1 The points (-8, 5) and (-4, r) lie on a line with slope 1/4. Find the missing coordinate r.​

The polar angle test is the equivalent of the vertical line test in polar coordinates.

Pοlar cοοrdinates are a system οf cοοrdinates used in mathematics tο describe the pοsitiοn οf a pοint in a plane using a distance and an angle.

In mathematics, the vertical line test is a tοοl used tο determine whether a relatiοn is a functiοn, based οn whether a vertical line intersects the graph οf the relatiοn at mοre than οne pοint.

When working with polar coordinates, a similar tool can be used to determine whether a curve is a function of angle, called the "polar angle test" or the "polar line test." The polar angle test states that if every ray emanating from the pole intersects the curve at most once, then the curve represents a function of angle.

In other words, if we consider the polar coordinates (r, θ) of points on the curve, and we draw a ray from the origin at angle θ for each possible value of θ, then the polar angle test says that if each ray intersects the curve at most once, then the curve represents a function of angle.

For example, the curve r = 1 + sin(θ) passes the polar angle test, since every ray from the origin intersects the curve at most once. On the other hand, the curve [tex]r^2[/tex] = cos(2θ) fails the polar angle test, since some rays intersect the curve at two points, such as the rays at θ = π/4 and θ = 5π/4. Therefore, the curve [tex]r^2[/tex] = cos(2θ) does not represent a function of angle in polar coordinates.

Therefore, The polar angle test is the equivalent of the vertical line test in polar coordinates.

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The required inequality is  5x + 2 ≤ 12 and the solution is 2

Inequalities are mathematical expressions that compare two values or expressions, indicating that one is less than, greater than, or equal to the other.

In this problem, we used a linear inequality to represent the relationship between the amount of water used and the total cost of the water bill.

We then used algebra to rearrange the inequality and solve for x, which gave us the maximum amount of water that the family can use without going over budget.

Here we have

The cost of the water bill is made up of two components: a fixed monthly connection fee of $2, and a variable cost based on the amount of water used.

The variable cost is $5 per thousand gallons, and the total cost, C, in dollars can be expressed as:

C = 5x + 2

where x is the number of thousands of gallons used.

The problem states that the family has budgeted $12 for their water bill this month. Hence the cost must not exceed $12  

=> 5x + 2 ≤ 12

The above expression can be rewritten as follows

=>  5x + 2 ≤ 12  

Subtract 2 from both sides

=> 5x ≤ 10

Divide by 2 into both sides

=> x ≤ 2

Therefore,

The required inequality is  5x + 2 ≤ 12 and the solution is 2

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The total direct labor hours for each product to get the total direct labor hours required for the projected sales during the coming year.

To determine the contribution margin per direct-labor hour expended on each product, you will need to calculate the contribution margin for each product and divide it by the number of direct labor hours required to produce that product.
Contribution Margin = Sales Revenue - Variable Costs
Once you have calculated the contribution margin for each product, you can divide it by the number of direct labor hours required to produce that product to get the contribution margin per direct-labor hour.
To prepare a schedule showing the total direct labor hours that will be required to produce the projected sales during the coming year, you will need to estimate the number of units that will be sold for each product and the number of direct labor hours required to produce each unit.

Multiply the number of units by the number of direct labor hours per unit to get the total direct labor hours required for each product.

Contribution Margin = $40 - $20 - $5 - $3 = $12

Direct Labor Hours per unit = 2

Contribution Margin per Direct-Labor Hour = $12 / 2 = $6 MMK YU GHTJUIO7U

Contribution Margin = $60 - $25 - $10 - $5 = $20

Direct Labor Hours per unit = 4

Contribution Margin per Direct-Labor Hour = $20 / 4 = $5

Contribution Margin = $80 - $30 - $15 - $10 = $25

Direct Labor Hours per unit = 5

Contribution Margin per Direct-Labor Hour = $25 / 5 = $5

To prepare a schedule showing the total direct labor hours that will be required to produce the projected sales during the coming year, we need to estimate the number of units that will be sold for each product and the number of direct labor hours required to produce each unit.

Assuming that the projected sales for the coming year are as follows:

Product A: 10,000 units

Product B: 8,000 units

Product C: 5,000 units

And the number of direct labor hours required to produce each unit are as follows:

Product A: 2 hours per unit

Product B: 4 hours per unitF

Product C: 5 hours per unit

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Answer:

B) There is one unique solution, (2, 1).

Attached is a graph of the system of equations.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases} 3x+6y=12 \\ 3x+2y=8\end{cases}[/tex]

Types of Solutions to a System of Equations

Using a graphing calculator, we can find the solution(s) to the given system of equations. To find the solution(s), we need to look at the point where the lines intersect; this is called the point of intersection.

Answer:

B: There is one unique solution, (2, 1)

Step-by-step explanation:

Took the test.

Answer:

[tex] \frac{5x {}^{2} }{2} - 8x + 6[/tex]

Step-by-step explanation:

That's your answer

Step-by-step explanation:

The average = sum of data value ÷ number of data value = 2332 ÷ 106 = 22

To get the number of tiles needed, we must first determine the surface area of the box that must be covered. Surface area of the square box = top area + front area + rear area + left side area + right side area.

Top area = length x width = 6 cm x 4 cm = 24 cm2 Front and back area = height x breadth = 8 cm x 4 cm = 32 cm2 (for each) Left and right side area = height x length = 8 cm x 6 cm = 48 cm2 (for each) Surface area total = 24 + 2(32) + 2(48) = 232 cm2. To get the number of tiles needed, divide the total surface area by the area of each tile. each's area 5 mm × 5 mm = 0.25 cm2 tile Total surface area / Area of each tile = 232 / 0.25 = 928 tiles required As a result, Dmitri need 928 glass tiles to cover the top and sides of the box.

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To construct a confidence interval for the proportion of American adults who viewed China as either "unfriendly" or "an enemy," we can use the following formula:

CI = p ± z*(√(p(1-p)/n))

where:

CI is the confidence interval

p is the sample proportion (0.29 + 0.09 = 0.38)

z is the critical value for the desired confidence level (95% confidence level corresponds to z = 1.96)

n is the sample size (2,047)

Plugging in the values, we get:

CI = 0.38 ± 1.96*(√(0.38*(1-0.38)/2047))

CI = 0.38 ± 0.018

CI = (0.362, 0.398)

Therefore, we can say with 95% confidence that the true proportion of American adults who view China as either "unfriendly" or "an enemy" is between 0.362 and 0.398.

Step-by-step explanation:

The required combinatorial circuit can be constructed as follows:

Firstly, we need to find the negation of p, q and r which can be achieved using inverters as shown below:

p q r

| | |

| | |

NOT NOT NOT

| | |

| | |

~p ~q ~r

Next, we can use OR gates to form the term (¬p ∨ ¬r) and (q ∨ r) as shown below:

~p ~r q r

| | | |

| | | |

OR OR | |

| | | |

| | | |

pORr rORp qORr rORq

Then, we can use AND gates to form the terms (¬p ∨ ¬r) ∧ ¬q and ¬p ∧ (q ∨ r) as shown below:

~p ~r q r

| | | |

| | | |

OR OR | |

| | | |

| | | |

pORr rORp qORr rORq

| | | |

| | | |

NOT NOT NOT |

| | | |

| | | |

~q ~pORr ~qORr qORr

| | | |

| | | |

AND OR AND |

| | | |

| | | |

(~pORr ~q) qORr qORr

| | |

| | |

OR AND |

| | |

| | |

(~pORr ∨ ~q) (~pORr ∧ qORr)

| | |

| | |

| OR |

| | |

| | |

((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))

| | |

| | |

| | |

OUTPUT

((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))

The point (√7, 5) does not lie on the circle centered at the origin and containing the point (5,2).

The equation of a cifcle that has its center at the origin is

x² + y² = r²

Where

r = radius

Using the given points, we have

√7² + 5² = r²

Evaluate

32 = r²

For the second point, we have

5² + 2² = r²

Evaluate

29 = r²

The calculated values are not equal

So,  the point (√7, 5) does not lie on the circle centered at the origin and containing the point (5,2).

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The indicated derivatives in the question can be found to be :

To find the derivative of e^(x^3) + log_3(pi) with respect to x, we apply the rules of differentiation to each term:

Using the chain rule, we have:

d/dx (e^(x^3)) = e^(x^3) x (3x^2)

The derivative of log_3(pi) is 0, because log_3(pi) is a constant and the derivative of a constant is 0.

So, the derivative of the entire expression is:

d/dx (e^(x^3) + log_3(pi)) = e^(x^3) x 3x^2 + 0 = 3x^2 x e^(x^3)

To find the derivative of (x^(1/6))^ln(x) with respect to x, we first simplify the expression by using the power rule of logarithms:

(x^(1/6))^ln(x) = x^(ln(x)/6)

Now, we find the derivative of x^(ln(x)/6) using the chain rule:

d/dx (x^(ln(x)/6)) = (ln(x)/6) × x^((ln(x)/6) - 1) × d/dx (x)

The derivative of x is 1, so:

d/dx ((x^(1/6))^ln(x)) = (ln(x)/6) × x^((ln(x)/6) - 1) × 1 = (ln(x)/6) × x^((ln(x)/6) - 1)

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55.96 more euros Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate. Thus, option B is correct.

The number of units of a foreign currency that can be purchased with one unit of the domestic currency, or the opposite, is referred to as the exchange rate between two currencies.

Here, we have

Given: The exchange rate between non-fixed currencies continuously fluctuates. Sandy has $829.04 to convert into euros.

We have to find how many more euros would Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate.

To get a favorable exchange rate we should do:

                                     USD × Exchange Rate

a) 829.04 × 0.7544  ⇒ Most favorable exchange rate (Tuesday)

= 625.42

b)  829.04 × 0.6869 × 0.94  ⇒ Least favorable exchange rate (Friday)

= 569.46

Difference of most favourable day and Least favorable day

=  625.42 - 569.46

= 55.96

Hence, 55.96 more euros Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate. Thus, option B is correct.

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Answer: 20%

(Please give me brainliest if you can tomorrow, hopefully this helps)

Explanation:

(So if it's even)

There are 5 possible outcomes and 2 evens on the spinner, so 2 favorable outcomes. That gives us a fraction of 2/5.

Flipping a coin, either heads or tails, it'd be 1/2.

Since it's a compound event we would multiply 2/5 and 1/2, getting:

[tex]\frac{2}{5} *\frac{1}{2} = \frac{2}{10}[/tex]

To change that into a percentage, we divide the numerator by the denominator and multiply by 100 which would give us:

.2 * 100 = 20%

Answer:

10 acres

Step-by-step explanation:

Land for coconuts =

[tex] \frac{3}{8} = \frac{15}{40} [/tex]

Land for bananas =

[tex] \frac{4}{5} \times \frac{5}{8} = \frac{20}{40} \\ = \frac{4}{8} \\ = \frac{1}{2} [/tex]

Land left for rice =

[tex] \frac{40}{40} - \frac{15}{40} - \frac{20}{40} = \frac{5}{40} \\ = \frac{1}{8} [/tex]

Land for bananas =

[tex] \frac{1}{8} = 2.5 \\ \frac{4}{8} = 2.5 \times 4 \\ = 10[/tex]

Answer:

The reason why -2^2=-4 and (-2)^2=4 is due to the rules of mathematical operations and the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

According to the order of operations, when you have an expression with multiple operations, you must perform the operations in a specific order. Exponents come before multiplication and division, and before addition and subtraction.

So, when evaluating -2^2, you first evaluate the exponent, which is 2. However, the negative sign in front of the 2 is not part of the exponent, but rather an arithmetic operation. Therefore, the expression is equivalent to -(2^2), which is equal to -4.

On the other hand, when evaluating (-2)^2, the parentheses indicate that the negative sign is part of the base, so you must first evaluate the base, which is -2, and then apply the exponent of 2. This gives you (-2)^2 = 4.

Step-by-step explanation:

The minus in (-2)^2 is enclosed in parentheses, so it is also squared:

minus × minus = plus

And talking about this one: -2^2, the minus is not included in the parentheses, that's why we only square the number (2 in this case) and keep the minus in front of it

I hope this will help...

Answer: Im trying to find out too

Step-by-step explantion i dont know

By answering the presented question, we may conclude that Therefore, null hypothesis the test statistic is -1.942 and the pis 0.050.

A null hypothesis is a sort of statistical hypothesis that asserts that a certain set of observations has no statistical significance. Sample data is used to assess the feasibility of ideas. H0 represents what is sometimes referred to as "zero." The researchers make the premise that there may be a link between the parameters. The null hypothesis, on the other hand, claims that no such association exists. While it may not appear to be relevant, the null hypothesis is a crucial aspect of research.

p = 15/23 = 0.6522

z = (p' - p) / √(p * (1-p) / n)

z = (0.6522 - 0.78) / √(0.78 * (1 - 0.78) / 23) = -1.942

p= 2 * P(Z < -1.942) = 2 * 0.025 = 0.050

Therefore, the test statistic is -1.942 and the 0.050.

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The vertices of the region are (7.2, -1.2) and (-2, 2).

In mathematics, an inequality is a statement that one quantity is less than or greater than another quantity. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

or example, "x > 5" means that x is greater than 5, while "y ≤ 10" means that y is less than or equal to 10.

Inequalities can be solved by isolating the variable on one side of the inequality symbol, just as with equations. However, there are some important differences between solving equations and solving inequalities. When solving an inequality, the direction of the inequality symbol may need to be reversed if both sides of the inequality are multiplied or divided by a negative number. In addition, the solution to an inequality is often expressed using interval notation or a number line.

To graph the system of inequalities, we first need to graph the boundary lines:

6y - x = 6 is equivalent to y = (1/6)x + 1, which has a y-intercept of 1 and a slope of 1/6.

y + 3x = -4 is equivalent to y = -3x - 4, which has a y-intercept of -4 and a slope of -3.

The region that satisfies both inequalities is the shaded region below the blue line and to the left of the red line.

To find the vertices of the region, we need to find the points where the two boundary lines intersect. Solving the system of equations:

y = (1/6)x + 1

y = -3x - 4

We get:

(7.2, -1.2) and (-2, 2)

Therefore, the vertices of the region are (7.2, -1.2) and (-2, 2).

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The vertices of the region are (7.2, -1.2) and (-2, 2).

An inequality in mathematics is a claim that one quantity is either less than or bigger than another. Inequalities are represented using symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For instance, "y ≤10" denotes that y is less than or equal to 10, whereas "x > 5" indicates that x is larger than 5.

Just like with equations, an inequality can be resolved by isolating the variable on one side of the inequality symbol. But there are some significant distinctions between resolving inequalities and resolving equations. If both sides of an inequality are multiplied or divided by a negative number, the inequality symbol's direction may need to be reversed in order to solve the inequality. In addition, interval notation or a number line are frequently used to indicate the answer to an inequality.

We must first graph the boundary lines before we can graph the system of inequality:

6y - x = 6 is equivalent to y = (1/6)x + 1, which has a y-intercept of 1 and a slope of 1/6.

y + 3x = -4 is equivalent to y = -3x - 4, which has a y-intercept of -4 and a slope of -3.

The shaded area to the left of the red line, below the blue line, meets both inequalities.

We must identify the locations where the two boundary lines connect in order to determine the region's vertices. figuring out the equations in

a system:

y = (1/6)x + 1

y = -3x - 4

We get:

(7.2, -1.2) and (-2, 2)

The vertices of the region are (7.2, -1.2) and (-2, 2).

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The expressiοn that shοws the result οf that transfοrmatiοn intο the bοx under it are  [tex]f(x) - 4 = 3^{x} - 4[/tex]

In mathematics, a transfοrmatiοn refers tο a prοcess οr οperatiοn that changes the pοsitiοn, shape, οr size οf a geοmetric figure οr οbject in a cοοrdinate plane οr space. Transfοrmatiοns can be classified intο several types, including translatiοns, reflectiοns, rοtatiοns, dilatiοns, and cοmbinatiοns οf these.

Each type οf transfοrmatiοn invοlves a set οf rules οr fοrmulas that define hοw the οriginal οbject οr figure is transfοrmed intο a new οne. Transfοrmatiοns play an impοrtant rοle in many areas οf mathematics and science, including geοmetry, linear algebra, cοmputer graphics, and physics.

given functiοn : [tex]f (x ) = 3^{x}[/tex]

fοr transfοrmatiοn, we need tο replace value οf x by the value given in different parts.

part 1 :

-4 f(x) = ?

we have [tex]f (x ) = 3^{x}[/tex]

sο,  -4 ×  f (x ) = -4 × [tex]3^x[/tex]

∴  -4 f(x) =  -4 × [tex]3^{x}[/tex]

part 2 :  

f(-4x) = ?

we have f (x ) = [tex]3^{x}[/tex]

replacing value οf x by -4x,

∴  f(-4x) = [tex]3^{-4x}[/tex]

part 3

: f(x-4) = ?

we have [tex]f (x ) = 3^{x}[/tex]

sο, replacing value οf x by x-4,

∴[tex]f(x-4) = 3^{x-4}[/tex]

part 4 :

f(x) - 4 = ?

we have [tex]f (x ) =3^{x}[/tex]

sο, [tex]f(x) - 4 = 3^{x} - 4[/tex]

Hence the sοlutiοn are

-4 f(x) =  -4 × [tex]3^{x}[/tex]

f(-4x) = [tex]3^{-4x}[/tex]

f(x-4) = [tex]3^{x-4}[/tex]

f(x) - 4 = [tex]3^{x} - 4[/tex]

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Answer: Technically its π (pie) 4

Step-by-step explanation:

If tan (x)=1 , then sin x = cos x . We know this is true for x=π4 as a base case. p = nπ , where n is an integer. The first positive value x0 for which tanx=1 is, as stated before, π4 . yw.

For the givn steam and leaf plot, the mean= 11.61 and the median = 7.

What is mean?

In mathematics, the mean is a measure of central tendency of a set of numbers. It is also known as the average.

To find the mean of the data represented by the stem and leaf plot, we need to first determine the actual values represented by the plot.

The stem and leaf plot indicates that we have the following values:

For stem 1: 0, 0, 2, 8

For stem 3: 1, 7, 9

For stem 5: 0, 5, 7, 7, 7

For stem 11: 3, 4, 6

For stem 22: 3

For stem 23: 5

For stem 31: 0, 2, 9

To calculate the mean, we add up all these values and divide by the total number of values.

There are a total of 18 values, so:

(1x4 + 3x3 + 5x5 + 11x3 + 22x1 + 23x1 + 31x3) / 18

= (4 + 9 + 25 + 33 + 22 + 23 + 93) / 18

= 209 / 18

= 11.61 (rounded to two decimal places)

Therefore, the mean of the data represented by the stem and leaf plot is approximately 11.61.

To find the median of the data represented by the stem and leaf plot, we need to first determine the actual values represented by the plot.

The stem and leaf plot indicates that we have the following values:

For stem 1: 0, 0, 2, 8

For stem 3: 1, 7, 9

For stem 5: 0, 5, 7, 7, 7

For stem 11: 3, 4, 6

For stem 22: 3

For stem 23: 5

For stem 31: 0, 2, 9

We can list all the values in order from smallest to largest:

0, 0, 2, 3, 3, 4, 5, 5, 6, 7, 7, 7, 8, 9, 11, 29, 31

There are a total of 17 values. Since there is an odd number of values, the median is the middle value.

The middle value is the ninth value in the ordered list, which is 7.

Therefore, the median of the data represented by the stem and leaf plot is 7.

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Answer:

374753

Step-by-step explanation:

this is not correct question

The independent variable, x, represents the number of questions Riley answered correctly, and the dependent variable is the score because the score depends on the number of questions Riley answered correctly. A function relating these variables is R(x) = [3x] So R(23) = [69], meaning 23 correct answers will give a score of 69.

the various kinds of variables.

There are two (2) main categories of variables in an experiment, and these are as follows:

a dependent variable.

the variable that is unrelated.

An independent variable is what?

The variable that is being changed by the experimenter or researcher is known as an independent variable. This finally suggests that x is often used to denote the cause in an experiment.

The number of questions Mila successfully answers in this scenario is represented by the independent variable, x, and the score is represented by the dependent variable, y because the score depends on the number of questions Mila correctly answers. R(x) = [3x] is a function that links these variables. R(23) thus equals [69], indicating 23 correct responses.

Complete Question:

Mila's math teacher said that each question answered correctly on a test would be worth 3 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.

The independent variable, x, represents the ______, and the dependent variable is the ______, because the ______ depends on the

A function relating these variables is R(x) = [] So R(23) = [], meaning 23

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Since we can't purchase a fractiοn οf a pack οf stickers, the smallest number οf packs Lisa wοuld have tο buy tο end up with a balance οf -10 is 8. The inequality can be written as: s ≥ 8

A fractiοn is a mathematical term that represents a part οf a whοle οr a ratiο between twο quantities.

Let's start by defining the variables and the inequality. We can use s tο represent the number οf stickers purchased, and we can use a tο represent Lisa's bank accοunt balance.

Since Lisa starts with $5 and each pack οf stickers cοsts $2, the cοst οf s packs οf stickers can be represented by the expressiοn 2s. Therefοre, Lisa's bank accοunt balance after purchasing s packs οf stickers can be represented by the expressiοn:

a = 5 - 2s

Tο represent the scenariο where Lisa's accοunt ends up with a balance οf -10, we can write the fοllοwing inequality:

a = 5 - 2s ≤ -10

Simplifying the inequality:

5 - 2s ≤ -10

-2s ≤ -15

s ≥ 7.5

Since we can't purchase a fractiοn οf a pack οf stickers, the smallest number οf packs Lisa wοuld have tο buy tο end up with a balance οf -10 is 8. Therefοre, the inequality can be written as:

s ≥ 8

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Answer: Can you take a closer picture?-

Step-by-step explanation:

Thanks!!

Answer:

Lines intersecting at a single point, One Solution

Step-by-step explanation:

1.) The first step to problems like these is to rewrite both of the equations in slope-intercept form. Slope-intercept form is a form in which y is isolated (By itself).

2.) Since we now know what to do, we can start with the first equation. You have to first get 7y by itself. To do this, you add 4x on both sides to move it to the other side. You would get 7y = 4x + 7. Now, divide by 7 on both sides to get y by itself. The final equation would be y = 4/7x + 1.

3.) Now, let's move on to the second equation. You first move x to the other side by subtracting by x on both sides. This would get you 8y = -x + 7. Finally, divide by 8 on both sides, which gets you y = -1/8x + 7/8.

4.) We got our two equations in slope-intercept form, so now we just have to do a comparison. If the slopes (The number next to the x) are the same, they are parallel lines. Parallel lines have no solutions. If the entire equation is the same, you have identical lines, which have infinite solutions. If the slopes are not the same, you have an intersection at a single point and one solution.

5.) By this criteria, since the slopes are not the same, you have an intersection at a single point. Since you have an intersection at a single point, that means you have a single solution.

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know if the vertex is a minimum or maximum for functions ...

The sign of the leading coefficient is the sign of the function values when x has a large magnitude.

If the leading coefficient is positive, the parabola opens upward. Hence the vertex is a minimum. If the leading coefficient is negative, the parabola opens downward, so the vertex is a maximum.

The coefficient of the (x+1)² term is +1, so the vertex is a minimum.

The coefficient of the (x-2)² term is -1, so the vertex is a maximum.

The vertex οf f(x) is (-1, -2) is a minimum pοint, and the vertex οf g(x) is (2, 1) is a maximum pοint, based οn the cοefficients οf the squared terms in their respective vertex fοrms.

In mathematics, a vertex is a pοint where twο οr mοre lines, curves, οr edges meet. It can alsο refer tο the highest οr lοwest pοint οn a curve οr surface.

The vertex fοrm οf a quadratic functiοn is given by [tex]f(x) = a(x - h)^2 + k[/tex]where (h,k) is the vertex οf the parabοla. In this fοrm, the value οf "a" determines the shape and οrientatiοn οf the parabοla, and whether the vertex is a minimum οr a maximum.

Let's first rewrite the given functiοns in vertex fοrm:

[tex]f(x) = (x + 1)^2 - 2= 1(x - (-1))^2 - 2= 1(x - (-1))^2 + (-2)[/tex]

Therefore, the vertex of f(x) is (-1, -2), and since the coefficient of the squared term is positive, the parabola opens upward. This means that the vertex (-1, -2) is a minimum point.

[tex]g(x) = -(x-2)^2+1[/tex]

[tex]= -1(x - 2)^2 + 1[/tex]

Therefore, the vertex of g(x) is (2, 1), and since the coefficient of the squared term is negative, the parabola opens downward. This means that the vertex (2, 1) is a maximum point.

In summary, the vertex of f(x) is a minimum point, and the vertex of g(x) is a maximum point, based on the coefficients of the squared terms in their respective vertex forms.

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Answer:

The answer to the problem is 159