What is the perimeter of a rectangle with a base of 9 ft and a height of 10 ft?

the solutions to the quadratic equation 1 = 2x^2 + 7x are:

[tex]x= \frac{(-7+\sqrt{51} )}{4}[/tex] and [tex]x= \frac{(-7-\sqrt{51})}{4}[/tex]

ToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToTo solve this quadratic equation by completing the square, we need to rewrite the equation in the form of (x + p)^2 + q = 0, where p and q are constants. This will allow us to solve for x.

First, we can factor out the coefficient of the x^2 term, which is 2:

[tex]2x^2 + 7x - 1 = 0[/tex]

Next, we can isolate the x^2 and x terms on one side of the equation by subtracting 1 from both sides:

[tex]2x^2 + 7x = 1[/tex]

Now, we need to add and subtract a constant term inside the parentheses to create a perfect square trinomial. To determine this constant term, we take half of the coefficient of the x term (which is 7/2) and square it:

[tex](\frac{7}{2} )^{2} = \frac{49}{4}[/tex]

So we add and subtract 49/4 inside the parentheses:

[tex]2x^2 + 7x + \frac{49}{4} - \frac{49}{4} = 1[/tex]

We can simplify the left side by factoring the perfect square trinomial:

[tex]2(x + \frac{7}{4} )^2 - \frac{51}{8} = 0[/tex]

Now, we can solve for x by isolating the perfect square term and taking the square root of both sides:

[tex]2(x + \frac{7}{4} )^2 = \frac{51}{8}[/tex]

[tex](x + \frac{7}{4} )^2 = \frac{51}{16}[/tex]

[tex]x + \frac{7}{4}=±\sqrt{\frac{51}{16} }[/tex]

[tex]x = -\frac{7}{4} ± \sqrt{\frac{51}{16} } /2[/tex]

Simplifying this expression, we get:

[tex]x = (-7 ±\sqrt{51} )/4[/tex]

Therefore, the solutions to the quadratic equation 1 = 2x^2 + 7x are:

[tex]x = (-7 + \sqrt{51} )/4 and x = (-7 -\sqrt{51} )/4.[/tex]

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The interval in which the inequality is true is:

-1 < x < 1

Here we know that:

f(x) = |x|

g(x) = x²

Now, remember that in a product:

a*A

we have:

|a*A | > a   if A > 1.

|a*A| < a    if A < 1.

So, in a square like in g(x) = x²

if  -1 < x < 1

Then the outcome will be smaller than the input, because we are multiplying by a numer smaller than 1.

Then:

f(x) > g(x)

|x| > x²

In the interval -1 < x < 1

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The value of every variable in the parallelogram is: a = 9 HK = 27.0 GK = 46 G = 63.5°

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.These shapes include squares, rectangles, rhombuses, and rhomboids. All of these shapes have four sides, four corners, and four angles

We know that sides of a parallelogram are parallel and congruent, as opposite angle

According to question  that GA equals HK, as:

46 is equal to 3a plus 19 When we subtract 19 from both sides, we get:

27 x 3a is the result of dividing both sides by 3:

we know that opposite angles in a parallelogram are congruent, we can use a = 9. Since angle H is 56 degrees, angle K must also be 56 degrees. The length of side HK can be determined using the Law of Cosines:

HK2 = GA2 + GK2 - 2(GA)(GK)cos(H) When we substitute the values we are familiar with, we obtain:

After solving the equation we obtain: HK2 = 462 + (3a + 19)2 - 2(46)(3a + 19)cos(56°).

HK2 = 2112 + 9a2 + 342a - 2764cos(56°) HK2 = 2112 + 9(9)2 + 342(9) - 2764cos(56°) HK2  732.4 By taking the square root of both sides, we obtain the following results:

∵ GA = 46, we can use the parallelogram's opposite sides being congruent to determine the length of side GK: HK  27.0

Then, we can use the Law of Cosines to determine the angle G's measurement:

cos(G) = (HK2 + GA2 - GK2) / (2(HK)(GA)) Using the values we are familiar with, we get,

cos(G) = (27.02 + 462 - 462) / (2(27.0)(46)) cos(G)  0.465 Using the inverse cosine, we get the following:

G ≈ 63.5°

Hence, the worth of every variable in the parallelogram is:

a = 9 HK = 27.0 GK = 46 G = 63.5°

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There is a 1.8% probability that a customer will buy clothes, shoes, AND jewelry.

This statement is false. The probability that a customer buys clothes, shoes, and jewelry is not given

How to solve the problem ?

Let's denote the event that a customer buys clothes by C, the event that a customer buys jewelry by J, and the event that a customer buys shoes by S. We are given that the probabilities of these events are independent. Therefore, the probability of a customer buying clothes and shoes, denoted by C and S, is simply the product of the probabilities of buying clothes and buying shoes, which is 0.6 × 0.3 = 0.18. Similarly, the probability of a customer not buying shoes and buying jewelry, denoted by S' and J, is simply the product of the probabilities of not buying shoes and buying jewelry, which is 0.7 × 0.1 = 0.07.

Using these probabilities, we can now check the statements:

There is a 15% probability that a customer buys NO clothes, NO shoes, and NO jewelry.

This statement is true. The probability that a customer buys none of these items is simply the complement of the probability that the customer buys at least one of them. Using the inclusion-exclusion principle, we have:

P(C ∪ J ∪ S) = P(C) + P(J) + P(S) - P(C ∩ J) - P(C ∩ S) - P(J ∩ S) + P(C ∩ J ∩ S)

P(C ∪ J ∪ S) = 0.6 + 0.1 + 0.3 - 0 - 0.18 - 0 + P(C ∩ J ∩ S)

P(C ∪ J ∪ S) = 0.52 + P(C ∩ J ∩ S)

Therefore, the probability that a customer buys none of these items is:

P((C ∪ J ∪ S)') = 1 - P(C ∪ J ∪ S) = 0.48 - P(C ∩ J ∩ S)

We are not given the value of P(C ∩ J ∩ S), but we know that it cannot be negative. Therefore, the maximum value of P((C ∪ J ∪ S)') is 0.48, which corresponds to the case where P(C ∩ J ∩ S) = 0. In this case, the probability that a customer buys none of these items is 0.48, which is 15% of 1.

There is a 70% probability that a customer does NOT buy shoes.

This statement is true. The probability that a customer does not buy shoes is simply the complement of the probability that the customer buys shoes, which is 0.3. Therefore, the probability that a customer does not buy shoes is 1 - 0.3 = 0.7, which is 70% of 1.

There is an 8.5% chance that a customer buys jewelry.

This statement is false. The probability that a customer buys jewelry is not given directly. However, we can use the information about the probability of not buying shoes and buying jewelry to find it. We have:

P(S' ∩ J) = P(S') × P(J) = 0.7 × 0.1 = 0.07

Therefore, the probability that a customer buys jewelry is:

P(J) = P(S' ∩ J) + P(S ∩ J) = 0.07 + 0 = 0.07

This is 7% of 1, not 8.5%.

There is a 1.8% probability that a customer will buy clothes, shoes, AND jewelry.

This statement is false. The probability that a customer buys clothes, shoes, and jewelry is not given

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Answer: -8x +10

Step-by-step explanation:

-2(2x -5) -4x

1. simplify parthentheses

-4x +10 -4x

add like terms

-8x +10

Now, we can write the matrix equation as:

AX = B

| 2 -6 -2 | | x | | 1 |

| 0 3 -2 | | y | = | -5 |

| 0 2 2 | | z | | -3 |

To write the given system of equations as a matrix equation, we will represent it in the form AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.

Given a system of equations:

We can represent the matrices as follows:

A = | 2 -6 -2 |

| 0 3 -2 |

| 0 2 2 |

X = | x |

| y |

| z |

B = | 1 |

| -5 |

| -3 |

Now, we can write the matrix equation as:

AX = B

| 2 -6 -2 | | x | | 1 |

| 0 3 -2 | | y | = | -5 |

| 0 2 2 | | z | | -3 |

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Answer:

3878.65

Step-by-step explanation:

Answer: 3876

Step-by-step explanation:

If you are asking how many months are in 323 years, then the answer is 3,876 months

323(12)

Answer: The image of (8, 7) after a reflection over the line y = -x is (-7, -8).

Step-by-step explanation:

The percent markdown rounded to the nearest percent is 13%.

Markdown represents the difference between the original or full price of an item and the current price that's reduced. It's typically expressed as a percentage.

To find the percent markdown, we first need to calculate the amount of markdown, which is the difference between the original price and the sale price:

Markdown = $175.90 - $153.77 = $22.13

Next, we need to find the percent markdown by dividing the markdown by the original price and multiplying by 100:

Percent Markdown = (Markdown / Original Price) x 100

Percent Markdown = ($22.13 / $175.90) x 100

Percent Markdown = 0.1258 x 100

Percent Markdown = 12.58%

Rounded to the nearest percent, the percent markdown is 13%.

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Step-by-step explanation:

Vertical angles of two crossing lines are equal so y = 163 degrees

  ... and  z = x    

Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.

The standard deviation is a measurement of how widely spaced out a set of data is from the mean. The bigger the dispersion or variability, the higher the standard deviation and the greater the magnitude of the value's divergence from its mean. It represents the absolute variability of a distribution.

Given data:

Number of population n = 300

probability p = 0.267

Mean is given as np:

np = 300*0.267

np = 80.1

standard derivation: √np(1 - p)

√np(1 - p) =  √80.1(1 - 0.267)

√np(1 - p) =  √58.7133

√np(1 - p) =  7.66

Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.

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Correct question:

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe 300 randomly selected individuals’ habits as they sneeze.

What are the mean and standard deviation?

Answer:

(x^2+3)(3x-4)

Step-by-step explanation:

To answer this question we can employ a technique called factor by grouping. This strategy has us factor out values from the first two numbers and last two numbers to simplify the expression.

3x^3-4x^2+9x-12

x^2(3x-4)+3(3x-4)

(x^2+3)(3x-4)

Therefore, the answer is the second option.

Answer:

Step-by-step explanation:

-(2x^2-x-3)

-(2x^2-3x+2x-3)

-[2x(x+1)-3(x+1)]

(x+1)(3-2x)

The period of a sinusoidal graph is the distance between two consecutive peaks or troughs of the graph. From the given graph, we can see that the graph completes one full cycle from x = 0 to x = 2π. Therefore, the period of the graph is 2π.

The period of a sinusoidal graph is the distance between two consecutive peaks or troughs of the graph. It can be determined by calculating the length of one complete cycle of the graph.

The period of a sinusoidal graph tells us how often the function repeats itself. It is an important characteristic of the function that can help us analyze its behavior and make predictions about its future values.

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Product A is priced at Ksh 55,000, while Product B is priced at Ksh 32,000.

Assume that the selling price for both the two items A and B is "S" and the cost price for both is "C". Using this knowledge, we can create two equations that relate the costs and revenues of the two items, one for Tom and one for John:

Tom: 5C - 2(5S) = [tex]P_1[/tex]

John: 3(5C) - 13C = [tex]P_2[/tex]

where [tex]P_1[/tex] and [tex]P_2[/tex] represent Tom's and John's respective profits.

We are aware that John deposits Ksh. 110,000 while Tom deposits Ksh. 230,000 at the end of the business day. Thus, we can say:

[tex]P_1[/tex] = 230,000 - 5C

[tex]P_2[/tex] = 110,000 - 18C

These values are what we obtain when we enter them into the equations for Tom and John:

5C - 2(5S) = 230.000 - 5C

When we simplify these equations, we obtain:

10C - 10S = 230,000

2C = 110,000

Solving for C, we get:

C = 55,000

We may determine S by adding this value back into the original equation:

10(55,000) - 10S = 230,000

Simplifying this equation, we get:

S = 32,000

Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

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Thus, remaining seats on the school bus that are empty is found as: 6 seats.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given data:

Total seats in bus = Total rows of seats * Number of seats in each row

Total seats in bus = 22 * 4

Total seats in bus = 88

Filled seats = 19 * 4 = 76

Left seats = 88 - 76 = 12

Now, 1/2 of the 12 seats is filled = 6 seats.

remaining seats = 6

Thus, remaining seats on the school bus that are empty is found as: 6 seats.

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Answer: x = [tex]\frac{1}{2}[/tex] , y= [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Answer:

LM = 40

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{LM}{LO}[/tex] = [tex]\frac{LN}{LP}[/tex] ( substitute values )

[tex]\frac{LM}{5}[/tex] = [tex]\frac{14+2}{2}[/tex] = [tex]\frac{16}{2}[/tex] = 8 ( multiply both sides by 5 )

LM = 5 × 8 = 40

Answer:

Solving 8x ÷ 4 = 100, we have:

2x = 100

x = 50

So the value of x is 50.

Answer:

x = 50

Step-by-step explanation:

To answer this question, we have to isolate the x. To do this, we have to get rid of any other numbers around it by doing the inverse of the operation.

1)

2)

This means that x is 50!

To check our answer is correct we can substitute 50 to x in the question...

It is correct!

Hope this helps, have a lovely day! :)

Answer:

w = -20

"The beautiful thing about learning is that no one can take it away from you." :)

Below 10 in.*6 in.*14 in., the triangular prism's volume is 420 cubic inches.

The area of the base must be multiplied by the prism's height in order to determine the volume of a triangular prism.

The base of this triangular prism is a triangle with a base of 6 inches and a height of 10 inches, so its area is:

Area of base = (1/2) × base × height = (1/2) × 6 in × 10 in = 30 in²

The height of the triangular prism is given as 14 inches.

Hence, the triangular prism's volume is:

Volume = Area of base × height = 30 in² × 14 in = 420 cubic inches.

So, the volume of the triangular prism is 420 cubic inches.

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The expression 1 -25x² +10xy-y² in product form is (1-5x-y)(1+5x-y).

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation. Expressions can be simple, such as a single number or variable, or complex, involving multiple operations and variables. Expressions are used in a variety of mathematical contexts, including algebra, calculus, and geometry. They can be evaluated to obtain a numerical value, simplified by combining like terms or using algebraic identities, or used to represent mathematical relationships and patterns.

Here,

The given expression can be written as a product of two binomials as follows:

(1-5x-y)(1+5x-y)

Expanding this product gives:

1(1) + 5x(1) - y(1) - 5x(1) - 25x² + 5xy + y(1) - y(5x) - y²

Simplifying this expression gives:

1 - 25x² + 10xy - y²

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(a) The probability of the questions being history, literature, and science in that order is 5/18 x 6/17 x 7/16, which is 0.04.

(b) The probability of all three questions being literature questions is 6/18 x 5/17 x 4/16, which is 0.024.

(c) The probability of the first question being science, the second history, and the third science is 7/18 x 5/17 x 7/16, which is 0.05.

In playing cards, it can be used to predict the likelihood of a certain outcome or to make decisions based on the probability of certain events occurring.

(a) The probability of the questions being history, literature, and science in that order is 5/18 x 6/17 x 7/16, which is 0.04.

(b) The probability of all three questions being literature questions is 6/18 x 5/17 x 4/16, which is 0.024.

(c) The probability of the first question being science, the second history, and the third science is 7/18 x 5/17 x 7/16, which is 0.05.

The probabilities of each of these scenarios can be calculated by multiplying the probabilities of drawing each of the three cards in the desired order.

For the first scenario, the probability of drawing a history question is 5/18, the probability of drawing a literature question is 6/17 (since there is one fewer card), and the probability of drawing a science question is 7/16 (since there are two fewer cards).

Multiplying these together gives us the probability of the questions being history, literature, and science in that order, which is 0.0771.

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Answer: 50 mph

Step-by-step explanation:  

Answer:

x = -2,  y = 6

Step-by-step explanation:

First, find the opposite of 10 by multiplying 5x+3y=8 by -2 to eliminate 10x.

10x+10y=40

-2(5x+3y=8)

10x+10y=40

-10x-6y=-16       (Subtract 10y - 6y)   (Subtract 40 - 16)

      4y = 24      (Divide by 4 on both sides)

       y = 6

Substitute 6 in the y value in any of the equations.

 10x+10(6)=40       (Replaced 10y with 10(6) )

 10x+60=40

      -60 = -60     (Subtract 60 from both sides)

10x     = -20        (Divide by 10 on both sides)

10           10

x = -2

The simplified expression would be 11a + 2.

In order to simplify the given expression, we first need to combine like terms.

The terms can be combined by adding their coefficients:

Now we can substitute these combined terms back into the original expression:

(7a + 9) + (4a - 7) = 7a + 4a + 9 - 7

And then simplify further:

= 11a + 2

Therefore, the simplified form of the expression (7a + 9) + (4a - 7) is 11a + 2.

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Based on these calculations, Option 3 yields the highest future value at age 35.

To compare the investment options at different ages, we can use the future value formula:

FV = PV * (1 + r)^t

where:

FV = future value of the investment

PV = present value or initial investment

r = annual growth rate (as a decimal)

t = number of years the investment grows

Here are the general equations for each option:

To compare the options at ages 20, 25, 30, and 35, calculate the future value for each option at those ages by plugging in the corresponding value of t.

Age 20:

FV1 = N/A (Option 1 hasn't started yet)

FV2 = 50 * (1 + 0.08)^0 = $50

FV3 = N/A (Option 3 hasn't started yet)

Age 25:

FV1 = N/A (Option 1 hasn't started yet)

FV2 = 50 * (1 + 0.08)^5 ≈ $73.86

FV3 = 100 * (1 + 0.07)^0 = $100

Age 30:

FV1 = 50 * (1 + 0.09)^0 = $50

FV2 = 50 * (1 + 0.08)^10 ≈ $107.95

FV3 = 100 * (1 + 0.07)^5 ≈ $140.26

Age 35:

FV1 = 50 * (1 + 0.09)^5 ≈ $77.16

FV2 = 50 * (1 + 0.08)^15 ≈ $157.46

FV3 = 100 * (1 + 0.07)^10 ≈ $196.72

Based on these calculations, Option 3 yields the highest future value at age 35.

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Comparing the box plots, the statements which are not true are Class A has greater variability and over half of the students in Class A have two or more siblings.

Based on the given box plots, we can make the following observations:

a) Class B has a higher median: True. We can see from the plot that the median line for Class B (represented by the orange line inside the box) is higher than the median line for Class A (represented by the blue line inside the box).

b) Class A has greater variability: False. We can see from the plot that the boxes for both classes have similar lengths, indicating similar variability. However, Class A has a few more outliers compared to Class B, which indicates some extreme values that are far from the median.

c) Both A and B have students who are only children: True. We can see from the plot that both classes have a box plot labelled "0" indicating that some students in each class are only children.

d) Over half of the students in class A have two or more siblings: False. We can see from the plot that the box labelled "2+" in Class A only covers about a third of the box, indicating that less than a third of the students have two or more siblings. Therefore, the statement is not true.

Therefore, the answer is b) Class A has greater variability and d) Over half of the students in Class A have two or more siblings.

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