Explain why you cannot factor the trinomialx² - 12x + 6
There are no factors of 6 that add up to -12
There are no factors of -12 that add up to 6.
It can be factored

Answers

Answer 1

The quadratic equation x² - 12x + 6 = 0 is factorized and the solution to the equations are x = 6 ± √30

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² - 12x + 6 = 0   be equation (1)

Now , to calculate the solution of x ,

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = 12 ± √ ( 144 ) - ( 24 ) / 2

x = 12 ± 2√30 / 2

x = 6 ± √30

Hence , the solutions to the equation are x = 6 + √30 or x = 6 - √30

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Related Questions

[tex]\lim_{x\to \023}[/tex][tex]\sqrt{x+2}-5/x-23[/tex]

Answers

The limit of the expression [tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex] when evaluated is -18.22

What is a Limit?

Limit is a value that a function approaches the output for the given input values.

How to determine the limit of the expression

From the question, we have the following limit expression that can be used in our computation:

[tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex]

To find the limit tends to 23, we substitute 23 for x in the above equation

So, we have the following representation

[tex]\lim_{x \to \223} \sqrt{23+2} -\frac{5\\}{23} -23[/tex]

Evaluate the sum in the expression

[tex]\lim_{x \to \223} \sqrt{25} -\frac{5\\}{23} -23[/tex]

Evaluate the exponent and the fractions

Limit = 5 -5/23 -23

When the expression is evaluated, we have

Limit = -18.2173913043

Approximate

Limit = -18.22

Hence, the solution is -18.22

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Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated?

One-fifth x + three-fourths y = 9

Two-thirds x minus five-sixths y = 8
–10 times the first equation and 3 times the second equation
10 times the first equation and 3 times the second equation
–3 times the first equation and 5 times the second equation
3 times the first equation and 5 times the second equation

Answers

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is: A. –10 times the first equation and 3 times the second equation.

How to solve these system of linear equations?

In order to determine the solutions to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

1/5(x) + 3y/4 = 9                .........equation 1.

2x/3 - 5y/6 = 8          .........equation 2.

In this scenario, the number that should be used to multiply first equation can be calculated by using the following ratio:

Ratio =  -(x-coefficient of second equation)/(x-coefficient of first equation)

Ratio = -(2/3)/(1/5)

Ratio = -10/3

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How many milliliter in 1 microliter?

Answers

From the given  information provided, by converting the units there are 0.001 milliliters in 1 microliter.

This means that if you have 1 microliter of liquid, it is equal to 0.001 milliliters of liquid.

The conversion factor between milliliters (mL) and microliters (μL) is:

1 mL = 1000 μL

Therefore, to convert microliters to milliliters, you divide the number of microliters by 1000.

For example, if you have 500 μL of liquid, you can convert it to milliliters by dividing 500 by 1000:

500 μL / 1000 = 0.5 mL

So, 500 microliters of liquid is equal to 0.5 milliliters of liquid.

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How many inches are there in 150 meters?

1 m≈39.37 in.

Responses

3.8 in.
3.8 in.

1554.1 in.
1554.1 in.

4355.5 in.
4355.5 in.

5905.5 in.
5905.5 in.

Answers

Answer: 5905.512 inches

What are the topics of algebra 1?

Answers

Algebra 1 covers a variety of topics in algebraic mathematics, including linear and quadratic equations, graphing, polynomials, exponents, factoring, rational expressions, inequalities, functions, and data analysis.

Algebra 1 is typically a high school level course that covers a variety of topics in algebraic mathematics. The specific topics covered can vary somewhat depending on the school or district, but some common topics in Algebra 1 include:

1. Linear equations: Solving for unknowns in linear equations and systems of linear equations.

2. Quadratic equations: Solving for unknowns in quadratic equations and understanding their properties.

3. Graphing: Graphing linear and quadratic functions, and understanding their properties such as slope and intercepts.

4. Polynomials: Understanding and manipulating polynomials of different degrees.

5. Exponents: Understanding and working with exponential functions and expressions.

6. Factoring: Factoring polynomials and other algebraic expressions.

7. Rational expressions: Simplifying and manipulating rational expressions, and solving equations involving them.

8. Inequalities: Solving and graphing inequalities, including absolute value inequalities.

9. Functions: Understanding the concept of a function, and working with linear and quadratic functions.

10. Data analysis: Using algebraic methods to analyze and interpret data, including creating and interpreting graphs and tables.

These are some of the main topics that are typically covered in Algebra 1, though the exact curriculum can vary depending on the specific school or district.

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Write some examples of quadrilaterals

Answers

A two-dimensional form having four sides, four vertices, and four angles is referred to as a quadrilateral. Examples are: Trapezium, Parallelogram, Rectangle, Rhombus, Square and Kite.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we might have several sorts of quadrilaterals. Hence a Quadrilateral is of 4 sides, vertices and angles. It consists of 360 degrees.

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You want to purchase
a pair of shoes for the
summer. Normally
they cost $79.99.
They are on sale for
15% off, or you also
have a $10 off
coupon. Including
sales tax at 10.3%,
what is the total
savings between
using the coupon and
taking the discount?

Answers

Answer:

  $2.21

Step-by-step explanation:

You want to know the savings between using a $10 off coupon and taking a 15% discount, if the tax rate is 10.3%.

Coupon

The price with the coupon is ...

  $79.99 -10.00 = $69.99

When tax is added, the total becomes ...

  $69.99 × 1.103 ≈ $77.20

Discount

The price with the discount is ...

  $79.99 × (1 -0.15) ≈ $67.99

When tax is added, the total becomes ...

  $67.99 × 1.103 ≈ $74.99

Savings

The savings by making use of the discount is ...

  $77.20 -74.99 = $2.21

The total savings between the coupon and the discount is $2.21. That is, you save $2.21 more by using the discount instead of the coupon.

__

Additional comment

The question seems a bit ambiguous. The word "or" suggests you cannot use both discounts. If you do, the total amount saved will depend on the order in which they are applied.

You get the best result by taking the $10 off the sale price. Doing that gives you a total savings of about $24.27 off the normal price with tax.

please help me on this

Answers

"Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all" is the true statement.

How to determine which statement is true?

This a problem on addition and subtraction of fractions

Since Hope's dad gives her 7/8 of a chocolate bar one day and then gives her 6/12 of a chocolate bar the next day. Hope received approximately 1 chocolate bar. Total chocolate  received will be:

Total chocolate received = 7/8  + 6/12 = 1 3/8

This statement is not true

Since Dee has 10/12 of a cake and gives 4/8 to her neighbor. Dee has approximately 1 cakes left. The cakes left will be:

cakes left = 10/12 - 4/8 = 1/3

This statement is not true

Since Joe ran 8/15 of a mile on Thursday. He ran 4/5 of a mile on Friday. Joe ran approximately 1/2 mile in all. The total mile ran will be:

total mile ran =  8/15 + 1/2 = 2 1/10

This statement is not true

Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all.

mile swam =  9/16 +  1 5/8 = 2 3/16

This statement is true

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4. Suppose you draw four balls from a bag containing seven pink, four white, three yellow, and two stripped balls. What is the probability of drawing 1 pink, 2 yellow and, stripped ball in succession without replacing the ball each time?

5. If a pair of dice is rolled, what is the probability that we roll a total of five if we are given that the total is less than nine?

6. Suppose a card is chosen at random from a deck of cards, replaced, and a second card is chosen. What is the probability that both cards are 7s?

7. It cost $1 to play a game in which two dice are rolled. If both dice show the same number you win $5; otherwise, you lose. What is the expected value of this game?

Answers

4. The probability of drawing 1 pink, 2 yellow and, stripped ball in succession without replacing the ball each time is (7/16) x (1/35) x (1/13) = 1/2540.

5. The probability that we roll a total of five if we are given that the total is less than nine is (1/36) / (4/36) = 1/4.

6. The probability that both cards are 7s is (6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17.

7. The expected value of the game is a loss of 17 cents per play.

Probabilities of Games

4. The probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is given by the product of the probabilities of drawing each ball without replacement.

The probability of drawing 1 pink ball is 7/16, the probability of drawing 2 yellow balls is (3/15) x (2/14) = 1/35 (because there are 3 yellow balls in the bag out of 15 total balls on the first draw, and 2 yellow balls out of 14 total balls on the second draw), and the probability of drawing 1 stripped ball is 2/13. Therefore, the probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is:

(7/16) x (1/35) x (1/13) = 1/2540

5. If the total is less than nine, then there are only 4 possible outcomes: (1, 4), (2, 3), (3, 2), and (4, 1). The probability of rolling each of these outcomes is 1/36, since each die has 6 equally likely outcomes. The only outcome that adds up to 5 is (1, 4), which has probability 1/36. Therefore, the probability of rolling a total of 5, given that the total is less than nine, is:

(1/36) / (4/36) = 1/4

6. The probability of drawing a 7 on the first card is 4/52, since there are four 7s in a deck of 52 cards. Since the card is replaced, the probability of drawing a 7 on the second card is also 4/52. Therefore, the probability of drawing two 7s in a row is:

(4/52) x (4/52) = 1/169

7. The expected value of the game is the sum of the products of the outcomes and their probabilities. There are 6 x 6 = 36 possible outcomes, each with probability 1/36. Of these outcomes, 6 are winning outcomes (where both dice show the same number), and 30 are losing outcomes. The payout for a winning outcome is $5, and the cost of playing the game is $1. Therefore, the expected value is:

(6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17

Therefore, the expected value of the game is a loss of 17 cents per play.

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find the length of the missing side leave your answer in simplest radical form

Answers

The length of the missing side in the given triangle is equal to option c. 5.

Figure is attached.

In the attached figure of a right angle triangle,

Let the triangle be named as ABC.

AC is the hypotenuse of a triangle.

AB is the altitude of a triangle.

BC is the base of a triangle.

Form the attached figure

Length of altitude AB = 3

Length of base BC = 4

Using Pythagoras theorem we have,

Hypotenuse² = Altitude² + Base²

⇒ AC² = AB² + BC²

Substitute the value we get,

⇒ AC² = 4² + 3²

⇒AC = √ 16 + 9

⇒ AC = √25

⇒ AC = 5

Therefore, the length of the missing side in the given triangle is equal to option c . 5.

The above question is incomplete, the complete question is:

Find the length of the missing side. Leave your answer in simplest radical form.

The triangle is not drawn to scale.

A.) 25

B.) 144

C.) 5

D.) Square root of 5

Figure is attached .

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The regular price on a pair of jeans is $54. The store advertises a back to school sale at 40% of the regular price of the jeans. Two weeks later, the store advertises a sale at an additional 20% off the sale price of the jeans. Two friends decided to purchase the jeans. Shannon says these jeans are now 60% of the regular price. Mary disagrees because she figures that the total discount is less than 60%. What is the cost of the jeans at the 40% off back-to-school sale. What is the cost of the jeans during the additional 20% off sale

Answers

Answer:

See explanation

Step-by-step explanation:

40% of the original $54 is $21.60, therefore the pants are $21.60 off of their original price. This makes the pants $32.40.

20% of the new $32.40 is $6.48, therefore the pants are $6.48 off of the 40%-off price. This makes the pants $25.92 for their final price.

20,−10,5,___ what comes next

Answers

The next term is -25.

What is the number pattern?

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers. In Maths, number patterns are the patterns in which a list number that follows a certain sequence. usaually, the patterns establish the relationship between two numbers. It is known as the sequences of series in numbers.

Given;

The pattern20,−10,5,___

Here, first term is 20, second is -10

Difference=20+10

=30

Now,

=5-30

=-25

Therefore, the answer of the given pattern will be -25.

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divide 3x^3-2x^2+4x-3 by x^2+3x+3

Answers

On dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.

What is algebraic expression?

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to divide (3x³ - 2x² +4x - 3) by (x² + 3x + 3).

Let us assume that -

f(x) = (3x³ - 2x² + 4x - 3)

g(x) = (x² + 3x + 3)

We can write -

h(x) = f(x)/g(x)

h(x) = (3x³ - 2x² + 4x - 3)/(x² + 3x + 3)

h(x) = 3x + {(- 11x² - 5x - 3)/(x² + 3x + 3)}

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}

Therefore, on dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.

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There are 128 teams in a softball tournament. In each
round, half of the teams are eliminated. Which function
can be used to find the number of teams remaining in
the tournament after x rounds?

Answers

We can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.

What are functions?

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain.

The usual way to refer to a function is as f(x), where x is the input.

One function, many. function onto (Surjective Function) into perform.

The function of a polynomial.

So, by observation we can find out the function:

y = 128(0.5)ˣ

Assume the teams after 1st round:

y = 128(0.5)ˣ

y = 128(0.5)¹

y = 128*0.5

y = 64 (Half od 128)

Therefore, we can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.

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Use the triangles to answer the question. Triangle A B C with A B = square root of 13, B C = 2, A C = 3, and angle C is labeled as a right angle. Also shown is triangle D E F with E F = 4, D F = 6, and angle F is labeled as a right angle. © 2016 StrongMind. Created using GeoGebra. If △ABC∼△DEF, what is the scale factor for the dilation that maps △ABC to △DEF? Enter your answer as a number.

Answers

The scale factor for the dilation that maps △ABC to △DEF is 0.75.

What is triangle?

A triangle is a geometric shape that consists of three line segments that connect to form three angles. These angles always add up to 180 degrees. A triangle has three sides and three vertices (corners). Triangles can have different shapes and sizes, and they are often classified based on the length of their sides or the size of their angles. Some common types of triangles include equilateral triangles (where all sides are equal in length and all angles are equal to 60 degrees), isosceles triangles (where two sides are equal in length), and right triangles (where one angle is a right angle, or 90 degrees). Triangles have many properties and are an important part of geometry and mathematics.

Here,

To determine the scale factor for the dilation that maps △ABC to △DEF, we need to find the ratio of the corresponding side lengths of the two triangles.

Since △ABC ∼ △DEF, we know that the corresponding angles of the two triangles are congruent. Therefore, angle B in △ABC corresponds to angle E in △DEF, and angle A in △ABC corresponds to angle D in △DEF.

Using the Pythagorean theorem, we can find the length of the missing side of △DEF:

DF² = DE² + EF²

6² =DE² + 4²

DE=√20

DE=2√5 units

3/4=2/2√5=√13/6=0.75

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Translation: 2 units left and 1 unit down. Q(0,-1), D(-2,2), V (2,4), J(3,-3)

Answers

Translation: 2 units left and 1 unit down. Q(0,-1), D(-2,2), V (2,4), J(3,-3)

New coordinates are respectively, (-2, -2), (-4, 1), (0, 3), (1, -4)

What is the point?

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given the points Q(0,-1), D(-2,2), V (2,4), and J(3,-3),

we can see that each point has been translated 2 units to the left and 1 unit down.

This is because each x-coordinate has decreased by 2 and each y-coordinate has decreased by 1.

So, the translation of 2 units left and 1 unit down has moved each point along the plane in the negative x-direction and the negative y-direction.

the points are respectively (-2, -2), (-4, 1), (0, 3), (1, -4)

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What is the difference between positive and negative z-score table?

Answers

Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean according to the z-score table.

The statistical measurement known as the Z-score describes the relationship between a value and the mean of a group of values. Z-score is quantified by the standard deviations from the mean. The mean score and the data point's score are equal when the Z-score is 0. The Z-score for a value that deviates by one standard deviation is 1.0. Z-scores are binary, with a positive value denoting a score above the mean and a negative value denoting a score below the mean.

Equation of the z-score: z = ( x - μ ) / σ

Get the value corresponding to one decimal place of the z-score by first looking at the left side column of the z-table.

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What does 500x235 equal?

Answers

Answer:

[tex]117500[/tex]

Step-by-step explanation:

[tex]500 \times 235=100\times (5\times 235)=1175 \times 100=117500[/tex]

Answer: 117,500

Step-by-step explanation: 500 x 235 = 117,500

if y varies inversly as x², and y=11/4
when x=4, find y when x=2​

Answers

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with }x^2}{y = \cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=\frac{11}{4} \end{cases} \\\\\\ \cfrac{11}{4}=\cfrac{k}{4^2}\implies \cfrac{11}{4}=\cfrac{k}{16}\implies \cfrac{(11)(16)}{4}=k\implies 44=k~\hfill \boxed{y=\cfrac{44}{x^2}} \\\\\\ \textit{when x=2, what's "y"?}\qquad y=\cfrac{44}{2^2}\implies y=\cfrac{44}{4}\implies y=11[/tex]

Answer:

y = 11 when x = 2

Step-by-step explanation:

This is indirect proportionality where:

y ∝ [tex]\frac{1}{x^{2}}[/tex]

This means:

[tex]y_{1} x_{1}^{2} = y_{2}x_{2}^{2}[/tex]

Substitute the following values in the above equation to solve for [tex]y_{2}[/tex]

[tex]y_{1} = \frac{11}{4}[/tex]

[tex]y_{2} = ?[/tex]

[tex]x_{1} = 4[/tex]

[tex]x_{2} = 2[/tex]


= [tex](\frac{11}{4})(4^{2}) = y_{2}(2^{2})[/tex]

= [tex](\frac{11}{4})(16) = y_{2}(4)[/tex]

= [tex]44 = 4y_{2}[/tex]

= [tex]y_{2} =\frac{44}{4}[/tex]

y = 11

Write an explicit formula for a(n) the n^th term of the sequence 36,−6,1

Answers

I’m he msjs sindbdjdbdjdb

how much 3 million yen to usd ?

Answers

Answer:

about 23,000 usd

Step-by-step explanation:

If you want a quick way to translate yen to usd, take the yen amount and take away two zeros. So 3 mil yen would be 30,000. This method is a bit off but is quick and easy.


1 us dollar is about 130 yen

A successful lawyer ownsthree vintage cars. The ratio of car is value to 1's value is 3:4. The ratio of car 2's value tocar 3's is 8:5. d the total value of three cars is $1115900, fins the value of each car

Answers

Answer: Let's represent the value of car 1 as x. Then, the value of car 2 is 3/4 of x, and the value of car 3 is 4/5 of the value of car 2.

So, we can write the following equations:

x = (3/4) * y

y = (4/5) * z

Where y is the value of car 2, and z is the value of car 3.

Adding all the values, we have:

x + y + z = 1115900

We can substitute the values of y and z in terms of x:

x + (3/4) * x + (4/5) * (3/4) * x = 1115900

Simplifying the expression on the left side, we get:

7/4 * x = 1115900

Finally, dividing both sides by 7/4, we get:

x = 359900

So, the value of car 1 is $359900, the value of car 2 is (3/4) * x = (3/4) * 359900 = 269925, and the value of car 3 is (4/5) * (3/4) * x = (4/5) * (3/4) * 359900 = 213140.

Step-by-step explanation:

Answer: the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.

Step-by-step explanation:

Let's call the value of car 1 "x".

From the first ratio, we know that the value of car 2 is 4/3 times greater than the value of car 1, and the value of car 3 is 3/4 times greater than the value of car 1.

So, the value of car 2 is 4/3 * x, and the value of car 3 is 3/4 * x.

From the second ratio, we know that the value of car 2 is 8/5 times greater than the value of car 3.

So, the value of car 2 is 8/5 * (3/4 * x) = 6/5 * x.

The total value of all three cars is $1115900, so we can set up an equation to solve for x:

x + 4/3 * x + 3/4 * x = 1115900

Expanding and simplifying the right side:

x + 4/3 * x + 3/4 * x = 1115900

8/3 * x = 1115900

x = 1115900 * 3 / 8

x = 467125

So, the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.

Write an exponential function for a graph that passes through the points (3, 2.8) and (4, 5.6) . Write the function in the form y=a(b)x.

Answers

The formula of the given exponential function whose graph passes through the points (3, 2.8) and (4, 5.6) is :

   y = 0.35* (2)ˣ

What is an exponential function?

When the input variable x appears as an exponent in the formula

f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. It is mostly used to determine exponential growth or decay.

When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. In exponential decay, the quantity initially falls very quickly and then gradually. Over time, the rate of change slows. As time goes on, change happens at a slower rate.

The general formula of an exponential function is:

y = abˣ

It is said that points (3, 2.8) and (4, 5.6) are present on the graph of the given exponential function.

W can substitute these value values in the above formula.

2.8 = ab³

5.6 = ab⁴

Dividing the above equations,

2.8 /5.6 = b³/b⁴

1/2 = 1/b

b = 2

Now substituting this value in one of the equations to find the value of a.

2.8 = a. (2)³

a = 2.8/8 = 0.35

Therefore the formula of the given exponential function is :

   y = 0.35* (2)ˣ

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Two polygons that has 3 more sides then the other

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The attachment shows different types of polygons that have 3 more sides then the other.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now depending on these we have following five possibilities:

Case 1: Triangle and hexagon

If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.

Case 2: Quadrilateral and heptagon

If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.

Case 3: Pentagon and Octagon

If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.

Case 4: Hexagon and Nonagon

If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.

Case 5: Heptagon and Decagon

If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.

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PLS HELP i rlly don't understan this

Answers

Answer:

SInce 2 is 2 less than 4, the value of x+2 is 4 less than 31. So x+2=29

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since 2 is 2 less than 4, the value of x + 2 is 2 less than 31.

So, x + 2 = 29.

Fine the value of each variable show proofs

Answers

The value of x is 11.3

The value of y is 11.3

How to determine the values

Using the different trigonometric identities such as sine, cosine, tangent, secant, cosecant, cotangent.

To determine the value of x, we use the sine identity

sin θ = opposite/hypotenuse

sin 45 = x/16

Find the value

0.7071= x/16

cross multiply

x = 11.31

To determine the value of y, we get;

tan 45 = 11.3/y

Determine the value and cross mutiply

1 = 11.3/y

Then,

y = 11.3

Hence. the values are equivalent

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What is the value of 186 lb in kg

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The formula for converting pounds (lb) to kilograms (kg) is 1 lb = 0.45359237 kg. To convert from lb to kg, you simply multiply the value in lb by 0.45359237.

For example, to convert 186 lb to kg, you would need to perform the following calculation: 186 lb × 0.45359237 kg/lb = 83.99 kg. Therefore, the answer to the question is that 186 lb is equivalent to 83.99 kg. This can be written in a short form as 186 lb = 83.99 kg. It is important to note that this conversion is based on the International System of Units (SI) and is the most commonly used method for measuring weight. When converting between measurements, it is also important to consider the accuracy of the conversion. In this case, the conversion is accurate to nine decimal places. This means that the result is accurate to within 0.000000001 kg, which is an extremely small amount. As such, this conversion should be suitable for most practical applications.

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At what points does the helix r(t) = sin(t), cos(t), t intersect the sphere x2 + y2 + z2 = 26? (round your answers to three decimal places. If an answer does not exist, enter dne. ).

Answers

At (0.958, 0.287, 5) and (0.958, -0.287, -5) points, the helix r(t) = sin(t), cos(t), t intersect the sphere x^2 + y^2 + z^2 = 26.

The sphere x^2 + y^2 + z^2 = 26 is a sphere with center at the origin and radius sqrt(26).

The helix r(t) = sin(t), cos(t), t is parameterized by sine and cosine functions, which oscillate between -1 and 1.

To find the points at which the helix intersects the sphere, we need to find the values of t such that the distance between r(t) and the origin is equal to sqrt(26).

The distance between a point (x, y, z) and the origin is given by the formula:

d = sqrt(x^2 + y^2 + z^2)

So, substituting the values from r(t), we have:

d = sqrt(sin^2(t) + cos^2(t) + t^2)

Setting d equal to sqrt(26), we have:

sqrt(sin^2(t) + cos^2(t) + t^2) = sqrt(26)

Squaring both sides, we have:

sin^2(t) + cos^2(t) + t^2 = 26

Recall that sin^2(t) + cos^2(t) = 1, so we have:

1 + t^2 = 26

Subtracting 1 from both sides, we have:

t^2 = 25

Taking the square root of both sides, we have:

t = ±5

So, the two points of intersection are (sin(5), cos(5), 5) and (sin(-5), cos(-5), -5).

Rounding the results to three decimal places, we have:

(sin(5), cos(5), 5) = (0.958, 0.287, 5)

(sin(-5), cos(-5), -5) = (0.958, -0.287, -5)

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In the figure, triangle UVW is similar to triangle RST, VU=48, VW=18, and SR=24.

What is the value of x? Show all your work.

Answers

Answer:

x=9

Step-by-step explanation:

18/48=x/24

Cross multiply

48x=432

Divide

432/48=9

x=9

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Convert 8400 kilograms into tons. Round your answer to the nearest hundredth.

Answers

Answer:

9.26 tons

Step-by-step explanation:

8400 kilograms is 9.259415 tons and when you round to the nearest hundredth it is 9.26.

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