Which graph best represents the solution to the following system?

5x - 2y < (less than or equal to) 10
x + y < 5

Answer: D. w = 4xz - 2z/y - 2.

Step-by-step explanation: 2x - 1/y = w + 2/2z                                                             2z (2x - 1) = y (w+2)                                                                                     4xz - 2z/y = w +2                                                                                w = 4xz - 2z/y - 2

Answer:

There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

Step-by-step explanation:

Sample response :)

Answer:

y=0.5x+3 is the right answer

Answer:

(C)

Step-by-step explanation:

It is given that JK is perpendicular to LM, since JK and LM both are lines which lie in the same plane, therefore JK and LM are coplanar.

Since JK is perpendicular to LM, then JK and LM will  intersect.

Thus, option A is not correct.

And, as JK is perpendicular to LM, then they will meet each other at a right angle as perpendicular lines make a right angle with each other.

Thus, Option C is correct.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression for the expression

3(2x + 1) + 2(x + 4) is 8x + 7.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example:

2 + 3x + 4y = 7 is an expression.

3X + 4X + 4 is an expression.

We have,

3 (2x + 1) + 2 (x + 4)

Remove the parenthesis.

3 x (2x) + 3 + 2x + 4

6x + 3 + 2x + 4

8x + 7

Thus,

The final expression for the expression

3(2x + 1) + 2(x + 4) is 8x + 7.

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The logarithmic equation log2(8) = 3 convert to exponential form as 2^3 = 8.

Converting the logarithmic equation log2(8) = 3 to exponential form involves recognizing the base and the exponent.Logarithms state that if logb(A) = C, then the equivalent exponential form would be bC = A. In this case, since 2 is the base and 3 is the exponent to which 2 must be raised to get 8, we can write 2^3 = 8.

To further clarify, logarithms are simply a way to represent exponents, and they are widely utilized in mathematics to simplify the multiplication and division of exponents. A logarithm with a base of 10 is known as the common logarithm and is often written without a base as log(A). In contrast, when another base is used, it is indicated as logb(A). The relationship between logarithms and exponents is leveraged in various scientific and engineering fields to represent and calculate large numbers conveniently.

Answer: 270

Step-by-step explanation:

Given: [tex]f(x)=7+4x[/tex] and [tex]g(x)=\dfrac{1}{2x}[/tex]

Then, the rational function (f/g) is given by :-

[tex](f/g)(x)=\dfrac{f(x)}{g(x)}\\\\\Rightarrow\ (f/g)(x)=\dfrac{7+4x}{\dfrac{1}{2x}}\\\\={2x(7+4x)} [/tex]

Now, the value of (f/g) is given by :-

[tex](f/g)(5)=2(5)(7+4(5))=270 [/tex]

Hence, the value of (f/g) (5) = 270.

The expression 3(5 + 6) is equal to: 15 + 18

The correct answer is option D.

The expression you have is "3(5 + 6)."

To find the equivalent expression, you need to simplify it step by step.

First, apply the distributive property by multiplying 3 by each term inside the parentheses:

3 * 5 + 3 * 6

Now, perform the multiplications:

15 + 18

So, the expression "3(5 + 6)" simplifies to "15 + 18."

Now, let's compare this result to the given options:

A. 5 + 18

This option is equal to 23, which is not the same as 3(5 + 6).

B. 15 + 6

This option is equal to 21, which is not the same as 3(5 + 6).

C. 3 + 11

This option is equal to 14, which is not the same as 3(5 + 6).

D. 15 + 18

This option is equal to 33, which is the same as 3(5 + 6).

So, the expression "3(5 + 6)" is equal to option D, which is "15 + 18."

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The evaluation of[tex]\( \oint_C \mathbf{F} \cdot d\mathbf{r} \)[/tex]  using Stokes' Theorem is [tex]\( \pi e - \pi \).[/tex]

To evaluate[tex]\( \oint_C \mathbf{F} \cdot d\mathbf{r} \)[/tex]  using Stokes' Theorem, we first need to find the curl of the vector field [tex]\( \mathbf{F}(x, y, z) = yz\mathbf{i} + 9xz\mathbf{j} + e^xy\mathbf{k} \)[/tex] . The curl is given by[tex]\( \nabla \times \mathbf{F} \)[/tex] , which, for this vector field, is [tex]\( (e^x - 9z)\mathbf{k} \).[/tex]

Now, we compute the surface integral over the surface ( S) bounded by the circle  C . The given circle is[tex]\( x^2 + y^2 = 1 \)[/tex] with ( z = 3 ). The surface is the disk in the plane (z = 3) with radius ( r = 1 ). The surface integral is then [tex]\( \iint_S \nabla \times \mathbf{F} \cdot d\mathbf{S} = \iint_S (e^x - 9z) \, dS \)[/tex] , where  dS is the area element. The projection of  S  onto the xy-plane is the circle  C , so [tex]( dS = dA = \pi \).[/tex]

The final step is to evaluate[tex]\( \iint_S (e^x - 9z) \, dS \)[/tex] over the disk. Since  z = 3 over the entire surface, the integral simplifies to [tex]\( \iint_S (e^x - 9 \cdot 3) \, dS = \pi e - \pi \).[/tex]  Therefore, the final answer is[tex]\( \pi e - \pi \)[/tex] after applying Stokes' Theorem to evaluate the circulation of [tex]\( \mathbf{F} \)[/tex] around the circle C .

The mathematical statement 4⊂A means 4 is a subset of A, option A is correct.

In set theory, the symbol "⊂" represents the subset relationship.

So, when we write "4⊂A," it means that the element 4 is a member of the set A and is included as part of the set.

It does not imply that 4 is an intersection or an element of the set, but rather that 4 is a subset of A.

Therefore, option A is the correct interpretation.

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On dividing 646.1 by 34, we get 19.

Dividing 646.1 by 34:

Set up the division: 646.1 ÷ 34.

Perform the division to get the result: 646.1 ÷ 34 = 19.

The greatest common factor of the monomials 25x^5 and 20x^6 is 5x^5.

To find the greatest common factor (GCF) of the monomials 25x^5 and 20x^6, we first break down each monomial into its prime factors and include the variables.

25x^5 = 5 × 5 × x × x × x × x × x

20x^6 = 2 × 2 × 5 × x × x × x × x × x × x

Next, we find the common factors between the two:

The common prime number is 5.

The common variable factor is x raised to the minimum power between the two terms, which is x^5 (since x^5 is the lower power compared to x^6).

Therefore, the greatest common factor is 5x^5.

"The correct answer is [tex]\(52/7\)[/tex] written as a mixed number is [tex]\(7\frac{3}{7}\).[/tex]

To convert an improper fraction to a mixed number, one must divide the numerator by the denominator and express the result as a whole number plus a proper fraction.

For the fraction [tex]\(52/7\)[/tex] we divide 52 by 7:

[tex]\(52 \div 7 = 7\)[/tex] with a remainder of 3.

 This means that is equal to 7 whole units and [tex]\(3/7\)[/tex] of another unit. Therefore, as a mixed number,[tex]\(52/7\)[/tex] is written as [tex]\(7\frac{3}{7}\)."[/tex]

The equivalent ratios to 4/28 are obtained by dividing both the numerator and the denominator by 4 to get 1/7, and then by multiplying the resulting ratio to get the other two equivalent ratios, 2/14 and 3/21, which correspond to answer choice b.

The question is asking to write three ratios that are equivalent to the ratio 4/28. To find equivalent ratios, you can either multiply or divide both the numerator (top number) and the denominator (bottom number) of a ratio by the same non-zero number.

For the ratio 4/28, if we divide both the numerator and the denominator by 4, we get 1/7. If we then multiply 1/7 by different numbers, we can find additional equivalent ratios. Therefore, multiplying by 2 gives us 2/14, and multiplying by 3 gives us 3/21. This means that the set of equivalent ratios is 1/7, 2/14, 3/21, which corresponds to answer choice b.

Each share of common stock would receive approximately $1,122.45 from the total distribution of $275,000.00.

One of the fundamental arithmetic operations in mathematics is division, which is the process of dividing a group of things into equal pieces.

Given that,

Number of shares of common stock: 245

Total amount to be distributed: $275,000.00

To calculate the amount each share would receive,

Divide the total amount of $275,000.00 by the number of shares, which is 245.

Therefore,

$275,000.00 ÷ 245

≈ $1,122.45 per share

Hence,

Each share would receive approximately $1,122.45.

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Answer:        

3)[tex]y = x^2[/tex], [tex]y = 2x^2[/tex], [tex]y = 3x^2[/tex]

4) [tex]y = -x^2[/tex],[tex]y = -5x^2[/tex], [tex]y = -4x^2[/tex]

5) It is shifted 1 unit up.

Step-by-step explanation:

3) Since, the general equation of parabola is,

[tex]f(x) = a(x-h)^2+k[/tex]

If 0<a<1 then f(x) is wider than [tex]f(x)=x^2[/tex]

If a>1 then f(x) is narrow that [tex]f(x)=x^2[/tex]

Thus, the required sequence of equations from widest to narrow graph,

[tex]y = x^2[/tex], [tex]y = 2x^2[/tex], [tex]y = 3x^2[/tex]

4) Again if a<0 then [tex]f(x)=-a(x-h)^2+k[/tex] is wider than [tex]f(x)= -x^2[/tex]

Thus, the required sequence from widest to narrowest graph is,

[tex]y = -x^2[/tex],[tex]y = -5x^2[/tex], [tex]y = -4x^2[/tex]

5) Since, In equation of parabola,

[tex]f(x) = a(x-h)^2+k[/tex]

k shows the y-coordinate of the vertex of the parabola,

⇒ k shows the shifting along y-axis.

Thus, If the graph [tex]y=4x^2[/tex] is transformed to [tex]y=4x^2+1[/tex]

Then we will say it is shifted 1 unit up or shifted vertically by the factor 1.

Therefore, First Option is correct.

Question (3): The correct option is [tex]\boxed{\bf option (d)}[/tex].

Question (4): The correct option is [tex]\boxed{\bf option (c)}[/tex].

Question (5): The correct option is [tex]\boxed{\bf option (a)}[/tex].

Further explanation:

Question (3):

Solution:

The best method to find which graph is widest and narrowest is graphing a quadratic function.

The vertically stretching of graph of [tex]f(x)[/tex] by a factor of [tex]c[/tex] can be obtained by [tex]g(x)=cf(x)[/tex] if [tex]c[/tex] is greater than [tex]1[/tex].

The graph is stretched as we increase the value of [tex]c[/tex] in first case the value of [tex]c[/tex] is [tex]1[/tex] and in the second case the value of [tex]c[/tex] is [tex]2[/tex] and the third case is value of [tex]c[/tex] is [tex]3[/tex].

It means that the third case has maximum stretching that leads to a narrow graph, and similarly in second case the value of [tex]c[/tex] is [tex]2[/tex] it is also stretches but less than the third case.

Therefore, the order of quadratic functions from widest to narrowest graph is as follows:

[tex]\boxed{(y=x^{2})>(y=2x^{2})>(y=3x^{2})}[/tex]

Figure 1 (attached in the end) represents the graph of the functions [tex]y=x^{2},y=2x^{2},y=3x^{2}[/tex].

Thus, the correct option is [tex]\boxed{\bf option (d)}[/tex].

Question (4):

Solution:

The reflection of graph of [tex]f(x)[/tex] about [tex]x[/tex]-axis can be obtained by [tex]g(x)=-f(x)[/tex].

The graph of the function [tex]y=-x^{2}[/tex] is obtained when each point on the curve of the function [tex]y=x^{2}[/tex] is reflected across the [tex]x[/tex]-axis.

Similarly, the graph of the function [tex]y=-4x^{2}[/tex] [tex]y=-5x^{2}[/tex] and is obtained when each point on the curve of the function [tex]y=4x^{2}[/tex] and [tex]y=5x^{2}[/tex] is reflected across the [tex]x[/tex]-axis respectively.

From figure 2 (attached in the end) it is observed that the graph of the function [tex]y=-x^{2}[/tex] is the widest and the graph of the function [tex]y=-5x^{2}[/tex] is the narrowest.

Therefore, the correct option is [tex]\boxed{\bf option (c)}[/tex].

Question (5):

Solution:

If a constant is added to a function, the graph of the function shifts vertically upwards if the constant is positive and it shifts vertically downwards if the constant is negative.

For example: The graph of the function of the form [tex]y=f(x)+a[/tex] is obtained when each point on the curve of [tex]y=f(x)[/tex] is shifted along the [tex]y[/tex]-axis. If [tex]a[/tex] is positive then the curve shifts vertically upwards and if [tex]a[/tex] is negative then the curve shifts vertically downwards.

Similarly, the graph of the function [tex]y=4x^{2}+1[/tex] is obtained when each point on the curve of [tex]y=4x^{2}[/tex] shifts [tex]1\text{ unit}[/tex] vertically upwards.

Figure 3 (attached in the end) represents the graph of the function [tex]y=4x^{2}[/tex] and [tex]y=4x^{2}+1[/tex].

Therefore, the correct option is [tex]\boxed{\bf option (a)}[/tex].

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1. Representation of graph https://brainly.com/question/2491745

2. Quadratic equation: https://brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Topic: Shifting of graph

Keywords: Graph,inequality ,y=x^2 ,y=-4x^2 ,y=-5x^2 ,y=x^2 ,y=2x^2 , y=3x^2,  shifted, stretches, widest, narrowest, quadratic function shifting, translation, curve.

we know that

The solution of the system of linear equation graphed is the intersection both graphs

so

The point of intersection is [tex](-2,2)[/tex]

therefore

the answer is

The solution is the point [tex](-2,2)[/tex]

see the attached figure to better understand the problem

The solution to the system of equations is (-2,2).

A system having more than one equation is known as a system of equations.

The solution of a system of two equations is the point where both graphs intersect.

The graphs of the given equations intersect at (-2,2).

Therefore, the solution to the system of equations is (-2,2).

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The absolute value of the complex number -4 - square root of -2i is 2sqrt(6).

The absolute value of a complex number is the distance between the complex number and the origin on the complex plane. In this case, the complex number is -4 - square root of -2i. To find the absolute value, we calculate the magnitude of the complex number using the Pythagorean theorem.

The magnitude is given by the formula |z| = sqrt(a^2 + b^2), where a and b are the real and imaginary parts of the complex number, respectively.

By substituting the values a = -4 and b = -sqrt(-2i) into the formula, we have |z| = sqrt((-4)^2 + (-sqrt(-2i))^2)).

Since the square root of -2i can be simplified as 2sqrt(2), we have |z| = sqrt((-4)^2 + (-2sqrt(2))^2) = sqrt(16 + 8) = sqrt(24) = 2sqrt(6).

In a second it will go 90

In a minute it will go 5400

The Greek letter ω is often used to represent the SI unit of angular motion, the radian per second. Additionally, the SI unit for angular frequency is the radian per second. The shift in an object's orientation measured in radians per second is known as a radian per second.

Given

A computer’s hard disk is spinning at 90 revolutions per second.

In 1 second --- hard disk spins 90 revolutions

in 1 min = 60 sec = 90*60 = 5400 revolutions

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The computer's hard disk travels 4 degrees in a second and 240 degrees in a minute.

To find the number of degrees traveled by a computer's hard disk in a second, we need to know the time taken for one revolution. Since the disk is spinning at 90 revolutions per second, the time taken for one revolution is given by:

Time taken for one revolution = 1 / 90 seconds

Now, to find the number of degrees, we can use the formula:

Degrees = (Revolutions) x (360 degrees)

Therefore, the number of degrees traveled in a second is:

Degrees = (1 / 90) x (360) = 4 degrees

To find the number of degrees traveled in a minute, we multiply the number of degrees per second by the number of seconds in a minute:

Degrees per minute = (Degrees per second) x (60 seconds)

Degrees per minute = 4 x 60 = 240 degrees

Answer:

Step-by-step explanation:

We can find the numbers of male students and female students by making the system of equations using the given data:

Let:

Then:

Now we have the system of equations:

[tex]\begin{cases} m=7a+1 &\text{... [1]}\\f=\frac{1}{2} m &\text{... [2]}\\a+m+f=82 &\text{... [3]}\end{cases}[/tex]

[1] & [2]

By substituting [1] into [2], the [2] equation becomes:

[tex]f=\frac{1}{2} m[/tex]

[tex]f=\frac{1}{2} (7a+1)\ ...\ [4][/tex]

[1] & [3] & [4]

By substituting [1] & [4] into [3], the [3] equation becomes:

[tex]a+m+f=82[/tex]

[tex]a+(7a+1)+\frac{1}{2} (7a+1)=82[/tex]

[tex]\frac{23}{2} a+\frac{3}{2} =82[/tex]

[tex]23a+3=164[/tex]

[tex]23a=164-3[/tex]

[tex]a=161\div23[/tex]

[tex]\bf a=7[/tex]

Now, we can find the numbers of male and female students by substituting the value of a into equation [1] & [2]

[1] [tex]m=7a+1[/tex]

   [tex]m=7(7)+1[/tex]

   [tex]\bf m=50[/tex]

[2] [tex]f=\frac{1}{2} m[/tex]

    [tex]f=\frac{1}{2}(50)[/tex]

    [tex]\bf f=25[/tex]

The division rule for exponents demonstrates that when a number is raised to the zero power, it equates to 1 since the subtraction of equal exponents (as in division) yields an exponent of zero, and any number with zero instances in a multiplication chain results in the multiplicative identity, which is 1.

The division rule for exponents is integral to understanding why anything raised to the zero power is 1. The division rule for exponents states that if you divide two expressions with the same base, you can subtract the exponents.

For example, consider [tex]3^4[/tex] divided by [tex]3^4[/tex], which simplifies to [tex]3^{4-4} = 3^0[/tex]. According to the rule, when we have the same base with exponents subtracted during division, we subtract the exponents. This results in an exponent of zero for the base. Since [tex]3^4[/tex] divided by [tex]3^4[/tex] is equal to 1, and we expressed that as [tex]3^0[/tex], it logically follows that any non-zero number raised to zero power equals 1.

To further clarify, anything to the zero power signifies zero instances of the number in a multiplication chain and the implicit factor of 1 is all that remains, meaning that you're left with 1 as the result. This understanding is consistent with the properties of exponents across different types of numbers, be they integers, fractions, or irrational numbers.