Evaluate x+y^2(2+x) if x=3 and y= -1

Answer:

<BAC ≅ BCA by rule Base angle theorem

Step-by-step explanation:

What we know:

BAC = DAC

BC = BA

ΔBCA is an isosceles so ∠BCA  =  ∠DCA and ∠BAC

and we found that out by base angle theorem since

Base angle Theorem  = Two base angles of a icosceles triangle are equal.

And since ΔBCA is an isoceles then ∠A and ∠C will be equal. And so we can prove BC is a parallel to AD

The proof that BC ∥ AD from the given statements is that;

BC ∥ AD because of the definition of alternate angles

We are given;

AB = BC  

 AC is ∠ bisector of ∠BAD

Since AC is the angle bisector of ∠BAD, it means that;

∠BAC  = ∠DAC (definition of a bisected angle)

Now, since AB = BC, it means that ΔBCA is an isosceles triangle.

Thus; ∠BCA = ∠BAC  (base angle theorem)

Now, since ∠BCA = ∠BAC, and ∠BAC  = ∠DAC, we can say that;

∠BCA = ∠DAC

This means  ∠BCA and ∠DAC are alternate angles. Thus, we can say that AC is the transversal line carrying the two equal angles.

Thus, we can say that BC is parallel to AD as they are the parallel lines cut by the transversal line AC.

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The number of possible permutations of the three letters C, D, and E is d.6

A permutation is an arrangement of objects in a specific order. In this case, we are looking at the number of possible arrangements of the three letters C, D, and E. To find the number of permutations, we can use the formula:

n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1

where "n" is the number of distinct objects to be permuted.

So for our problem, we have three distinct objects (C, D, and E). Therefore, we can plug in n=3 to get:

3! = 3 x 2 x 1 = 6

This means there are 6 possible ways to arrange the letters C, D, and E in different orders. We can list all of these permutations as follows:

CDE

CED

DCE

DEC

ECD

EDC

So the answer to the question is 6, as given in option (d).

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Answer:

72 dentists

Step-by-step explanation:

In this case, we can multiply 80 by 9/10 or .9 to get our answer.

If we were to multiply by 9/10 it would look like this:

\(80 * \frac{9}{10} \\\frac{720}{10} = 72\)

But, if we were to multiply by .90 (remember that 9/10 = .9) it would look like this:

\(80(.90) = 72\)

Therefore, if 9 out of 10 dentists recommended PurWhite toothpaste and 80 were surveyed then 72 out of the 80 would have recommended it.

I hope this helps!!

If you have any questions feel free to ask!

- Kay :)

Answer:

C. 113.04 square inches

The approximate surface area of the orange is 113.04 square inches. Therefore, the correct option is: 113.04 square inches.

To find the surface area of an orange, we need to calculate the surface area of its sphere. The formula for the surface area (SA) of a sphere is:

SA = 4πr²

where r is the radius of the sphere.

Given that the radius of the orange is 3 inches, we can plug this value into the formula:

SA = 4π(3)²

SA = 4π(9)

SA = 36π

Now, to get an approximate value for the surface area, we can use the approximation π = 3.14:

SA = 36 × 3.14

SA = 113.04 square inches

So, the approximate surface area of the orange is 113.04 square inches. Therefore, the correct option is: 113.04 square inches.

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Answer:

4/9

Step-by-step explanation:

The probability that the spinner lands on a 5 or a multiple of 3 will be 0.4444 or 44.44%.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

You spin a spinner with 9 equal spaces numbered 1 through 9.

Then the probability that the spinner lands on a 5 or a multiple of 3 will be

The total number of the event will be

Total events = 9

The favorable event will be

Favorable = 1 {5} and 3 {3, 6, 9}

Then the probability will be

P = 1/ 9 + 3/ 9

P = (1 + 3) / 9

P = 4/9

P = 0.4444

P = 44.44%

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Greetings from Brasil...

The type of quadrilateral is formed by the points A(1, 2), B(3, 5), C(3, 8), and D(1, 5) is parallelogram.

Given points:

A(1, 2), B(3, 5), C(3, 8), and D(1, 5)

we know that distance formula,

Distance between AB = \(\sqrt{(x_{2} - x_{1})^{2} +( y_{2} - y_{1})^{2} }\)

= \(\sqrt{(3 - 1)^{2} +( 5 - 2)^{2} }\)

= \(\sqrt{2^{2}+3^{2} }\)

AB = \(\sqrt{13}\)

BC = \(\sqrt{(3 - 3)^{2} +( 8 - 5)^{2} }\)

= \(\sqrt{0^{2}+3^{2} }\)

= \(\sqrt{9}\)

= 3

BC = 3

CD = \(\sqrt{(1 - 3)^{2} +( 5 - 8)^{2} }\)

= \(\sqrt{(2^{2} +3^{2} }\)

CD = \(\sqrt{13}\)

AD = \(\sqrt{(1 - 1)^{2} +( 5 - 2)^{2} }\)

= \(\sqrt{0^{2}+3^{2} }\)

AD = 3

AC = \(\sqrt{(3 - 1)^{2} +( 8- 2)^{2} }\)

= \(\sqrt{2^{2} +6^{2} }\)

AC = \(\sqrt{40}\)

BD = \(\sqrt{(1 - 3)^{2} +( 5 - 5)^{2} }\)

= \(\sqrt{2^{2} +0^{2} }\)

BD = 2

Here AB = CD,BC = DA . But AC ≠ BD

Hence the pairs of opposite sides are equal but diagonal are not equal so it is a parallelogram.

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Answer:107.2

Step-by-step explanation:

So u know how much he gets in 4 days so u subtract 4 days by 2 and u get 2 so then divide 214.40 by 2 and u get 107.2

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1200\\ r=rate\to 5.2\%\to \frac{5.2}{100}\dotfill &0.052\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases}\)

\(A = 1200\left(1+\frac{0.052}{12}\right)^{12\cdot 4} \implies A = 1200( 1.004\overline{33})^{48}\implies A \approx 1476.79\)

The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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To find the marginal density of X/Y, we need to integrate the joint density function fXY(x, y) over the range of Y. By performing the integration, we obtain the marginal density of X/Y as a function of X. The resulting marginal density provides information about the distribution of the ratio X/Y.

The marginal density of X/Y can be obtained by integrating the joint density function fXY(x, y) over the range of Y. In this case, the joint density function is given by:

fXY(x, y) =

  24xy    if x >= 0, y >= 0, and x + y <= 1

  0       otherwise

To find the marginal density of X/Y, we integrate fXY(x, y) with respect to y, while keeping x as a constant. The integration limits for y can be determined based on the given conditions x >= 0, y >= 0, and x + y <= 1. Since y must be non-negative, the lower limit of integration is 0. The upper limit of integration can be determined by the constraint x + y <= 1, which implies y <= 1 - x.

Integrating fXY(x, y) over the range of y, we obtain the marginal density of X/Y as follows:

fX/Y(x) = ∫[0 to (1 - x)] 24xy dy

Evaluating the integral, we have:

fX/Y(x) = 24x * ∫[0 to (1 - x)] y dy

       = 24x * [(y^2)/2] evaluated from 0 to (1 - x)

       = 12x * (1 - x)^2

The resulting marginal density fX/Y(x) represents the distribution of the ratio X/Y. It provides information about the likelihood of different values of X/Y occurring. The shape of the distribution can be further analyzed to understand the characteristics of the random variable X/Y.

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Answer:

(2)

Step-by-step explanation:

-3,2

-1,-1

\(y = ax + b \\ 2 = - 3a + b \\ - 1 = - a + b \\ 3 = - 2a \\ a = - 1.5\)

slope is -1.5

Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.

Given function is: \(f(x) = -2x^{2}+12x+5\)

\(f(x) = a(x-h)^{2} +k\) , where (h,k) is the vertex

Apply completing the square method to find vertex

\(f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5\)

Lets take half of coefficient of x is -6

divide by 2 that is -3

square it \((-3)^{2}\) that is 9

Add and subtract 9

\(f(x) = -2(x^{2}-6x+9-9)+5\)

Take out -9 and multiply by -2

\(f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23\)

Now factor the parenthesis part

\(f(x) = -2(x-3)^{2} +23\)

The value of h=3  and k=23

So vertex is (3,23)

The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum

Hence the answer is the vertex is maximum at (3,23)

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(a) The system with impulse response h(t) = e^(-|t|) is causal but not BIBO stable.(b) The system with impulse response h(t) = (1-|t|)[u(t+1)-u(t-1)] is both causal and BIBO stable.(c) The system with impulse response h(t) = e^(2t)u(-t) is neither causal nor BIBO stable.(d) The system with impulse response h(t) = e^(2t)u(t) is causal but not BIBO stable.(e) The system with impulse response h(t) = cos(2t)u(t) is causal and BIBO stable.(f) The system with impulse response h(t) = t+1/1 is both causal and BIBO stable.

(i) Causality: A system is causal if the output at any time depends only on past and present inputs. For the given impulse responses:

(a) The exponential function e^(-|t|) is symmetric around t=0, so it depends on future values and is not causal.

(b) The function (1-|t|) is a linear function that depends on both past and present inputs, making it causal.

(c) The impulse response e^(2t)u(-t) involves a unit step function with a negative argument, indicating dependence on future inputs and making it non-causal.

(d) The impulse response e^(2t)u(t) is causal as it depends on past and present inputs only.

(e) The cosine function cos(2t)u(t) is causal as it depends on past and present inputs only.

(f) The impulse response t+1 is a linear function that is causal.

(ii) BIBO Stability: A system is BIBO (Bounded-Input Bounded-Output) stable if bounded inputs produce bounded outputs. For the given impulse responses:

(a) The exponential function e^(-|t|) does not decay for large |t|, indicating that it is not BIBO stable.

(b) The function (1-|t|) is a bounded function, and the unit step function ensures boundedness, making it BIBO stable.

(c) The exponential function e^(2t) grows without bound for positive t, indicating that it is not BIBO stable.

(d) The exponential function e^(2t) grows without bound for positive t, making it not BIBO stable.

(e) The cosine function cos(2t) is bounded, and the unit step function ensures boundedness, making it BIBO stable.

(f) The linear function t+1 is bounded for any input, making it BIBO stable.

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cos 48° = b / √(a²+b²)

tan 48° = a/b

sin 48° = a / √(a²+b²)

Answer:

-44

Step-by-step explanation:

Using distribute property of multiplication

=> \(7\sqrt{5} + (\sqrt{5} )^2-49-7\sqrt{5}\)

(\(7\sqrt{5}\) will be cancelled with each other)

=> 5 - 49

=> -44

The quadrilateral that has diagonals that always bisect its angles and also bisect each other is a (1) rhombus.

In a Rhombus, the diagonals are perpendicular bisectors of each other, and they bisect each other at their point of intersection, dividing the rhombus into four congruent triangles.

Each angle of a rhombus is = 180° divided by number of sides, so each angle of a rhombus is 90°.

In a rectangle, the diagonals bisect each other, but they do not necessarily bisect the angles of rectangle.

In a parallelogram, the diagonals bisect each other, but they do not necessarily bisect the angles of parallelogram.

In an isosceles trapezoid, the diagonals do not bisect each other.

Therefore, the correct answer is option (1) rhombus.

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The given question is incomplete, the complete question is

Which quadrilateral has diagonals that always bisect its angles and also bisect each other?

1) rhombus

2) rectangle

3) parallelogram

4) isosceles trapezoid.

The probability that exactly 10 are yellow out of 9 random selections is 0.

To calculate the probability of exactly 10 jelly beans being yellow out of 9 selected at random, we need to consider the total number of favorable outcomes (selecting exactly 10 yellow jelly beans) divided by the total number of possible outcomes (selecting any 9 jelly beans).

The total number of jelly beans in the box is 23 (yellow) + 33 (green) + 37 (red) = 93.

The number of ways to select exactly 10 yellow jelly beans out of 9 is 0, as we have fewer yellow jelly beans than the required number.

Therefore, the probability of exactly 10 yellow jelly beans is 0.

In this case, it is not possible to have exactly 10 yellow jelly beans out of the 9 selected because there are not enough yellow jelly beans available in the box.

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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that: exactly 10 are yellow?

Step 1

Given; What equation results from completing the square and then factoring? x2 + 4x = 5

A.(x + 2)2 = 7

B.(x + 2)2 = 1

C.(x + 2)2 = 9

D.(x + 2)2 = 3

Magnus still has 3 games left to play

Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}\)

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

\(\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}\)

Answer:

1/16IB

Step-by-step explanation:

Differnce means to subtract which means we need to subract the two fractions. First find the the lowest of common factor for both fractions. In this case it is 16 because 4 can go into 16 four times as 4x4=16.

Since we know that 4 goes into 16 four times we get the 4 and then multiply it by the numerator (the top number of the fraction) for the fracion 1/4. Now the fraction 1/4 is 4/16. Keep the 3/16 the same as the denominator  (bottom number of fraction) is already our common factors between the two fractions.

Work Shown:

Orginal Equation: 1/4-3/16

Get common Denomiantors: Convert 4 to 16. 4 goes into 16 four times, multiply by 4 by numerator. 4X1=4.

Final Step: Since both are now common fractions just subtract the numerators keeping the denominators the same of the fractions.

4/16-3/16= 1/16

Final Answer: 1/16IB

two million four hundred seventy thousand

Answer:

Step-by-step explanation:

here x1=8 , y1=9 , x2=4 , y2=4

using formula

slipe(m)=y2-y1/x2-x1

=4-9/4-8

=-5/-4

=5/4

The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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The oblique asymptote of the function is 7x

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

x² + x - 5 | 7x³ + 7x² + 4x - 2

When the polynomial is divided, we have

                7x

x² + x - 5 | 7x³ + 7x² + 4x - 2

                7x³ + 7x² - 35x

--------------------------------------------

                39x - 2

From the above, we have

Quotient = 7x

This means that the oblique asymptote is 7x

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The value of P(0) and P(6) of The Polynomial Function above are 2 and 253/2 respectively.

Polynomial function refers to the algebraic expression that consists of several terms.

Polynomial function can be of different degrees, like linear polynomial (degree 1), quadratic polynomial (degree 2), cubic polynomial (degree 3), and so on.

The given polynomial function is P(w) = 6w² - 20w + 2.

To find P(6), substitute w = 6 in P(w).

Therefore,P(6) = 6(6)² - 20(6) + 2P(6) = 6(36) - 120 + 2P(6) = 216 - 120 + 2P(6) = 96

Adding P(6) = 349 to this equation, we get:2P(6) = 349 - 96 = 253

Therefore, P(6) = 253/2

Now, to find P(0), substitute w = 0 in P(w).

Therefore, P(0) = 6(0)² - 20(0) + 2 = 2

Therefore, P(0) = 2

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Answer:

Step-by-step explanation:

\(d = \frac{m}{V} \\Cross\:Multiply\\\\dV = m\\\\Divide\:both \:sides \:of\:the\:equation\:by\:d\\\\\frac{dV}{d} = \frac{m}{d} \\\\\\V = \frac{m}{d}\)

Ans:12*3=36 the answer is D

Step-by-step explanation