Solve by Elimination:

5x+2y=−3
2x+3y=−10

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 6-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~6 - \cfrac{ 16 }{ 4 } \right) \\\\\\ \left( -2 ~~~~ ,~~~~ 6 -4 \right)\implies (-2~~,~~2)[/tex]

It is vertically stretched by a factor of 200 and shifted 10 units up.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

You write functions with the function name followed by the dependent variable.

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Answer:

Step-by-step explanation:

i cant see the answer

As per the proportion, the number of males rabbits in the population is 1000.

Let's first find the proportion of female rabbits in the population using the given information. We are told that 8 out of every 75 rabbits in the population are females. Therefore, we can write:

Proportion of females = 8/75

We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor, which is 1:

Proportion of females = 8/75 = 0.1067

This means that for every unit of 75 rabbits in the population, there are 8 female rabbits.

Then, the total number of rabbits in the population is:

Total number of rabbits = r x 75

Since we know that the proportion of females is 0.1067, we can find the number of female rabbits in the population as follows:

Number of female rabbits = Proportion of females x Total number of rabbits

= 0.1067 x (r) x 75

We also know that the total number of rabbits in the population is 1500. Therefore, we can set up an equation as follows:

Number of male rabbits + Number of female rabbits = Total number of rabbits

Number of male rabbits + 0.1067 x (r) x 75 = 1500

Now, we can solve for the number of male rabbits by rearranging the equation:

Number of male rabbits = 1500 - 0.1067 x (r) x 75

We can simplify this expression by first multiplying 0.1067 and 75:

Number of male rabbits = 1500 - 8.003 x r

Finally, we can substitute the value of x in terms of the total number of rabbits in the population (1500) to find the number of male rabbits:

Number of male rabbits = 1500 - 8.003 x (1500/75)

Number of male rabbits = 1000

Therefore, there are 1000 male rabbits in the population.

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Answer:

V = 226.08 ft³

Step-by-step explanation:

the volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius and h the height ) , then

V = 3.14 × 6² × 2

   = 3.14 × 36 × 2

  = 3.14 × 72

  = 226.08 ft³

If the area of a pad is 17. 5 square yards, the length of the pad is 5 yards, the width of the pad is 3.5 yards.

The formula for the area of a rectangle is:

Area = length x width

We know that the area of the pad is 17.5 square yards, and the length is 5 yards. We can use this information to solve for the width.

Let's substitute the values we know into the formula:

17.5 = 5 x width

To solve for the width, we need to isolate it on one side of the equation. We can do this by dividing both sides by 5:

17.5/5 = width

Simplifying the left side gives:

3.5 = width

In conclusion, Mr. Tomas should make a rectangular concrete pad that is 5 yards long and 3.5 yards wide to have an area of 17.5 square yards.

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Answer:

The mean of a group is calculated by adding up all the values in the group and then dividing by the number of values. In this case, the mean age of the original group of 20 people is 12 years. This means that the sum of their ages is 20 * 12 = 240 years.

When three new people with ages 10, 11, and 15 join the group, the total number of people in the group increases to 23. The sum of their ages becomes 240 + 10 + 11 + 15 = 276 years. The new mean age of the group is calculated by dividing the sum of their ages by the number of people in the group: 276 / 23 ≈ 12 years.

So, after three new people join the group, the mean age remains approximately the same at around 12 years.

Step-by-step explanation:

workers = k× number of days (k= constant of proportionality)

w = k× days

20= 15× k

k = 20/15

w = k× days

substitute the values

w = 20/15 × 12

w = 16

Number of workers required = 16

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Answer:

5

Step-by-step explanation:

15d -- 20l

12d -- (x)l

x= 15×20

12

x= 25

25-20= 5

Ans = 5.

we need to know how many students each circle represents to calculate how many chose chicken Maybe try 4 3/4 but im not quite sure

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

24 students said veggie and there is 6 circles in the pictogram for veggie so we can divide 24 by 6 to find the value of one circle.

[tex]\frac{24}{6} = 4[/tex]

Now we have the value of a circle we can figure out how many students chose chicken.

There are 4 full circles which is [tex]4*4 = 16[/tex]

Finally, there is a 3/4 of a circle which is [tex]4*\frac{3}{4} = 3[/tex]

Then we add all the values together to find the number of students who chose chicken.

16+3=19

Hope this helps!

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Mr. Razon paid 87 percent of his Php 100 for his lunch.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage. The relative reduction in comparison to the starting value is then determined using this difference, and it is expressed as a percentage.

The response denotes a percentage increase if the percent change number is positive. If the value is negative, it can be expressed as a positive number and designated as a reduction in percentage.

To find the percentage that Mr. Razon paid for his lunch, we can use the formula:

percentage = (part / whole) x 100%

Substituting the values we get:

percentage = (87 / 100) x 100%

percentage = 87%

Therefore, Mr. Razon paid 87% of his Php 100 for his lunch.

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The height of the base if it is 2 in. wide  is 3 inches. Option B

Let's call the height of the triangular base h (in inches).

The volume of the triangular prism can be calculated using the formula:

Volume = (1/2) x Base x Height x Length

In this case, the length is given as 4 inches, the width (or base) is given as 2 inches, and the volume is given as 12 cubic inches. Substituting these values into the formula, we get:

12 = (1/2) x 2 x h x 4

Simplifying this equation, we get:

12 = 4h

Dividing both sides by 4, we get:

h = 3

Therefore, the height of the triangular base is 3 inches.

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Answer: 3

Step-by-step explanation:

Answer:

7.8 x (12/6)-0.8

the average rate of change in the number of cattle from 2006 to 2014 is approximately -1.1125 million head of cattle per year.

To find the average rate of change in the number of cattle from 2006 to 2014, we need to divide the total change in the number of cattle over that period by the number of years.

The total change in the number of cattle is:

87.7 million - 96.6 million = -8.9 million

The number of years is:

2014 - 2006 = 8

So, the average rate of change is:

-8.9 million / 8 years = -1.1125 million per year

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The number Chrissie is thinking of is 900. This is obtained by solving the equation 0.3x = 270.

Let's call the number Chrissie is thinking of "x". We know that 30% of x is equal to 270.

We can write this as an equation:

0.3x = 270

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.3:

x = 270 ÷ 0.3

x = 900

So the number Chrissie is thinking of is 900.

An equation is used to find the number Chrissie is thinking of. 30% of the number is equal to 270, so we can solve for the number by dividing 270 by 0.3, which gives us x = 900. Therefore, the number Chrissie is thinking of is 900.

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We can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

Given the triangles EFG and BCD, you can identify that:

By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.

In this case, you can identify that you know two pairs of corresponding sides. Then, you can find that they are in proportion. Set up that:

[tex]\frac{EF}{BC}=\frac{FG}{CD}[/tex]

Substituting values and simplifying, you get:

[tex]\frac{18}{90}=\frac{16}{80}\\\\\frac{1}{5}=\frac{1}{5}[/tex]

Notice that they are in proportion.

You can also identify that the corresponding angles F and I are congruent because they have equal measures.

Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

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D)probability that the sample proportion is between 0.56 and 0.59 is 0.7912.

E)Probability that the sample proportion is less than 0.51 is 0.0002

D. To calculate the probability that the sample proportion is between 0.56 and 0.59, we can use the Standard Normal Probability Distribution Table. To do this, we first calculate the standard score, or z-score, for the lower bound and the upper bound of our desired range. The formula for calculating the z-score is:


z = (x - μ) / σ


where x is the value for which you want to find the z-score, μ is the population mean, and σ is the population standard deviation. In this case, x is the sample proportion, μ is 0.61, and σ is 0.01. Therefore, the z-score for the lower bound (0.56) is -2.90, and the z-score for the upper bound (0.59) is -0.33. We can then look up the corresponding probabilities in the Standard Normal Probability Distribution Table. The probability that the sample proportion is between 0.56 and 0.59 is 0.7912.

E. To calculate the probability that the sample proportion is less than 0.51, we can use the same process as above. The z-score for 0.51 is -3.90. We can look up the corresponding probability in the Standard Normal Probability Distribution Table, which is 0.0002. Therefore, the probability that the sample proportion is less than 0.51 is 0.0002.

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The volume of the frustum is 19840cm³

A frustum is a cut out section of a defined shape. The volume of the frustum is calculated as;

Volume of the Big shape - Volume of the small shape.

The shape here is a pyramid. And the volume of a pyramid is given as ;

1/3 bh

The height of the big pyramid is obtained by using similar shape theorem

10/10+x = 6/30

= 60+6x = 300

6x = 240

x = 240/6 = 40

Therefore the height of the pyramid = 40+10 = 50cm

Therefore volume of the big pyramid = 1/3 × 30×40× 50

= 10× 40 × 50

= 20000cm³

The volume of the small pyramid = 1/3 bh

The width of the small pyramid = 6/30 = x/40

30x = 240

x = 8

= 1/3 × 8× 6× 10

= 8× 2 × 10

= 160cm³

therefore the volume of the frustum = 20000-160

= 19840cm³

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Answer:

Option C: The skaters path intersect twice, but only one of those points is inside the rink.

Step-by-step explanation:

Coordinates of center of ice rink: (0,0) Radius of ice rink circle = 35 m

We know that the equation of a circle with center coordinates (a,b) and radius of (r) is given as; (x - a)² + (y - b)² = r²

Thus, the total area on which the skaters are skating will be given by the equation;

x² + y² = 35²

Now, we are told the path along which Susan is skating is modeled by the equation: y = 6x - x² - 5

While Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9)

From equation of a parabola, the path along which like is skating can be modeled by;

(x - 8)² = 4a(y + 9)

To find a, we will substitute the coordinate started at to get;

(10 - 8)² = 4a(-21 + 9)

4 = 4a × -12

Divide both sides by 4 to get;

a = -1/12

Thus;

(x - 8)² = 4(-1/12)(y + 9)

(x - 8)² = (-1/3)(y + 9)

This gives: 3(x - 8)² = -(y + 9)

I've drawn the graph on demos and attached it.

From the graph we can see that the skaters points intersect twice but one is inside the rink circle while the other is outside the rink circle. The point at which they intersect outside the rink was slightly cropped out because of size. But it is clearly seen that they are both approaching point of intersection.

Thus, correct answer is Option C.

The domain of the given function is (-∞, 1) ∪ [1, ∞) and  the range of the function is [1/4, ∞)

The domain of a function is the set of all possible values for which the function is defined. In the given function, there are two separate definitions: one for x < 1 and another for x ≥ 1. Hence, we can say that the domain of the given function is (-∞, 1) ∪ [1, ∞).b. Range: The range of a function is the set of all possible values that the function can take. Since the function is a quadratic function, it is always positive, and the minimum value occurs at x = -b/2a. The minimum value of the function occurs at x = -b/2a = 1/2.

Thus, the range of the function is [1/4, ∞). Computing the values of f(x): Now, we have to compute the following values of f(x): f(0), f(1/2), and f(2).f(0): The value of the function when x = 0 is given by the second part of the definition:f(0) = (0² + 3 - 0 + 1) = 4f(1/2): The value of the function when x = 1/2 is given by the first part of the definition: f(1/2) = (1/4 + 3 - 1/2 + 1) = 13/4f(2): The value of the function when x = 2 is given by the second part of the definition: f(2) = (2² + 3 - 2 + 1) = 8Therefore, f(0) = 4, f(1/2) = 13/4, and f(2) = 8.

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Step-by-step explanation:

4 1/2(2)=9. Multiply by 2 to get total

9- 3 1/2=z. Subtract 3 1/2 from total to get Z

5 1/2= Z

Answer:

-7x - 12

Step-by-step explanation:

To simplify the expression, we need to get rid of the parentheses and combine like terms. We can use distributive property to multiply each term inside the parentheses by the sign outside.

Therefore, the expression (-2x-10) - (-5x + 2) - 10x simplified is -7x - 12.

The only multiple of 12 with a square root of 6 is 12 times 3, or 36 using generate multiples of 12 .

The multiples of 12 are numbers that are divisible by 12 without a remainder. We can generate multiples of 12 by multiplying 12 by any integer. For example, the first few multiples of 12 are 12, 24, 36, 48, 60, and so on.

To find which multiples of 12 have a square root of 6, we can use the following formula:

√(12n) = √(12) * √(n)

Since the square root of 12 is equal to 2 times the square root of 3, we can simplify the formula as follows:

√(12n) = 2 * √(3n)

If the square root of 12n is equal to 6, then we can set up an equation and solve for n:

2 * √(3n) = 6

√(3n) = 3

3n = 9

n = 3

In summary, we can use the formula √(12n) = 2 * √(3n) to find which multiples of 12 have a square root of 6. By solving for n, we find that the only multiple of 12 with a square root of 6 is 36.

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By looking at the degree, we conclude that we have 4 roots.

Here we want to see how many roots the function:

x⁴ - 2x³ - 6x² + 22x - 15 = 0

The numer of roots (repeated, complex, or real) is given by the degree of the g

In this case we can see that the maximum exponent is 4, so the degree is 4, which means that we have 4 roots

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The balance in Howard's savings account increased by $374 in 5 months. This works out to an average of $74.80 per month.

To calculate the change in the balance of Howard’s savings account per month, we need to subtract the initial balance of $250 from the balance after 5 months of $624. This gives us a difference of $374. To find the change in the balance per month, we need to divide this difference by the number of months (5). This gives us a final answer of $74.80, which is the change in the balance of Howard’s savings account per month. To summarize, the balance in Howard’s savings account increased by $374 in 5 months, which works out to an average of $74.80 per month.

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There is a 34.39% chance that at least one patient will worsen to severe sepsis or septic shock after three days.

Assuming that the probability of sepsis worsening to severe sepsis or septic shock after three days is 0.10, the probability of a patient with sepsis not worsening to severe sepsis or septic shock after three days is 0.90.

Therefore, the probability that all four patients with sepsis do not worsen to severe sepsis or septic shock after three days is:

[tex](0.90)^4 = 0.6561[/tex]

This means that there is a 65.61% chance that none of the four patients will worsen to severe sepsis or septic shock after three days.

To estimate the probability that at least one patient will worsen to severe sepsis or septic shock after three days, we can use the complementary probability. That is, the probability that none of the four patients will worsen to severe sepsis or septic shock after three days is 0.6561, so the probability that at least one patient will worsen to severe sepsis or septic shock after three days is:

[tex]1 - 0.6561 = 0.3439[/tex]

Therefore, there is a 34.39% chance that at least one patient will worsen to severe sepsis or septic shock after three days.

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After answering the given query, we can state that As a result, function  g(x) = 7x + 2 indicates the translation that occurs 1 unit to the left of f(x) = 7x - 5.

Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.

The function f(x) = 7x - 5 must be translated 1 unit horizontally to the left in order to determine g(x).

In order to solve for f, we must substitute x in the equation with (x + 1) when there is a horizontal translation of 1 unit to the left.(x). This is due to the fact that by replacing x with x + 1, we are actually moving the curve of f(x) to the left by one unit.

So, g(x) = f(x + 1) can be expressed as:

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

g(x) = 7x + 2

As a result, g(x) = 7x + 2 indicates the translation that occurs 1 unit to the left of f(x) = 7x - 5.

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Answer:

-8

Step-by-step explanation:

5r= -40 | :5

r= -8

.....

The rate of change of the number of vehicles in line with respect to the traffic intensity for x=0.2 is -1.2000. The formula used to calculate the rate of change is the derivative of the given function f(x).

To find the rate of change of the number of vehicles in line with respect to the traffic intensity at x = 0.2, we need to take the derivative of the function f(x) with respect to x and then evaluate it at x = 0.2.

f(x) = 5(2 - x)x^2

f'(x) = 5[(2 - x)(2x) + x^2(-1)]

f'(x) = 5(4x - 3x^2)

f'(0.2) = 5(4(0.2) - 3(0.2)^2) = 0.68

Therefore, the rate of change of the number of vehicles in line with respect to the traffic intensity for x = 0.2 is 0.68.

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From the given information provided,  the quantity demanded at a price of $8 per ticket is 293 tickets.

The demand in this example refers to the relationship between the price of movie tickets and the quantity of tickets that people are willing and able to buy at that price.

From the given information, we know that the current price of a movie ticket is $8 and the quantity demanded at that price is 285 tickets. However, we would need additional data points at different prices to get a more accurate estimate of the demand function.

Assuming that the demand for movie tickets is downward sloping (i.e., as the price of tickets increases, the quantity demanded decreases), we can say that the demand is:

Inverse: The price and quantity demanded move in opposite directions. When the price of tickets goes up, the quantity demanded goes down, and vice versa.

Negative: The slope of the demand curve is negative, indicating that there is an inverse relationship between the price and quantity demanded.

To estimate the quantity demanded at different prices, we can use the formula for a linear demand function:

Q = a - bP

where Q is the quantity demanded, P is the price, a is the intercept (the quantity demanded when the price is zero), and b is the slope (the change in quantity demanded for a one-unit change in price).

Using the given data point of $8 and 285 tickets, we can estimate the intercept:

285 = a - 8b

Assuming a relatively elastic demand, we can use a slope of -2:

Q = a - 2P

Substituting the intercept value we solved for earlier, we get:

Q = 309 - 2P

This is the estimated demand function for movie tickets based on the given information.

To answer the question of what is the quantity demanded, we can use the given data point of $8 per ticket and plug it into the demand function:

Q = 309 - 2(8)

Q = 293

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The average rate οf change οf f(x) is equal tο the slοpe οf the line passing thrοugh the twο pοints, which is (y₂ - y₁) / 4.

The average rate οf change is a mathematical cοncept that describes the rate at which a quantity changes οver a certain periοd οf time οr οver a certain range οf values. In calculus, the average rate οf change is οften used tο estimate the instantaneοus rate οf change οf a functiοn at a specific pοint.

Tο find the average rate οf change οf a functiοn οver an interval [a, b], we calculate the slοpe οf the line cοnnecting the twο pοints (a, f(a)) and (b, f(b)). This is given by the fοrmula:

average rate οf change = (f(b) - f(a)) / (b - a)

Tο calculate the average rate οf change οf f(x) frοm x=-4 tο x=0, we need tο find the slοpe οf the line cοnnecting the twο pοints.

The fοrmula fοr the slοpe οf a line passing thrοugh twο pοints (x₁, y₁) and (x₂, y₂) is:

slοpe = (y₂ - y₁) / (x₂ - x₁)

In this case, the twο pοints are (-4, f(-4)) and (0, f(0)). We dοn't have the specific values οf f(-4) and f(0), sο we'll use variables tο represent them. Let's say f(-4) = y₁ and f(0) = y₂.

Then the slοpe οf the line is:

slοpe = (y₂ - y₁) / (0 - (-4)) = (y₂ - y₁) / 4

Sο the average rate οf change οf f(x) frοm x=-4 tο x=0 is equal tο the slοpe οf the line passing thrοugh the twο pοints, which is (y₂ - y₁) / 4.

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