Write System of Equations from Context
Kennedy has $0.81 worth of pennies and nickels. She has 9 more nickels than
pennies. Write a system of equations that could be used to determine the number of
pennies and the number of nickels that Kennedy has. Define the variables that you
use to write the system.
Let __=_________
Let__=___________

System of Equations:
_________________

_________________

The value of the limit of the rational function evaluated x = - 5 is equal to - 6.

In this problem we find the limit of rational function evaluated at a given value. According to the statement, there is apparently a discontinuity at x = 5. The expression can be simplified by algebra properties:

[tex]\lim_{x \to - 5} \frac{x^{2} + 4 \cdot x - 5}{x + 5}[/tex]

[tex]\lim_{x \to -5} \frac{(x + 5)\cdot (x - 1)}{(x + 5)}[/tex]

[tex]\lim_{x \to - 5} (x - 1)[/tex]

Then, we can complete the table by means of the following expression:

f(x) = x - 1

x = - 5.01

f(- 5.01) = - 5.01 - 1

f(- 5.01) = - 6.01

x = - 5.001

f(- 5.001) = - 5.001 - 1

f(- 5.001) = - 6.001

x = - 5.0001

f(- 5.0001) = - 5.0001 - 1

f(- 5.0001) = - 6.0001

x = - 5

f(- 5) = - 5 - 1

f(- 5) = - 6

x = - 4.9999

f(- 4.9999) = - 4.9999 - 1

f(- 4.9999) = - 5.9999

x = - 4.999

f(- 4.999) = - 4.999 - 1

f(- 4.999) = - 5.999

x = - 4.99

f(- 4.99) = - 4.99 - 1

f(- 4.99) = - 5.99

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Answer:

Step-by-step explanation: We can start the problem by using the principle of Proportional Equivalents. We can write two equations based on the given information:

Let's say that the rate of filling the pool with one large pump is x and the rate of filling the pool with one small pump is y.

Then, we can write the following two equations:

2x + 1y = 1/4 (because two large and one small pump can fill the pool in 4 hours)

1x + 3y = 1/4 (because one large and three small pumps can fill the pool in 4 hours)

Now we have two equations with two unknowns, x and y. We can solve for x and y using either substitution or elimination method. Let's use substitution method.

Solving for x:

From equation (1), we have 2x = 1/4 - 1y

Substituting this value of x in equation (2), we get:

1 (1/4 - 1y) + 3y = 1/4

Expanding and simplifying, we get:

1/4 - 1 + 3y = 1/4

3y = 1/2

y = 1/6

So, the rate of filling the pool with one small pump is 1/6.

Now that we have found the value of y, we can find the value of x.

x = 1/4 - 1y = 1/4 - 1 * 1/6 = 1/4 - 1/6 = 1/12

So, the rate of filling the pool with one large pump is 1/12.

Now that we have found the rate of filling the pool with each large and small pump, we can find the time it will take 4 large and 4 small pumps to fill the pool.

Let's call the rate of filling the pool with 4 large and 4 small pumps as R.

Then, R = 4 * 1/12 + 4 * 1/6 = 1/3

So, it will take 1/R = 3 hours to fill the pool with 4 large and 4 small pumps.

To answer this question, we need to use some basic trigonometry. We know that Dirk's shadow is as tall as the town hall and that Dirk is 1.40m tall. So, if we can determine the angle of elevation of the spotlight, we can calculate the height of the town hall.

Let's call the angle of elevation "α" and the distance from the spotlight to the town hall "d". To determine α, we can use the tangent function.
tan α = opposite/adjacent = (d-5)/35 = (30/35) = 0.8571

The angle of elevation is arctan(0.8571) = 53.13°.

Now, we can use the sine function to calculate the height of the town hall:
sin α = opposite/hypotenuse = 1.4/d
d = 1.4/sin 53.13° = 16.2m

Therefore, the town hall is 16.2m tall.

Answer:

y = ( x - 4 )² - 4

Step-by-step explanation:

a² ± 2ab + b² = ( a ± b )²

~~~~~~~~~~~~

y = x² - 8x + 12

y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4

y = ( x - 4 )² - 4

Answer:

The percentage of students in Kiri's brother's class who think aliens exist is 11/25 = 44%.

Since the number of students in Kiri's class is not given, it's not possible to compare the percentage of students in Kiri's class who think aliens exist to the percentage in her brother's class. We need to know the number of students in Kiri's class and the number of students who believe in aliens in order to compare the percentages.

Answer:

The island is 728 feet off the coast.

Step-by-step explanation:

The solution of the logarithm expression  logₐ 60 is 2.1. Therefore, the answer is D.

The logarithm expression can be solved as follows; Using the logarithm rule,

Law of multiplication of logarithm,

logₐ x + logₐ y = logₐ xy

Therefore,

logₐ 2 = 4

logₐ 3 = 5

logₐ 5 = 8

Hence, let's find logₐ 60.

logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60

Hence,

0.8 + 0.5 + 0.4 + 0.4 = 2.1

Therefore,

logₐ 60 = 2.1

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The value of log a 60 is 21. The correct option is D.

Logarithms are another way of writing exponents.

Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.

log a 60 = log a (12 x 5)

log a 60 = log a 12 x log a 5

log a 60 = log a (4 x 3) x log a 5

log a 60 = log a 4 x log a 3 x log a 5

log a 60 = 2 log a 2 x log a 3 x log a 5

Substituting the values for the logs

log a 60 = 2 (4) + 5 + 8

log a 60 = 21

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The transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.

Given that, a function f(x) undergo some transformations to become f(x+9)-1,

We know that,

Vertical Shifting:

Adding a constant to a function will shift its graph vertically (i.e. y = f (x) + c). Adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.

Horizontal Shifting:

Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

Therefore, there is transformation of a horizontal and vertical shift.

Hence, the transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

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The reason why AC must be congruent to BD is the hypotenuse - leg theorem and CPCTC

According to the hypotenuse-leg (HL) theorem, a right triangle is congruent if each of its hypotenuse and one leg are congruent with their corresponding hypotenuse and one leg in another right triangle.

The problem have the hypotenuse and a leg of the two triangles stated to be equal. This completes the requirement for the theorem and hence the two triangles are said to be equal

Then applying the CPCTC theorem which says that if two triangles are congruent, every corresponding part of one triangle is congruent to the other side hence, the sides AC = BD

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Side a will be 58cm.In mathematics, a side is a feature of a geometric shape.

The "A-side" of a record, which is the main song, is issued as a single. The "A-side" of an album is the side that this track is on. The word "side" is most frequently employed as a noun, however it can also be used as an adverb or a verb. The shapes we observe are made of points and lines (line segments) (vertices).

Finding the side, we obtain:

Given ∠A= 30°, b =100 cm .

In ΔABC,

tan A = [tex]\frac{a}{100}[/tex],

tan 30°=  [tex]\frac{a}{100}[/tex]

0.577×100=a

a=57.7≅58 cm.

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Answer:

The difference in height is 8cm

Step-by-step explanation:

Volume of a cylinder=hπr²

When the bottle is full 5652:

5652=hπr²

5652=h*3.14*7.5²

5652=h*176.625

5652/176.625=h

Height=32cm

When the bottle is full by 4239:

4239=hπr²

4239=h*3.14*7.5²

4239=h*176.625

4239/176.625=h

Height=24cm

Difference in height:

32-24=8

The difference in height is 8cm

The solution for x is not possible because the information is not enough, the correct option is D.

Its a parallelogram but all sides of same length.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

We are given that;

m∠AEB of rhombus ABCD is 7x+6

Now,

To find the value of x we need atleast one more information

Since the measure of diagonals are not given and the length of sides are also not provided.

So, that the calculation could not be made.

Therefore, the information of rhombus is insufficient.

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The value of the expression √4x-3 /9-2x =0 will be B. 2.

Rearrange the radical on the left side of the equation:

√4x-3=√9-2x

Power on both sides: (√4x − 3)²=(√9 – 2x)² -

Simplify the radical expression: 4x-3=9-2x Rearrange unknown terms to the left side of the

equation: 4x+2x=9+3

Combine like terms: 6x=9+3

Calculate the sum or difference: 6x=12

Divide both sides of the equation by the coefficient

of variable: x=12÷6

Calculate the product or quotient: x=2

Substitute into one of the equations: √4 x 2 3-√9-2 × 2=0

Calculate the product or quotient: √8

9-2×2

Calculate the product or quotient: √8 3 - √9 4

Calculate the sum or difference: √5-√9

Calculate the sum or difference: √5-√5

Calculate the sum or difference: 0=0

Combine the results: x=2

x=2

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Answer:

32/13

Step-by-step explanation:

To evaluate the expression Z₂ * Z3 / Z₁, we first need to find the complex numbers Z₂ * Z3 and Z₁.

Z₂ * Z3 = -2 + 3i * 4 + 2i = (-8 + 14i) + (-6 + 6i) = -8 + 8i

Z₁ = 3 - 2i

So, Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i)

We can simplify this expression by multiplying the numerator and denominator by the complex conjugate of the denominator, which is (3 + 2i).

Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i) * (3 + 2i) / (3 + 2i) = (-8 + 8i) * (3 + 2i) / (3 - 2i) * (3 + 2i)

Z₂ * Z3 / Z₁ = ((-8 * 3 + 8 * 2i) + (8 * 3 + 8 * 2i)) / (3^2 + (-2i)^2) = (16 + 16i) / 13

Therefore, Z₂ * Z3 / Z₁ = (16 + 16i) / 13.

By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

According to the information in question:

Total salt = 90.45 grams

Amount of salt poured = 55.2 grams

Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:

Amount of salt left = 90.45 - 55.2

                               = 35.25 grams

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The length of x is 6 in the given triangle.

The branch of Mathematics which studies relationships between side lengths and angles of triangles.

We have to find the value of x in the given triangle.

We know that tan theta is the ratio of opposite side by adjacent side.

The opposite side is x and the adjacent side has √12

tan60=x/√12

√3=x/√12

x=√12√3

x=√36

x=6

Hence, the length of x is 6.

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The probability distribution does not add up to 1.0, in other words.

The complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

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Answer:

It is not accurate

Step-by-step explanation:

If the complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

THEN:

To determine whether the probability distribution is accurate, we need to check two conditions:

The sum of the probabilities should be equal to 1.

All probabilities should be between 0 and 1.

Let's check these conditions:

Sum of probabilities:

p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05

The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.

All probabilities should be between 0 and 1:

The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.

However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.

Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.

The perimeter of the given figure is: 36 +16√5 ft ≈ 71.777 ft

The area of the figure is: 288 ft²

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

We know that the perimeter is the total length of all the sides. The length of the horizontal sides is; 8 ft + 10 ft = 18 ft.

The length of the slant sides can be found by the Pythagorean theorem.

For side length s, we have;

s^2 = 8^2 + 16^2

 s^2 = 64 +256 = 320

 s = √320 = 8√5

Then the perimeter;

 P = 2(8√5 + 18) = 36 +16√5 ≈ 71.777 . . . feet

Area,  A = bh

where b is the base and h is the height.

 A = (18 ft)(16 ft) = 288 ft²

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Answer:

10 minutes

Step-by-step explanation:

1/4 in 2 minutes

1 1/4 = 1/4 x 5

2 x 5 = 10

(That's REALLY good honestly)

The slope is 2.5

The y-intercept is 5.8.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = 5.8 + 2.5x

This is in the form of y = mx + c

So,

m = 2.5

And,

The y-intercept is when x = 0.

So,

y = 5.8 + 2.5x

Substitute x = 0,

y = 5.8

Thus,

Slope is 2.5

The y-intercept is 5.8.

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Someone who is not a stakeholder in this business does not have any interest or concern in Biketown's decision to purchase a new automated machine.

In this scenario, stakeholders for Biketown's decision to purchase are Customers who appreciate the workmanship of Biketown's bicycles, Employees who are involved in the assembly process, Shareholders who have invested in the company, Suppliers who provide materials or components for the bicycles.

Local community members who may be impacted by the company's operations or decisions. An individual who has no knowledge of or interaction with Biketown or the bicycle industry, and therefore has no stake in the decision.

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Equivalence means to be same, whether it be value, temperature, size, etc.

First, let's convert [tex]\frac{3}{4}[/tex] into a different fraction.

We know this because each side of the fraction [tex]\frac{3}{4}[/tex] can be multiplied by 25 to get [tex]\frac{75}{100}[/tex].

Now that we know this, we can convert the fraction [tex]\frac{75}{100}[/tex] into a percentage.

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

if we know that percentages are expressed as a fraction of 100, we know that [tex]\frac{75}{100}[/tex] is equal to %75.

To convert percentages into decimals, we can just take the percentage (%75) and fit it into 0.00, making it 0.75.

Therefore, the fraction [tex]\frac{3}{4}[/tex] as a percentage is %75, and as a decimal it is 0.75.

Answer:

the scale factor that Samir used in his drawing is 5/1.

Step-by-step explanation:

Here's a step by step explanation of how to find the scale factor of a drawing:

Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.

Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.

Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.

The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.

So, the scale factor that Samir used in his drawing is 5/1.

Answer:

To make x the subject of the formula, we can isolate x by subtracting 1 from both sides of the equation:

x + 1 = 4y

x + 1 - 1 = 4y - 1

x = 4y - 1

So x is equal to 4y minus 1.

Answer:

[tex]x = 4y - 1[/tex]

Step-by-step explanation:

Currently x is on the left side of the equal sign and is being added to 1. x has to be isolated and be by itself on one side of the equal sign in order to be made the subject of the formula. Therefore the 1 needs to be moved to the other side of the equal sign:

             [tex]x = 4y - 1[/tex]

The tape diagram helped to understand by that we can subtract the combined $25 at the concession stand from the total and divide it by 5.

A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication. It is also known as a divided bar model, fraction strip, length model or strip diagram.

Given that, a family of 5 went to a matinee movie on a Saturday afternoon. The movie tickets for the matinee were a special price for each person. The family spent a combined $25 at the concession stand on drinks and popcorn. Altogether, the family spent $57.50 at the movies.

By using the tape diagram we get an equation,

5x+25 = 57.50

5x = 32.5

x = 6.5

Therefore, the special price for each person was $6.5

The figure is attached

Hence, the tape diagram helped to understand by that we can subtract the combined $25 at the concession stand from the total and divide it by 5.

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Answer:

14v-2

Step-by-step explanation:

1. distribute

2. combine like terms

see photo for more information

Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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Their ages are 5 years, 25 years

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let L and Y represent the age of the older person and younger person respectively.

Using the given information, we can write:

L = 4Y + 5 --- (1)

L + Y = 30 --- (2)

From (2):

L = 30 - Y --- (3)

Put (3) in (1):

L = 4Y + 5

30 - Y = 4Y + 5

4Y + Y = 30 - 5

5Y = 25

Y = 25/5

Y = 5 years

Put Y = 5 into (3):

L = 30 - Y

L = 30 - 5

L = 25 years

Their ages are 5 years, 25 years

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Answer:

Step-by-step explanation:

its Reduced to 2 / 5, which is 40 percent. Maria has 40 percent of her work completed

The amount of natural oil needed to make 869 liters of Petrolyn oil is given as follows:

1520.75 liters.

The necessary amount of natural oil is obtained applying the proportions in the context of this problem.

Considering the ratio given in the problem, a rule of three is established, as follows:

7 liters of natural oil - 4 liters of Petrolyn oil.

n liters of natural oil - 869 liters of Petrolyn oil.

Applying cross multiplication, the desired amount is obtained as follows:

4n = 7 x 869

n = 7 x 869/4

n = 1520.75 liters.

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