solve the following system of equations algebraically for all values of x and y

Answer:

Step-by-step explanation:

The size of each interior angle of the polygon is 4x+28 °

The value of x is 34 degree and y is 56 degree.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.

here, we have,

We have, BOA is an isosceles triangle.

< CBO = 90°

So, < DBO = 90 - 56

<DBO = 34

and, <ODB = 34°

Now, let the angle ODB be x

As, from the figure < EBD is also 90°

So, <y = 180 - (90+34)  (Angle sum property)

<y = 56

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complete question:

Work out the size of angle x and work out the size of angle y

The grams of each food she feeds this group of rats each day is 80 grams of food A and 100 grams of food B each day.

Let us consider that the researcher feeds x grams of food A and y grams of food B each day. Then we can restructure the  two equations on the basis of  the amount of niacin and retinol present in the food
0.11x + 0.35y = 28.4 (equation 1)
190x + 95y = 37,335 (equation 2)

We can evaluate this system of equations applying the substitution or elimination method.
Let us apply substitution method:
In case of equation 1, we can evaluate concerning x:
x = (28.4 - 0.35y) / 0.11
Staging this value for x in equation 2
190[(28.4 - 0.35y) / 0.11] + 95y
= 37,335
Applying simplification and evaluating for y
y = 100
Staging this value for y in equation 1 to evaluate x

x = 80

Then, the researcher feeds 80 grams of food A and 100 grams of food B each day.
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Note that the graph of the function ((x+1)²+(y+2)²=9) is attached accordingly

A coordinate graph is one that has two axes that are perpendicular to each other. These two axes are known as the x- and y-axes. The y-axis is represented by the vertical line, while the x-axis is represented by the horizontal line. A coordinate plane, a Cartesian plane, and a Cartesian coordinate system are other names for it.

The given circle has a radius of 3 units and centre is (-1,-2).

This circle can thus be drawn by first plotting the point (-1,-2) and then with this point as centre draw a circle of radius 3.

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Full question:

graph the circle

((x+1)²+(y+2)²=9)

The length of OP in the given circle figure is 2.

We know that the area of a sector which obtain 'A' degree at center in a circle with radius 'r' is given by,

A = (A/360)*πr²

Here length of OP represents the radius of the circle with center O.

Let OP = R.

The area of the whole circle will be = πR²

Given that the sector which intends an angle of 72 degrees in center has area 4π/5.

According to the condition,

(72/360)* πR² = 4π/5

R²/5 = 4/5

R² = 4

R = 2 [since length cannot be negative so the negative value of square root is ignored.]

Hence the length of OP is 2.

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840 different numbers can be created selecting 4 of the digits from the number

From the question, we have the following parameters that can be used in our computation:

Number =  8712395

Digits = 4

The count of digits in the number is 7

Using the above as a guide, we have the following:

So, we have

Numbers = 7 * 6 * 5 * 4

Evaluate

Numbers = 840

Hence, 840 numbers can be formed

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Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

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Note that given the factors above, Orr should replace the above plant. This has to do with depreciation and book value.

We need to first compute the current total cost of keeping the old plant.

Book value = $4,500,000 - $1,000,000/year x 4 years

= $500,000

Thi smean that the current total cost of keeping the old plan tfor the reamining 10 year is

Total cost of keeping old plant = $1,000,000/year x 10 years - $500,000 + $150,000

= $9 650 000

Now lets calculate the total cost of purchasing the new plant for 10 years.

$600,000 - $150,000

= $450,000 per year.

The salvage value after 10 years is $0.

Total cost of new plant = $3,500,000 + $450,000/year x 10 years = $8,000,000

Since the cost of keeping is higher than the new one, then Orr should get a new plant.

$9 650 000 > $8,000,000

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Answer:

f(1) = 1

Step-by-step explanation:

Open holes on a graph means that the function is not defined at that point, so we ignore the open hole.

At f(1), there is both an open hole at y=-2 and a closed hole at y=1

We ignore the open hole as it is not defined so the answer would be the closed hole, y = 1

So f(1) is 1

The statement that is true about the numbers above include the following: C. (i) is rational and (ii) is rational.

In Mathematics and Geometry, there are six (6) common types of numbers and these include the following:

In Mathematics and Geometry, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 2/3, 0.12345678901234567890.

In Mathematics and Geometry, an irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11 or √11.

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The equation that can be used to determine the cost of each admission ticket is 4x + $25.00 = $175.00.

The cost in dollars of the admission ticket is $ 37.50.

Let x be the cost, in dollars, of each admission ticket, including tax.

The total cost of 4 admission tickets can be expressed as 4x, since the cost of each ticket is the same.

The total cost of 4 admission tickets and parking is given as $175.00, so we can write:

4x + $25.00 = $175.00

Simplifying the equation, we can solve for x:

4x = $175.00 - $25.00

4x = $150.00

x = $37.50

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One advantage of using a dot plot is that it makes it easy to identify outliers. Option A is correct.

An outlier is a data point that is significantly different from the others in the data set, either in terms of its value or its position within the range of values. In a dot plot, outliers are represented by individual dots that are far away from the other dots, either above or below them.

By looking at the dot plot, researchers can quickly identify any outliers and investigate them further to determine why they are different and whether they should be included or excluded from the analysis.

Hence, A. is the correct option.

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The balanced equation of the hanger is 3z = 45 and the solution is z = 15

From the question, we have the following parameters that can be used in our computation:

The hanger image

On the hanger image, we have the following

One side = z + z + z

The other side = 45

The expressions on either sides must be equal to have a balanced equation

So, we have

z + z + z = 45

Evaluate the like terms

3z = 45

Divide both sides of the equation by 3

z = 15

Hence, the balanced equation is 3z = 45 and the solution is z = 15

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Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499

To solve this problem, we need to know the minimum sample size required. The formula for this is given as;

n = (z² * p(1 - p))/ E²

Substituting the values into the formula;

n = (1.645² * 0.21(1 - 0.21))/ 0.03²

n = 498.8

The sample size should be at least approximately 499

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The order of the equations from least number of solutions to greatest number of solutions is: C, B , and A.

In algebra, an expression is made up of several numbers, variables, and mathematical operations including addition, subtraction, multiplication, and division. One expression is, for instance, 3x + 2y - 5.

In algebra, an equation is a claim that two expressions are equal to one another. Often, it asks us to determine the value of a variable that would make the equation true.

Equation A:

4x + 12 = 2(2x + 3) + 6

4x + 12 = 4x + 12

This equation has infinitely many solutions, as 0 = 0 is always true.

Equation B:

5(x - 1) = 3(x + 7)

5x - 5 = 3x + 21

2x = 26

x = 13

This equation has one solution, which is x = 13.

Equation C:

2x - 4 = 2(x + 18)

2x - 4 = 2x + 36

-4 = 36

This equation has no solutions.

Hence, the order of the equations from least number of solutions to greatest number of solutions is: C, B , and A.

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Answer:

a. Let's denote the number of bacterial cultures after n hours by B_n. We know that the number of bacteria triples every hour, so we can write:

- Recursive formula: B_n = 3*B_(n-1) with initial condition B_0 = 250.

- Explicit formula: B_n = 250 * 3^n.

b. To predict the number of bacterial cultures after 8 hours, we can use the explicit formula and substitute n=8:

B_8 = 250 * 3^8 = 250 * 6561 = 1,640,250

Therefore, there will be 1,640,250 bacterial cultures in the dish after 8 hours.

c. Yes, this sequence represents a function. For each input value (number of hours), there is a unique output value (number of bacterial cultures). The explicit formula gives a direct way of computing the output for any input, so it satisfies the definition of a function.

The statements that are true include the following:

B. Lisa paints more square feet per minute than Sally.

C. Lisa will finish painting before Sally.

D. After 10 minutes of painting Sally will have less to paint than Lisa.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 360)/(30 - 0)

Slope (m) = -360/30

Slope (m) = -12

At data point (0, 360) and a slope of -12, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 360 = -12(x - 0)  

y = -12x + 360

A = 360 - 12x

For Sally, the time to finish;

360 = 12x

x = 360/12 = 30 min.

For Lisa, the time to finish;

392 = 14x

x = 392/14 = 28 min (Lisa will finish painting before Sally)

For Sally, when x = 10;

A = 360 - 12(10)

A = 240 sq. feet.

For Lisa, when x = 10;

A = 392 - 14(10)

A = 252 sq. feet.

For Sally, when x = 20;

A = 360 - 12(20)

A = 120 sq. feet.

For Lisa, when x = 20;

A = 392 - 14(20)

A = 112 sq. feet.

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The best-fit linear regression equation gives us the equation y = 0.0804x + 1.1794, where the slope is 0.0804 and the y-intercept is 1.1794.

The trendline equation will give us the equation for the linear regression line, which can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

Once we have the trendline equation, we can use it to make predictions about future enrollment percentages based on the number of years after 1820.

The slope of the line tells us the rate at which the enrollment percentage is increasing or decreasing over time, and the y-intercept tells us the enrollment percentage when x is equal to zero (i.e., in 1820).

Here we have find that the best-fit linear regression equation gives us the equation

=> y = 0.0804x + 1.1794,

where the slope is 0.0804 and the y-intercept is 1.1794.

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Answer: Let's first convert Cheryl's walking speed to meters per minute. Since she takes 80 steps per minute and each step is 81 cm, her walking speed is:

80 steps/min x 81 cm/step = 6480 cm/min

To convert this to meters per minute, we can divide by 100:

6480 cm/min ÷ 100 cm/m = 64.8 m/min

Now, let's find out the distance Cheryl walks to school. Since she walks for 12 minutes at a speed of 64.8 m/min, the distance she covers is:

distance = speed x time = 64.8 m/min x 12 min = 777.6 m

Next, let's find out how many steps Diane takes per minute on average:

90 steps/min

Since each of Diane's steps is 72 cm long, her walking speed is:

90 steps/min x 72 cm/step = 6480 cm/min

To convert this to meters per minute, we can divide by 100:

6480 cm/min ÷ 100 cm/m = 64.8 m/min

So Diane's walking speed is the same as Cheryl's. To find out how long it takes Diane to walk to school, we can use the formula:

distance = speed x time

Since Diane and Cheryl walked the same distance, we can use the distance we found for Cheryl:

777.6 m = 64.8 m/min x time

Simplifying this equation, we get:

time = 12 minutes

Therefore, Diane takes 12 minutes to walk to school.

Answer:

  12 min

Step-by-step explanation:

You want to know how long it takes Diane to walk to school if she takes 90 steps of 72 cm per minute, while Cherly takes 80 steps of 81 cm per minute and traverses the distance in 12 minutes.

The speed of each girl is the product of the number of steps per minute and the length of the step:

  Cheryl: (80 step/min)(81 cm) = 6480 cm/min

  Diane: (90 step/min)(72 cm) = 6480 cm/min

Both girls travel at the same speed, so will take the same amount of time to get to school. It takes Diane 12 minutes to walk to school.

i) The length of the arc is approximately 73.148 meters.

ii) The area of the sector is approximately 85.584 square meters.

(i) The length of an arc can be calculated using the formula:

Arc Length = (θ/360) × 2πr

where;

θ = central angle in degrees

r = radius of the circle

π = mathematical constant approximately equal to 3.14159.

Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:

Arc Length = (85/360) × 2π × 7

= (17/72) × 2 × 3.14159 × 7

≈ 1.7454 × 6.28318 × 7

≈ 73.148 meters (rounded to three decimal places.

(ii) The area of a sector can be calculated using the formula:

Sector Area = (θ/360) × πr²

Given that the central angle is 85° and the radius is 7 meters, we can substitute these values into the formula:

Sector Area = (85/360) × π × 7²

= (17/72) × 3.14159 × 7²

≈ 1.7454 × 3.14159 × 49

≈ 85.584 square meters (rounded to three decimal places)

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The correct question is:

Find:

(i) the length of an arc

(ii) the area of a sector in a circle of radius 7 meters subtended by the central angle of 85°.

Answer:

y = (3/4)x + 2

Step-by-step explanation:

A line (or linear function) can be represented by the equation y = mx + b where "m" is the slope and "b" is the y-intercept.

The y-intercept is when x = 0 or when the line crosses the y-axis. In the graph, notice that the line crosses at (0, 2). Thus, the y-intercept is at y = 2 and "b" must be "2".

Next, we have to find the slope, "m". The slope is defined as a change in "y" divided by a change in "x". Lets use the two points which are marked on the graph already, (4, 5) and (0, 2). We first subtract the y-values, and then divide that by the difference between corresponding x-values:

(5 - 2)/(4 - 0) = 3/4                           The slope is 3/4, so m = 3/4

Now, plug "m" and "b" into the equation:

y = (3/4)x + 2

Answer:

y=(3/4)x+2

Step-by-step explanation:

So first you need to find the slope (3/4). To find that you can use the rise over run method. In this case they have already chosen two points on the line, but you could use any exact points. Count how many up from 2 to 5 (in green), which is 3 then how many across (in red) which is 4. Then put the rise (3) over the run (4) so 3/4.

Then b (2) is equal to y in the y intercept which is (0,2)

Answer:

No I don't. The editor will receive 360 undelivered mail.

Step-by-step explanation:

He sends 12000 emails, 3/100 of them come back undelivered.

Multiply to find the answer:

12000 x 3/100 = 36000/100 = 360

Simple as that; the editor will find that 360 of his sent emails will come back undelivered.

The total cost for the first 25 units is given as follows:

$140.

The marginal cost function is defined as follows:

[tex]c(x) = \frac{14}{\sqrt{x}} = 14x^{-\frac{1}{2}}[/tex]

The total cost function is the integral of the marginal cost function, hence it is given as follows:

[tex]t(x) = \int c(x) dx[/tex]

[tex]t(x) = 28\sqrt{x}[/tex]

Applying the Fundamental Theorem of Calculus, the total cost from x = 0 to x = 25 is given as follows:

t(25) - t(0).

Thus:

Hence:

140 - 0 = $140.

(Applying the Fundamental Theorem of Calculus, we subtract the numeric values at each endpoint of the integral).

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Answer: The function given is f(x) = (x^2 + 8x + 7)/(x + 1).

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function f(x) is defined for all real numbers except for x = -1, because division by zero is undefined in mathematics. Therefore, the domain of f(x) is all real numbers except x = -1, or in interval notation: (-∞, -1) ∪ (-1, ∞).

The range of a function is the set of all possible output values that the function can produce. For this rational function, the range depends on the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function f(x) approaches 0, because the highest power of x in the numerator (x^2) and the highest power of x in the denominator (x) have the same degree, and their coefficients (1 in the numerator and 1 in the denominator) are equal. Therefore, the range of f(x) is all real numbers except 0, or in interval notation: (-∞, 0) ∪ (0, ∞). Note that f(x) never actually equals 0, because the function is defined for all real numbers except x = -1. However, it can arbitrarily approach 0 as x approaches positive or negative infinity. So, 0 is excluded from the range. Therefore, the correct answer is: Range = (-∞, 0) ∪ (0, ∞). Note that the range is expressed in interval notation, which uses parentheses to indicate open intervals (excluding the endpoints) and the union symbol (∪) to indicate the combination of two or more sets. In this case, the range consists of all real numbers except 0, expressed as two separate open intervals. The domain is also expressed in interval notation, with the union symbol (∪) used to indicate the combination of two disjoint sets. In this case, the domain consists of all real numbers except -1, expressed as the union of two separate intervals. So, the final answer is: Domain = (-∞, -1) ∪ (-1, ∞) and Range = (-∞, 0) ∪ (0, ∞). I hope this helps! Let me know if you have any further questions. I am here to help! Keep in mind that if you need to use the function f(x) in a real-world context, you should also consider any additional restrictions or conditions that may apply. It's always important to carefully analyze the properties of a function in the context of the problem you are trying to solve.

Step-by-step explanation:

The probability that Rosie does her homework is: 27/44

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Thus, we can solve this probability as:

(6/11 * 1/2) + ((1 - (6/11) * 3/4)

= (3/11) + (5/11 * 3/4)

= (3/11) + 15/44

= 27/44

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The first four elements of the sequence are:

a11 = 5350

a12 = 10702

a13 = 21406

a14 = 42814

Starting with a11 = 5350, we can use the recursive formula to find a12:

a12 = 2a11 + 2 = 25350 + 2 = 10702

a13 = 2a12 + 2 = 210702 + 2 = 21406

a14 = 2a13 + 2 = 221406 + 2 = 42814

Therefore, the first four elements of the sequence are:

a11 = 5350

a12 = 10702

a13 = 21406

a14 = 42814

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For the function "f (x) = 120/x²", the domain of the function "f" is (b) All non zero real numbers.

The "Domain" of a function is the set of all possible "input-values" for which the function is defined. In this case, the function is defined as:

f (x) = 120/x²

The only restriction on the input values is that the denominator cannot be equal to zero, because division by zero is undefined.

So, the domain of the function f is all non-zero real numbers.

Therefore, the correct option is (b): All non-zero real numbers.

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The given question is incomplete, the complete question is

Given that f (x) = 120/x², What is the domain of the function f ?

(a) only positive integers,

(b) All non zero real numbers,

(c) only negative integers,

(d) All real numbers including zero.

The line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).

A line of reflection is a line that acts as a mirror, reflecting a figure across it. Each point on the original figure is reflected over the line and the resulting image is the same size and shape as the original, but appears to be "flipped" or "mirrored" across the line of reflection. The line of reflection is the perpendicular bisector of the segment connecting each point on the original figure to its corresponding point on the reflected image.

In the given question,

To determine the line of reflection, we need to find the perpendicular bisector of each line segment between the point and its image.

First, we find the midpoint of the line segment between A and A': (A + A')/2 = (-3 + (-5))/2, (3 + 3)/2 = (-4, 3)

The perpendicular bisector of the line segment AA' is a vertical line passing through (-4, 3).

Similarly, we find the midpoints and perpendicular bisectors of the line segments BB', CC', DD', and EE'.

The perpendicular bisectors of the line segments BB', CC', DD', and EE' are also vertical lines passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1), respectively.

Therefore, the line of reflection is the vertical line passing through (-5, 6), (-9, 6), (-9, 3), and (-7, 1).

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The amount that will be in Andy's account in 2 years after the addition of interest is $112.36

Andy has $100 in an account

An interest rate of 6% is compounded annually

The amount that will be present in the account after 2 years can be calculated as follows

= 100(1+ 6/100)²

= 100(1 + 0.06)²

= 100(1.06)²

= 100(1.1236)

= 112.36

Hence the amount that will be present in the account after 2 years with the addition of interest is $112.36

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