What is the area of this trapezoid

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The value of x is -1 and 3 for which x makes the equation.

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

Given: 1 + (x-1)² = 5

We have to solve it for x and find the value of x.

1 + (x-1)² = 5

We solve this equation by factorization and we get

1 + x² - 2x + 1 = 5

x² - 2x + 2 -5 = 0

x² - 2x - 3 = 0

x² + x - 3x - 3 = 0

x(x+1) -3(x+1) = 0

(x+1)(x-3) = 0

x= -1, 3

Hence, the value of x is -1 and 3 for which x makes the equation.

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3x^2 + 4x - 3 = ( 3x -2 ) (x + 2) + 1

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.

Given:- p(x) = 3x^2 + 4x - 3 and g(x) = 3x - 2

p(x) ÷ g(x)

3x^2 + 4x - 3  ÷ ( 3x - 2)  

[tex]\frac{3x^2+4x-3}{3x-2} =(x+2 )+ \frac{1}{3x-2}[/tex]

Quotient =  x + 2

Remainder = 1

Hence, 3x^2 + 4x - 3 = ( 3x -2 ) (x + 2) + 1

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The size of each payment for the sinking fund must be $1586.87.

A sinking fund is a collection of funds that have been put up or saved to pay off bonds or debts. A corporation that issues debt will eventually have to pay that loan back, and the sinking fund lessens the burden of a significant outflow of revenue. The corporation creates a sinking fund so that it may make contributions to it in the years before the bond matures.

The sinking fund formula is given as:

A = P * ((1 + r/n)ⁿˣ - 1) / (r/n)

61000 = P * ((1 + 0.009833/6)⁽⁶⁽⁹⁾ ⁻ ¹⁾/ (0.009833/6)

61000 = P * 38.4647

P = 1586.87

Hence, the size of each payment for the sinking fund must be $1586.87.

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The surface formed by the equation 25x²+4y²+z²=100 is an ellipse.

In mathematics, an ellipse is a planar curve with two focus points, where the total of the two distances from any point on the curve to the focal points is a constant. It generalises the shape of a circle, a unique variety of ellipse in which the two focus points coincide. The eccentricity of an ellipse is used to calculate its length.

We may set one of the variables at a constant value and then plot the resulting 2D curve in the plane created by the other two variables in order to sketch the surface. This procedure can be repeated for various constant values to get a rough surface drawing.

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The organized list has the following outcomes:

H1                 T1        

H2                T2

H3                T3

H4                T4

H5                T5

H6                T6

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given:

Two events take place.

Let event A be flipping a coin

Let event B be rolling a 6-sided die.

Now, a coin has two faces; one is the head and the other is the tail.

So, the possible outcomes of event A are: {H, T}

H → Head, T → Tail.

Now, a six-sided die has six faces each marked with a number. The numbers marked ranges from 1 to 6.

So, the possible outcomes of event B are {1, 2, 3, 4, 5, 6}

Now, each element of set A should match all the elements of set B.

Now, the tabular form should have a row of outcomes of B and a column of outcomes of event A. Thus,

Outcomes          1          2       3        4         5          6  

   H                 H1         H2     H3     H4       H5      H6

   T                 T1         T2     T3        T4      T5         T6

Therefore, the organized list has the following outcomes:

H1                 T1        

H2                T2

H3                T3

H4                T4

H5                T5

H6                T6

Finally, the correct tree diagram is attached below.

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Complete question:

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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Answer:

  y = -3

Step-by-step explanation:

You want the equation of a line with slope 0 through the point (-2, -3).

The point-slope form equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Adding k to both sides gives the "y =" form ...

  y = m(x -h) +k

When m=0 and (h, k) = (-2, -3), this becomes ...

  y = 0(x -(-2)) + (-3)

  y = -3 . . . . . . simplified

__

Additional comment

Anything times 0 is 0. So, the product 0(x +2) is 0.

Anything added to 0 is unchanged. So, the sum y = 0 -3 is y = -3.

When the slope is zero we get y= -3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

As, the Point-slope form

The point-slope form equation for a line with slope m through point (h, k) is

y = mx + b

When m=0 and (h, k) = (-2, -3)

y = 0(x -(-2)) + (-3)

y = -3

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For the polynomial 9x² - 49, the values of a and b include the following:

a = 3x

b = 7

In Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:

a² - b² = (a + b)(a - b).

Where:

a and b are numerical values (numbers or numerals).

Based on the information provided, we have the following polynomial function:

9x² - 49

By using the sum-product pattern, we have the following:

9x² + 21x - 21x - 49

By writing the common factor from the two pairs, we have the following:

(9x² + 21x) + (-21x - 49)

3x(3x + 7) - 7(3x + 7)

By rewriting in factored form, we have the following:

9x² - 49 = (3x - 7)(3x + 7)

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The solutions of  x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,

which is the x-coordinate of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9

"It is a polynomial equation with degree two."

"The general form of quadratic equation is  , where a, b, c are real numbers with a ≠ 0."

here, we have,

For given question,

We have been given an quadratic equation  x² - 2x - 4 =  -3x + 9

We simplify above quadratic equation.

=>  x² - 2x - 4 =  -3x + 9

solving we get,

=>  x = -4.14 and x = 3.14

Consider the graphs for y = x² - 2x - 4 and y = -3x + 9 as shown below.

Therefore, the solutions of  x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,

which is the x-coordinates of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9

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The slope of the linear function is given as follows:

3/2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope represents the rate of change of a linear function, meaning that it is calculated as the change in y divided by the change in x.

Considering points (-4,-4) and (-2, -1), we have that when x increases by 2, y increases by 3, hence the slope is given as follows:

m = 3/2.

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Step-by-step explanation:

=6+(-4)(2-3)²

=6+(-4)(-1)²

=6-4×1

=2

Answer:

30k^2+55k+25

Step-by-step explanation:

30k^2+30k+25k+25

=30k^2+55k+25

[tex]30k { }^{2} + 30k + 25k + 25[/tex]

[tex]30k ^{2} + 55k + 25[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{65}~,~\stackrel{y_1}{149})\qquad (\stackrel{x_2}{105}~,~\stackrel{y_2}{221}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{221}-\stackrel{y1}{149}}}{\underset{\textit{\large run}} {\underset{x_2}{105}-\underset{x_1}{65}}} \implies \cfrac{ 72 }{ 40 } \implies \cfrac{ 9 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{149}=\stackrel{m}{ \cfrac{ 9 }{ 5 }}(x-\stackrel{x_1}{65})\implies y-149=\cfrac{ 9 }{ 5 }x-117 \\\\\\ y=\cfrac{ 9 }{ 5 }x-117+149\implies \boxed{y=\cfrac{ 9 }{ 5 }x+32} \\\\\\ \stackrel{\textit{Celsius is 70, so x = 70}}{y=\cfrac{ 9 }{ 5 }(70)+32}\implies \boxed{y = 158}[/tex]

The correct option is - D. The degree of F(x) is at most 9, shows the largest number of turning points of polynomial function.

Several kinds of polynomial functions exist. They include linear, quadratic, cubic, among many other types.

A polynomial function with degree n is provided to us.

The largest number of turning points is what we're looking for.

The most turning points a polynomial function can have are:

n - 1

Thus, the degree of F(x) is at most 9.

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The quantity 8 to the power of x end quantity over 16

In mathematics, two expressions are said to be equivalent if they have the same value for all possible values of the variables involved. In other words, equivalent expressions represent the same mathematical object or concept, but they may be expressed in different forms or notations.

Equivalent expressions are expressions that have the same value for all possible values of the variables involved, and they can be used to simplify or manipulate algebraic expressions.

Then we have;

8^x/16

= 2^3(x)/2^4

Then we use the laws of exponents;

2^3x - 4

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The probability and the likelihood, that the marble drawn is not red is high which is 4/5.

To determine how likely something is gonna occur, use probability. Several things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty.

It is stated that there is a 2/10 chance of drawing a red marble at random.

We can deduct the likelihood of drawing a red marble from one to determine the likelihood that the drawn marble is not red (since the probability of an event and its complement add up to 1).

So, the probability of drawing a marble that is not red is -

1 - 2/10 = 8/10 = 4/5

Therefore, the probability that the marble drawn is not red is 4/5.

The likelihood of an event is a measure of how plausible it is, given some evidence or knowledge.

In this case, we can say that the likelihood of drawing a marble that is not red is high, since there are more marbles in the jar that are not red than those that are red.

Therefore, the likelihood of drawing a marble that is not red is high.

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Answer: 10

Step-by-step explanation: any number to the first power is the number being multiplied

Answer: 10

Step-by-step explanation: Any number to the first power equals the same number, for example: 4 to the first power is 4, or in this case 10 to the first power = 10.

Answer:

Step-by-step explanation:

We can simplify the expression using the rules of exponents:

(-27)^(-2/3) = 1/(-27)^(2/3)

Now, we can use the fact that (-a)^(2/3) = (a^(2/3)) to simplify the expression further:

1/(-27)^(2/3) = 1/(3^3)^(2/3) = 1/3^(3*2/3) = 1/3^2 = 1/9

Therefore, x = 1/9.

To show how c and b are related, we can draw a line through these points. A positive sloped straight line should appear on the graph.

Identifying the slope and y-intercept is necessary before putting the equation in y-intercept (y=mx+b) form and figuring out the equation of a graphed line. The slope is the y-to-x change ratio.

Plotting points on the coordinate plane with values for b and calculating the appropriate values for c is necessary to graph the equation c = 2b + 6.

Let's pick some b values and determine the matching c values:

c = 2(0) + 6 = 6 when b = 0.

If b = 1, then c = 2(1) + 6 = 8.

c = 2(2) + 6 = 10 when b = 2

These points can be used to plot the graph:

Set the scene (0, 6)

Set the scene (1, 8)

Set the scene (2, 10)

Now we may illustrate the relationship between c and b by drawing a line across these locations. A positive sloped straight line should appear on the graph.

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Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.

An equation in mathematics is a claim that two expressions are equivalent. Mathematical operations like addition, subtraction, multiplication, division, and exponentiation may be used. It typically includes one or more variables. A connection between two or more variables can be represented by an equation, and it can also be used to determine the value of an unknown variable. Finding the values of the factors that make the equation true is the first step in solving an equation.

given

The projectile is in the air for a maximum of three seconds, so the domain of h(t) is [0, 3], since the equation depicts the projectile's height in feet after t seconds.

Any input number of t outside of the range [0, 3] would therefore be meaningless given the circumstances of the issue.

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Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

300000000000000000000000000

Answer:

$45

Step-by-step explanation:

I = prt

I = interest earned

p = principal = amount invested

r = interest rate; 5.25% = 5.25/100 = 0.0525

t = time in years; 6 months = 0.5 years

$4,000.00 at 5.25% interest

I = 4000 × 0.0525 × 0.5 = 105

$105 interest in 6 months

$2,000.00 at 6.00% interest

I = 2000 × 0.06 × 0.5 = 60

$60 earned in 6 months

$105 - $60 = $45

The difference is $45.

By answering the above question, we may infer that The inaccuracy, equation when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The following formula may be used to get the percent error:

percent error is calculated as follows: 100% divided by (actual value - measured value).

Whereas, "|" stands for absolute value.

In this instance, the measured measurement is 8.5 inches, whereas the real value is 9.1. Hence, by entering these values into the formula, we may obtain:

error = |(9.1 - 8.5) / 9.1| x 100% error = 6.59%

The inaccuracy, when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

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Answer:

376.8

Step-by-step explanation:

Area of circle: A = πr^2 = π12^2 = 144π

Area of shade: A = (θ/360º) x πr^2 = (60/360) x 144π = 24π

Area not shaded = 144π - 24π = 120π = 120(3.14) = 376.8

For this equation our term is root of -24

What is verbal sentence ?

Verbal sentences consist of a verb + subject + object or adverbial phrase. The subject and object can be either nouns or pronouns.

After solving the equation we get square of n which is equal to three times of eight

If the subject is a pronoun, it is always a suffix; and if the object is pronoun, it is always a dependent pronoun. When the subject is a pronoun, the word order is normal, meaning that the subject follows the verb and precedes the object.

If the subject is a noun and the object is a dependent pronoun, the pronoun object is before the noun subject.

The dative has a special place in the word-order of verbal sentences. It is expressed by the preposition n in addition to a noun or pronoun referring to a person, if the subject is a pronoun. It assumes a third place following the verb and its subject. However, if the subject is a noun, the dative is allocated a forward position and occurs before the subject.

If the subject is a noun and the object is a pronoun and the sentence consists of a dative, the word order is thus:

Verb + dative + dependent pronoun (object) + subject

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The retailer estimates that about 254,623 regular cell phones will be sold 7 years from now.

Since the retailer estimates that 28% fewer regular cell phones will be sold every year, this means that the number of regular cell phones sold each year will be 72% of the number sold the previous year. We can use this information to find the number of regular cell phones sold 7 years from now as follows:

Let x be the number of regular cell phones sold 7 years from now. Then we have:

x = 0.72^7 * 917160

where 0.72 is the percentage of regular cell phones sold each year.

Using a calculator, we get:

x ≈ 254,623

Therefore, the retailer estimates that about 254,623 regular cell phones will be sold 7 years from now.

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Answer:

91,997

Step-by-step explanation:

y = a(1–r)t

y = 917,160(1–0.28)7 Plug in values

y = 917,160(0.72)7 Subtract

y = 917,160(0.10030…) Simplify

y = 91,996.77023… Multiply

Round to the nearest whole number.

91,996.77023… → 91,997

To the nearest whole number, 91,997 regular cell phones will be sold.

Answer:

Step-by-step explanation:

Josslyn burns 7 calories per minute while swimming and 5 calories per minute while practicing yoga. Let x be the number of minutes she spends swimming and y be the number of minutes she spends practicing yoga.

The total number of calories burned, C, is given by:

C = 7x + 5y

To burn at least 500 calories each day, we can write the inequality:

7x + 5y ≥ 500

This inequality states that the total number of calories burned from swimming and practicing yoga, 7x + 5y, must be greater than or equal to 500. Josslyn can achieve this goal by spending a combination of x minutes swimming and y minutes practicing yoga.

The coordinates of the fourth vertex are (0, -4).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;

Midpoint = [(3 - 6)/2, (6 - 6)/2]

Midpoint = [-3/2, 0/2]

Midpoint = (-1.5, 0).

For the fourth vertex, we have:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(-1.5, 0) = [(-3 + x₂)/2, (4 + y₂)/2]

-3 + x₂ = 2(-1.5)

x₂ = -3 + 3

x₂ = 0.

4 + y₂ = 0

y₂ = -4.

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Answer:

look in the comments and have a good day