Solve the systems by graphing.
y = -2x - 8
X-Y = 5

Answer:

(x - 4)(x - 7)

Step-by-step explanation:

x² - 11x + 28

consider the factors of the constant term (+ 28) which sum to give the coefficient of the x- term (- 11)

the factors are - 4 and - 7 , since

- 4 × - 7 = + 28 and - 4 - 7 = - 11

then

x² - 11x + 28 = (x - 4)(x - 7) ← factored form

The coordinate of the complex numbers are plotted on a graph below

i) Z₁ + Z₂ = (2+j4) + (3-j) = (2+3) + (j4-j) = 5 + j3

ii) Z₁ - Z₂ = (2+j4) - (3-j) = (2-3) + (j4+j) = -1 + j5

iii) Z₂ - Z₁ = (3-j) - (2+j4) = (3-2) + (-j-4j) = 1 - j5

iv) To represent these complex numbers on an Argand diagram, we plot the real part on the x-axis and the imaginary part on the y-axis.

Z₁ = 2 + j4 can be represented as a point in the complex plane with coordinates (2,4).

Z₂ = 3 - j can be represented as a point in the complex plane with coordinates (3,-1).

Using these coordinates, we can plot the results from parts (i) to (iii) as follows:

(i) Z₁ + Z₂ = 5 + j3 can be represented as a point in the complex plane with coordinates (5,3).

(ii) Z₁ - Z₂ = -1 + j5 can be represented as a point in the complex plane with coordinates (-1,5).

(iii) Z₂ - Z₁ = 1 - j5 can be represented as a point in the complex plane with coordinates (1,-5).

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Answer:

4550

Step-by-step explanation:

Answer:

4,550

Step-by-step explanation:

4,550 x 2% = 91

In Converse: a positive integer is a prime if it has no divisors besides 1 and itself. A positive integer has other divisors besides 1 and itself if it is not a prime; this is Contrapositive. Inverse: A positive integer is not a prime if it has divisors other than 1 and itself.

The conditional statement reads, "A positive integer is a prime only if it has no divisors other than 1 and itself."

In converse: "a positive integer is a prime if it has no divisors other than 1 and itself." This is not always the case, however, as some composite numbers, like 15, have only themselves and the number one as divisors.

Contrapositive: "If a positive integer is not a prime, then it has divisors other than 1 and itself," is the contrapositive. This is true because a prime number cannot have any divisors than itself and the number 1, which means that any number that is not a prime must have other divisors.

Inverse: "A positive integer has divisors other than 1 and itself is not a prime." This is also true since a prime number is defined as having no divisors besides itself and 1. Hence, any number with divisors other than 1 and itself cannot be a prime number.

The converse, contrapositive, and inverse of a conditional statement are typically not logically identical to the original statement and may or may not be true.

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Answer:

Change 6 1/3 into a mixed number so 19/3 then multiply 19 * 4 then divide by 4. So C

Step-by-step explanation:

The relationship between the lines are they have same slope and they are parallel.

What is slope?

If [tex](x_1,y_1) \: and \: (x_2,y_2) [/tex] are two points on line then slope of the line will be [tex]m= \frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

To determine the relationship between the two lines, we need to find out if they are parallel, perpendicular, or neither.

First, we can find the slope of the line passing through (7,1) and (10,5) using the slope formula:

[tex]m_1 = \frac{(y_2 - y_1)}{(x_2 - x_1)} \\ m_1 = \frac{ (5 - 1)}{(10 - 7)} \\ m_1 = \frac{4}{3} [/tex]

Similarly, we can find the slope of the line passing through (-8,5) and (-5,9):

[tex]m_2 = \frac{ (y_2 - y_1) }{ (x_2 - x_1)} \\ m_2 = \frac{(9 - 5) }{(-5 - (-8))} \\ m_2 = \frac{4}{3} [/tex]

Since both lines have the same slope of 4/3, they are parallel to each other.

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There were 21 quarters, 26 dimes, and 10 nickels in the piggy bank.

Quarters are a type of coin used as currency in many countries, including the United States, Canada, and Mexico. In the United States, quarters are worth 25 cents each and have a diameter of 0.955 inches (24.26 mm). Quarters feature the image of George Washington, the first president of the United States, on the obverse (front) side, and an eagle on the reverse (back) side.

Let's use variables to represent the number of each type of coin. Let:

q be the number of quarters

d be the number of dimes

n be the number of nickels

From the problem statement, we have the following information:

The total value of the coins is $8.50, so we can write:

0.25q + 0.10d + 0.05n = 8.50

There were twice as many quarters as nickels, so:

q = 2n

There were 5 less quarters than dimes, so:

q = d - 5

We can use the third equation to substitute for q in the first two equations:

2n = d - 5

n = (d - 5)/2

q = d - 5

Now we can substitute these expressions for n and q in the first equation:

0.25(d-5) + 0.10d + 0.05((d-5)/2) = 8.50

Simplifying and solving for d:

0.25d - 1.25 + 0.10d + 0.025d - 0.125 = 8.50

0.375d = 9.875

d = 26.333...

Since we can't have a fraction of a coin, we need to round this to the nearest whole number. We also know that q = d - 5 and n = (d-5)/2, so:

d = 26

q = 21

n = 10

Therefore, there were 21 quarters, 26 dimes, and 10 nickels in the piggy bank.

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Answer:

4000/3 * π

Step-by-step explanation:

The formula for the volume of a sphere is;

V = (4/3) * π * r^3

Where;

r = the radius of the sphere

Substituting the given value, we get;

r = 10

V = (4/3) * π * (10)^3

= (4/3) * π * 1000

= 4000/3 * π

Therefore the volume of the sphere is (4000/3)π cubic units.

Suzie must pay $27,864 on delivery for the new truck. To determine how much Suzie must pay on delivery, we need to add the extra charges to the base price of the truck and subtract the down payment she already made.

Let's first list the extra charges:

Freight and PDI: $1,650

Air Tax: $100

Tire Tax: $20

GST (Goods and Services Tax): 5%

To calculate the extra charges, we can use the following formula:

Extra charges = Freight and PDI + Air Tax + Tire Tax + (GST x Base Price)

Substituting the given values, we get:

Extra charges = 1650 + 100 + 20 + (0.05 x 27280)

Extra charges = 1650 + 100 + 20 + 1364

Extra charges = 3134

Therefore, the total cost of the truck, including extra charges, is:

Total cost = Base price + Extra charges - Down payment

Total cost = 27280 + 3134 - 2450

Total cost = 27864

Thus, Suzie must pay $27,864 on delivery for the new truck.

It's important to note that the amount Suzie will actually pay will depend on the financing and payment options available to her. She may be able to spread out the payments over a longer period of time or negotiate a different down payment amount. It's always a good idea to research and compare different financing options before making a major purchase like a new vehicle.

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Answer:

Step-by-step explanation:

99+988

Answer:

Step-by-step explanation:

Answer:

the first car drove 30 miles and the second drove 35

Step-by-step explanation:

1. add how many mile they can travel together.

15+20=35

2. subtract 35 from 65 and whats left is how youll determine which car drove how many the lower number goes to the lower miled vehicle.

A circle graph would be best to display the data.

A circle graph, also known as a pie chart, is useful for displaying categorical data where the parts represent a percentage of a whole. In this case, the whole is the total number of purchases, which is 125. The different types of items purchased can be represented as sections of a circle, with the size of each section proportional to the percentage of purchases that fall into that category. A circle graph would allow the viewer to easily see the relative frequency of each category in the data set.

Box plots, scatter plots, and histograms are all graphical representations that are better suited for displaying continuous data, rather than categorical data.

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According to given graph, the equation of the blue graph is [tex]G(x)=(x+3)^3[/tex].

What is graph?

Graph is a mathematical and computer science concept that consists of nodes or vertices, connected by edges to represent the relationships between objects.

Let's plug in x = -3 into both options and see which one gives the y-value of the blue graph at x = -3:

For g(x) = [tex](x+3)^3[/tex], when x = -3, we have g(-3) = ( -3 + 3 )^3 = 0.

For g(x) = [tex](x-3)^3[/tex], when x = -3, we have g(-3) = ( -3 - 3 )^3 = (-6)^3 = -216.

Since the blue graph passes through (-3,0), the correct option is g(x) = [tex](x+3)^3[/tex].

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-3 ≤ x ≤ 5 and -4 ≤ y ≤ 2. gives the correct range for the graph.

The correct range for the graph can be determined by looking at the minimum and maximum values of the x and y coordinates of all the points on the graph.

For the given coordinate plane with two line segments, the x-coordinates range from -3 to 5, which means -3 ≤ x ≤ 5. The y-coordinates range from 1 to 2 (on the first segment) and from -4 to 1 (on the second segment), which means -4 ≤ y ≤ 2.

Therefore, the correct range for the graph is -3 ≤ x ≤ 5 and -4 ≤ y ≤ 2.

So, the answer is -3 ≤ x ≤ 5 and -4 ≤ y ≤ 2.

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The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

A rectangular is a four-sided polygon in geometry with opposite sides that are parallel and of equal length. It contains four diagonals that cross one another at 90 degree angles. A rectangle is also a rhombus, a rectangle with all sides of equal length, and a parallelogram, a trapezoid with the opposite sides parallel. In the formula A = l w, where l stands for length and w for width, the area of such a rectangle is determined. P = 2l + 2w is a formula that yields the perimeter. In the fields of engineering, design, and architecture, rectangles are used frequently.

given

The Pythagorean theorem can be used to determine the base of the smaller triangle, which equals the pyramid's slant height.

Slant height is equal to (12.5 + 12.9) in (rounded to one decimal place)

Hence, the smaller triangle's area is:

A(small triangular) = 1/2 x 17.8 in, 17.8 in, and 12.9 in, or 115.1 in2.

By summing the areas of all the pyramid's faces, we can determine the overall surface area of the structure:

A (base) + 2 x A (big triangle) + A Equals total surface area (small triangle)

Surface area total = 238 in2 + 2 x 84 in2 + 115.1 in2

Surface area total = 622.1 in2 (rounded to one decimal place)

The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

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Answer: Not true

Step-by-step explanation:

This isn't true.

There is no way to manipulate the number 20 to get the number 5908 by subtraction or any other arithmetic operation.

Therefore, "20-4=5908" is false.

Answer:

[tex]2 {x}^{2} + 10x - 48[/tex]

[tex]2( {x}^{2} + 5x - 24)[/tex]

[tex]2(x + 8)(x - 3)[/tex]

So C is correct.

The final answer for linearizing the function f(x) = cos^5(x) around a = 0 is:

f(x) ≈ 1.

Linearizing a function is the process of approximating the behavior of a function by a linear function (i.e., a function of the form y = mx + b) in a certain region around a specific point.

Linearization is useful because linear functions are easy to work with mathematically, and they can provide a good approximation of the original function near the point of interest. By linearizing a function, we can simplify calculations and make predictions about the behavior of the function in the vicinity of the point of interest.

In the given question,

To linearize the function f(x) = cos^5(x) around a point a, we can use the first two terms of the Taylor series expansion:

f(x) ≈ f(a) + f'(a)(x - a)

where f'(a) is the first derivative of f evaluated at x = a.

In this case, we want to linearize around a = 0, so we have:

f(x) ≈ f(0) + f'(0)(x - 0)

To find f(0) and f'(0), we need to evaluate the function and its derivative at x = 0:

f(x) = cos^5(x)

f(0) = cos^5(0) = 1

f'(x) = 5cos^4(x)(-sin(x))

f'(0) = 5cos^4(0)(-sin(0)) = 0

Therefore, the linearization of f(x) = cos^5(x) around a = 0 is:

f(x) ≈ 1 + 0(x - 0) = 1

So the linearization is simply the constant function f(x) = 1. This means that for small values of x, the function cos^5(x) can be approximated by the constant function 1. The accuracy of this approximation depends on how small x is and how far away x is from 0.

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What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.

How do I find the volume of a rectangular prism?

The rectangular prism volume formula is:

volume = h × w × l,

where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:

Find the box length. For example, it can be equal to 18 in.

Determine its width. Let's say you measured 12 in.

Find out the rectangular prism height. Assume it's 15 in.

Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².

Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To determine the diagonal of a rectangular prism, apply the formula:

diagonal = √(l² + h² + w²)

where h is prism height, w is its width, and l is its length.

Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.

The probability is [tex]0.0922 approx[/tex] [tex]9.22%[/tex]%

Probability theory is an area of mathematics that determines the likelihood that an event will occur or a claim will be true.

The probability of an event is a number between[tex]0[/tex] and [tex]1[/tex], where [tex]0[/tex] is the likelihood of the event occurring and [tex]1[/tex] is the chance that it will happen.

The probability that a certain event will occur is simply represented numerically as a probability.

The percentages [tex]0%[/tex]% to [tex]100%[/tex]% or even[tex]0[/tex] to[tex]1[/tex] can be used to express probabilities.

The probability of occurrence in an entire set of equally likely possibilities that results in a particular event divided by the number of outcomes.

We need to know the standard deviation of the sampling distribution of the mean in order to calculate the likelihood that the sample mean will be within one week of the population mean.

The standard error of the mean can be calculated as follows if the population standard deviation is known:

These steps are used to compute standard error: sample size squared / standard deviation of the population

If the sample standard deviation is unavailable, we can estimate the population standard deviation and compute the standard error of the mean as follows:

These steps are used to compute standard error: sample size squared / standard deviation of the population

If we assume that the population's standard deviation is [tex]1[/tex], we can use the standard error of both the mean formula to determine

The probability  that a simple random sample of [tex]55[/tex] unemployed people will somehow generate a sample mean that is within one week of the population average. In this context, "within one week" means within one standard error of something like the population mean, or one.

The standard error of the mean for a sample size of [tex]55[/tex]

Standard error =[tex]\frac{1}{\sqrt{55} }[/tex]

 error                 ≈[tex]0.1348[/tex]

To find the probability that a sample mean is within one standard deviation of the population mean, we can use the standard normal distribution with a mean of [tex]0[/tex] and a standard deviation of [tex]1[/tex].

We want to find the probability that a z-score is between [tex]-1 and 1[/tex], which represents one standard deviation from the mean.

This chance is roughly [tex]0.6827[/tex], as determined by a calculator or a conventional normal distribution table.

In light of this, the probability  that a straightforward random sample of [tex]55[/tex] unemployed people will yield a possession of tiny sums that is close to the population mean in just one week is approximately:

[tex]0.6827*0.1348= 0.0922[/tex](rounded to four decimal places) (rounded to four decimal places)

Therefore , the probability is [tex]0.0922[/tex], or roughly[tex]9.22%[/tex]%.

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The base and height could also be converted to meters to maintain consistency in units, resulting in an area of 0.3 square meters

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To calculate the area of the shaded triangle, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

Given that the base of the triangle is the width of the rectangle, which is 6 cm, and the height is the diagonal line connecting the top corners of the rectangle, which is 10 m, we can now substitute these values into the formula and calculate the area of the shaded triangle.

Converting the height to centimeters for consistency:

Height = 10 m * 100 cm/m = 1000 cm

Plugging in the values:

Area = 1/2 * 6 cm * 1000 cm = 3000 cm²

So, the area of the shaded triangle is 3000 square centimeters. Please note that it's important to use consistent units when performing calculations, so make sure to convert measurements to the same unit if necessary. In this case, we converted the height to centimeters to match the units of the base, which was given in centimeters.

Therefore, the base and height could also be converted to meters to maintain consistency in units, resulting in an area of 0.3 square meters.

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Answer:

C

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

The quotient will have a larger value than the dividend.

Step-by-step explanation:

Example:

15 ÷ [tex]\frac{1}{2}[/tex]

[tex]\frac{5}{\frac{1}{2} }[/tex]

[tex]\frac{\frac{15}{1} }{\frac{1}{2} }[/tex]  x [tex]\frac{\frac{2}{1} }{\frac{2}{1} }[/tex] = [tex]\frac{\frac{30}{1} }{1}[/tex] = 30

Our quotient of 30 has a larger value than the dividend of 15.

Helping in the name of Jesus.

Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:

Italian restaurant:

Donation = $462 + $1 per diner

Donation = $462 + $1x

Mexican restaurant:

Donation = $235 + $2 per diner

Donation = $235 + $2y

Since both restaurants will donate the same total amount, we can set their donations equal to each other:

$462 + $1x = $235 + $2y

Simplifying this equation, we get:

$2y - $1x = $227

We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.

For example, if we try x = 200, then we can solve for y:

$2y - $1(200) = $227

$2y = $427

y = 213.5

Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:

$2y - $1(250) = $227

$2y = $477

y = 238.5

Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:

$2y - $1(300) = $227

$2y = $527

y = 263.5

Still not a whole number, so we try x = 350:

$2y - $1(350) = $227

$2y = $577

y = 288.5

Finally, we get a whole number for y, so we have our solution:

Italian restaurant: x = 350 diners, donation = $812

Mexican restaurant: y = 289 diners, donation = $812

Therefore, 350 diners promised to participate and each restaurant would donate $812.

It appears that the "adjusted balance method" would be best for Judy, as it results in no interest charged for this billing cycle.

What is an interest ?

To calculate the interest charged by each method, we need to determine the average daily balance for the billing cycle, which is calculated as the sum of each day's balance divided by the number of days in the billing cycle.

For the opening balance of $930 that remained for the first 10 days, the average daily balance is:

($930 x 10 days) / 30 days = $310

For the balance of $1480 that remained for the next 10 days, the average daily balance is:

($1480 x 10 days) / 30 days = $493.33

For the balance of $690 that remained for the last 10 days, the average daily balance is:

($690 x 10 days) / 30 days = $230

Part III: Previous balance method

The previous balance method calculates the interest charged on the balance at the end of the previous billing cycle. For Judy's last 30-day billing cycle, the previous balance was $930. Therefore, the interest charged for the previous balance method would be:

$930 x (26%/365) x 30 days = $16.44

Part IV: Adjusted balance method

The adjusted balance method calculates the interest charged on the balance at the end of the billing cycle after subtracting any payments made during the billing cycle. For Judy's last 30-day billing cycle, the adjusted balance would be:

$690 - $790 = -$100

Since Judy made a payment that exceeded her balance, there is no balance on which to charge interest for the adjusted balance method.

Based on these calculations, it appears that the adjusted balance method would be best for Judy, as it results in no interest charged for this billing cycle.

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We can conclude after answering the presented question that As a probability result, the likelihood of discovering a package that deviates from the target weight by more than 12 grammes is around 0.4014.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

The mean of the box's overall weight is:

n * mu X = mu Y

With a mean weight of 500/n grammes for each chocolate, we get:

mu Y =n * (500/n) = 500

The standard deviation of the box's total weight is:

sqrt(n) * sigma X = sigma Y

When we substitute the provided values, we get:

= 2 * P(Z > 0.8485)

= 2 * (1 - P(Z < 0.8485))

= 2 * (1 - 0.7993) (1 - 0.7993)

= 0.4014 (rounded to four decimal places) (rounded to four decimal places)

As a result, the likelihood of discovering a package that deviates from the target weight by more than 12 grammes is around 0.4014.

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The "Angle-Angle (AA) Similarity Theorem" should be used as the justification in #6 based on the assertions made in the proof.

According to the Angle-Angle-Angle (AAA) criterion, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are similar."

The "Angle-Angle (AA) Similarity Theorem" should be used as the justification in #6 based on the assertions made in the proof.

This is due to the proof demonstrating the congruence of two sets of corresponding angles in the triangles ABC and EDC: ACB  DCE and BDE  DBA.

According to the AA Similarity Theorem, two triangles are similar if two sets of corresponding angles in each triangle are congruent.

As a result, the AA Similarity Theorem leads us to the conclusion that ABC equals EDC.

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If good is worth K2 500 cash and it can also be purchased by K200 deposit and monthly instalments of K103.50 for 2 years in hire purchase, the interest charged on hire purchase is K184.

To find the interest charged on the hire purchase, we need to compare the total amount paid through hire purchase to the cash price of the good.

The monthly instalments are K103.50 and the hire purchase term is 2 years, so the total amount paid through hire purchase is:

K103.50/month × 24 months = K2,484

In addition, there is a deposit of K200, so the total amount paid through hire purchase and deposit is:

K2,484 + K200 = K2,684

Since the cash price of the good is K2,500, the interest charged on hire purchase is:

K2,684 - K2,500 = K184

In summary, if someone wants to purchase the good through hire purchase, they need to pay a deposit of K200 and monthly instalments of K103.50 for 2 years. The total amount paid through hire purchase and deposit is K2,684, and the interest charged on hire purchase is K184.

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Answer:

true

Step-by-step explanation: