How do you compute this? 4(-2, 3) - 2(6, -7)

Answer:

[tex]P(x) -0.1(x+1)(x-3)^2[/tex]

Step-by-step explanation:

So you can express a polynomial in factored form, where each factor of the polynomial is being multiplied by each other to get the original polynomial as such: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex] notice the a in front? Sometimes the value is 1, sometimes it's not, and I'm assuming it's not 1, since the y-intercept is given.

Anyways, when we express a polynomial in factored form: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex], it's pretty easy to see that -a, -b, and -c are roots, since if we plug in -a, the factor (x+a) becomes (-a + a) = 0, and since the factors are being multiplied by each other, the value p(-a) will be 0, since 0 * some value = 0.

The next thing to know is what multiplicity means. It essentially means when you have the same root "multiple times", or in other words it's the degree of the factor. For example: [tex]f(x) = (x+a)^3(x+b)^2(x+c) = (x+a)(x+a)(x+a)(x+b)(x+b)(x+c)[/tex], if you took each factor, you would see that the root -a shows up 3 times, thus the multiplicity is 3, which can also be determined by just looking at the initial degree... 3. The same thing goes for b and c, except for c, the degree isn't explicitly said, it's just 1.

Since we have a zero at x=3 one of the factors will be (x-3) since plugging in 3 to this makes it 0. But this has a multiplicity of 2, so the degree of the this factor is 2. So for we have the polynomial: [tex]p(x) = (x-3)^2[/tex]

Since we have a zero at x=-1, one of the factors will be at (x+1), since plugging in 1 into this makes the value 0. This has a multiplicity of 1, and you can write the degree 1, but if you don't explicitly write it, it can just be assumed to be 1, since a^1=a

So now we have the polynomial: [tex]p(x) = (x+1)(x-3)^2[/tex]

So let's just assume we have an "a" value in front as mentioned in the very beginning, we have the polynomial: [tex]p(x) = a(x+1)(x-3)^2[/tex] and we can solve for this value, using any point except for the zeroes. We can use the y-intercept given to solve for a

Plug in 0 as x (by definition of y-intercept) and set p(x) = -0.9

[tex]-0.9 = a(0+1)(0-3)^2[/tex]

Subtract/add values

[tex]-0.9 = a(1)(-3)^2[/tex]

Simplify

[tex]-0.9 = 9a[/tex]

Divide both sides by 9

-0.1 = a

So now let's plug this into our polynomial to get the final result!

[tex]P(x) -0.1(x+1)(x-3)^2[/tex]

Answer: 5/11

Solution: x = 5/11

Step-by-step explanation:

Question: -(x+3)=-8+10x

Result -x-3=10x-8

Hope this help :)

Please give brainless

-(×+3)=-8+10× is a math equation with the solution of 5/11

Answer:

Step-by-step explanation:

e^-6 = 1/e^6 = about 0.00248

The value of the probability P(A and D) is 0.30

Using the probabilities on the tree diagram, we have the following parameters

P(A) = 0.5

P(D/A) = 0.6

The probability P(A and D) is then calculated using the following formula

P(A and D) = P(A) * P(D/A)

Substitute the known values in the above equation

P(A and D) = 0.5 * 0.6

Evaluate the product

P(A and D) = 0.30

Hence, the value of the probability P(A and D) is 0.30

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The area of this regular polygon is 46.8 square units

The given parameters are:

Perimeter, p = 54 m

Apothem, a = √3

The area of this regular polygon is then calculated as:

Area = 0.5 * Apothem * Perimeter

Substitute the known values in the above equation

Area = 0.5 * √3 *  54

Evaluate the product

Area = 46.8

Hence, the area of this regular polygon is 46.8 square units

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Answer:

[tex]\sqrt[3]{192} x^{\frac{3}{5} }y^{\frac{3}{8} }[/tex]

Step-by-step explanation:

You have to simplify all of the terms individually

[tex]\sqrt[3]{192} = 5.769[/tex]

Since that isn't a whole number, it doesn't simplify

Use the root to exponent rule for the variables

[tex]\sqrt[3]{x^{5} } =x^{\frac{3}{5} }[/tex]

[tex]\sqrt[3]{y^{8} } =y^{\frac{3}{8} }[/tex]

Then put them all together to get

[tex]\sqrt[3]{192} x^{\frac{3}{5} }y^{\frac{3}{8} }[/tex]

Make sure the variables aren't under the root when you give your answer

I hope this helps!

pls mark brainliest

The theoretical probability of randomly getting a black counter is P = 2/5.

In this case, we have 8 black counters and 12 white counters, so there is a total of 20 counters.

We assume that all the counters have the same probability of being randomly selected, then the probability of randomly selecting a black counter is just given by the quotient between the number of black counters and the total number of counters.

There are 8 black counters and 20 in total, then the probability is given by:

P = 8/20

Now we can simplify that fraction to get:

P = 2/5

The theoretical probability of randomly getting a black counter is P = 2/5.

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The number sets that each number belong too are given as follows:

1. Rational.

2. Irrational.

3. Rational.

4. Whole.

5. Whole.

6. Integer.

It is a terminating decimal, hence it is a rational number.

The square root of 5 is not exact, hence it is a non-terminating decimal, meaning that is an irrational number.

It is a fraction, hence it is a rational number.

It is a positive non-decimal number, hence it is a whole number.

The square root of 16 is of 4, which is a positive non-decimal number, hence it is a whole number.

The result of the division is of -4, which is a negative non-decimal number, hence it is an integer number.

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Answer:

[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]

=

[tex]\frac{ \sqrt{2} }{a + b} [/tex]

Step-by-step explanation:

[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]

[tex](a - b)( \frac{ {2}^{ \frac{1}{2} } }{(a + b)(a - b)} )[/tex]

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

The value of tan 0 as given in question is 0

Trigonometric identities are equations involving the trigonometric functions that are true for every value of the variables involved. They are written in terms of sine, cosine and tangent.

According to the question, we are to find the value of tan0. This is as shown below;

tan 0 = 0

Note that the tangent angle is positive in the first and third quadrant. Hence the result of the given tangent expression will also be positive.

Hence the value of tan 0 as given in question is 0

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a. Central angle in the circle is: Angle BAC

b. A major arc is: Arc BEC

c. A minor arc is: Arc BC

d. measure of arc BEC is: 260°

e. m(BC) = 100°

A central angle has two of its sides as radii of the circle, forming an angle at the center of the circle, where the vertex is at the center of the circle.

A major arc has a measure that is greater than 180 degrees. That is, it is more than half a circle (semicircle). Thus, measure of major arc > 180 degrees.

A minor arc has a measure that is less than 180 degrees. That is, it is not more than half a circle (semicircle). Thus, measure of minor arc < 180 degrees.

a. Central angle in the circle is: Angle BAC

b. A major arc in circle A is: Arc BEC

c. A major arc in circle A is: Arc BC.

d. Measure of arc BEC = 360 - 100 [according to the central angle theorem]

Measure of arc BEC = 260°.

e. Measure of angle BAC = 100°  [given]

Measure of arc BC = angle BAC [according to the central angle theorem]

Measure of arc BC = 100°

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Answer:

6t tomato plants

Step-by-step explanation:

There are 6 rows, Tamala places t in each row. We multiply 6 by t.

If t were 5, the tomato plants would be 30 since we multiply the rows by the number of tomato plants

Answer:

6t

Step-by-step explanation:

number of rows × number of plants per row = total number of plants

6 × t = 6t

Answer: 6t

See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

Transverse axis

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

The vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

The co-vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola

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Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.

In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:

c = 17/0.83 = $20.48.

In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:

c = 288/18 = $16.

16 < 20.48, hence the souvenir would be less expensive in Egypt.

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Answer:

a) [tex]\angle QST[/tex]

b) Arc QT

c) Arc QRS

d) 105 degrees

e) 255 degrees

Answer:

69500

Step-by-step explanation:

695 x 100 = 69500

to check answer divided 69500 by 100

which is equals to 695

695 is a hundred times smaller than 69500

multiplication is a method of finding the product of two or more numbers.

We need to find the number which 695 is a hundred times smaller than

Six hundred ninety five times smaller than

Let us consider the number to be x.

Let us multiply 695 with 100 to  get the value or answer of the above question.

Six hundred ninety five into hundred is sixty nine thousand five hundred

695 x 100 = 69500

To verify the answer is correct or not , divide 69500 by 100. if we get 695 out answer is correct

69500/100=695

Hence 695 is a hundred times smaller than 69500

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Answer:

2 1/8

Step-by-step explanation:

I counted from 29 to 31 and then saw that for 29 it was 3/8 and for 31 it was 2/8 so i knew that the answer would be 2 1/8

Answer:

7 weeks, £35, and £21.

Step-by-step explanation:

Every week, Suzie saves £5 and gets £3 from her Mum. Altogether, Suzie gets £8 every week. All we need to do is divide 56 by 8, which gives us 7. Suzie will take 7 weeks to collect enough money. To find out how much she has saved and been given by her mum individually, we need only times these values by 7. 5x7=35, and 3x7=21.

Answer:

no habla espanol

Step-by-step explanation:

Using the combination formula, it is found that six of these five-ball selections contain exactly five red balls.

The order in which the balls are selected is not important(as balls A, B, C, D and E is the same outcome as balls B, A, C, D and E), hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, five red balls can be chosen from a set of six, hence the number of selections is the combination of 5 elements from a set of 6, that is calculated from the formula given above:

[tex]C_{6,5} = \frac{6!}{1!5!} = 6[/tex]

Hence six of these five-ball selections contain exactly five red balls.

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Answer:

[1 , +∞)

Step-by-step explanation:

Solving the inequality 6x ≥ 6

6x ≥ 6

⇔ x ≥ 1   (Divide both sides by 6)

⇔ x ∈ [1 , +∞)

The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

According to the statement

we have given that the Smith family's sprinkler was 25L per hour and

Stewart family's sprinkler was 30L per hour and The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1750L.

And we have to find the How long was each sprinkler used.

So, For this purpose,

The given statements in the equation form become:

Let Smith family's sprinkler be x

Let Stewart family's sprinkler be y then

The equation become

x + y = 65 -(1)

25x + 30y = 1750 -(2)

Here we use the elimination method.

So, Multiply (1) by 25 and (2) by 1 then

25x + 25y = 1625

25x + 30y = 1750

Now eliminate x from the equations then

-5y = -125

y = 25

then x value becomes

x + y = 65

x + 25 = 65

x = 40.

So, The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

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By solving a quadratic equation we will see that the number can be:

8 or -5.

The product of a number N, and 3 less than the number, is equal to 40.

This is written as:

[tex]N*(N - 3) = 40[/tex]

Now we need to solve this for N.

[tex]N^2 - 3N = 40[/tex]

[tex]N^2 - 3N - 40 = 0[/tex]

Then we need to solve this quadratic equation:

[tex]N = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*1*(-40)} }{2} \\\\N = \frac{3 \pm 13 }{2}[/tex]

Then we have two solutions:

These are the two possible solutions.

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Answer:

True

Step-by-step explanation:

Plotting the point of any linear equation on a graph gives a straight line

The revenue function in terms of q will be 200q - 3q².

The following can be deduced based on the information given:

P(q) = 200 - 3q

C(q) = 75 + 80q - q²

The revenue function in terms of q will be:

= Price × Quantity

= (200 - 3q) × q

= 200q - 3q²

The profit will be:

= Total revenue - Total cost

= (200q - 3q²) - (75 + 80q - q²)

= 200q - 3q² - 75 + 80q + q²

= -2q² + 280q - 75

= 2q² - 280q + 75

The average cost function will be:

= Total cost / Quantity

= (75 + 80q - q²) / q

= 75/q + 80 - q

The marginal cost will be 80 - 2q.

The marginal revenue will be 200 - 6q.

The marginal cost when q = 20 will be:

= 80 - 2q

= 80 - 2(20)

= 80 - 40

= 40

The marginal revenue when q = 20 will be:

= 200 - 6q

= 200 - 6(20)

= 200 - 120

= 80

The company should decrease production from 20 units in order to gain more profit.

The production level that gives the largest profit for the company will be gotten by finding the second derivative for the profit function as illustrated in the question. The profit function is 2q² - 280q. Then the production level will be 4.

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The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

The quadratic expression in its standard form is;

ax² + bx + c

Given the expression in the question;

x² - 2x + ------

Compared with the standard for a quadratic expression

Let the missing value be represented by "c"

x² - 2x + c

Now, to find the value of c, we divide the coefficient of x by 2 and then square the result.

Note that, coefficient of x is b

c = ( b/2 )²

We substitute

c = ( -2/2 )²

c = ( -1 )²

c = 1

The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

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The graphs of the equations are:

In fig. 1:

a) y = x (red line)

b) y = -x (blue line)

c) y = x + 5 (green line)

In Fig. 2:

a. y = 3x + 2 (red line)

b. y = 3x - 2 (blue line)

A linear equation can be expressed in slope-intercept form as, y = mx + b, where m is the slope of the line and b is the y-intercept where the line cuts across the vertical axis (y-axis).

Given the equations:

a) y = x, the slope is 1, while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the red line on the graph plotted).

b) y= -x, the slope is -1 (declining slope), while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the blue line on the graph plotted).

c) y = x + 5, the slope is 1 (rising slope), while the y-intercept is 5. This means the line of the graph passes the y-axis at 5. (It is the green line on the graph plotted).

In Figure 2, we have the second graph with the following equations:

a. y = 3x + 2, the slope is 3 (rising slope), while the y-intercept is 2. This means the line of the graph passes the y-axis at 2. (It is the red line on the graph plotted).

b. y = 3x - 2, the slope is 3 (rising slope), while the y-intercept is -2. This means the line of the graph passes the y-axis at -2. (It is the blue line on the graph plotted).

In summary, the graphs of the equations are:

In fig. 1:

a) y = x (red line)

b) y = -x (blue line)

c) y = x + 5 (green line)

In Fig. 2:

a. y = 3x + 2 (red line)

b. y = 3x - 2 (blue line)

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