Write the standard form of the equation of a parabola passing through the point (1, 32) with a minimum point at (-2, 5).

Therefore, the function is not defined on the parabola y - x² = 0.

The function f(x,y) = sin(xy)/y - x² will not be defined for the parabola y - x² = 0.

This is because the denominator will be zero in this case.

We can see this as follows:

f(x,y) = sin(xy)/(y - x²)

Thus, the function will not be defined when the denominator is zero, i.e., y - x² = 0.

We can also see this by looking at the graph of the parabola y = x².

This is a U-shaped curve that opens upwards.

The function will not be defined at any point on this curve since the denominator will be zero everywhere on the curve. This is because the curve is the set of all points where y - x² = 0.

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Answer:

Irrational

Step-by-step explanation:

Answer:

x = -2

y = -4

Step-by-step explanation:

x - 3y = 10 --------------(1)

x + 5y = -22 -----------(2)

Taking Eq. (1)

x - 3y = 10

x = 10 + 3y ------------(3)

10 + 3y + 5y = -22

8y = -22 - 10

8y = -32

y = -32/8

x = 10 + 3(-4)

x = 10 - 12

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

To solve the given system, let's begin by solving for x in x- 3y=10:-

\(\tt x-3y=10\)

Add 3y to both sides:-

\(\tt x-3y+3y=10+3y\)

\(\tt x=10+3y\)

Substitute x= 10+3y into x+5y=-22:-

\(\tt 10+3y+5y=-22\)

Simplify:-

\(\tt 10+8y=-22\)

Now, solve for y in 10+8y=-22:-

\(\tt 10+8y=-22\)

Subtract 10 from both sides:-

\(\tt \tt 10+8y-10=-22-10\)

\(\tt 8y=-32\)

Divide both sides by -8:-

\(\boxed{\bf y=-4}\)

Now, substitute y=-4 into x=10+3y:-

\(\tt x=10+3y\)

\(\tt x=10+3\times-4\)

Simplify:-

\(\boxed{\bf x=-2}\)

Therefore, x=-2 and y=-4

_________________________

Hope this helps! :)

The number of cicadas that will be put into each terraiums will be 72.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Bella is putting 576 cicadas into 8 different terrariums the same number of cicadas will be put into each one.

The number of cicadas will be calculated as follow

Number of the cicadas = 576 / 8

number of the cicadas = 72

Therefore, the number of cicadas that will be put into each terrarium will be 72.

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The X value corresponding to z = -2.00 is 60. The X value corresponding to z = -2.00 is 60. This means that the observation with a z-score of -2.00 is 60 units below the population mean of 80.

To find the X value corresponding to z = -2.00, we can use the formula:
z = (X - µ) / σ
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

The z-score measures the number of standard deviations an observation is from the mean. In this case, the given z-score of -2.00 indicates that the observation is 2 standard deviations below the mean.
To find the corresponding X value, we use the formula:
z = (X - µ) / σ
Where z is the standard normal distribution value, X is the corresponding raw score, µ is the mean of the population, and σ is the standard deviation of the population.
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

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The height of the rectangular prism is 3√2 units.

Given is a rectangular prism.

Using the Pythagoras theorem, we can write -

(√34)² = h² + 4²

h² = 34 - 16

h² = 18

h = √18

h = 3√2 units

Therefore, the height of the rectangular prism is 3√2 units.

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The exact trigonometric function values of

a) cos (π/12) = √(1/2 - 1).

b) cos (3π/8) = √(2(2/4) - 1).

a) cos (π/12):

To find the exact value of cos (π/12), we need to use the properties of trigonometric functions and special angles.

The angle π/12 is not one of the commonly known angles, but we can express it in terms of angles we do know. We can rewrite π/12 as (π/6) / 2, where π/6 is a special angle that we can work with.

The value of cos (π/6) is a well-known value. In a right triangle with an angle of π/6, the adjacent side is half the hypotenuse. Therefore, cos (π/6) = 1/2.

Now, let's halve the angle π/6 again to get π/12. When we halve the angle, we need to use the double-angle formula for cosine, which states that cos (2θ) = 2cos²(θ) - 1.

Let's substitute π/6 for θ in the double-angle formula: cos (2(π/6)) = 2cos²(π/6) - 1.

Simplifying this equation, we have: cos (π/3) = 2(1/2)² - 1.

cos (π/3) simplifies further to: cos (π/3) = 1/2 - 1.

Finally, cos (π/12) can be obtained by taking the square root of the resulting value: cos (π/12) = √(1/2 - 1).

b) cos (3π/8):

To find the exact value of cos (3π/8), we'll follow a similar process as we did for the previous example.

The angle 3π/8 is not a well-known angle, so we'll try to express it in terms of special angles we know.

We can rewrite 3π/8 as (π/8) * 3. The angle π/8 is not a special angle, but we can express it as (π/4) / 2, where π/4 is a well-known angle.

The value of cos (π/4) is √2 / 2. Now, let's halve the angle π/4 to get π/8.

Using the double-angle formula for cosine, we have: cos (2(π/8)) = 2cos²(π/8) - 1.

Substituting π/4 for θ in the double-angle formula, we get: cos (π/4) = 2(cos²(π/4) - 1).

Simplifying this equation, we have: cos (π/2) = 2((√2 / 2)²) - 1.

cos (π/2) simplifies further to: cos (π/2) = 2(2/4) - 1.

Finally, cos (3π/8) can be obtained by taking the square root of the resulting value: cos (3π/8) = √(2(2/4) - 1).

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There is a proportional relationship between two quantities which are 950 and 4,845 as 950*5.1 = 4,845.

If all of the ratios of the variables are equal, then there is a proportional link between the two variables.

In proportional relationships, one variable is, in other words, always a constant value multiplied by the other variable.

The proportionality constant is the name given to the constant value.

So, find the proportional relationship as follows:

950 * 3 = 2,850

The given number is 2852.

NO proportional relationship.

950 * 5.1 = 4,845

The given number is 4,845.

It is a proportional relationship.

Therefore, there is a proportional relationship between two quantities which are 950 and 4,845 as 950*5.1 = 4,845.

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Answer is 5/4The slope is the number next to the “x” in the y intercept formula

y= m (slope) x + b

Answer: m= 5/4

Step-by-step explanation:

La ecuación general de la recta es y=mx+by=mx+b, donde m es la pendiente y b es la intersección en y

y=mx+by=mx+b

Since there are 16 ounces in a pound, we multiply 2 pounds by 16 to get ounces: 2 pounds equals 32 ounces (2 x 16 ounces). This is our last response because the number is already expressed in its most basic form: 38/1

Since there are 16 ounces in a pound, we multiply 2 pounds by 16 to get ounces:

2 pounds equals 32 ounces (2 x 16 ounces).

We thus have:

32 ounces in 2 pounds

The additional 6 ounces give us:

32 ounces plus 6 ounces plus 2 pounds equals 38 ounces.

The simplest way to write 38 ounces as a fraction is as follows:

38/1

This is our last response because the number is already expressed in its most basic form:

38/1

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The length and height of the box with a volume of 70 cubic feet to reduce construction costs is 8.572 and 3.81.

Given that,

The base of an open box must be built with the length of the base being four times more than the width of the base. If building the base costs two dollars per square foot and building the four sides costs one dollar per square foot.

We have to identify the dimensions of a box with a volume of 70 cubic feet to reduce construction costs.

We know that,

The volume =70 cubic feet

L=4w    ------>equation(1)

Volume= l×w×h

70=4w×w×h

h=70/4w²     ------>equation(2)

The construction cost is

C= 4(lw)+2(wh)+2(hl)

C=4(4w×w)+2(w×70/4w²)+2(4w×70/4w²)

C=4(4w²)+2(70/4w)+2(70/w)

C=16w²+70/2w+140/w

Now,

To determine the minimum cost,

dC/dw

16w-70/4w²-140/w²=0

16w³=1/w²(70/4+140)

16w³=1/w²(315/2)

16w³=315/2

w³=315/32

w=2.143

From equation(1)

L=4w=4×2.143=8.572

H=70/4w²=70/4(2.143)²=3.81

Therefore, The length and height of the box with a volume of 70 cubic feet to reduce construction costs is 8.572 and 3.81.

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Asample of n = 25 scores from the same population would have a standard error of 6.

The standard error of the mean is given by the formula:

SE = s / sqrt(n)

where s is the standard deviation of the population and n is the sample size.

In this case, we are given that for a sample of n = 9, the standard error is 10. So we can write:

10 = s / sqrt(9)

Simplifying, we get:

s = 30

Now we can use the same formula to find the standard error for a sample of n = 25:

SE = s / sqrt(n) = 30 / sqrt(25) = 6

Therefore, a sample of n = 25 scores from the same population would have a standard error of 6.

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Answer:

Carl is correct. So the 2nd option

Step-by-step explanation:

A rectangle- a quadrilateral

it also had 4 sides and vertices.

I hope this Helps!

Using the concept of subject of formula, the only correct steps are:

bx + bc = d

x + c = d/b

The given Algebraic expression is given as:

b(x + c) = d

Using distributive property on the bracket, we can have that:

bx + bc = d   ------(1)

Divide through by b to get:

x + c = d/b

Use subtraction property of equality to subtract c from both sides to get:

x = (d/b) - c

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Answer:

(v - 6)(-5v + 1)

Step-by-step explanation:

\( - 5 {v}^{2} + 31v - 6\)

\( - 5 {v}^{2} + 30v +v - 6\)

\( - 5v(v - 6) +(v - 6)\)

\( (v - 6)( - 5v + 1)\)

Therefore , the solution to the given problem of probability comes out to be P =0.6.

Probability theory, a subfield of mathematics, calculates the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where 1 denotes certainty and around 0 denotes how probable the event is to occur. A likelihood is a numerical representation of the likelihood that a particular event will occur. Probabilities may alternatively be stated as percentages with a range of 0% to 100% or as a number between 0 and 1. the percentage of events over a wide range of comparably likely outcomes that happen in comparison to all other conceivable outcomes.

Here,

Given :

Twelve 16 GB and 18 32 GB pen drives are packaged together in a box.

To find the probability of 16gb pen drive is defective:

Thus,

Total pendrive = 30

Event = 16gb pen drive or defective:

The probability of it is 16gb pendrive = 12/30 = 0.4

The probability of it is defective pendrive = 6/30 = 0.2

thus,

total probability (16gb pen drive or defective) = 0.4 +0.2 =0.6

Therefore , the solution to the given problem of probability comes out to be P =0.6.

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the equation of the line is y = 3x - 5

Answer:

WOOF WOOF

Step-by-step explanation:

i love getting extra points :)

Answer:

Q' would be (5, 6)

Answer:

-51 months

Step-by-step explanation:

To solve, we can use the second model since we're told the money is compounded monthly

\(A=P(1+r/n)^n^t\\\\1000=4000(1+0.027/12)^1^2^t\\\\1/4=(4009/4000)^1^2^t\\\\log(1/4)=log(4009/4000)^1^2^t\\\\log(1/4)=12t*log(4009/4000)\\\\log(1/4)/log(4009/4000)=12t\\\\1/12*(log(1/4)/log(4009/4000))=t\\\\-51.40197623=t\\-51=t\)

To solve this problem, we'll use the formula A=P(1+r/n)^nt, where A is the future value, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

In this case, we know that P=$4000, r=2.7%, and n=12 (since interest is compounded monthly). We're trying to find the time required for the account to earn $1000, so A=P+$1000=$5000.

Plugging these values into the formula, we get:

$5000=$4000(1+0.027/12)^(12t)

Simplifying, we can divide both sides by $4000 and take the natural logarithm of both sides:

ln(1.25)=ln(1+0.027/12)^(12t)

Using the properties of logarithms, we can bring the exponent down:

ln(1.25)=12t*ln(1+0.027/12)

Dividing both sides by 12ln(1+0.027/12), we get:

t=ln(1.25)/(12ln(1+0.027/12))

Using a calculator, we find that t is approximately 3.5 years. Rounded to the nearest month, this is 42 months.

Therefore, it would take approximately 42 months (or 3 years and 6 months) for the account to earn $1000 with an initial investment of $4000 at an interest rate of 2.7% compounded monthly.

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The least change in temperature is in the eastern region.

What is meant by the temperature of a place?

The physical concept of temperature indicates in the numerical form how hot or cold something is. A thermometer is used to determine temperature. It denotes the direction of the spontaneous movement of heat energy, i.e., from a hotter body (one with a higher temperature) to a colder body (one at a lower temperature).

Thermometers are calibrated according to different temperature scales that used different reference points and thermometric substances as definitions. The Celsius scale, denoted by the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale are the most popular scales (K).

To find the change in temperature we can use the following formula:

Temperature change = Final temperature - Initial temperature

                                    = Maximum temperature - Minimum temperature

Using the above relation, we can find the change in temperature in each region.

North

Temperature change = 10 °F - (-8°F) = 18°F

South

Temperature change = 2 °F - (-3°F) = 5°F

East

Temperature change = 0 °F - (-2°F) = 2°F

West

Temperature change = 3 °F - (-4°F) = 7°F

Hence from the above calculations, it is clear that the least change in temperature is in the eastern region.

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The area of the sign is 35 square feet. The solution has been obtained by using the area of the trapezoid.

The entire area occupied by the sides of a trapezoid is its area. A trapezoid's area is determined by how many unit squares fit inside of it.

We know that area of the trapezoid is

Area (A) = (a + b ) * h/ 2

Now, here we are given the following:

a = 8

b = 6

h = 5

Now, on substituting these values in the formula, we get

⇒A = (8 + 6 ) * 5 / 2

⇒A = (14 * 5) / 2

⇒A = 70 / 2

⇒A = 35 square feet

Hence, the area of the sign is 35 square feet.

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Answer:

4,950

Step-by-step explanation:

4,500*.10=450

4,500+450=4,950

Hope this helps:)

Answer:    72

Step-by-step explanation: just ask safary, 80% of 90 to get 72

A student must answer 72 questions correctly out of the 90 questions on the test to achieve an 80% accuracy rate and pass the test.

To pass the test with an 80% score, a student must answer 72 questions correctly out of the total 90 questions. This can be calculated by first finding out what 80% of 90 is, which can be done by multiplying 0.8 (the decimal form of 80%) by 90:

0.8 x 90 = 72

Therefore, a student needs to answer at least 72 questions correctly to pass the test with an 80% score.

To determine the number of questions a student must answer correctly to pass the test, we will use the given criteria: the student needs to achieve 80% accuracy, and there are 90 questions on the test.

To find the required number of correct answers, we will multiply the total number of questions (90) by the percentage required to pass (80%). The formula for this calculation is:

(Number of correct answers) = (Total questions) × (Percentage required to pass)

In our case, this translates to:

(Number of correct answers) = (90) × (80%)

Converting the percentage to a decimal value by dividing it by 100, we get:

(Number of correct answers) = (90) × (0.8)

Now, we multiply the values:

(Number of correct answers) = 72

Therefore, a student must answer 72 questions correctly out of the 90 questions on the test to achieve an 80% accuracy rate and pass the test.

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Step-by-step explanation:

5x+4<16

or,5x<16-4

or,5x<12

or,x<12÷5

or,x<12/5

or,x<2.4

:.x<2.4

Answer:

hope it helps.

The sum of the given fraction is -1/3

Fractions are expressions written as a ratio of two integers

Given the expression below;

5/6+(-1 1/6)

Convert the mixed fraction into improper fraction

5/6+(- 7/6)

Expand

5/6 - 7/6

Subtract

-2/6

-1/3

Hence the sum of the given fraction is -1/3

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Crime rates in the UCR (Uniform Crime Report) are expressed as the number of reported crimes per 100,000 population.

This allows for a standardized comparison of crime levels across different areas and time periods, taking into account population size. The UCR presents raw figures, crime rates, and changes in both the number and rate of crime over time to provide a comprehensive view of crime trends.

This is calculated by dividing the number of reported crimes by the population of the area and multiplying the result by 100,000. This helps to standardize the data and allows for comparison across different jurisdictions and time periods. Additionally, the UCR also presents changes in crime rates over time, allowing for the identification of trends and patterns in crime.

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To determine the measures of the angles of a polygon are necessary the concepts of algebra by using the formula of the sum of interior angles and creating equations and obtaining the measures of unknown angle.

First, it is important to remember the formula for the sum of interior angles of a polygon, which is (n-2) x 180°, where n is the number of sides of the polygon.

Next, you can use algebra concepts to solve for the unknown angle measures. For example, if you know the sum of the interior angles and the measures of some of the angles, you can create an equation and solve for the unknown angle measures.

Here is an example:
If a quadrilateral has interior angles of 70°, 110°, and 120°, you can use the formula (4-2) x 180° = 360° to find the sum of the interior angles. Then, you can create the equation 70° + 110° + 120° + x = 360° and solve for x to find the measure of the unknown angle.

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Answer:

B. The quilt consisted of 1,008.

Step-by-step explanation:

You take the initial number of squares the quilt had, which was 126. If that number was repeated 8 times for the entire quilt you would have to take 126*8 and the answer would be 1,008.

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