Using the substitution method, find the solution to this system of equations.
-2x+y=4
-2x+2y=7

The solution of the given quadratic equation is [tex]x=-4-\sqrt{5}[/tex], [tex]x=-4+\sqrt{5}[/tex].

To solve the equation, we can start by dividing both sides by -5, which gives:

[tex](x+4)^{2} = 5[/tex]

Next, we can take the square root of both sides, remembering to consider both the positive and negative square roots:

[tex]x+4=[/tex]±[tex]\sqrt{5}[/tex]

[tex]x=-4+\sqrt{5}[/tex]

[tex]x=-4-\sqrt{5}[/tex]

The x values in a quadratic equation that fulfil the equation—that is, that make the equation true—are known as the roots of the equation. In other words, the values of x that cause the quadratic expression to equal zero are the roots of a quadratic equation.

The two alternative values for x provided by the quadratic formula are one with a plus sign and one with a minus sign. The quadratic equation's roots are these two numbers. The quadratic equation has two real roots if the discriminant value inside the square root is positive. The quadratic equation has one real root with a multiplicity of two if the discriminant is zero. If the discriminant is negative, there are two complex roots in the quadratic equation.

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The length of missing side AC ≈ 10.9.

What is length of side?

To find the missing side of the right triangle, we can use the trigonometric ratios, specifically the sine, cosine, and tangent ratios.

Given that B is a right angle, we know that:

sin A = opposite/hypotenuse = BC/AB

cos A = adjacent/hypotenuse = AC/AB

tan A = opposite/adjacent = BC/AC

Substituting the known values, we get:

sin 33° = BC/13

cos 33° = x/13

tan 33° = BC/x

Solving for x, we can use the cosine ratio:

cos 33° = x/13

x = 13 cos 33°

x ≈ 10.88

Therefore, the missing side AC ≈ 10.9.

What is hypotenuse?

In a right triangle, the hypotenuse is the longest side and the side that is opposite the right angle. It is also the side that connects the two legs of the right triangle. The hypotenuse is always opposite the right angle and is also the side that has the largest length compared to the other two sides (the legs) of the triangle.

The hypotenuse plays a crucial role in the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. The Pythagorean theorem is expressed mathematically as: a² + b² = c²

where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.

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Let's think of this number as T|U where T is the tens position digit and U is the units position digit.

Original number has value 10T+U.  U=3T (first sentence).

Second sentence deals with U|T, which has value ('new number') 10U+T.

Half the new number is 21 < twice the original means:

 ½(10U+T) = 2(10T+U) - 21

There you have a system of two equations in two unknowns.  You may now solve it.

Check the answers for reasonableness and correctness. (Also check my work producing the last equation)

Note I have used the vertical separation symbol "|" to segregate the two digits of a 2-digit number.

Answer:

x = 15°

Step-by-step explanation:

We Know

(2x + 45) + x = 90°

Let's solve

2x + 45 + x = 90°

3x + 45 = 90°

3x = 45°

x = 15°

Answer: 13/100

Step-by-step explanation:

As per the given data, Mark is buying different nuts to make a mixed nut platter to serve at a party. the total weight in grams of the nuts Mark purchased is 4000.

He buys 1.5 kilograms of peanuts, 500 grams of almonds and 200 dekagrams of cashews. We need to calculate the total weight in grams of the nuts he purchased.Calculation:Total weight in grams of peanuts = 1.5 × 1000 = 1500 grams. Total weight in grams of almonds = 500 grams. Total weight in grams of cashews = 200 × 10 = 2000 grams. . Adding all the weights: Total weight = 1500 + 500 + 2000 = 4000. Therefore, the total weight in grams of the nuts Mark purchased is 4000. The gross weight is the total weight of the goods carried, including all packaging but excluding the tare weight of the transport unit. The tare weight is the weight of a transport unit before any cargo is loaded.

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Answer:

20

Step-by-step explanation:

So there is a total of 1/5 chance of getting an answer right, because there are 5 possibilities and only 1 is correct.

Now because there are 100 Questions, we will multiply our probability with the total value (in this case its a 100).

So 1/5 = .2

.2 × 100 = 20

The standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.

The standard deviation of the number of questions answered correctly in a multiple-choice test of 100 questions with 5 possible answers for each question, assuming random selection of one answer per question, can be calculated using the formula for the binomial distribution, which is the square root of n times p times q, where n is the total number of trials, p is the probability of success on each trial, and q is the probability of failure on each trial.

Using the formula for the binomial distribution, the standard deviation of the number of questions answered correctly can be calculated as follows:

n = 100 (total number of trials)

p = 1/5 (probability of success on each trial, i.e., selecting the correct answer)

q = 4/5 (probability of failure on each trial, i.e., selecting one of the incorrect answers)

Therefore, the standard deviation is:

√(100 x 1/5 x 4/5) = √16 = 4

Therefore, the standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.

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The nearest whole number, we get that we can expect about 419 students on campus to prefer Movie B.

How to calculate addition?

Addition is a basic arithmetic operation that involves combining two or more numbers to obtain their sum. Here's how to calculate addition:

Write the numbers to be added one below the other, aligning the digits according to their place value (ones below ones, tens below tens, and so on).

Start by adding the digits in the ones column (the rightmost column). If the sum is less than 10, write it down below the line. If the sum is 10 or greater, carry the 1 to the next column (the tens column).

Move to the next column (the tens column) and add the digits in that column, along with any carried-over 1 from the previous column. Again, if the sum is less than 10, write it down below the line. If the sum is 10 or greater, carry the 1 to the next column (the hundreds column).

Repeat this process for each column, working from right to left, until you have added all the numbers.

The final result is the sum of the numbers.

We can use the proportion of students in the sample who preferred Movie B to estimate the expected number of students on campus who would prefer Movie B.

The proportion of students in the sample who preferred Movie B is:

Proportion of students who prefer Movie B in the sample = Number of students who prefer Movie B in the sample / Sample size

= 66 / (39 + 66 + 2 + 25)

= 0.524

So, we can expect that approximately 0.524 * 800 = 419.2 students on campus would prefer Movie B.

Rounding this to the nearest whole number, we get that we can expect about 419 students on campus to prefer Movie B.

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according to the question, the selling price of each book is $13.18.

When the quantity supplied and wanted are equal, prices are in equilibrium. The quantity provided and demanded are equal at the price of equilibrium.

Let's denote the selling price of each book as "x". The markup for each book is 56% of its selling price, so the profit that Binder's Bookstore makes on each book is:

0.56x

If we add this profit to the cost of the book, we get the selling price:

x = 5.80 + 0.56x

Solving for x, we can simplify as follows:

0.44x = 5.80

x = 13.18

Therefore, the selling price of each book is $13.18.

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The equation that can be used to determine the charge for a computer repair for any possible number of hours is y = 25x + 5, where x is the number of hours and y is the charge in dollars for a computer repair of x hours.

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Answer:  [tex]\textsf{Option B, 44}[/tex]

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Given:  [tex]\textsf{Perimeter of the rectangle is 110. Width is 4 times the length}[/tex]

Find: [tex]\textsf{The width}[/tex]

Solution:  So, we are given two different statements in the problem.  The first one states that the perimeter of the given rectangle is 110.  We know that the perimeter formula is equal to 2(length + width).  Since we know that the perimeter is equal to 110 that means that we can set the perimeter formula equal to 110.  

Therefore, the first equation would be [tex]\textsf{2(length + width) = 110}[/tex].

The second statement states that the width is 4 times the length.  Using simple algebra we can make an equation which states that the width on one side is equal to the length multiplied by 4 on the other side.

Therefore, the second equation would be [tex]\textsf{width = 4 * length}[/tex].

Now that we have created two equations these two would be considered as a system of equations.  We can now plug in the second formula into the first one and solve for the length.

Now that we have the length, we can plug the length into the second formula and solve for the width.

In conclusion, after creating two equations and forming them into a system of equations we were able to solve for the width and determine that the value of it is 44.  Therefore, the option that matches our answer would be [tex]\textsf{Option B, 44}[/tex].

The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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Answer: 125

Step-by-step explanation:

Answer:

diameter = 2× radius

circumference = [tex]2\pi r[/tex]

Area = [tex]\pi r^{2}[/tex]

use this formulas and put the given values and you will get the answers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Malia determined that "x" is equal to LIT * 3 as a result as by the left side of the equation .

A mathematical assertion that two expressions are equal is known as an equation. The leading edge (LHS) and the right hand side (RHS), which are normally two independent portions, are denoted by the equals sign (=). Depending on the equation, the values on either side of the equals sign are all either equal or not. In a variety of disciplines, including science, law, finance, and economics, equations can be used to represent real-world events and address issues.

given

First, let's make the left side of the equation easier to understand:

LIT / 7 = x / (3 * 7)

LIT / 7 = x / 21

We can now cross-multiply to obtain:

LIT * 21 = 7 * x

Streamlining the left side:

LIT * 3 * 7 = 7 * x

LIT * 3 = x

Malia determined that "x" is equal to LIT * 3 as a result as by the left side of the equation .

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Answer:

Step-by-step explanation:

As a result, x²-18x+81 is a perfect square trinomial and can be represented as (x-9)².

Perfect square trinomials are illustrated by the following:

x²+6x+9

=(x+3)²

x²-10x+25

=(x-5)²

4x²+12x+9

=(2x+3)²

a²+2ab+b²=(a+b)²

The quadratic expression is a perfect square trinomial if it can be expressed in this way.

As an illustration,

let's determine whether x²-18x+81 is a perfect square trinomial:

The square of x is the first term, x².

The square of 9 is the final term (81).

Its result 2(x)(-9)=-18x is

twice as long as the middle term.

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A function that describes the number of pythons now living in the park in the 11th year would be P(11) = 2(1 + 0.0063)^11.

To describe the number of pythons in the swamp, we can use the exponential growth function:

P(t) = P₀(1 + r)^t

Given that the number of pythons increases by 1.9% every three years, we first need to find the annual growth rate:

1.9% every three years = (1.9 / 3) % per year = 0.63% per year

One mating pair of pythons was released in 2010, so the initial number of pythons is 2:

P₀ = 2

We want to find the number of pythons in the 11th year, so we need to find P(11):

P(t) = P₀(1 + r)^t

P(11) = 2(1 + 0.0063)^11

The function that describes the number of pythons living in the park in the 11th year is:

P(11) = 2(1 + 0.0063)^11

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Step-by-step explanation:

different to the suggested graphic representation, which goes wild with several complex sub-figures, I see simply a rectangle (2×9 × 4) at the bottom and a triangle standing on top of it (2×(9-6) × (16-4)).

the area of the rectangle is

2×9 × 4 = 18×4 = 72 ft²

the area of the triangle (remember : baseline × height / 2) is

2×(9-6) × (16-4) / 2 = 2×3 × 12 / 2 = 3×12 = 36 ft²

the total area is then

72 + 36 = 108 ft²

The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

To calculate the mean value, we add up all the values and divide by the

number of values:

(990 + 1030 + 950 + 1050 + 1000 + 980) / 6 = 1000

So the mean value is 1000 rpm.

To calculate the standard deviation, we need to first calculate the

variance:

Variance =[tex][(990 - 1000)^2 + (1030 - 1000)^2 + (950 - 1000)^2 + (1050 - 1000)^2 + (1000 - 1000)^2 + (980 - 1000)^2] / 6[/tex]

Variance = 12000 / 6 = 2000

So the variance is [tex]2000 (rpm)^2[/tex].

The standard deviation is the square root of the variance:

Standard deviation = √(2000) = 44.7 rpm

The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

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Leah and Josh should expect to pay approximately $1,204.31 in prepaid interest at the closing.

What is interest?

Interest is the amount of money that is paid or earned for the use of borrowed or invested funds. When someone borrows money, they typically have to pay back the principal (the amount borrowed) plus interest, which is usually calculated as a percentage of the principal.

To calculate the prepaid interest at closing, we need to first determine the loan amount, which is the purchase price of the home minus the down payment:

Purchase price = $550,000

Down payment = 14% of $550,000 = $77,000

Loan amount = $550,000 - $77,000 = $473,000

Next, we need to calculate the daily interest rate by dividing the APR by 365:

Daily interest rate = 3.70% / 365 = 0.010137%

Finally, we can calculate the prepaid interest by multiplying the loan amount by the daily interest rate and the number of days from the closing date to the end of the month:

Number of days from September 6 to September 30 = 25

Prepaid interest = $473,000 x 0.010137% x 25 = $1,204.31

Therefore, Leah and Josh should expect to pay approximately $1,204.31 in prepaid interest at the closing.

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The value of three times the number plus 17 - that same number is found to be 7.

It is provided that if twice a number is equal to that number minus then we have to find what is three times that number plus 17 minus that number.

Let's say that the number we are talking about his x.

From the given condition we can write at the twice of x will equal to x minus x - 5.

2x = x-5

Solving this simple algebraic equation.

x = -5.

Now, to find the answer,

3x + 17 - x

Putting values,

= 3(-5) + 17 -(-5)

= -15 + 17 + 5

= 7.

So, the value of thrice the number added to number minus from 17 is 7.

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To find the measure of angle B, we can use the inverse tangent function:

tan(B) = opposite / adjacent = a / b

tan(B) = 500 / 300

B = arctan(500 / 300)

B ≈ 59.0 degrees

Therefore, the measure of angle B is approximately 59 degrees (rounded to the nearest degree).

Mr. Olakunle needs to divide the total amount of soil he has by the number of planters he wants to fill, which is 10/8 = 5/4. This can be simplified by dividing both the numerator and denominator by 4, resulting in 5/4 = (5  4) / (4  4) = 5/12.

To find out how much soil Mr. Olakunle will use for each planter, we need to divide the total amount of soil he has by the number of planters he wants to fill.

The total amount of soil he has is 10 bags.

He plans to fill 8 planters with the soil.

Therefore, the amount of soil he will use for each planter is:

10/8 = 5/4

This can be simplified by dividing both the numerator and denominator by 4, to get:

5/4 = (5 ÷ 4) / (4 ÷ 4) = 5/4

So the answer is C) 5/12.

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From the given coordinates geometry function will be y=-3x+1.

Plotting points on a coordinate plane will provide the graph of the function y = -3x + 1. To accomplish this, we can select various x values, enter them into the equation, and then solve for y. As an illustration, if x = 0, then y = -3(0) + 1 = 1. We now get the graph's point (0, 1) thanks to this. Similar to the previous case, if we select x = 1, then y = -3(1) + 1 = -2. This results in the graph's point (1, -2) for us. By repeating this procedure, we can identify more points, which we can then join with a straight line to create the function's graph. A straight line with a slope of -3 and the point appears on the graph as a result (0, 1).

from graph we can write coordinates ,

(-1,4),(0,1),(1,-2),(2,-5)

so from these coordinates ,function will be

y=-3x+1.

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However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem .

To solve this problem, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's first find the measure of angle P:

m∠P + m∠Q + m∠R = 180

Substituting in the given measures:

(x + 13) + (10x + 13) + (2x - 2) = 180

Simplifying and solving for x:

13x + 24 = 180

13x = 156

x = 12

So m∠P = (x + 13) = 25 degrees.

Next, we can use the fact that the angles opposite equal sides in a triangle are congruent. Since we know that PR and QR are equal, we have:

m∠P = m∠R

So m∠R = 25 degrees.

Finally, we can find m∠Q:

m∠Q = m∠P + m∠R - 180

Substituting in the values we found:

m∠Q = 25 + 25 - 180 = -130

However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem.

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Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.

The products of a measurements of the segments of two chords are equal if they overlap in a circle.

For the given arc length  of circle:

Let the intersection of the both chords be 'O'.

m∠KOL = 180 - x  ...eq 1 (linear pair).

By the  intercept chord theorem:

m∠KOL = (arc JM + arcKL)

Put the value of eq 1.

180 - x = 1/2(30 + 2x - 30)

180 - x = 1/2 * 2x

180 = x + x

x = 180/2 = 90

Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.

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If the sample size in part c is larger, then the sample standard deviation will be a better estimate of the population

standard deviation.  If the sample size is smaller, then the sample standard deviation will be less reliable and may not

be a good estimate of the population standard deviation.

To describe the standard deviation in part c relative to the population standard deviation from which the samples were

generated, you can use the concept of the sample standard deviation.

The sample standard deviation is a measure of the variation in a set of data that is calculated by taking the square root

of the variance of the data set. The variance is the average of the squared differences from the mean. It is important to

note that the sample standard deviation is an estimate of the population standard deviation, which is the true measure

of the variability in the population. The larger the sample size, the closer the sample standard deviation will be to the

population standard deviation. Therefore, if the sample size in part c is larger, then the sample standard deviation will

be a better estimate of the population standard deviation.

Conversely, if the sample size is smaller, then the sample standard deviation will be less reliable and may not be a

good estimate of the population standard deviation.

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