Suppose G(x)=2x+3/x-4
find x such that G(x) = -3.

Answer:

11/15

Step-by-step explanation:

The total cost for Janissa is given by the equation A = $ 297,312

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost for the home by Janissa be represented as A

Now , the equation will be

The initial cost of the house C = $ 125,000

The total number of payments n = 40 x 12

The total number of payments = 480 payments

The monthly rate i = 5.2 % / 12

The monthly rate i = 0.004333

Now , the monthly payment is M = C [ i ( 1 + i )ⁿ ] / [ ( 1 + i )ⁿ⁻¹ ]

Substituting the values in the equation , we get

Monthly payment M = 125000 [ ( 0.00433 ) ( 1.00433 )⁴⁸⁰ ] / [ 1.00433 )⁴⁷⁹ ]

On simplifying the equation , we get

Monthly payment M = $ 619.40

Now , the total cost of the house A = total number of payments x Monthly payment M

Substituting the values in the equation , we get

The total cost of the house A = 480 x 619.40

The total cost of the house A = $ 297,312

Hence , the equation is A = $ 297,312

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The answer is Z-score. Z-score measures the number of standard deviations that a particular value is away from the mean.

A z-score is a numerical measure used in statistics to measure the number of standard deviations between data point and the mean. It is calculated by the subtracting of the population mean from the individual raw score and then dividing the difference by population standard deviation.

The resulting number is  z-score, which can then also be used to determine the probability of a raw score in the population. Z-Scores are useful for comparing scores on different tests because they allow you to compare scores on different scales.

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The expanded form of the expressions is 3y + 3x

These are mathematical expressions that are composed of terms, variables, constants and  factors with coefficients,

These expressions are also known to include mathematical or arithmetic operations, such as;

They could also be made up of fractions and decimlals

We have the expression;

3(y + x)

expand the parentheses

3y + 3x

Hence, the expression is 3y + 3x

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Step-by-step explanation:

(10x + 8x) +( 45x +10)- 2

18x + 45x + 10 - 2

63x + 10 - 2

71x

Step-by-step explanation:

18x + 45x+10-2

63x+8(unlike terms)

To complete the explanation, the table needs the following explanations and equations, respectively: (-2 + 2)*3 = 0 Put the distributive property to use. Take 6 away from both sides. -2*3 = -6

An equal sign is located between the two algebraic expressions to form an equation, which is a mathematical statement. It indicates that the left and right sides of the equation are equal. Mathematical operators, variables, symbols, and integers all appear in algebraic expressions.

The initial stage in this technique is to insert any real number its opposite, which is zero. These results;

(-2 + 2)*3 = 0

The following step is to get using distributive property;

-2*3 + 2*3 = 0

That this next is to remove 6 away from both corners to get at;

-2*3 = 0 - 6

Lastly, we distill to obtain;

-2*3 = -6

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One of the main goals of making a frequency distribution for quantitative data is to summarize the data in a way that properly depicts data as a whole.

A frequency distribution is a representation of the number of times each value or range of values appears in a set of data. By constructing a frequency distribution, we can get a better understanding of the distribution of values and the overall pattern of the data. This information can help us identify any outliers, the center or average of the data, and the spread or variability of the data.

Additionally, a frequency distribution allows us to compare different sets of data and make informed decisions based on the information presented. For example, if we compare the frequency distributions of two groups, we can determine if there are any significant differences between the two groups. This can be useful in various fields such as market research, psychology, and medicine.

In summary, the goal of constructing a frequency distribution is to summarize the information contained within the data and gain a better understanding of the distribution of values. This information can be used to make informed decisions and compare different sets of data.

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Answer:B I’m not sure if it is correct

Step-by-step explanation:

After 20 hours, Eric and Jennifer will each have 340 signatures.

We may begin by constructing an equation that solves for the number of signatures and the number of hours that have passed. Let's name the number of signatures "x" and the number of hours "h" respectively. Then there's:

20 + 17h Eric's signatures

Jennifer's signatures: 19h

We may put their signatures equal to each other because they will eventually have the same amount of signatures:

20 + 17h = 19h

We can now solve for h by removing h from one side of the equation. To begin, remove 19h from both sides:

20 = -h

Then we divide both sides by -1 to get h on its own:

h = 20

So, after 20 hours, Eric and Jennifer will have both gathered the same amount of signatures, which is:

Eric's autographs total 340 (20 + 17 * 20).

Jennifer has 19 * 20 = 380 signatures.

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Augmented matrix is a matrix that is composed of the coefficients of the variables of a system of linear equations and the constants on the right side of the equal signs of the linear equation.

For the given system of equations, the augmented matrix is:

|  7  -6  8  |  0  |

|  6  -2  -3 | -3  |

The first row consists of the coefficients of the variables x and y, and the constant 0 from the equation 7-6y+8x=0.

The second row consists of the coefficients of the variables x and y, and the constant -3 from the equation 6x=-3-2y.

The augmented matrix can be written in a short form as:

|  7  -6  8  |  0  |

|  6  -2  -3 | -3  |

This augmented matrix can be used to solve the system of equations by using the Gaussian Elimination Method or the Gauss-Jordan Elimination Method.

The columns of two matrices are combined to create a new matrix, which is known as an augmented matrix. When using matrices to solve straightforward linear equations, the augmented matrix is a crucial tool. The number of variables in the linear equation is the same as the number of rows in the augmented matrix.

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Answer:

Step-by-step explanation:

The required exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is y = 86 * (1.20)ˣ.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Let's let the variable x represent the number of weeks after opening the shop, and let y represent the weekly sales in dollars. We know that in the first week, her sales were $86. After that, her sales increased by 20% each week. This means that her sales in the second week were,

We can see that her sales are increasing by a factor of 1.20 each week. This means that we can model her sales using an exponential equation of the form:

y = a * (1.20)ˣ

Where a is the amount of the initial sales in the first week (which we know is $86).

So the exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is:

y = 86 * (1.20)ˣ

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Answer:

24

Step-by-step explanation:

The total number of students in the three sections is 36 + 40 + 48 = 124.

To find the maximum number of students in each row, we need to divide the total number of students by the number of rows, rounded down to the nearest integer.

Let's call the maximum number of students in each row "x". Then, we can write the equation:

x * n = 124

To find the maximum value of x, we need to find the maximum value of n such that the result of x * n is less than or equal to 124.

Starting with n = 1, we can increment n and calculate x for each value of n until x * n is greater than 124.

For n = 1, x * n = 124, so x = 124.

For n = 2, x * n = 62, so x = 62.

For n = 3, x * n = 41, so x = 41.

For n = 4, x * n = 31, so x = 31.

For n = 5, x * n = 24.8, which is not an integer, so we round down to 24.

Therefore, the maximum number of students in each row is 24, with a total of 5 rows.

Answer:

Step-by-step explanation:

Let's call the maximum number of students in each row "r". To find this value, we need to divide the total number of students by the number of rows. To ensure that all the students can fit into the rows, the number of students in each section must be divisible by the number of rows.

First, we find the least common multiple (LCM) of the number of students in each section, which will be the total number of students if we arrange them in the same number of rows. The LCM of 36, 40, and 48 is 240.

Next, we divide the LCM by the number of students in each section to find the number of rows:

r = LCM / 36 = 240 / 36= 6.67 (rounded down to 6)

So, the maximum number of students that can be in each row is 24

Answer:

x = -2/3

y = -7/3

Step-by-step explanation:

2x-4y=8

4x+y= -5

Times the first equation by -2

-4x + 8y = -16

4x + y = -5

9y = -21

y = -7/3

Now put -7/3 back in for y and solve for x

4x - 7/3 = -5

4x - 7/3 = -15/3

4x = 8/3

x = -2/3

Answer:

Step-by-step explanation:

You want the x- and y-intercepts of each of the given lines:

The x-intercept is the x-value when y = 0. For an equation of the form ...

  ax +by = c

setting y = 0, we have ...

  ax = c

Solving for x gives ...

  x = c/a . . . . . x-intercept

Similarly, setting x=0 and solving for y gives the y-intercept:

  by = c

  y = c/b

X-intercept: 8/2 = 4

Y-intercept: 8/-4 = -2

X-intercept: -5/4

Y-intercept: -5/1 = -5

X-intercept: -14/14 = -1

Y-intercept: -14/-7 = 2

X-intercept: 10/2 = 5

Y-intercept: 10/6 = 5/3

Answer:

C. Yes, if both pairs of opposite sides are congruent, they must also be parallel.

Step-by-step explanation:

a parallelogram means a quadrilateral with 2 pairs that are parallel. If one pair is congruent, that means that if it is parallel, the other pair must be congruent as well. That proof can be pretty complex to explain, but i hope this helps.

Answer:

Step-by-step explanation:

B. No; both pairs of opposite sides can be congruent without being parallel.

A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. This particular quadrilateral has four sides, two of which are parallel and equal in length, and both of which have equal-sized opposite angles.

A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. This particular quadrilateral has four sides, two of which are parallel and equal in length, and both of which have equal-sized opposite angles. A parallelogram has equal-length opposite sides and diagonals that cut each other in half. It possesses all the characteristics of a parallelogram, including diagonals that are split in half and angles that add up to 360 degrees. Additionally, it is the only quadrilateral in which the angles on either side are equal.

In two dimensions, a parallelogram is a shape with four sides and four angles. It is a particular kind of quadrilateral where the opposing sides are parallel and all sides are the same length. In terms of the intersection of the two sides, it is also symmetrical. A parallelogram has equal opposed angles and diagonals that cut each other in half.A parallelogram's internal angles add up to 360°. The parallelogram is a rectangle if two of its adjacent angles are supplementary. Whenever a parallelogram's angles are all at right angles, it is a square.

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Answer:

The total debits in the trial balance add up to $99,050, while the total credits add up to $88,100. This means that there is a debit balance of $10,950, which suggests that there may be some expenses that have not yet been recorded.

Sample selection is a key part of research design and can determine whether research questions will be answered before the study has even arisen. Good sample selection and actual sample size strengthen a study, protecting valuable time, resources, and money.

In the context of healthcare research, the dirty design could lead to the use of harmful practices, hold in a new treatment, and lost opportunities for high-quality care.

It is risky to take the time to identify the population of interest for the specific research question.

Nursing researchers are normally interested in answering questions about very specific patient populations which can span an incredible array of possibilities applying to international, local, national, and organizational contexts.

Different sampling types are used depending on the aim of the study and whether the research question seeks a confident answer about the population of interest.

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Answer: The angle measures cannot be determined from the information given. The equation m1 = (x+84)° and m2 = 2x° only specify a relationship between two angles, but do not specify specific angle measures. To determine the angle measures, additional information or constraints are needed.

Step-by-step explanation:

Answer:

30.7

Step-by-step explanation:

sin 71° = 29/ ladder length

so length = 29/ sin 71° = 30.7

The second coterminal angle for x = 120° that is less than -500° is -620°.

Triangle is geometric figure that can be described as the amount of rotation between two straight line or planes and angle is measured in degree with a full circle being 360° the most common type of angle are the right angles 90° acute angles are less than 90°. Anglican also be classified as either complementary or supplementary depending on how they relate to each other.

Coterminal angles are angles that are the same distance from 0° but in the opposite direction. To find the second coterminal angle for x = 120° we subtract 360° from it. Thus, the second coterminal angle for x = 120° that is less than -500° is -620°.

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Answer: 2/21

Step-by-step explanation:

2/3x6-3+5/3x3

2/18-3+5

2/21

Answer:

According to the equation given, the slope-intercept form is y = -3/2 x - 17/2. To graph this function, you need to first plot the y-intercept at (-17/2, 0) on the graph. Then, use the slope (-3/2) to find the next point and draw a line between the two points. That will be your graph for the equation. Good luck!

The sales are expected to drop by 20%, this represents a total estimated loss in income from operations of $213,200.

Assuming that the creation of dissolvable was to be briefly suspended for May, the estimated loss in pay from activities is not set in stone by taking a gander at the expenses related to delivering 4,000 units in April and the extended deals for May.

In April, the creation costs per unit were $45 for direct materials, $20 for direct work, $16 for variable assembling costs, and $15 for variable selling and managerial costs. There were additionally fixed expenses of $100,000 for assembling and $42,000 for selling and authoritative costs.

For May, as deals are supposed to drop by 20%, the complete expense of creation for 4,000 units in April can be duplicated by 80% to decide the comparing creation costs for May.

Similar turns out as expected for fixed costs. In this way, the complete expense of creation in May would be,

$71,200 ($45 × 4,000 × 0.8) for direct materials, $32,000 ($20 × 4,000 × 0.8) for direct work, $25,600 ($16 × 4,000 × 0.8) for variable assembling costs, and $24,000 ($15 × 4,000 × 0.8) for variable selling and authoritative costs.

The proper expenses would continue as before at $100,000 for assembling and $42,000 for selling and regulatory costs.

Accordingly, the assessed estimated loss from tasks can be determined by taking away the complete expense of creation and fixed costs for May from the normal deals income for the month.

Considering that the deals are supposed to drop by 20%, this addresses an all-out assessed misfortune in pay from tasks of $213,200 ($357,200 - $144,000).

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The question is -

The production costs and selling and administrative expenses, based on the production of 4,000 units in April, are as follows:

Direct materials $45 per unit

Direct labor 20 per unit

Variable manufacturing cost 16 per unit

Variable selling and administrative expenses 15 per unit

Fixed manufacturing cost $100,000 for April

Fixed selling and administrative expenses 42,000 for April

Sales for May are expected to drop about 20% below those of the preceding month. No significant changes are anticipated in the fixed costs or variable costs per unit. No extra costs will be incurred in discontinuing operations in the portion of the plant associated with solvent. The inventory of solvent at the beginning and end of May is expected to be inconsequential.

What would be the estimated loss in income from operations if the solvent production were temporarily suspended for May?

The probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

In the given question a parking row has 8 spaces.and four cars are pulled in randomly to park in the parking row.

We have to find the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs.

Number of ways to arrange 4 cars in 8 places = P(8,4)

Number of ways to arrange 4 cars in 8 places = 1680

Number of ways to arrange 4 cars in 2 pairs = N

(Choose 2 pairs of consecutive place from 8 and arrange 4 cars) = 15*4!

= 360

Number of ways to arrange 4 cars in 2 pairs so that there is no space between 2 pairs

= 5*4!

= 120

therefore,

Number of ways no two pairs are consecutive = 360-120

Number of ways no two pairs are consecutive = 240

probability=240/1680

Probability = 1/7

Therefore, the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

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First, subtract 4 from both sides:

[tex]5t\geq 15[/tex]

Now, divide both sides of the equation by 5 to isolate variable t:

[tex]t\geq 3[/tex]

Therefore, we know that t must be greater than or equal to 3 for this inequality to be true!

The correct option regarding the area and the flow rate when the engine speed is decreased and the tractor speed is increased is given as follows:

B. Area rate would increase and flow rate would decrease.

From the first table, when the tractor's speed increases, the area also increases, hence they are direct proportional and the area rate would decrease.

From the second table, when the engine's speed increases, the flow rate also increases, hence if the engine's speed decreases, the flow rate would also decrease, as the variables are also direct proportional.

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The solutions to the quadratic equation are;

[tex]x = \frac{ \sqrt{10} + 5 }{2} [/tex]

[tex]x = \frac{ - \sqrt{10} + 5 }{2} [/tex]

The correct answer choice is option A and E

4x² - 20x + 25 = 10

Equate the equation to 0

4x² - 20x + 25 - 10 = 0

4x² - 20x + 15 = 0

Solve the quadratic equation using formula

[tex]4x^2 - 20x + 15 = 0[/tex]

using Quadratic Formula where,

a = 4,

b = -20, and

c = 15

[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

[tex]x = \frac{ -(-20) \pm \sqrt{(-20)^2 - 4(4)(15)}}{ 2(4) }[/tex]

[tex]x = \frac{ 20 \pm \sqrt{400 - 240}}{ 8 }[/tex]

[tex]x = \frac{ 20 \pm \sqrt{160}}{ 8 }[/tex]

[tex]x = \frac{ 20 \pm 4\sqrt{10}\, }{ 8 }[/tex]

[tex]x = \frac{ 20 }{ 8 } \pm \frac{4\sqrt{10}\, }{ 8 }[/tex]

[tex]x = \frac{ 5}{ 2 } \pm \frac{ \sqrt{10}\, }{ 2 }[/tex]

Therefore, the solution to the quadratic equation using formula is

[tex]x = \frac{ 5}{ 2 } \pm \frac{ \sqrt{10}\, }{ 2 }[/tex]

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The diameter of the circle is 12.5 inches

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: 157 breaks required to make a circular garden and cover the boundary.

Now each brick is 4 inches long

Thus total length of the circumference of the circular garden we get

157/4=39.25 inches long

Thus the circumference of the circle is given by

2πr=39.25

2r=39.25/3.14

d=12.5 inches

Thus the diameter is 12.5 inches.

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Answer:

1. Amplitude = 2 feet (max height level of water on the beach)

2. Periodicity = 24 hours (water level reaches 2 ft max every 24 hours or 0 feet minimum every 24 hours

3. Graph attached with explanation

Step-by-step explanation:

For a sine function, sin(x), the maximum value is 1 when x is π/2, 5π/2, 9π/2...

The minimum value is -1 at x = 0, π, 3π/2, 2π,...

a sin(x) will have the maximum value(amplitude) of |a · 1| = |a|

The given function is
[tex]f(t) = 2 \sin\left(\dfrac{2\pi t}{24}\right)\\\\\dfrac{2\pi t}{24} = \dfrac{\pi t}{12}\\\\\textrm{So the function is:}}\\\\f(t) = 2 \sin \left(\dfrac{\pi t}{12}\right)[/tex]

1. The amplitude is 2 and this is the maximum water level in feet at the beach. This occurs when [tex]\textstyle {\dfrac{\pi t }{12} = \dfrac{\pi}{2}}[/tex]

or, when t = 6. It repeats every 24 hours (see #2)

2. The periodicity of a function is when the function starts repeating itself

The periodicity of sin(x) is 2π i.e. the sinusoidal wave starts repeating itself every 2π radians

Since our sine function has πt/12 as its argument we have that
πt/12 = 2π

or t = 24

So every 24 hours, the water level which starts at 0 feet at 0 hours, becomes 0 again

3) Graph of the function attached. Note that water level cannot be negative which is the sine value from π/2 to 2π so we have to set it equal to 0

Water level goes to zero every 12 hours and stays at zero for 12 hours when it starts rising again.

As can be seen from the graph, every 24 hours, the water level reaches a peak height of 2 feet

I hope that this helps