protection from injury. Motorcycles have virtually no ability to absorb the impact from another vehicle; there is the potential for serious injuries or even death for any rider as a result of a motorcycle crash or accident.

Unfortunately, according to statistics motorcycle deaths accounted for 14% of all motor vehicle crash deaths. A motorcyclist is about 35 times more likely to die in an accident compared to passengers in cars.

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Answer:

C

Step-by-step explanation:

C It makes the line become steeper. When the coefficient in front of x is increased, the slope of the line becomes larger, so the line becomes steeper. The other responses are not correct.

All the possible values of each expression is given as an inequality as;

0 < a - b < 4

We are given the inequalities of the domain and range as;

2 < a < 5

1 < b < 2

Thus, we can say that the maximum value of a - b will be the difference between the maximum value of a and the minimum value of b to give;

(a - b)max = 5 - 1

(a - b)max = 4

Similarly, minimum value of a - b will be the difference between the maximum value of b and the minimum value of a to give;

(a - b)min = 2 - 2

(a - b)min = 0

Thus, all possible values would be expressed as;

0 < a - b < 4

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Answer:

[tex]f(-2) = -20[/tex]

Step-by-step explanation:

Plug -2 into the function for x.

[tex]f(x) = 7x - 6[/tex]

For [tex]x=-2[/tex]:

[tex]f(-2) = 7(-2) - 6[/tex]

[tex]f(-2) = -14 - 6[/tex]

[tex]f(-2) = -20[/tex]

The distance scale between San Antonio and Houston on Vicki's map is 7.3 centimeters. The sane distance in millimeters in millimeters is

Distance measurement is a linear measurement and the unit can be inches, feet, yard, meters, kilometers and so on

In the problem the unit is in centimeters and conversion of centimeters to millimeters is done by the factor 10

Applying the factor of 10 to 7.3 centimeters will to convert it to millimeters and this shown below

= 7.3 * 10

= 73 millimeters

The distance in millimeters is solved to be 73 millimeters

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The side length of PQ = 5.6 unit and angle C = arc sin [sin A (0.70)]

The mathematical law that shows the relationship between the size of an angle and opposite side length of a triangle is called sine rule. It is an equation that express the ratio of the side length of a triangle to the sine of the opposite angle.

The laws can be shown as

a/ sin A = b /sin B = c /sin C

Given, triangle ABC ≈ triangle PQR

for the triangle PQR, PR = 8

angle Q = 63 degrees

angle R = 38.5 degrees

we need to determine the length PQ

as per the sine rule for triangle PQR

PQ/ sin R = PR / sin Q

PQ = PR × sin R / sin Q

PQ = (8 × sin 38.5) / sin 63

PQ = 5.59

PQ = 5.6 unit

As triangle ABC ≈ triangle PQR

AB/PQ = BC/PR = AC / QR

and sin A / sin Q = sin B/ sin P = sin C /sin R

sin C = (sin A / sin Q) × sin R

sin C = sin A (0.70)

C = arc sin [sin A (0.70]

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The coordinates of point R are (5.17, 7.33), which is answer choice C.

To find the coordinates of point R, we can use the formula for finding the coordinates of a point that divides a line segment into a given ratio:

R = [(1 - ratio) * A + ratio * B] / (1 + ratio)

In this case, the ratio is 1 : 5, which means that point R divides the line segment EF into a ratio of 1 : 5. The coordinates of points E and F are (4, 8) and (11, 4), respectively. Plugging these values into the formula, we get:

R = [(1 - (1/6)) * (4, 8) + (1/6) * (11, 4)] / (1 + (1/6))

= [(5/6) * (4, 8) + (1/6) * (11, 4)] / (6/6)

= [(20/6, 40/6) + (11/6, 4/6)] / (6/6)

= [(20/6 + 11/6, 40/6 + 4/6)] / (6/6)

= [(31/6, 44/6)] / (6/6)

= [(31/6)/(6/6), (44/6)/(6/6)]

= (31/6, 44/6)

= (5.17, 7.33)

Thus, the coordinates of point R are (5.17, 7.33), which is answer choice C.

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The coordinates of point r to be (5.17, 7.33) which is in option c.

To calculate the coordinates of point r, we must first determine the length of each section of the line segment. To do this, we can use the distance formula. The distance formula is given by d = √( (x2-x1)^2 + (y2-y1)^2 ). Using this formula, we can calculate the length of the line segment connecting points e and f to be 7 units.

We can then use the ratio of 1:5 to calculate the length of each segment. The length of the section starting at e is 1/6 of the total distance (7 units). The length of the section starting at f is 5/6 of the total distance (7 units).

To find the coordinates of point r, we can use the midpoint formula. The midpoint formula is given by (x, y) = ( (x1 + x2)/2, (y1 + y2)/2 ). Using this formula, we can calculate the coordinates of point r to be (5.17, 7.33). Therefore, the correct answer is c. (5.17, 7.33).

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Answer:

35/3

Step-by-step explanation:

To find the product of 3 1/3 and 3 1/2, we first need to convert both numbers to fractions with a common denominator.

3 1/3 is equal to 10/3, and 3 1/2 is equal to 7/2.

To find a common denominator, we can find the least common multiple of 3 and 2, which is 6.

Then, we can express both fractions as fractions with a denominator of 6:

10/3 becomes 20/6, and 7/2 becomes 21/6.

Now that both fractions have a common denominator, we can multiply them together:

(20/6) * (21/6) = 420/36

This fraction can be simplified to:

420/36 = 35/3

So, the product of 3 1/3 and 3 1/2 is 35/3.

[tex]3\dfrac{1}{3} \times3\dfrac{1}{2}[/tex]

In order to multiply mixed numbers, you need to convert them into improper fractions.

[tex]3\dfrac{1}{3} \rightarrow\dfrac{10}{3}[/tex]

[tex]3\dfrac{1}{2} \rightarrow\dfrac{7}{2}[/tex]

Multiply:

[tex]\dfrac{10}{3} \times\dfrac{7}{2}[/tex]

[tex]=\fbox{$\dfrac{35}{3} $}or\fbox{11$\dfrac{2}{3} $}[/tex]

Answer:

Step-by-step explanation:

To evaluate an integral by interpreting it in terms of area, one should first sketch the region indicated by the integrand and limits of integration. Once the region is visualized, the integral can be thought of as the total area under the curve of the integrand within the given limits. If the integrand is a sum, the integral is the sum of the areas under each individual curve, provided they exist.

To evaluating an integral by interpreting it in terms of area is a powerful technique that allows you to visualize the problem and understand the meaning of the integral. By sketching the region indicated by the integrand and limits of integration, you can gain a better understanding of what the integral represents. The integrand is the function whose area is being calculated, and the limits of integration are the boundaries of the region over which the integral is being taken. The integral can be thought of as the total area under the curve of the integrand within the given limits.

For example, consider the definite integral of a function f(x) between the limits of a and b. This integral represents the area between the curve of the function f(x) and the x-axis, between the values of x = a and x = b. By sketching this region, you can visualize the area being calculated and understand the meaning of the integral. It's also important to note that when the integrand is a sum, the integral is the sum of the areas under each individual curve, provided they exist. This allows you to break down a complex function into simpler parts and evaluate them separately.

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Answer:

Whatever has the answer of 80.

Step-by-step explanation:

In the United States, long-term capital gains and short-term capital gains are treated differently from income tax purposes. Long-term capital gains are gains from the sale of assets that have been held for more than one year, while short-term capital gains are gains from the sale of assets that have been held for one year or less.

The tax rate on long-term capital gains is generally lower than the tax rate on ordinary income, such as wages or salaries. For example, in 2021, the tax rate on long-term capital gains for individuals in the highest income tax bracket is 20%, while the tax rate on ordinary income for those same individuals is 37%. Lower-income individuals may also be eligible for 0% rate on long term capital gains.

Short-term capital gains, on the other hand, are taxed at the same rate as ordinary income. It's worth noting that these tax rates can also be changed by legislation, and can be different at state level as well, So it is best to consult a tax professional for the most up-to-date information on capital gains tax rates and the rules that apply to your specific situation.

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The minimum y-value after which the exponential function will always be greater than the linear function is y = 4.

How do functions work?

A law relating two dependent and independent variables is known as a function.

An illustration of a linear function is

y =mx+c

and represents the exponential function as follows:

y = aˣ

By looking at the graph, one may identify the lowest y-value after which the exponential function will always be bigger than the linear function.

When y = 4, they are equal, and from that point on, the linear function's value exceeds that of the exponential function.

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The surds equation x√40 = x√5 + √10 is resolved into (4√2) / 7  which a and b are 4 and 2 respectively.

A surd equation is a mathematical formula that comprises one or more surds, or irrational numbers, in the form of square, cube, or higher-order roots. Surds, such as √2, √3, 5, etc., are numbers that cannot be expressed as the ratio of two integers. The symbol "√" for them is frequently used.

Because surds are irrational numbers that cannot be stated as a ratio of integers, calculating a surd equation can be more challenging than solving a regular equation. The first step in solving a surd equation is to make the equation as simple as feasible by deleting any surds from any fractions' denominators or numerators. You will then separate the surd on one side of the equation from the numbers on the other side using algebraic manipulation. Once the square root has been eliminated, you can square both sides of the equation to get a polynomial equation that can be solved using conventional algebraic methods.

In the given problem;

x√40 = x√5 + √10

Collect like terms;

x√40 - x√5 = √10

x√(8 * 5) - x√5 = √10

x√(2 * 4 * 5) - x√5 = √10

2x√10 - x√5 = √10

x = (4√2) / 7

The value of a and b are 4 and 2

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The value of the base angles of triangle ABC formed by the given polygon is; 80°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, the number of sides of the given polygon when completed will be 18 sides. Thus, we can say that;

Central angle = 360/18

Central angle = 20°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠B = ∠C = [180 - 20]/2

∠B = ∠C = 80°

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a) The data modeling in this problem is an exponential function.

b) The function is defined as follows: y = 1.5(2)^x.

c) The rate of change from x = 2 to x = 4 is of 4.

The general format for an exponential function is presented as follows:

y = a(b)^x.

For which the parameters are given as follows:

From the data, when x increases by one, the output y is multiplied by two, hence the rate of change is given as follows:

b = 2.

Hence, when x increases by two, as is the case from x = 2 to x = 4, the rate of change is given as follows:

b² = 2² = 4.

When x = 1, y = 3, hence, applying the recursion of the rate of change, the parameter a is given as follows:

a = 3/2 = 1.5.

Meaning that the function is defined as follows:

y = 1.5(2)^x.

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The simplification of the expression −5.55− 8.55c+ 4.35c by combining the like terms is - 5.55 - 4.20c.

Like terms can be defined as terms which has the same variable and power.

For instance,

4a + 5a²

They are not like terms, though they have the same variable a but different power of 1 and 2 respectively.

So,

−5.55− 8.55c+ 4.35c

The like terms are - 8.55c and + 4.35c

−5.55− 8.55c+ 4.35c

= - 5.55 - 4.20c

Consequently, - 5.55 - 4.20c is the simplification of −5.55− 8.55c+ 4.35c.

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Answer:

yES, THIS IS CORRECT THE ANSWER IS 2

Step-by-step explanation:

Answer:

7.35 miles

Step-by-step explanation:

Example: [tex]\frac{66}{6} = 11[/tex]

Given 1 week = 7 days.

Given the athlete has ran 8.5 miles on Sunday, the remaining distance to run is:

[tex]52.6-8.5\\=44.1 miles[/tex]

Distance to run each day for the remaining 6 days is:

[tex]\frac{44.1}{6} \\=7.35 miles[/tex]

The value of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm.

A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:

Operands: Operands are the numbers that an operation uses. The terms that are given to the operands vary according to the kind of operation.

Operator: An operator is the symbol that denotes a math operation, such as: division, addition, subtraction, and multiplication.

Given length of wooden plank AB is 252 cm

divides it into four parts by inserting the points C, D and E

parts of plank are AC, CD, DE, EB

CD = 3AC,

DE = 2CD, and DE = 2(3AC) = 6AC

EB = 4AC

AB = AC + CD + DE + EB

substitute the values,

AB = AC + 3AC + 6AC + 4AC

252 = 14AC

AC = 252/14 = 18cm

CD = 3AC = 3(18) = 54 cm

DE = 6AC = 6(18) = 108 cm

EB = 4AC = 4(18) = 72 cm

Hence length of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm.

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The derivative of the function is

A) dw/dz=z^5 (7z-18)

B) dh/dx=192x^11+36x^5-6x^2+19

C) dy/dx=24x^2-38x-15

In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.

A) w = z^7 – 3z^6 + 14

dw/dz=7z^6-18z^5

dw/dz=z^5 (7z-18)

B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7

dh/dx=192x^11+36x^5-6x^2+19

C) y = (8x + 5)(x^2 – 3x)

dy/dx=  d/dx  [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]

dy/dx=(8*  d/dx  [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])

dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)

dy/dx=8(x^2-3x)+(2x-3)(8x+5)

dy/dx=24x^2-38x-15

Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).

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Answer:

X/3 < -9

(x/3) 3 < -9(3)

x < -27

Step-by-step explanation:

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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The shortest path from a vertex to the opposite side is an altitude, but the designer used a median. The foundation should be located at the orthocentre.

In order to obtain the shortest side, they actually want the shortest pathways from each side to the opposing vertex, as seen in the triangle below, which shows the medians drawn from each angle to the middle of the opposite side.

In its place, you would draw a straight line the shortest distance from the vertex to the opposite side, add a perpendicular, and then do the same thing here, draw a straight line out of a perpendicular, and then pulled down it, a perpendicular; this center, where they all come together, is referred to as the ortho center. In order to respond to the query, I will say that the point of concurrency would be the shortest route from the vertex to the opposite. Go precisely across to the side.

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