Factor the expression completely.
x^4-15x^2+54

Answer:

74,779,038,221

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

[tex]5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6[/tex]

We can eliminate all the zeroes.

[tex]5^3*7^5+9^8+9^7*5^6[/tex]

Evaluate each term.

Raise 5 to the power of 3.

[tex]125*7^5+9^8+9^7*5^6[/tex]

Raise 7 to the power of 5.

[tex]125*16807+9^8+9^7*5^6[/tex]

Raise 9 to the power of 8.

[tex]125*16807+43046721+9^7*5^6[/tex]

Raise 9 to the power of 7.

[tex]125*16807+43046721+4782969*5^6[/tex]

Raise 5 to the power of 6.

[tex]125*16807+43046721+4782969*15625[/tex]

Multiply 125 by 16807.

[tex]2100875+43046721+4782969*15625[/tex]

Multiply 4782969 by 15625.

[tex]2100875+43046721+74733890625[/tex]

Add 2100875 and 43046721.

[tex]45147596+74733890625[/tex]

Add 45147596 and 74733890625.

[tex]74779038221[/tex]

A calculator would help but here you go.

Answer:you just have to find the slope

Step-by-step explanation:

so all you have to do is start by doing y=Mx+b. You start by placing down you b point on the y axis and then Do your Mx it should look something like this

The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]

A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.

A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.

[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]

[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]

[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]

=1+x^2+y^2

[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]

[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]

[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]

[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]

[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]

[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]

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Answers:

1.  6x + 7 = 17

2.  5x - 4 = 11

3.  6(x - 2) = 24

4.  6x - 3 = 2x + 5

5.  (-3x) + 2 = 11

Step-by-step explanation:

Since your only translating the sentence and not actually solving, we don't need to determine a specific number.  So in that case, whenever the question says "a number," use a variable such as x.  

1.  Seven more would mean +7, so your adding 7 to x.  X is multiplied by 6, so your answer is 6x + 7 = 17.  

2.  X is being multiplied by 5, and 4 less means -4 so you get 5x - 4 = 11

3.  X-2 is being multiplied by 6, so indicate that in parenthesis.  You should then get 6(x - 2) = 24

4.  This one is a little different, since it doesn't equal a direct number.  X is being multiplied by 6, and 3 is getting subtracted from it so the first part is 6x - 3 and it equals X multiplied by 2 plus 5.  Put it all together and you get 6x - 3 = 2x + 5

5.  The word product means multiplication so you know that -3 is being multiplied with X.  Again, indicate this in parenthesis.  You should get (-3x) + 2 = 11

I hope this helps you!  Have a good day/night!  :)

Triangle ABD is a right-angled triangle. The value of s which is the hypotenuse of the triangle ABD is 17 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

Given information:

From the given figure, the following information can be extracted:

Triangle ABD is a right-angled triangle.

Base AB is 8 units, Height BD is 15 units.

s is the hypotenuse of the triangle ABD.

Use the Pythagoras theorem to solve for the value of s or AD,

AD²=AB²+BD²

s²=8²+15²

s²=289

s=17 units

Therefore, the value of s which is the hypotenuse of the triangle ABD is 17 units.

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Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].

Therefore,

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)

[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex]  units

B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex]  units

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex]  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]

[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

Answer:

-5 = |5|

Step-by-step explanation:

Absolute value is the number of distance from zero. Therefore, it doesn't matter if the number is positive or negative in absolute value it is always positive.

Answer:

77.472222 etc

Step-by-step explanation:

Answer:

Conclusion: Straight line upwards from point (0,3) to (3, 5.25)

Step-by-step explanation:

Your part (a) answer is absolutely correct.

Equation is y = 3/4x + 3

For part (b), you are correct to say that the y-intercept of the graph is 3. The implication is that the initial height of the tree is 3 feet tall. (When the tree just starts to grow at time = 0 years)

Your part (c) answer is absolutely correct as well.

For the graph part,

x = years (independent variable)

y = height (dependent variable)

From the equation you have constructed in part (a), the y-intercept of the graph is 3. Hence, a point (0, 3) can be first plotted in the graph.

Secondly, for part (c), you have also obtained the answer (3, 5.25). Plot that point on the graph as well.

Next, we can see that the graph in (a) is a linear graph in the form y = mx + c, where m is the gradient and c is the y-intercept.

Hence, you can easily draw a straight line upwards from (0,3) to (3,5.25) . It is expected as the gradient of the graph is 3/4, which is a positive number.

It can be written in standard form as [tex]5x^2-2+3[/tex] and the degree of polynomial is 2 with leading coefficient as 2.5.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). When attempting to solve systems of two linear equations, this form is also very helpful.

The values on which mathematical operations take place in an algebraic expression are known as terms in mathematics. Let's explain with the help of a term example. This algebraic expression has terms 8x and 9, respectively.

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There is no shape with exact 3 sides and 3 right angles.

The shape with three sides is a triangle. A triangle is a polygon with three edges and three vertices. It is a basic shape in geometry and can be classified into several types based on the length of its sides and the measure of its angles. Triangles can be classified as acute, right, or obtuse, depending on the measure of their angles.

A right triangle is a triangle with one right angle (90 degrees ). But there can not be a triangle with 2 or more right angle.

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The better deal would be 500 individual nerds candy for $5.

One of the four basic mathematical operations, along with addition, subtraction, and multiplication, is division. The equal partition of bigger groupings into smaller parts is referred to as division.

The order of work assigned to and completed by the team of employees in order to optimize efficiency is known as the division of labor.

The splitting down of a job into multiple separate parts that make up the total is referred to as the division of labor. 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.

Thus, The better deal would be 500 individual nerds' candy for $5 since you will have more candy and it will last longer.

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Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.

A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.

In Computer technology, there are various examples of a computer hardware and these include the following:

Based on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.

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Answer: c 1/6

Step-by-step explanation

Becouse it has six numbers so that means that 1 is a factor so taking in every other number the answer should be 1/6

The coefficient of y2 in 9xy2z is 9xy.

In mathematics, a coefficient is any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value. It is typically a number, however, in other expressions, a letter might be used instead. In the formula: ax2 + bx + c, for instance, x is the variable and a and b are the coefficients.

A coefficient is what?

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it. It is assumed that the variables with no associated number have a coefficient of 1.

coefficient of y 2  in 9x(y 2 )z is 9xy.

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The Least Common Multiple (LCM) of 2, 6, and 11 is 66.

We shall divide the numbers (6, 11) by their prime factors in order to determine the LCM of 6 and 11 using the division method (preferably common). The LCM of 6 and 11 is determined by the product of these divisors.

Step 1:Find the smallest prime number that at least one of the numbers, 6, or 11, can be factored into. As indicated by the ladder arrangement, place this prime number (2) to the left of the supplied numbers (6 and 11).

Step 2: Divide any of the supplied integers (6, 11) by 2 and write the quotient below it if it is a multiple of 2. Any number that is not divisible by the prime number should be brought down.

Step 3: Continue the procedure until there are only 1s left in the

The LCM of 6 and 11 is the product of all prime numbers on the left, i.e. LCM(6, 11) by division method = 2 × 3 × 11 = 66

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The missing angle of a triangle where only the measure of all sides are given can be calculated by using the Cosine Law .

What is Law Of Cosine ?

The law of cosine is also known as Cosine Rule. This law is useful in finding  the missing information of  any triangle.

For example, if you know the lengths of three sides of a triangle , this rule helps to find the angle between the two sides of the triangle.

Let a , b and c be the sides of the triangle and let A , B and C be the angle corresponding to the respective sides .

Then by the Cosine Law the angles are represented as : [tex]CosA = \frac{b^{2} +c^{2} -a^{2} }{2bc}[/tex] ;

[tex]CosB = \frac{c^{2} +a^{2} -b^{2} }{2ac}[/tex] ; [tex]CosC = \frac{a^{2} +b^{2} -c^{2} }{2ab}[/tex] .

Therefore , The Law Of Cosines is used to find the missing angle .

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The three examples of quadratic equations are x(x - 2) = 4, x(2x + 3) = 12 and 3x(x + 8) = -2

The term quadratic equation also known as quadratic expression referred as an equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.

Here the examples of quadratic equations in other forms is written as follows:

=> x(x - 2) = 4

Here we have to multiply and then moving the 4, then we get the quadratic expression as,

=> x² - 2x - 4 = 0

Another example like the following,

=> x(2x + 3) = 12

Here we have to multiplying and moving the 12, then we get the resulting expression as,

=> 2x² - 3x - 12 = 0

Final example for quadratic expression is written as

=> 3x(x + 8) = -2

When we multiplying and moving the -2, then we get the simplified form as

=> 3x² + 24x + 2 = 0

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Graphing exponential functions and logarithms involves understanding the key characteristics of these functions and how they are represented on a graph.

Asymptotes: The graph of an exponential function does not have any asymptotes.

Domain and range: The domain and range of an exponential function are all real numbers.

Increasing or decreasing: An exponential function is always increasing.

Shape: The graph of an exponential function is concave up.

y-intercept: The y-intercept is (0,1)

x-intercept: The x-intercept does not exist.

To graph an exponential function, you can start by plotting the y-intercept (0,1) on the graph. Then, you can use the information about the shape of the graph (concave up) and the increasing nature of the function to determine the general shape of the graph.

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To begin, our game organizer will introduce participants to the escape game instructions and backstory. Teams will have 60 minutes to complete their chosen quest

An escape room, also known as an escape game, puzzle room, exit game, or riddle room is a game in which a team of players discover clues, solve puzzles, and accomplish tasks in one or more rooms in order to accomplish a specific goal in a limited amount of time. The goal is often to escape from the site of the game.

Once you’re ready to start the game, your team will watch a mission video. This video explains the world your team is now a part of, what you’re trying to accomplish, and why you only have 60 minutes to do so!Some missions are about escaping the room, like in a prison break room. Other missions might not be centered around escaping, but instead, you might be completing a heist or launching a martian spaceship.Here’s an example of the type of mission video that plays at the beginning of a game. This one is from The Escape Game’s The Heist!

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Answer:21 teams

Step-by-step explanation:because if you cont the black dots and read the question that would be the answer

The amount invested by Dylan will be £1200.

Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate.

Given that Dylan invested some money in his bank. He agreed on a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period, the value of his investment increased by £72.

The amount of money invested will be calculated as,

SI = ( P x R x T ) / 100

72 = ( P x 3 x 2 ) / 100

7200 = 6P

P = 7200 / 6

P = £1200

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The probability that the bead taken from the bag is purple or red is total is 0.75 or 3/4.

The total number of beads in the bag is 12.

Out of these, 3 are purple and the rest are red (12-2-1-3 = 6). So, the probability of drawing a purple bead is 3/12 and the probability of drawing a red bead is 6/12.

To find the probability of drawing either a purple or red bead, we add the individual probabilities together: (3/12) + (6/12) = 0.25 + 0.5 = 0.75. This means that there is a 75% chance that the bead taken from the bag will be purple or red.

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The complete question is -

Write down the letter of the event that is likely. bag contains 12 beads_ 2 of the beads are blue: of the beads are green: 3 of the beads are purple: The rest of the beads are red: Julia takes a bead from the bag at random c) Show the probability that this bead is purple Or red is Totulmen.

The shaded region has a surface area of 7π.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

find the area of the circle with radius =3 cm,

then subtract the areas of the two circles with radius 1 cm

pir^2 = the area of a circle with radius = r

=pi(3)^2 -pi(1)^2 - pi(1)^2

= 9pi -pi-pi

= 9π-2π

= 7π

The area of shaded region is 7π.

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We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!

We can come up with two expressions:

Shaded Area:

[tex](5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2[/tex]

Blank area:

[tex](x)(x+7)\\x^2+7x[/tex]

Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.

[tex](15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2[/tex]

Therefore, your final answer should be:

14x^2 - 6x - 2

Hello there!

Answer:

y = ± 13

Step-by-step explanation:

[tex]y {}^{2} - 58 = 25 \times 4 + 11 \\ y {}^{2} - 58 = 100 + 11 \\ y {}^{2} - 58 = 111 \\ y {}^{2} - 58 - 111 = 111 - 111 \\ y {}^{2} - 169 = 0 \\ (y + 13)(y - 13) = 0 \\ y = - 13 \: \: \: and \: \: \: y = 13[/tex]

The average time is 7.5.  The average is calculated by dividing the total number of values in a given set by the sum of all the values in that set.

An average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. Average The arithmetic mean is calculated by adding a set of numbers, dividing by their count, and then taking the result.

If every number in a list is the same number, then that number also serves as the average for the list. Every one of the diverse varieties of average shares this characteristic.

An average of the values in a sample of data can be used to define a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.

Average = Sum /  Count

Sum = 7.48 + 7.45 + 7.90 + 7.37 + 7.25 + 7.40 + 7.55 + 7.60

= 60 / 8

= 7.5

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Answer:

The inverse property definition states when added together with its additive inverse, the sum of the two numbers will be zero. When a number is multiplied by its multiplicative inverse, the product will be one

Step-by-step explanation:

Answer:

[tex]80^{\circ}[/tex]

Step-by-step explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

Aisha has 2 chocolates left. You can represent the problem as an equation as follows:

Where x is the total number of chocolates, b is the number of boxes filled and 2 is the remaining chocolates left.

Since we know that Aisha has 50 chocolates, we can substitute this value for x in the equation:

50 = 3b + 2

Solving for b, we find that b = 16. So, Aisha filled 16 boxes and had 2 chocolates left over. The equation is true, and Aisha has 2 chocolates left.

It's worth noting that this is a simple algebraic equation, we can use the same equation to find the number of chocolates given the number of boxes and remaining chocolates, or to find the number of boxes given the number of chocolates and remaining chocolates or to find the remaining chocolates given the number of boxes and the number of chocolates.

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