Find the equation of the line through the points (−2,−10)
and (−2,−5).

Answer:

16 units.

------------------

According to triangle inequality theorem, any side of a triangle is less than the sum of the other two.

Let the missing side is largest, then it must be less than:

The closest whole number less than 17 is 16.

Therefore, a function equivalent to y = x² - 8x + 10 is: y = (x - 4)² + 4.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range), with the property that each input is associated with exactly one output. Functions are often denoted using function notation, such as f(x) or g(y), where the letter in parentheses represents the input and the expression to the right of the parentheses represents the output. Functions are used in many areas of mathematics, science, and engineering to model real-world phenomena and to solve problems. They are essential tools for analyzing data, making predictions, and creating mathematical models of physical and natural systems.

Here,

The function y = x² - 8x + 10 is a quadratic function, which has a U-shaped graph. To find a function that is equivalent to this function, we can start by completing the square, which involves adding and subtracting a constant term to create a perfect square trinomial. We can then write the function in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Completing the square, we get:

y = x² - 8x + 10

= (x² - 8x + 16) - 6 + 10 // Add and subtract (8/2)² = 16 to create a perfect square

= (x - 4)² + 4

Now we can see that the vertex of the parabola is at (4, 4). We also see that the coefficient of the squared term is 1, which means the parabola opens upward.

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The exact perimeter of the triangle is: 8+3√17 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:
The distance formula between two points (x1, y1) and (x2, y2) is:

[tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

So, to find the lengths of the sides of the triangle with vertices (-3, 5), (-3, 2), and (-1, -3), we can use the distance formula as follows:

Between (-3, 5) and (-3, 2):

[tex]d =\sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}[/tex]

= [tex]\sqrt{[(2 - 5)^2 + (-3 - (-3))^2]}[/tex]

= [tex]\sqrt{[(-3)^2 + 0^2]}[/tex]

= [tex]\sqrt{9}[/tex]

= 3

Between (-3, 2) and (-1, -3):

[tex]d = \sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}[/tex]

= [tex]\sqrt{[(-3 - 2)^2 + (-1 - (-3))^2]}[/tex]

= [tex]\sqrt{[(-5)^2 + 2^2]}[/tex]

= [tex]\sqrt{29}[/tex]

Between (-1, -3) and (-3, 5):

[tex]d = \sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}[/tex]

= [tex]\sqrt{[(5 - (-3))^2 + (-3 - (-1))^2]}[/tex]

= [tex]\sqrt{[8^2 + (-2)^2]}[/tex]

= [tex]\sqrt{68}[/tex]

Now we can add up the lengths of the sides to get the perimeter:

[tex]P = 3 + \sqrt{29} + \sqrt{68}[/tex]

So the exact perimeter of the triangle is:

8 + 3√17 units.

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Answer:

there were 15 almonds in the snack pack.

Step-by-step explanation:

Let's use variables to represent the unknown quantities. Let's call the number of almonds in the snack pack "a", and the number of cashews in the snack pack "c".

we can use the following equations to represent the problem:

c = 2a (the number of cashews is twice the number of almonds)

c - 10 = a + 5 (there are 5 more cashews than almonds after Sylvia eats 10 cashews)

Substituting the first equation into the second equation, we get:

2a - 10 = a + 5

Solving for "a", we get:

a = 15

So there were 15 almonds in the snack pack.

If a basketball player makes 40% of his shots from the free throw line, then the mean for  the number of shots that he makes is 0.928

Since the basketball player makes 40% of his shots from the free throw line and he takes 3 shots, the number of shots he makes, x, can take on the values 0, 1, 2, or 3.

The probability of making a shot is 0.4, so the probability of missing a shot is 0.6. Since each shot is independent, we can use the binomial probability formula to calculate the probability of making x shots:

P(X = x) = (3 choose x) × (0.4)^x × (0.6)^(3-x)

where (3 choose x) is the binomial coefficient that represents the number of ways to choose x items from a set of 3.

To find the mean for x, we need to multiply each possible value of x by its probability and then sum the results:

E(X) = 0 × P(X = 0) + 1 × P(X = 1) + 2 × P(X = 2) + 3 × P(X = 3)

Substituting the binomial probabilities into this formula, we get:

E(X) = 0 × (1) × (0.6)^3 + 1 × (3 choose 1) × (0.4)^1 × (0.6)^2 + 2 × (3 choose 2) × (0.4)^2 × (0.6)^1 + 3 × (1) × (0.4)^3 × (0.6)^0

E(X) = 0 + 0.432 + 0.432 + 0.064

E(X) = 0.928

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The loan that will have a lower balance is;

Option B: The PLUS Loan will have a lower balance by $70.47 at the time of repayment.

To determine which loan will have a lower balance at the time of repayment, we need to calculate the total amount of interest that will be accrued on each loan.

1) For the unsubsidized Stafford loan:

The loan amount is $3,725.

The annual interest rate is 4.65%, compounded monthly. This means the monthly interest rate is 4.65%/12 = 0.3875%.

The loan will be repaid in 6 months, so there will be 6 monthly compounding periods.

Using the formula for compound interest, the balance of the loan at the time of repayment will be:

balance = principal x (1 + monthly interest rate)^number of compounding periods

balance = $3,725 x (1 + 0.003875)^6

balance = $3,901.95

So the balance of the unsubsidized Stafford loan at the time of repayment will be $3,901.95.

2) For the PLUS loan:

The loan amount is $3,725.

The annual interest rate is 5.65%, compounded monthly. This means the monthly interest rate is 5.65%/12 = 0.4708%.

The loan will be deferred until graduation, which is in 6 months, so there will be 6 monthly compounding periods.

Using the formula for compound interest, the balance of the loan at the time of repayment will be:

balance = principal x (1 + monthly interest rate)^number of compounding periods

balance = $3,725 * (1 + 0.004708)^6

balance = $3831.47

So the balance of the PLUS loan at the time of repayment will be $3831.47

Difference in balance = $3,901.95 - $3831.47

= $70.47

Therefore, the PLUS loan will have a lower balance at the time of repayment, by an amount of $70.47

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Based on the information in the paragraph, we can infer that the order of the terms is as follows. Expected value, permutation and combination.

Some probability situations involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.

There are two ways to sort or combine dependent event results. Permutations are groupings in which the order of the objects matters. Combinations are groupings in which the content matters but the order does not. In accordance with the above, the terms must be arranged in the following order:

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Vera's location after three hours is thus 2,100 feet above sea level.

Division is a basic arithmetic operation used to find how many times one number (the divisor) is contained within another number (the dividend). The result of a division operation is the quotient. Division is often represented using the symbol "÷" or "/".  Sometimes division results in a remainder, which is the amount left over after dividing as much as possible.  Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. It is used in a wide variety of mathematical and real-world contexts, such as sharing equally, calculating rates, and solving equations.

Here,

To find Vera's location after three hours of climbing down the mountain, we first need to convert three hours into minutes. There are 60 minutes in one hour, so three hours is:

3 hours x 60 minutes/hour = 180 minutes

Vera descends at a rate of five feet per minute, so after 180 minutes, she will have descended:

180 minutes x 5 feet/minute = 900 feet

3,000 - 900 = 2,100

Therefore, Vera's location after three hours is 2,100 feet above sea level.

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In summary, A, B, E are valid linear programming relationships, while C, D, F are not.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

A. -1A+2B less than or equal to 70: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

B. 2A -2B= 50: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

C. 1A-2B^2 less than or equal to 10: This relationship is not acceptable for a linear programming model because it contains a quadratic term, B^2. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

D. 3(square root of) A + 2B greater than or equal to 15: This relationship is not acceptable for a linear programming model because it contains a square root function. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

E. 1A+1B=6: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

F. 2A+5B+1AB less than or equal to 25: This relationship is not acceptable for a linear programming model because it contains a product of variables, AB. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

Therefore, In summary, A, B, E are valid linear programming relationships, while C, D, F are not.

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The length of PR is 4.8 units.

In geometry, a trapezoid, also known as a trapezium in some countries, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs. The angle between the bases of a trapezoid determines its height.

Trapezoids can be classified into several types based on their properties, such as:

Isosceles trapezoid: a trapezoid with congruent legs.

Right trapezoid: a trapezoid with a right angle between one of its legs and one of its bases.

Scalene trapezoid: a trapezoid with no congruent sides.

Since QR is parallel to NO, we have:

∆PNQ ~ ∆PRO (by AA similarity)

So we can write:

PR/PQ = PO/PN

PR/7.2 = 6/9

PR = 7.2 × 6/9

PR = 4.8

Therefore, the length of PR is 4.8 units.

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The solution to the matrix is x1 = (-555 - 356x3)/90, x2 = (138 + 89x3)/10 and x3 = free variable

To find the solution to this matrix, we need to perform row operations to put it into row echelon form or reduced row echelon form. We can do this by adding multiples of one row to another row, multiplying a row by a nonzero scalar, and swapping two rows.

Here are the row operations we can use to put this matrix into row echelon form:

1. Add 5 times the first row to the third row to eliminate the 5 in the (3,1) entry:

0 0 -9 6

0 -1 -4 4

25 35 11 38

2. Multiply the second row by -1 to make the pivot in the second row, second column equal to 1:

0 0 -9 6

0 1 4 -4

25 35 11 38

3. Add 9 times the second row to the first row to eliminate the -9 in the (1,3) entry:

0 9 0 -30

0 1 4 -4

25 35 11 38

4. Add -25 times the second row to the third row to eliminate the 25 in the (3,1) entry:

0 9 0 -30

0 1 4 -4

0 10 -89 138

5. This matrix is now in row echelon form. We can solve for the variables by back-substitution. Starting with the last row:

0 10 -89 138 | x3

We have:

10x2 - 89x3 = 138

Solving for x2, we get:

x2 = (138 + 89x3)/10

Substituting this expression for x2 in the second row, we have:

Copy code

0 1 4 -4 | (138 + 89x3)/10

Solving for x1, we get:

9x1 + 4(138 + 89x3)/10 = -30

Simplifying and solving for x1, we get:

x1 = (-555 - 356x3)/90

So the solution to the matrix is:

x1 = (-555 - 356x3)/90

x2 = (138 + 89x3)/10

x3 = free variable

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Answer:

The investment in the fund was $19000 x 0.12 = $2280

The investment in the stock was $19000 - $2280 = $16720

The net profit was $520, so the amount of the profit from the fund was $520 x (2280/16720) = $136

The amount of the loss from the stock was $520 - $136 = $384

Answer:

Determine Your Budget.

Check Your Credit.

View Multiple Rentals.

Consider Roommates.

Consider a Cosigner.

Gather Your References.

Check Out the Neighborhood.

Check All the Websites.

The required choice is true of an observational study B, C, and D.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
Option a is not true of an observational study. In an observational study, the researcher cannot control the variables of interest, unlike in a true experiment where the researcher can manipulate the variables.

Option b is true of an observational study. Since the researcher cannot control the variables of interest, the study is entirely based on observing the subjects and collecting data.

Option c is true of an observational study. The data collected in an observational study is similar to the data collected in a true experiment, and the same statistical methods can often be used to analyze both types of data.

Option d is true of an observational study. Since the researcher cannot control the variables of interest, they have to take advantage of natural variation in the variables to draw conclusions.

Thus, Options B, C, and D are correct.

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Answer:

Sure In this context, a weak negative linear relationship between the number of hours worked and the amount of donations collected means that as the number of hours worked by Thor each week increases, the amount of donations collected by the organization each week decreases, but the relationship is not very strong.

When we say that the correlation between two variables is weak, we mean that there is a low degree of association between them. In this case, the negative correlation suggests that there is a tendency for the amount of donations collected to decrease as the number of hours worked increases, but the relationship is not very strong, meaning that there is a lot of variability in the data and it is difficult to make strong predictions or conclusions based on this relationship alone.

It is important to note that correlation does not necessarily imply causation, so a weak negative linear relationship between the number of hours worked and the amount of donations collected does not necessarily mean that one variable causes the other. Other factors may be influencing the amount of donations collected by the organization each week, and further analysis would be required to determine the nature and strength of these relationships.

Step-by-step explanation:

The length of ML in the line segment is 35 units.

The figure below has the following length as follows:

LN = 79 units

Let's find ML in the line segment as follows:

LM + MN = LN

Hence,

LM = 5y - 5

MN = 4y + 12

Therefore,

LN = 5y - 5 + 4y + 12

79 = 5y - 5 + 4y + 12

79 = 9y + 7

79 - 7 = 9y

72 = 9y

divide both sides by 9

y = 72 / 9

y = 8

Therefore,

ML = 5(8) -5

ML = 40 - 5

ML = 35 units

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Answer:

Step-by-step explanation:

If (x + a) is a factor of x³ + 8x² + 4ax - 3a, then we know that dividing x³ + 8x² + 4ax - 3a by x + a will give a quotient of x² + (8 - a)x + (4a - 3), and a remainder of 0.

We can write this as:

x³ + 8x² + 4ax - 3a = (x + a)(x² + (8 - a)x + (4a - 3))

Expanding the right-hand side, we get:

x³ + 8x² + 4ax - 3a = x³ + (8-a)x² + (4a-3)x + ax² + (8-a)ax + (4a-3)a

Collecting like terms, we get:

x³ + 8x² + 4ax - 3a = x³ + (a+8)x² + (5a-3) x + a(4a-3)

Comparing the coefficients of x², x and the constant term, we get the following equations:

a + 8 = 8   --> a = 0

5a - 3 = 0   --> a = 3/5

4a^2 - 3a = 0 --> a(4a-3) = 0

Therefore, we have:

a³ - 4a² + 3a = a(a² - 4a + 3) = a(a-1)(a-3) = 0

So, a can be 0, 1, or 3

Therefore, the possible values of a are 0, 1, and 3.

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

A polygon is any form having three sides. Although a circle is curved and devoid of sides and angles, it is not categorised as a polygon even if it is a plane figure.

If the polygon translates 3 units to the left and 1 unit down, the coordinates of the new vertices would be:

A' (0, 3)

B' (2, 2)

C' (0, 1)

D' (-2, 2)

To find the length of diagonal AC, we can use the distance formula:

AC = √[(3-3)^2 + (2-4)^2] ≈ 2 units

If the polygon translates 3 units further to the left and 4 units down, the coordinates of the new vertices would be:

A'' (-3, -1)

B'' (-1, -2)

C'' (-3, -3)

D'' (-5, -2)

To find the length of diagonal A'C', we can use the distance formula:

A'C' = √[(0-0)^2 + (1-3)^2] ≈ 2 units

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

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Answer:

181

Step-by-step explanation:

To simplify this expression, we need to apply the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses: 9 ÷ 3 = 3.

Then, we add 6 + 3 = 9.

Finally, we divide 1,629 by 9 to get the answer:

1,629 ÷ 9 = 181.

Therefore, 1,629 ÷ (6 + 9 ÷ 3) simplifies to 181.

The sum of 106 and h can be written as an expression in the following way:   106 + h

This expression represents the sum of the two numbers, 106 and h. We can simplify this expression by combining like terms, but since h is a variable and 106 is a constant, we cannot combine them. Therefore, the expression remains as 106 + h.

In conclusion, the sum of 106 and h is represented by the expression 106 + h.

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Answer:

B

Step-by-step explanation:

urheheyfthxhzhditoiytdyifxzydzyfuyrzuysriduyrsute

This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.

The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.

The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

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Answer:

Step-by-step explanation:

D, 57,500

Answer:

Step-by-step explanation:

o divide 6029 by 28, we can use long division:

             215

          ---------

28 |    6029

             56

             ---

            182

           168

             ---

           144

          140

           ---

            4

So 6029 divided by 28 is 215 with a remainder of 4. Therefore, the answer to the problem is:

6029/28 = 215 R 4

So overall, you can expect to make a profit of $166.67 if you play the game 100 times.

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

To determine how much you expect to win or lose if you play the game 100 times, we need to calculate the expected value of each round and then multiply it by the number of rounds.

Let X be the random variable that represents the amount you win in one round of the game. The possible outcomes of X are winning $14, winning $12, or losing $10. We can calculate the expected value of X using the following formula:

E(X) = P(win $14) × $14 + P(win $12) × $12 + P(lose $10) × (-$10)

To calculate the probabilities, we can use the fact that there are 5 red balls, 3 green balls, and 4 yellow balls in the bag. The probability of drawing a red ball is therefore 5/12, the probability of drawing a green ball is 3/12, and the probability of drawing a yellow ball is 4/12.

So we have:

E(X) = (5/12) × $14 + (4/12) × $12 + (3/12) × (-$10)

E(X) = $5/3

This means that on average, you expect to win $5/3 per round. Over 100 rounds, you can expect to win:

100 × $5/3 = $166.67

However, it's important to note that this is just an average - in reality, you may win more or less than this amount depending on the luck of the draw.

Therefore, overall, you can expect to make a profit of $166.67 if you play the game 100 times.

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The linear function that models this problem is y = 25x + 25 and the cost for 6 hours is $175

To solve this problem, we have to find the slope and y-intercept of the line.

m = y2 - y1 / x2 - x1

Taking two points from the line;

A = (2, 75)

B = (5, 150)

Substituting the values into the formula;

m = 150 - 75 / 5 - 2

m = 25

Using the slope;

y = mx + c

150 = 25(5) + c

150 = 125 + c

c = 150 - 125

c = 25

The equation of line is ;

y = 25x + 25

The cost for 6 hours will be

y = 25(6) + 25

y = 175

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Trigonometric functions have some interesting symmetry properties

If tan x= -2.5, then tan (-x)= 2.5 and If sin x= 0.4 then sin (-x)= -0.4

If cos x = 0.9 then cos (-x)= 0.9  If tan x = 1.5 then tan (pi+x)= -1.5

Trigonometric functions are mathematical functions that are widely used in various fields, including mathematics, physics, and engineering. The most commonly used trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Trigonometric functions have some interesting symmetry properties. For example, the sine and tangent functions are odd functions, which means that sin(-x) = -sin(x) and tan(-x) = -tan(x). On the other hand, the cosine function is an even function, which means that cos(-x) = cos(x).

These symmetry properties have important implications in many applications of trigonometric functions. For example, if we know the value of sin(x), we can immediately determine the value of sin(-x) by using the odd symmetry property. Similarly, if we know the value of cos(x), we can determine the value of cos(-x) by using the even symmetry property.

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Answer:

5 or -2

Step-by-step explanation:

|2x-3| can equal either (2x-3) or -(2x-3) thus

(2x-3) = 7

2x = 10

x = 5

-(2x-3) = 7

-2x = 4

x = -2

Answer: it’s 5 or -2, |2x-3| can equal either (2x-3) or -(2x-3) thus(2x-3) = 72x = 10x = 5-(2x-3) = 7-2x = 4x = -2

Step-by-step explanation: hope this helps0^0

The moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.

Since we know the tensions in cables AB and BC, we can find the horizontal and vertical components of the forces exerted by the cables at point B:

The horizontal component of the force exerted by the cable

AB = 630 cos(45) = 444.21 N

Similarly,

The vertical component of the force exerted by the cable  = 444.21 N

The horizontal component of the force exerted by the cable  = 637.55 N

The vertical component of the force exerted by cable  = 367.50 N

Total horizontal force = 444.21 N + 637.55 N = 1081.76 N

Total vertical force = 444.21 N + 367.50 N = 811.71 N

The moment about point O of the resultant force exerted on the tree by the cable at B is given by:

Moment = F * d

Using the Pythagorean theorem, we can find the magnitude of the resultant force,
= 1351.44 N

Perpendicular distance = 4 m * sin(45) = 2.828 m

Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is,

Moment = F * d = 1351.44 N * 2.828 m = 3830.06 N·m

Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.

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