the expression x^3+ax^3+bx-3 where a and b are constants, has a factor of x-3 and leaves a remainder of 15 when divided by x+2. find the value of a and b​

Answer:

y = 2x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (1, 0) ← 2 points on the line

m = [tex]\frac{0-(-2)}{1-0}[/tex] = [tex]\frac{0+2}{1}[/tex] = [tex]\frac{2}{1}[/tex] = 2

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = 2x - 2 ← equation of line

Answer:

y = 2x - 2

Step-by-step explanation:

The equation y = mx + b is a standard form of a linear equation in one variable. It represents a straight line on a graph

In this equation, y is the dependent variable, which is the variable that is being measured or predicted. The independent variable is x, which is the input or cause in the relationship.

The coefficient m is the slope of the line, which tells you the rate of change between the two variables. It represents how much the value of y changes for each unit change in the value of x. A positive slope means that the line goes up as you move from left to right, while a negative slope means that the line goes down.

- Our slope is positive

- slope (m) = rise / run = 2/1 = 2

The constant b is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of y when x is equal to 0.

- Our y-intercept is -2

m is 2 and b is -2, the equation y = 2x - 2 represents a line with a slope of 2 and a y-intercept of -2. This means that for every 1 unit increase in the value of x, the value of y increases by 2 units, and the line crosses the y-axis at the point (0, -2).

$18.24

You can find the answer to this by simply dividing the two numbers:

$383 ÷ 21 = $18.24

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

77.8%, blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw

According to our answer-

Probability is defined as the product of the number of successful outcomes over the total number of outcomes.

There are 36 different results for one draw because there are 36 marbles overall in the bag.

All draws that are conceivable but are not blue are considered successful outcomes. 28 of those are available.

Consequently, the probability of a non-blue option is 28/36 = 7/9 = 77.8%. (rounded)

Hence, 77.8%, blue marbles need to be added to the bag so that the probability of randomly drawing a blue marble is 3/4.

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The length of side BC is approximately 10.928.

What is the right triangle?

In a right triangle, the side opposite the right angle is called the hypotenuse. In triangle ABC, side AC is the hypotenuse, and sides AB and BC are the other two sides.

To find the length of side BC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

We can use the given information to write the Pythagorean theorem in the form:

AC^2 = AB^2 + BC^2

Substituting the given lengths, we get:

13² = 5² + BC²

Solving for BC, we get:

BC = √(13² - 5²)

= √(144 - 25)

= √(119)

= approximately 10.928

Therefore, the length of side BC is approximately 10.928.

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Answer:

Hope this helps good luck :)

see explanation

Step-by-step explanation:

Find relationship of length(L) and width(w)

Perimeter = L + W + L + W

[tex]20. = (w+2) + w + (w+2) +w 20. = 4w + 4 -4. -4 16 = 4w 16. = 4w 4. 4 4. = w w = 4 L. = w+2 = 4 +2 L = 6[/tex]

Answer width is 4 meters and length is 6 meters.

Answer:153000394836295938

Step-by-step explanation:

;)

Answer:

m∠QRS = 30°

m∠SRT = 75°

Step-by-step explanation:

Now,

The sum of m∠QRS and m∠SRT is equal to m∠QRT which is 105°

So,

m∠QRS + m∠SRT = m∠QRT

(6x)° + (14x + 5)° = (105)°

6x + 14x + 5 = 105

20x + 105 - 5

20x = 100

x = 100/20

x = 5

Thus, The value of x is 5°

Now,

m∠QRS = (6x)° = 6 × 5 = 30°

m∠SRT = (14x + 5)° = 14(5) + 5 = 70 + 5 = 75°

Answer:

x = 90 , y = 43

Step-by-step explanation:

Since AB and AC are congruent , then Δ ABC is isosceles with base angles congruent , that is

∠ ABD = ∠ ACD = 47°

AD is the perpendicular bisector of BC , so

∠ ADB = x = 90

the sum of the 3 angles in Δ ABD = 180° , then

y = 180° - (90 + 47) = 180 - 137 = 43

Answer:

360 in commission.

Step-by-step explanation:

If you received a 4% commission on the TVs you sold, and you sold $9,000 worth of TVs, then you would have received 4/100 * $9,000 = $<<4/100*9000=360>>360 in commission.

Answer:500

Step-by-step explanation:

[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]will be 4[tex]x^{3/2} y^{5/2}[/tex]

The number that, when multiplied four times by itself, yields the original number is the fourth root of a number. In other words, the square root of the square root of an integer equals the number's fourth root.

eg:

eg: [tex]\sqrt[4]{81}[/tex] = 3

We are asked

x> 0 and y> 0then

[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]    =  4 [tex]x^{3/2} y^{5/2}[/tex]

As 4 multiplied by 4 , 4 times given 256 and x to the power 6 and root 4 so that will be x to the power 3/2 and y to the 10 and root 4 will give 5/2

thus

[tex]\sqrt[4]{256x^{6}y^{10} }[/tex] will be equivalent to  4 [tex]x^{3/2} y^{5/2}[/tex]

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The height of the tree after 12 years is 21.401 feet.

In this problem we find the case of a tree that grows exponentially, the height of the tree is defined by the following formula:

h = a · (1 + r / 100)ⁿ

Where:

If we know that a = 4 ft, r = 15 and n = 12, then the final height of the tree is:

h = 4 · (1 + 15 / 100)¹²

h = 21.401

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The answer to this question based on limits is -4/3

What is limits?

Limits are very interesting concepts in mathematics which are veryuseful when we are dealing with numbers like infinity or numbers where some functions are not defined

Concepts of limits give us brief understanding that why these things are not defined

Solution;

We are asked to calculate a limit

By limits laws we can apply limit to both numerator and denominator respectively

Numerator = lim x--->2 2x-2

= just put 2 in place of x we will get 4 - 2 = 2 ans

Denominator = 2f(3x) - x

put limit as x = 2 in this we get

2 f(6) - 2

we need values of f(6) we can take from graph that f(6) = -3/2

hence answer to our question is 2 divided by -3/2

which in turn our answer for this limit problen is -4/3

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The algebraic expression is (3X + 4)²

Word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

From the question

To express the worded problem algebraically using X as your unknown

To express the worded problem algebraically using X as your unknown

The number is X

Now if we multiply the number X by 3 we get 3X

When we add 4 with 3X we get 3X + 4

Finally the squaring the result 3X + 4 we get (3X + 4)²

Hence the required algebraic expression for the worded problem is (3X + 4)²

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Answer: Puerto Rico

Step-by-step explanation:

the counterpart to sampling error is nonsampling error, which consists of all errors in a survey including those attributable to the sample plan and sample size is a True statement.

Non sampling error is an error that occurs due to various sources which are not related to sampling. These errors can occur due to improper selection of the sample, incorrect data collection and analysis, or due to errors in data reporting. Sampling error, on the other hand, occurs due to the differences between the sample and the population. It is caused by the randomness of the sample that is used and can be reduced by increasing the sample size. the counterpart to sampling error is nonsampling error, which consists of all errors in a survey including those attributable to the sample plan and sample size is a True statement.

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The expressions that are equivalent to -6x-4/2 are: -6x-4/2 and 1/2 (-3x-2)

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers

According to the given option, the required solution would be as:

A. -3x - 2 (if you multiply both sides of the equation -6x - 4 = 2 by -1/2, you get -3x - 2 = 1)

E. 1/2 (-3x-2) (if you multiply both sides of the equation -6x - 4 = 2 by 1/2, you get -3x - 2 = 1, and then divide both sides by -1 to get 1/2 (-3x-2) = -1/2)

Hence, the correct answer would be options (A) and (E).

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A class is planning a trip to the local City Museum of Art. The class needs 3 trucks and 1 car to transport all 22 people on the trip.

Generally, To solve this problem, we can set up a system of equations using the information given. Let C be the number of cars needed and T be the number of trucks needed.

The first equation will represent the number of people that can be transported in the cars: 4C + 6T = 22

The second equation will represent the number of drivers: C + T = 4

Now we can solve this system of equations using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and the second equation by 4 to get: 8C + 12T = 44 4C + 4T = 16

Then we can subtract the second equation from the first equation to get: 4C + 8T = 28

Then we can divide both sides by 4 to get: C + 2T = 7

Then we can substitute this value for C in the second equation to get: 7 - 2T = 4 T = 1.5

Since T represents the number of trucks, which must be a whole number, this solution is not possible.

Using substitution, we can solve for C in the second equation and substitute it into the first equation: C = 4 - T 4(4 - T) + 6T = 22 16 - 4T + 6T = 22 2T = 6 T = 3

Substituting this value for T into the second equation, we get: C = 4 - 3 C = 1

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Answer:

Step-by-step explanation:

You need to find the perimeter of the door in the scale drawing.

Not the perimeter of the door on the dollhouse.

If the dollhouse door is 7 cm by 5 cm use the scale factor of 3/4 to

find the dimensions on the scale drawing.

7 times 3/4 = 5.25

5 times 3/4 = 3.75

P = 2(length) + 2 (width)

P = 2 (5.25) + 2 (3.75)

P = 10.5 + 7.5

P = 18 cm

Answer choice C

Answer:

(A) ∠Y ≅ ∠C.

Step-by-step explanation:

To prove that two triangles are congruent by ASA (Angle-Side-Angle), you need to show that two angles in one triangle are congruent to two corresponding angles in the other triangle, and that the side between the two angles is congruent to the corresponding side in the other triangle.

Given that ∠X ≅ ∠D and ∠DE ≅ ∠XW, the third congruence needed to prove that ΔXWY ≅ ΔDEC by ASA is:

(A) ∠Y ≅ ∠C

This is because ∠Y and ∠C are the corresponding angles in the two triangles that have not been shown to be congruent.

So the answer is (A) ∠Y ≅ ∠C.

Tell me if this helped :)

A. True. The circumcenter is equidistant from all vertices of the triangle.

B. False. The circumcenter is equidistant from all vertices of the triangle.

C. False. By the definition of a bisector, [tex]MJ=6[/tex], meaning [tex]JG=6+6=12[/tex].

D. True. By the definition of a bisector, [tex]GK=4[/tex], meaning [tex]GH=4+4=8[/tex].

Answer:

P= RS. 9000

R=7.6%

T= 9 months

Simple Interest (SI}=?

By using formula,

SI= PTR/100

= 9000* 7.6* 9/ 100* 12

= 615600/1200

= 513

Answer:

39 inches

Step-by-step explanation:

All of the sides are the same length because all of the angles are equal

21 - x = 2x - 3  Set two sides equal to each other and solve for x.  Add x to both sides

21 = 3x - 3  Add 3 to both sides

24 = 3x  Divide both sides by 3

x = 8

Substitute in 8 for x to find the value of a side

2x - 3

2(8) - 3

16 - 3

13

Each side length is 13

3 x 13 = 39

Answer:

To calculate the interest rate for your account, you will need to use the formula for simple interest:

Interest = Principal x Rate x Time

In this case, the principal is the amount of money you deposited, or $600. The time is the number of months the money was in the account, or 18 months. And the interest is the amount of money you earned, or $31.50.

Plugging these values into the formula, we get:

$31.50 = $600 x Rate x 18

To solve for the rate, we can divide both sides of the equation by $600 and 18:

Rate = $31.50 / ($600 x 18)

Simplifying this expression gives us:

Rate = 0.01625

So, the interest rate for your account is approximately 1.625%.

Answer:  

A) 15

B) Summer Swim

Step-by-step explanation:

How to solve problem "A":

45+3.50x =6.50x

Take 3.50 from each side.

6.50-3.50=3

45=3x

Now you divide 45 divided by 3.

45/3=15

So after 15 visits, you'll be charged the same amount.

6.50 (15)=97.5

3.50 (15)+45= 97.5

So it's definitely correct.

_________________________________________________________

How to solve problem "B":

All we have to do is plug 32 into "x"

Equation 1: 45+3.50(32)= 157

Equation 2: 6.50 (32)=208

So equation 1 definitely is cheaper. So it's the Summer Swim that's cheaper

I hope this helps!!!

Answer:33/5

Step-by-step explanation:

Hope this helps <3

Answer:

1)1

2)3

Step-by-step explanation:

Have a look at some tables online