Use the method of equating coefficients to find the values of a, b, and c: (x+4)(ax2+bx+c)=−2x3−7x2+3x−4.

The missing reasons for each of the given statements are respectively;

1) Substitution

2) Definition of a Straight angle because a straight angle is 180°.

3) Congruent Angles have equal measures

We are given that;

m∠1 = 90°

m∠1 + m∠2 = m∠5

∠3 ≅ ∠4

Statement 1; 90° + m∠2 + m∠4 = 180°

Reason 1; Substitution

Statement 2; m∠1 + m∠2 + m∠3 = 180°

Reason 2; Definition of a Straight angle because a straight angle is 180°.

Statement 3; m∠3 = m∠4

Reason 3; Congruent Angles have equal measures

Thus, the missing reasons for each of the given statements are respectively;

1) Substitution

2) Definition of a Straight angle because a straight angle is 180°.

3) Congruent Angles have equal measures

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a.

Solution Given:

Slope of the line passing through the point is

m= [tex] \frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{-2-2}=\frac{8}{-4}=-2[/tex]

slope=-2

b.

Solution given:

equation is

2x-5y=-10

2x+10=5y

y=2x/5 +10/5

y=2/5 x +3

comparing above equation with y=mx+c

we get

m=2/5

slope=2/5

c.

Slope of the line passing through the point is

m=[tex] \frac{y_2-y_1}{x_2-x_1}[/tex]

-4=[tex] \frac{1-(-9)}{0-x}[/tex]

-4=10/-x

doing criss cross multiplication

-4*-x=10

4x=10

x=10/4

x=5/2

slope=5/2

d.

we have

equation of line passing through the one point is

[tex] y-y_1=m(x-x_1)[/tex]

y-5=-7(x-(-1))

y=-7(x+1)+5

y=-7x-7+5

y=-7x-2 is a required equation:

Answer: 2/6 2/3 11/12

Step-by-step explanation: if you do the common denominator, you will find the numbers 2/6= 4/12 11/12=11/12 2/3=8/12. So your answer should be 2/6 11/12 2/3

a. By replacing [tex]x[/tex] with [tex]-x^2[/tex] in the power series, we get

[tex]\displaystyle \frac1{1+x^2} = \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n}[/tex]

Integrate both sides to recover [tex]\arctan(x)[/tex] on the left.

[tex]\displaystyle \int \frac{dx}{1+x^2} = \int \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n} \, dx[/tex]

[tex]\displaystyle \arctan(x) = C + \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

By letting [tex]x=0[/tex] on both sides, we find [tex]C=0[/tex], so that

[tex]\displaystyle \arctan(x) = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

Then dividing both sides by [tex]x[/tex] gives

[tex]\displaystyle \boxed{\frac{\arctan(x)}x = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n} \, dx}[/tex]

b. Let [tex]x=\frac1{\sqrt3}[/tex]. Then

[tex]\displaystyle \frac{\arctan\left(\frac1{\sqrt3}\right)}{\frac1{\sqrt3}} = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} \left(\dfrac1\sqrt3\right)^{2n}[/tex]

[tex]\displaystyle \sqrt3 \arctan\left(\frac1{\sqrt3}\right) = \sum_{n=0}^\infty \frac1{2n+1} \left(-\frac13\right)^n[/tex]

Taking the first few terms from the infinite series, we can approximate

[tex]n=0 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1[/tex]

[tex]0\le n\le1 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1+\dfrac13\left(-\dfrac13\right) = \dfrac89[/tex]

which together suggest the value we want is bounded between 8/9 and 9/9 = 1, hence [tex]\boxed{p=8}[/tex].

Since the series is alternating and converges on [tex]-1<x<0\cup0<x<1[/tex],

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^0 a_n \right| < |a_1| = \left|\frac13 \left(-\frac13\right)^1\right| = \frac19[/tex]

and

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^1 a_n \right| < |a_2| = \left|\frac15 \left(-\frac13\right)^2\right| = \frac1{45}[/tex]

which tells us the first approximation is off by at most 1/9 from the actual value of [tex]\frac\pi{2\sqrt3}[/tex], whereas the second approximation is off by at most 1/45 from the actual value. In other words, the second approximation is closer, so [tex]\frac\pi{2\sqrt3}[/tex] is closer to [tex]\frac p9[/tex] :

[tex]\dfrac89 \approx 0.8889[/tex]

[tex]\dfrac{\pi}{2\sqrt3}\approx0.9069[/tex]

[tex]\dfrac99 = 1[/tex]

The probability that the person selected is 40 years old or younger is 0.61.

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the person selected is 40 years old or younger = number of people 40 years or younger / total number of people at the movie theatre = (6 + 17 + 18 + 10 + 4 + 6) / (6 + 17 + 18 + 10 + 4 + 6 + 16 + 3 + 20)

61 / 100 = 0.61

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Answer:

BC 1

AC 2

AABC 3

Step-by-step explanation:

BC=16

AC = 15

AABC= 15

Answer: C, B, A

Step-by-step explanation: It just is

So, K and L are located at K = -11 or L = -27 or K = -27 or L = -11

Givent that Point J is located at -19. Points K and L are each 8 units away from Point J. This implies that the modulus of K - J or modulus of L - J = 18.

So, |K - J| = 8

⇒ K - J = 8 or -(K - J) = 8

Substituting the value of J = -19 into the equation, we have

⇒ K - J = 8 or -(K - J) = 8

⇒ K - (-19) = 8 or -(K - (-19)) = 8

⇒ K + 19 = 8 or (K - (-19)) = -8

⇒ K + 19 = 8 or K + 19 = -8

⇒ K = 8 - 19 or K = -8 - 19

⇒ K = - 11 or K = -27

Also, |L - J| = 8

⇒ L - J = 8 or -(L - J) = 8

Substituting the value of J = -19 into the equation, we have

⇒ L - J = 8 or -(L - J) = 8

⇒ L - (-19) = 8 or -(L - (-19)) = 8

⇒ L + 19 = 8 or (L - (-19)) = -8

⇒ L + 19 = 8 or L + 19 = -8

⇒ L = 8 - 19 or L = -8 - 19

⇒ L = - 11 or L = -27

So, K and L are located at K = -11 or L = -27 or K = -27 or L = -11

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The positive square roots of the number 151,321 according to the task content can be determined by means of division as; 389.

It follows from.the task content above that the number given is; 151,321 whose positive square roots is to be determined.

Upon testing different integers as divisor on the number 151,321; it is concluded that the only positive integer by which 151,321 can be divided to result in a whole is; 389.

Hence, the positive square root of the number 151,321 is; 389.

Consequently, it can be concluded that the positive square root of the number, 151,321 as in the task content is; 389 which is itself a prime number as it is only divisible by 1 and itself.

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Answer:

Angle x= 60°

Step-by-step explanation:

For the triangle HIL, you're going to add 30+90=120

Angles in a triangle add up to 180.

So, therefore,

180-120=60   so angle L must equal 60.

HJ is a straight line and angles in a straight line add up to 180.

180-90=90

Angle JIL is equal to 90.

To find y you add 90+45 which equals 135.

Again, angles in a triangle add up to 180.

180-135=45

So,

y = 45

Now we are told that IJK is a right angle and that we are given that IJL is 45. 45 is half of 90 so LJK must be 45.

To find angle JLK we must add angle L and angle y.

60+45=105

Angles in a straight line add up to 180. So,

180-105=75

75 = Angle JLK

75+45=120

Angles in a triangle add up to 180 so,

180-120= 60

Angle x= 60°

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Answer:9[tex]a^{10}[/tex][tex]b^{-6}[/tex]=[tex]\frac{9a^{10} }{b^6}[/tex]

Step-by-step explanation:

Answer:

9*a^10*(1/(b^6))

Step-by-step explanation:

(-3a^5*b^-3)^2

(-3)^2 * (a^5)^2 * (b^-3)^2

9a^10*b^-6

9*a^10*(1/(b^6))

Answer:(3+3)(1+3) = 24

Step-by-step explanation: There is a 1 and 3 3's. We know that added up, the sum is not 24. So it can't be all addition. But, 3 is a factor of 6 which is a factor of 24. There are 2 3's, so we add them up to get 6. Then, we have a 1 and a 3 left. we add these up to get 4. 6x4= 24.

Answer: slope is 1/3

Step-by-step explanation: make a graph of y=1/3x+9

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

SA = 2(lw + lh + hw), where:

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

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Using the formula for the distance between two points, the length of the line segment PQ is of 30 units.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates of the endpoints for this problem are given by:

Hence the distance is given by:

D = sqrt[(-20 -10)² + (10 - 10)] = 30 units.

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Answer: 30 units

Step-by-step explanation:

Using the t-distribution, it is found that since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.

At the null hypothesis, it is tested if the average is not less than 25, that is:

[tex]H_0: \mu \geq 25[/tex]

At the alternative hypothesis, it is tested if the average is less than 25, that is:

[tex]H_1: \mu < 25[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

Considering the situation described, the values of the parameters are given as follows:

[tex]\overline{x} = 24.97, \mu = 25, s = 2.16, n = 10[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{24.97 - 25}{\frac{2.16}{\sqrt{10}}}[/tex]

t = -0.04

Using a t-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -0.04, the p-value is of 0.4844.

Since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.

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Answer:

line NM

Step-by-step explanation:

Since planes extend infinitely in all directions, planes intersect at a line, not at a line segment.

Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.

The equation is given by:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

In which:

In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

[tex]20 = 10\log{\frac{p}{p_0}}[/tex]

[tex]\log{\frac{p}{p_0}} = 2[/tex]

The logarithm is inverse of the function [tex]10^x[/tex], hence we apply the function to both sides to find the ratio.

[tex]\frac{p}{p_0} = 10^2[/tex]

[tex]\frac{p}{p_0} = 100[/tex]

Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.

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Answer:

1. x = 20

2. x = 3

3. RST = 22 degrees

Step-by-step explanation:

1. Since QR bisects PQS, the measure of the angles PQR and PQS should be equal, so we can set their expressions equal to each other, and then solve.

4x-10 = -3x+130

4x = -3x +140

7x = 140

x = 20

2. Since there is a CAB has a right angle, the measure of angles CAD and BAD should add up to 90 degrees. So we can set the sum of their expressions equal to 90 degrees.

(5x+57) + (x+15) = 90

6x + 72 = 90

6x = 18

x = 3

3. I can't see where the R is but if it is on the empty line then we can find RST by subtracting the measure of angle TSU from angle RSU.

TSU - RSU = RST

91 - 69 = 22 degrees

RST = 22 degrees

Answer:

7.  m∠PQR =70°   m∠PQS = 140°

8.  m∠CAD = 18°    m∠BAD = 72°

9.  m∠RST = 22°

Step-by-step explanation:

Question 7

If QR bisects (divides into two equal parts) ∠PQS then:

⇒ m∠PQR = m∠RQS

⇒ 4x - 10 = -3x + 130

⇒ 4x - 10 + 10 = -3x + 130 + 10

⇒ 4x = -3x + 140

⇒ 4x + 3x = -3x + 140 + 3x

⇒ 7x = 140

⇒ 7x ÷ 7 = 140 ÷ 7

⇒ x = 20

Substitute the found value of x into the expression for m∠PQR:

⇒ m∠PQR = 4(20) - 10 = 70°

As QR bisects ∠PQS:

⇒ m∠PQS = 2m∠PQR = 2 × 70° = 140°

Question 8

From inspection of the given diagram, ∠BAC = 90°.

⇒ m∠CAD + m∠BAD = 90

⇒ x + 15 + 5x + 57 = 90

⇒ 6x + 72 = 90

⇒ 6x + 72 - 72 = 90 - 72

⇒ 6x = 18

⇒ 6x ÷6 = 18 ÷ 6

⇒ x = 3

Substitute the found value of x into the expressions for the two angles:

⇒ m∠CAD = 3 + 15 = 18°

⇒ m∠BAD = 5(3) + 57 = 72°

Question 9

From inspection of the given diagram (and assuming R is on the empty line segment):

   m∠RSU = m∠RST + m∠TSU

⇒ 91° = m∠RST + 69°

⇒ 91° - 69° = m∠RST + 69° - 69°

⇒ 22° = m∠RST

⇒ m∠RST = 22°

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Answer:

233.35488 km (Rounded to 233 km)

Step-by-step explanation:

If you convert miles to kilometers then you would use this conversion factor:

1 mile = 1.609344 km (or 1.61 km)

so in this case,

145 mile = 1.609344 km x 145

145 mile = 233.35488 km

I could also round it to 233 km.

Since your on a trip... i hope u enjoy ur journey to Las Vegas!

In mathematical notation, the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set of integers less than -20 is the set of all whole numbers that are smaller than -20. Integers include both positive and negative whole numbers, as well as zero.

In mathematical notation, we can represent the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set includes all numbers that are smaller than -20, going indefinitely in the negative direction. Each number in the set is obtained by subtracting 1 from the previous number in the set.

For example:

-21 is the integer immediately smaller than -20, so it is included in the set.

-22 is the next integer, smaller than -20, so it is also included in the set.

And this pattern continues indefinitely, encompassing all the integers less than -20.

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Answer
5/9 is the dividend

Step-by-step explanation:

Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:

[tex]H_0: \mu = 16[/tex]

At the alternative hypothesis, it is tested if the mean is different, hence:

[tex]H_1: \mu \neq 16[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are:

[tex]\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150[/tex].

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}[/tex]

z = -2.1

Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.

Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

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The sum of the first 7 terms of the geometric series is 15.180

The formula for calculating the sum of geometric series is expressed according to the formula. below;

GM = a(1-r^n)/1-r

where

r is the common ratio

n is the number of terms

a is the first term

Given the following parameters from the sequence

a = 1/36

r = -3

n = 7

Substitute

S = (1/36)(1-(-3)^7)/1+3
S = 1/36(1-2187)/4
S = 15.180

Hence the sum of the first 7 terms of the geometric series is 15.180

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Answer:

the coordinates of equations

1.4x+y=-7

for x =0

f(0,y)=4(0)+y=-7

y=-7

for y=0

f(x,0)=4x+0=-7

4x=-7

x=-7/4

2.x-y=2

for x=0

f(0,y)=0-y=2

-y=2

y=-2

for y=0

f(x,0)=x-0=2

x=2

graph all of the equations coordinates or you can look the image

so the answers are : {-3,-1}

CMIIW

Answer:

The combination shows that the numbers of possible live card hands drawn without replacement from a standard deck of 52 playing cards is 2,598,960.

A permutation is the act of arranging the objects or numbers in order while combinations are the way of selecting the objects from a group of objects or collection such that the order of the objects does not matter.

Since the order does not matter, it means that each hand is a combination of five cards from a total of 52.

We use the formula for combinations and see that there are a total number of C( 52, 5 ) = 2,598,960 possible hands.

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Answer: 105 dollars

Step-by-step explanation:

Let's say that the original price x dollars, we can use the equation to find the original price.

80%x = 84

x = 105

Answer:

$105

Step-by-step explanation:

The multiplier is 0.8

To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8

Therefore to obtain the original price from the price after the discount, we use reverse percentage:

$84 ÷ 0.8 = $105

Answer:

0.85

Step-by-step explanation:

1 - 15% = 1 - 0.15 = 0.85

[tex] y = (0.85)^\frac{t}{12} [/tex]

Answer: 0.85

The number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

Ratio of flour to loaves of bread = 3 cups : 2 loaves

Number of loaves of bread can the baker make with a 10 lb-bag of flour

3 : 2 = 30 : x

3/2 = 30/x

3 × x = 2 × 30

3x = 60

x = 60/3

x = 20 loaves of bread

Therefore, the number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

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