1520−{64÷−4}−[37( √ 121+345)(43−|−583|)+405]−{1745÷5−64 }

Answer: x = √-6 - 4

Step-by-step explanation:

x^2+8x+22=0

(x+4)^2 - 16 + 22 = 0

(x+4)^2 + 6 = 0

(x+4)^2 = -6

√(x+4)^2 = √-6

x = √-6 - 4            

√6 = 2.449

Both Student A and Student B's representations of the expression 9/y³ⁿ are incorrect.

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a meaningful way. An expression can represent a value, a quantity, a function, or some other mathematical object. Expressions can be made up of one or more terms. A term is a group of numbers, symbols, and/or variables that are separated by a plus or minus sign. Expressions can also include mathematical operations, such as addition, subtraction, multiplication, and division, as well as exponents and parentheses. Expressions are used in various areas of mathematics, including algebra, calculus, and statistics, to represent mathematical relationships and to solve problems.

Here,

Student A represents the expression as the product of 9 and y times the product of 3 and t, which can be written as: 9 * y * 3 * t = 27yt.

This representation is incorrect because it does not include the exponent 3 in the denominator. The correct representation of the expression is: 9 / y^3t.

Student B represents the expression as the quotient of 9 and y times the sum of 3 and t, which can be written as: 9 / y * (3 + t) = (27 + 9t) / y.

This representation is also incorrect because it incorrectly combines the sum of 3 and t in the denominator. The correct representation of the expression is: 9 / y^3t.

To represent the expression correctly, we need to include the exponent 3 in the denominator, indicating that y is being raised to the power of 3, and include t as a separate factor in the denominator. Therefore, the correct representation of the expression is: 9 / (y^3 * t).

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Answer:

Student A says prodact of Tandy, but 9 is 9 y so it's quotient.

Step-by-step explanation:

The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = |x| - 2 and g(x) = 2 f(x)

The function g(x) is rewritten as,

g(x) = 2 (|x| - 2)

g(x) = 2|x| - 4

The function f(x) is an absolute function and the function g(x) will be twice the function f(x).

x           f(x) = |x| - 2               g(x) = 2f(x)

-2                0                               0

-1                -1                               -2

0                -2                              -4

 1                -1                               -2

2                0                                0

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{1, 3, 5, 7, 9, 11, ... , 47}

To Write The Following in Set-builder notation

\( \text{A} = \) {x : x ∈ N;x is an odd number, x ≤ 47}

The equation which represents the transformation of the y-intercept of the parent quartic function,\(f(x) = x^4\)   is given by     \(g(x)=(x-3)^4-1\) .

Transformation is the act or process of changing completely. In this also the graph changes or transform.

We have,

Parent Quadratic equation \(f(x)=x^4\)

And

It translated \(3\) units to the right and \(1\) unit down.

And the parent quadratic function is in the form of \(f(x) = a(x-h)^4 + k.\)

Here,

"h" tells if the vertex of the parabola is going left or right.

"k" determines if the vertex of the parabola is going up or down.

So, According to the question;

We have,

\((a)\)   \(3\)  units to the right

\((b)\)   \(1\) unit down

So,

Equation would be  \(g(x)=(x-3)^4-1\)  means that you have moved the vertex of the parabola  \(3\)  units to the right and  \(1\) units down.

(Always remember if moving right means \((x-3)\) sign would be minus because in parent quadratic function is in the form of \(f(x) = a(x-h)^4 + k\) we have minus sign.)

Hence, we can say that the equation which represents the transformation of the y-intercept of the parent quartic function,\(f(x) = x^4\)   is given by     \(g(x)=(x-3)^4-1\) .

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Answer:

(8,-6)

Step-by-step explanation:

Given

To find:

Which of the following is equivalent to the product?

Explanation:

It is given that,

That implies,

Hence, the answer is, 5√3.

The Probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

To find the probability that the randomly chosen coin is gold, given that it is small, we need to determine the number of small gold coins and the total number of small coins.

From the given information, Marco has 12 small gold coins and 3 small silver coins, making a total of 12 + 3 = 15 small coins.

The probability that the coin is gold, given that it is small, can be calculated as the ratio of the number of small gold coins to the total number of small coins:

P(Gold|Small) = Number of Small Gold Coins / Total Number of Small Coins

P(Gold|Small) = 12 / 15

Simplifying the fraction, we have:

P(Gold|Small) = 4 / 5

Therefore, the probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

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Answer:

The relation (13,14), (13,5). (16,7). (18,13) is not considered a function

Step-by-step explanation:

Relations are only considered functions if each x value, which is the first number in each ordered pair or set of parentheses, has only one corresponding y-value, which is the second number in each ordered pair. The third option has two y-values, 14 and 5, for one x-value, 13. This means that it does not satisfy the requirements to be a function and therefore it is not a function.

Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

The given histogram is uniform histogram.

Since we know that,

A histogram is a graphical depiction of data distribution in statistics. The histogram is represented by a series of neighboring rectangles, with each bar representing a different type of data.

Statistics is a branch of mathematics that is used in a variety of areas. When numbers are repeated in statistical data, this repetition is known as Frequency, and it may be put down in the form of a table, which is known as a frequency distribution.

A Frequency distribution may be represented graphically using several types of graphs, one of which is a Histogram.

Based on the frequency distribution of the data, the histogram may be categorised into distinct categories. Normal distribution, skewed distribution, bimodal distribution, multimodal distribution, comb distribution, edge peak distribution, dog food distribution, heart cut distribution, and so on are all examples of distributions. These many sorts of distributions can be represented by the histogram.

A histogram can be of several types:

Histogram that is uniform

Histogram with symmetry

Histogram with two modes

Probability distribution histogram

A uniform distribution demonstrates that the number of classes is too small, with the same amount of components in each class. It might involve a distribution with many peaks.

Since we can see in the given histogram,

The average frequency  is 5

And almost all the bars are ending at 5

Hence,

This histogram is uniform histogram.

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Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Hope this helps :)

......

The correct option D: the origin, has the symmetry of the volume of sphere for the graph of the function rule.

For the stated question.

The volume of the sphere is modeled by the power function with respect to the radius as;

V = f(r) = 4/3πr³

As, r is independent of any of the coordinate axis.

Thus, the function rule's graph, which describes the volume of the sphere, is symmetric with regard to the origin.

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Answer:

121

Step-by-step explanation:

firstly you arrange the numbers in ascending order the number in the middle is considered to be the median

Part A (Printer): $12.63

Part B (Computer): $180.83

A:

"take advantage of the cash discount" Since Janet is taking the cash discount we need to use the terms.

2/10 => Means if paid in 10 days apply a 2% discount

($880 - $100) = $780  (This is because of the trade discount stated also)

$780 * 0.98 = $764.40  

(Note: 0.98 is the term "2/10" it is the 2% discount, represented as (1-0.02) )

$764.40 * 0.07 * (20/360) = $2.9726666 (Note: Here 20/360, 20 represents the rest of the days left in the term agreement)

No Discounts: ($780 - 764.40) = $15.60

Discounts: $2.9726666

How much would Janet save?

$15.60 - $2.9726666 = $12.62733 = $12.63

===============================================

Question has a part B:

"On the computer, what is the difference in the final payment between choices 1 and 2?"

Note: Computer Price w/ Trade Discount => $4,000 - ($4,000*0.25) = $3000

(1) "$155 per month for 17 months" => $155 × 17 = $2,635

Last payment $3,000 – $2,635 = $365

(2)-------------- Note: 18 Months = 1.5 Years

$3,000 × 0.07× 1.5 = $315

$3,000 + $315 = ($3,315) / 18 Months = $184.1666

Difference in the final payment?

$365 - $184.1666 = $180.8334 = $180.83

A. Janet would save $12.63

B. Computer: $180.83

Since Janet is taking the cash discount we need to use the terms.

"take advantage of the cash discount"

2/10 => Means if paid in 10 days apply a 2% discount

($880 - $100) = $780  (This is because of the trade discount stated also)

$780 * 0.98 = $764.40  

[0.98 is the term "2/10" it is the 2% discount, represented as (1-0.02)]

$764.40 * 0.07 * (20/360) = $2.9726666 (Note: Here 20/360, 20 represents the rest of the days left in the term agreement)

No Discounts: ($780 - 764.40) = $15.60

Discounts: $2.9726666

Janet would save = $15.60 - $2.9726666 = $12.62733 = $12.63

Computer Price w/ Trade Discount => $4,000 - ($4,000*0.25) = $3000

(1) "$155 per month for 17 months" => $155 × 17 = $2,635

    Last payment $3,000 – $2,635 = $365

(2) 18 Months = 1.5 Years

    $3,000 × 0.07× 1.5 = $315

    $3,000 + $315 = ($3,315) / 18 Months = $184.1666

Difference in the final payment= $365 - $184.1666 = $180.8334 = $180.83

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So the parametric equation for the line through the point p(-2, 8, 5) and parallel to the vector v is:

x = -2 + t * vx

y = 8 + t * vy

z = 5 + t * vz

The vector equation for a line can be represented as:

p = p0 + t * d

where p0 is a point on the line, t is a scalar parameter, and d is the direction vector of the line. To find the vector equation for the line through the point p(-2, 8, 5) and parallel to the vector v, we need to find the direction vector d and the point p0.

Since the line is parallel to the vector v, the direction vector d will be equal to v. The point p0 can be found by using the point p(-2, 8, 5):

p0 = p - t * d

p0 = (-2, 8, 5) - 0 * (v) = (-2, 8, 5)

So the vector equation for the line through the point p(-2, 8, 5) and parallel to the vector v is:

p = (-2, 8, 5) + t * (v)

x = x0 + t * dx

y = y0 + t * dy

z = z0 + t * dz

where (x0, y0, z0) is a point on the line, and (dx, dy, dz) is the direction vector of the line.

x = -2 + t * vx

y = 8 + t * vy

z = 5 + t * vz

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The time it takes (1/x) + (1/(x + 5)) + (1/(4x + 20))

​

From the question,

Marla takes 5 hours more than Tom: M = T + 5

Bob takes 4 times as long as Marla: B = 4M

work is inversely proportional to the time hence

Tom: 1/T

Marla: 1/M

Bob: 1/B

When we express this,

Marla: 1/(T + 5)

Bob: 1/(4*(T + 5))

We would have to solve for the total work in a given hour

= (1/T) + (1/(T + 5)) + (1/(4*(T + 5))

In one hour, Tom cаn clеan 1/х оf thе building, Mаrlа cаn clеan 1/(x + 5) оf thе building, and Вob cаn clеan 1/(4х + 20) оf thе building.

then 1/T = 1/x

1/(T + 5) = 1/(x + 5)

1/(4*(T + 5)) = 1/(4x + 20)

The expression would be written as:

work in one hour = (1/x) + (1/(x + 5)) + (1/(4x + 20))

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Answer: It looks like you are trying to use the Law of Sines to find the value of x. The Law of Sines states that, in any triangle, the ratio of the sine of an angle to the length of the side opposite that angle is the same for all three angles and all three sides. In other words, if A, B, and C are the angles of a triangle and a, b, and c are the lengths of the sides opposite those angles, then:

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

To find the value of x, you need to plug in the values of the angles and the side lengths that you know, and then solve for x. Based on the information you provided, it looks like you know the values of A, B, and c. Therefore, you can use the Law of Sines to write the following equation:

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

You can then solve for x by cross-multiplying and rearranging the terms:

x = (b * sin A) / sin B

Plugging in the values you know, you get:

x = (b * sin 28°) / sin 83°

You can then use a calculator to find the value of x. When you do this, you will get a value of approximately 5.2. Rounded to the nearest tenth, the value of x is 5.2. The other options you gave are not equal to 5.2.

The value of x using sine rule is 8.5 (nearest tenth)

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Sine rule is used to find unknown side and unknown angle when the other side and corresponding angle is given.

The corresponding angle to 18 is 83°

The corresponding angle to x is 28°

Therefore;

x/sin28 = 18/sin83

18sin28 = xsin83

8.45 = 0.992x

divide both sides by 0.992

x = 8.45/0.992

x = 8.5 (nearest tenth)

Therefore the value of x to the nearest tenth is 8.5

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9514 1404 393

Answer:

  Pyramid B is 2.6888 times the volume of pyramid A

Step-by-step explanation:

The volume is proportional to the height, and to the square of the linear measure of the base.

Then the ratio of volumes will be ...

  B/A = (592²·247)/(492²·133) = 86564608/32194512 ≈ 2.6888

Pyramid B has the greater volume by a factor of about 2.6888.

_____

Additional comment

The actual volumes in cubic meters will be 1/48 of the numbers we used in the ratio above.

If you recall that the side length is related to the perimeter by ...

  P = 4s   ⇒   s = P/4

and the volume is ...

  V = 1/3s²h

Then you have ...

  V = 1/3(P/4)²h = 1/48·P²h . . . . . . P²h is the number we used above

Answer:

Step-by-step explanation:

Let |x-a|=b

then x-a=±b

so x-a=b

or x=a+b

so a+b=18   ...(1)

and x-a=-b

or x=a-b

or a-b=8   ...(2)

adding (1) and (2)

2a=26

a=26/2=13

subtract (2) from (1)

2b=10

b=10/2=5

|x-13|=5

In the given graph, the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

To find the equation of the quadratic function, we start by using the vertex form:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:

\(y = a(x - 4)^2 - 2\)

Next, we use the other two points to find two additional equations:

\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)

Simplifying these equations, we get:

\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)

So the equation of the quadratic function is:

\(y = (1/2)(x - 4)^2 - 2\)

Now, we can answer the questions:

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:

\(y = (1/2)(0 - 4)^2 - 2 = 6\)

So the y-intercept is (0,6).

To find the x-intercepts, we set y = 0 in the equation:

\(0 = (1/2)(x - 4)^2 - 2\)

Simplifying, we get:

\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)

So the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

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In the coordinate plane, the vertices of triangle PAT are P(-1,-6), A(-4,5), and T(5,-2) forms an isosceles triangle.

To prove that triangle PAT is an isosceles triangle, we need to show that at least two sides of the triangle are congruent.

Let's calculate the distances between the vertices:

Distance between P and A:

PA = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-4 - (-1))² + (5 - (-6))²]

= √[9 + 121]

= √130

Distance between P and T:

PT = √[(5 - (-1))² + (-2 - (-6))²]

= √[(5 + 1)² + (-2 + 6)²]

= √[36 + 16]

= √52

= 2√13

Distance between A and T:

AT = √[(5 - (-4))² + (-2 - 5)²]

= √[(5 + 4)² + (-2 - 5)²]

= √130

We can see that PA = AT = √130, and PT = 2√13.

Since PA = AT, we have shown that two sides of the triangle are congruent.

Therefore, triangle PAT is an isosceles triangle.

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Answer:

5km

Step-by-step explanation:

A - her office

E - her home

AB = 1km; BC = CE = 4km

AE - the shortest disctance between her office and home.

ADE - right triangle, where AD = 4km, ED = 3 (EC - CD) =>

According to the Pythagorean theorem , we make up the equation:

AE = √ED^2 + AD^2 = √25 = 5km

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

One way to estimate an answer is to round the numbers and then do the calculation