On August 1, Stacy had a debt of $43 in her checking account. After depositing $75 from her paycheck on August 15, what is her new account balance?

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is \((e - 2\sqrt{3} )^2\) = f - 20√3.

Expanding the left side of the equation we have:

\((e - 2\sqrt{3} )^2\) = (e - 2√3)(e - 2√3)

= \(e^2\) - 2e√3 - 2e√3 + 12

= \(e^2\) - 4e√3 + 12

Substituting back in the function

\(e^2\) - 4e√3 + 12 = f - 20√3

\(e^2\) - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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Answer:Alto 16cm Ancho 32cm

A+2A=48

3A=48

/3

A=16

Step-by-step explanation:

Usando conceptos de velocidad, distancia y tiempo, se encuentra que tardará 4 horas en llegar a su destino.

-----------------------------

La velocidad es la distancia dividida por el tiempo, o sea:

\(v = \frac{d}{t}\)

-----------------------------

Así, la distancia será de:

\(d = vt = 60(6) = 360\)

360 km.

-----------------------------

\(v = \frac{d}{t}\)

\(90 = \frac{360}{t}\)

\(90t = 360\)

\(t = \frac{360}{90}\)

\(t = 4\)

Tardará 4 horas en llegar a su destino.

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

From the information given, we can set up the following equations:

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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Answer:

25922.963

Step-by-step explanation:

the square root of 42 is 6.48074069841

4000*6.48074069841 is 25922.9627936

The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.

Let's calculate the fraction of the plot of land that is not occupied by the flowers.

Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.

After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.

Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.

Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.

To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:

1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.

Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.

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Answer:

B.

Step-by-step explanation:

Let's write an equation that expresses the relationship.

Let s denote the amount of spiders.

We know that every time Alex catches one spider, the remaining population doubles.

So, if s represent the population of spiders, if Alex catches 1, then the population will become (s-1).

However, for every catch, the population doubles, so, the new population will be 2(s-1).

Therefore, we can write the following equation:

\(s_n=2(s_o-1)\)

Where s_n represents the new population and s_o represents the original population.

We know that there are now 194 spiders in Alex's house. We want to find the number of spiders in his house before he caught the last 2 spiders. So, let's solve for s_o twice.

Substitute 194 for s_n. Solve for s_o:

\(194=2(s_o-1)\)

Divide by 2:

\(97=s_o-1\\\Rightarrow s_o=98\)

Therefore, before catching the last spider, there were 98 spiders.

So, to find the number of spiders before the last 2, we will solve for s_0 again. This time, we will use 98 for s_n. So:

\(98=2(s_0-1)\)

Solve for s_o:

\(\Rightarrow 49=s_o-1\\\Rightarrow s_o=50\)

Therefore, there were 50 spiders in Alex's house before he caught the last 2 spiders given that the current population is 194 spiders.

Our answer is B.

Edit: Typo

Answer:

the answer is 50, or B.

Step-by-step explanation:

The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

-2(x + y) = -2(1) --

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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Answer:

B

Step-by-step explanation:

Trust

The required simplified value of the given expression is given as -13/20.

Given that,
An expression is given, −1 4/5 + (−1/4) + (−1/5) we have to determine the sum of the expression.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
= -1 4/5 + (-1/4) + (-1/5)
= -1/5 -1/4 -1/5
= -2/5 -1/4
= -13/20

Thus, the required simplified value of the given expression is given as -13/20.

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The probability of drawing two numbers from both jars whose product is even = 5/9.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Total number of outcomes =9

Favorable cases = (1,2), (2,1), (3,2), (2,3), (2,2)

The probability of drawing two numbers from both the jars whose product is even = 5/9

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e) - x^2 + y ^2 = 1

The three statements that are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   .......equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

Based on the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

By comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x - 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

20+4=24=12=6=3

therefore the answer is three defect

Answer:

-16.7

Step-by-step explanation:

(2°F − 32) × 5/9 = -16.7°C

Answer:

B) (1/2, -8)

Step-by-step explanation:

(1, -6) and (0, -10)

Midpoint formula:

((x1+x2)/2, (y1+y2)/2)

Solving for x:

(x1+x2)/2

(1 + 0)/2

1/2

Solving for y:

(y1+y2)/2

(-6-10)/2

(-16)/2

-8

Answer:

884.4

Step-by-step explanation:

Answer:

The original price is 895.12$

I haven't done percent in ages, lmk if you get it right
kudos to any other answer besides this

Step-by-step explanation:

Answer:

120 cm²

Step-by-step explanation:

Applying,

A = Ph................... Equation 1

Where A = Literal Area of the triangular prism, P = Perimeter of the base, h = height.

But,

P = a+b+c............... Equation 2

Where a, b, c represent the three sides of the triangular base

Therefore,

A = h(a+b+c)............... Equation 3

From the question,

Given: h = 8 cm, a = 4 cm, b = 5 cm, c = 6 cm

Substitute these values into equation 3

A = 8(4+5+6)

A = 8(15)

A = 120 cm²

The relation and equation that is modelled by the graph is y = x - 1.

To determine the relation and equation that is modelled by the graph, we must analyze the characteristics of the graph.The graph is a straight line that passes through the points (0, -1) and (4, 3).

The slope of the line can be determined by using the slope formula:slope = (y2 - y1) / (x2 - x1) = (3 - (-1)) / (4 - 0) = 4/4 = 1

Therefore, the slope of the line is 1. We can use the point-slope form of the equation of a line to determine the equation of the line.y - y1 = m(x - x1)

where y1 = -1, x1 = 0, and m = 1Substituting these values, we get:y - (-1) = 1(x - 0)y + 1 = x Simplifying this equation, we get the relation y = x - 1.

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Answer: 540

Step-by-step explanation:

Given: A polling company reported that 53​% of 1018 surveyed adults said that rising gas prices are "quite annoying."

To find: The exact value of 53​% of 1018.

\(53\%\text{ of }1018 = \dfrac{53}{100}\times1018\)  [we divide a percentage by 100 to convert it into a fraction of decimal]

\(=\dfrac{53954}{100}=539.54\\\\\approx540\)

Hence, the 540  adults said that rising gas prices are "quite annoying."

Thus, the exact value = 540

Answer:

the answer is c.

Answer:

Let x represent the variety of tickets sold, and y represent the total amount of cash raised. Since each price tag is $2.50, the total amount of money raised is identical to $2.50 instances the wide variety of tickets. The equation would be y = 2.50x.

Step-by-step explanation:

The x variable represents the number of tickets sold.

The y variable represents the total amount of money raised from ticket sales.

The equation for the scenario is y = 2.50x.

Answer:

b

Step-by-step explanation:

Answer:

The range of the function is: -∞≤y≤∞.

Consider the provided function.

The range of the function is the set of all values which a function can produce or the set of y values which a function can produce after substitute the possible values of x.

The range of a cubic root function is all real numbers.

Now consider the provided function.

The above function can be written as:

Taking cube on both sides.

The graph of the function is shown in figure 1:

For any value of x we can find different value of y.

Here, the cube root function can process negative values. Since, the function can produce any values, the range of the given function is  -∞≤y≤∞ .

Therefore, the range of the function is: -∞≤y≤∞ (A).

Answer:

A

Step-by-step explanation:

use division to get 3.6

Answer:

3.6 is equivalent to \(\frac{18}{5}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sales Revenue:  $800.00

Cost of good sold:  $350,000.00

Subtract:                   $450,000.00

Sales Revenue:         $795,000.00

Cost of good sold:     $600,000.00

Subtract Sales             $195,000.00

Revenue from Cost

of goods sold.

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Step-by-step explanation:

P odd = spin of 1 or 3

P greater than 3  = spin of 4  

   three spins out of 4 possible spins   =  3/4

Answer:

B. (x - 3²)(y-6)

Step-by-step explanation:

Find the expression with a value of 30;

 when x  = -1 and y = 3:

   A.  (x - 3²).y-6

           (-1 - 9).3-6 = -10 x 3 -6  = -30 - 6 = -36

 B.  (x - 3²)(y-6)

          ( -1 -3²)(3 - 6) = (-1 -9)(-3) = 30

C.  x - 3² . (y-6) = -1 - 9.(3-6)

                         = -1-9.-3

                         = -1 - 9 x -3

                         = -1 + 27

                         = 26

D. x - 3².y-6 = -1 - 9. 3 - 6

                   = -1 - 27 - 6

                   = -34