Given the vertex of a quadratic function, find the axis of symmetry.

Answer:

d = [tex]\sqrt{29}[/tex]

Step-by-step explanation:

The distance between two points is given by

d = [tex]\sqrt{ ( x2 - x1) ^2 - ( y2-y1)^2}[/tex]  where ( x1,y1) and ( x2,y2) are the two points

d = [tex]\sqrt{( 0 - -5) ^2 + (4 - 2) ^2}[/tex]

d = [tex]\sqrt{5^2 + 2^2}[/tex]

d = [tex]\sqrt{25 +4}[/tex]

d = [tex]\sqrt{29}[/tex]

Answer: [tex]\Large\boxed{Distance=\sqrt{29} }[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(-5,~2)[/tex]

[tex](x_2,~y_2)=(0,~4)[/tex]

Given the distance formula

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

Substitute values into the formula

[tex]Distance =\sqrt{((0)-(-5))^2+((4)-(2))^2}[/tex]

Simplify values in the parenthesis

[tex]Distance =\sqrt{(0+5)^2+(4-2)^2}[/tex]

[tex]Distance =\sqrt{(5)^2+(2)^2}[/tex]

Simplify the exponents

[tex]Distance =\sqrt{25+4}[/tex]

Simplify values in the radical sign

[tex]\Large\boxed{Distance =\sqrt{29}\approx5.4}[/tex]

Hope this helps!! :)

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Answer:

Initial population: 222 fish

After 7 years: 871 fish

Step-by-step explanation:

Initial population size:

Let t=0

∴P(0)=[tex]\frac{2000}{1+8e^0}[/tex]

       =[tex]\frac{2000}{1+8}[/tex]

       =[tex]\frac{2000}{9}[/tex]

       =222 fish

After 7 years:

Let t=7

∴P(7)=871 fish

1 week = 7 days

10 weeks = 10×7 days

= 70 days

if Ellen reads 1 book in a day

Therefore,

1 day = 1 book

70 days = 70×1

= 70 books.

Thus Ellen reads 70 books in 10 weeks.

Hope helps

Answer:

70 books

Step-by-step explanation:

Ellen reads one book per day for 10 weeks.

All we need to do to know the number of books Ellen read overall is to multiply 1 (number of books he read each day) and 10 weeks (total number of days).

Each week is 7 days, so 10 weeks is equal to 70 days.

The equation will be: 1 x 70

We can conclude that Ellen read 70 books overall within 10 weeks.

Answer: [tex]4x^3 -29x^2 +10x-21[/tex]

Step-by-step explanation:

[tex](4x^2 -x+3)(x-7)\\\\=4x^3 -28x^2 -x^2 +7x+3x-21\\\\=4x^3 -29x^2 +10x-21[/tex]

Answer:

no solutions

Step-by-step explanation:

The coefficient of 2(3)(6)Q is 2(3)(6)

The expression is given as:

2(3)(6)Q

For an expression

AQ

Where A is a number or product of numbers and Q is a variable

The number A represents the coefficient

By comparing:

AQ and 2(3)(6)Q

We have

A = 2(3)(6)

Hence, the coefficient of 2(3)(6)Q is 2(3)(6)

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Answer:

16 liters of 70% alcohol

4 liters of 20% alcohol

Step-by-step explanation:

Let x = volume of 70% alcohol and y = volume of 20% alcohol. Since we need total of 20 liters, the first equation is x + y = 20. Next, calculate the amount of alcohol in the 20 liters of 60% alcohol. 60% is equivalent to 0.6, so there is 20*0.6 = 12 liters of alcohol in the 20 liter solution. Therefore the second equation is 0.7x + 0.2y = 12.

x + y = 20

0.7x + 0.2y = 12

2x + 2y = 40

7x + 2y = 120

-5x = -80

x = 16

16 + y = 20

y = 4

The standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

The quadratic function is given as

f(x) = -3x^2 + 6x - 2

The standard form of a quadratic function is represented as:

f(x) = ax^2 + bx + c

When both equations are compared, we can see that the function f(x) = -3x^2 + 6x - 2 is already in standard form

Where

a = -3

b = 6

c = -2

Hence, the standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Take HJ = a, GH = b and GJ = c

put the value of a from equation 1 in equation 2

[tex]\qquad❖ \: \sf \:c = (b + 2) + b - 17[/tex]

[tex]\qquad❖ \: \sf \:c = 2b - 15[/tex]

now, put the value of a and c in equation 3

[tex]\qquad❖ \: \sf \:b + 2 + b + 2b - 15 = 73[/tex]

[tex]\qquad❖ \: \sf \:4b - 13 = 73[/tex]

[tex]\qquad❖ \: \sf \:4b = 86[/tex]

[tex]\qquad❖ \: \sf \:b = 21.5 \: \: in[/tex]

Now, we need to find HJ (a)

[tex]\qquad❖ \: \sf \:a = b + 2[/tex]

[tex]\qquad❖ \: \sf \:a = 21.5 + 2[/tex]

[tex]\qquad❖ \: \sf \:23.5 \: \: in[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

23.5 in

Step-by-step explanation:

To find the length of HJ in triangle GHJ, create three equations using the given information, then solve simultaneously.

Equation 1

HJ is two inches longer than GH:

⇒ HJ = GH + 2

Equation 2

GJ is 17 inches shorter than the sum of HJ and GH:

⇒ GJ + 17 = HJ + GH

Equation 3

The perimeter of ΔGHJ is 73 inches:

⇒ HJ + GH + GJ = 73

Substitute Equation 1 into Equation 2 and isolate GJ:

⇒ GJ + 17 = GH + 2 + GH

⇒ GJ + 17 = 2GH + 2

⇒ GJ = 2GH - 15

Substitute Equation 1 into Equation 3 and isolate GJ:

⇒ GH + 2 + GH + GJ = 73

⇒ 2GH + GJ = 71

⇒ GJ = 71 - 2GH

Equate the two equations where GJ is the subject and solve for GH:

⇒ 2GH - 15 = 71 - 2GH

⇒ 4GH = 86

⇒ GH = 21.5

Substitute the found value of GH into Equation 1 and solve for HJ:

⇒ HJ = 21.5 + 2

⇒ HJ = 23.5

The nickels in the envelope is $0. 12

From the information given, we have that;

Dimes + nickels = $1. 20

1/4 dimes + dimes = $ 1. 35

Let dimes = d

Nickels = n

d + n = 1. 20    equation a

d/4 + d = 1. 35   equation b

Make 'd' subject from equation a

d = 1. 20 - n

Substitute into equation b

1. 20 - n/ 4 + 1. 20 - n = 1. 35

0. 3 - 0. 25n + 1. 20 - n = 1. 35

collect like terms

- 1. 25n = 1. 35 - 1. 5

- 1. 25 = - 0. 15

n = -0. 15/ -1. 25

n = 0. 12

Thus, the number of nickels in the envelope is $0. 12

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Answer:

Step-by-step explanation:

a-b=21

5a-2b=18

Using elimination, we have

5a-5b=105

5a-2b=18

So:

3b=-87 so b=-29

Substituting, a=-8

(a,b)=(-8,-29)

Answer:

y= -3x+4

Step-by-step explanation:

y=mx+c

m= y2-y1 ÷ x2-x1

m= -3

y=-3x+c

7=-3(-1)+c

c=4

y=-3+4

Answer:

68?

Step-by-step explanation:

multiples of 5 end in 5 or 0

_ _ _

last digit has 2 choices ( 5 and 0 )

1,3,5,7,9 are odd

so tens digit has 5 choices but we see that 5 is repeated so we split into more cases

when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40

when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28

40+28=68

Using the z-distribution, the p-value for the test is of 0.0040.

The test statistic is given by:

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

In which:

For this problem, the parameters are given as follows:

[tex]\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40[/tex]

Hence the value of the test statistic is given by:

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

z = (33.8 - 32)/(4.3/sqrt(40))

z = 2.65.

Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.

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The perimeter of the minor segment is 77. 4m

The formula for determining the perimeter of the minor segment is given as;

Perimeter = θ/360 × 2πr + 2r sin θ/2

where;

Substitute into the formula;

Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)

Perimeter = 30. 79 + 46. 60

Perimeter = 77. 4 m

Thus, the perimeter of the minor segment is 77. 4m

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Answer:

3

Step-by-step explanation:

First we look at our problem 1/2 + 5/2. We can see our denominator is the same so we can add our numerators. 1/2 + 5/2 equals 6/2 = 3.

Answer:

If you add this fraction in fraction strip instead of equivalent fraction method

Step-by-step explanation:

firstly draw 5 1/2 fraction strip

then draw 12 1/4 fraction strip

we taking 1/4 bcoz 1/4 is multiple of 1/2, under 1/2 there is 2 1/4.

The end product will be 12/4

cancel out it 12/4 by 2 ans = 6/2 still we can cancel so cancel out 6/2 by 2 at the end ans will be 3/1 = 3

if you think it wrong then use the equivalent fraction method to see the answer..

1/2 + 5/2

denominators are same so we will take only one denominator and will directly add the numerators

1 + 5 = 6 so

6/2 cancel it the ans will be 3/1 and it's equal to 3.

Answer:$2346

Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.

Answer:

xy-49

Step-by-step explanation:

x x y is xy and -7x7 is 49 so the answer is xy- 49

The correct option regarding the sampling is C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.

Sampling is a process that is used in statistical analysis in which a predetermined number of observations are taken from a larger population

In this case, since the claim is mean pulse rate of students in a large statistics classes is greater than 72. The sample mean pulse rate was found to be 98.9 then the sample is not unusual if the claim is true. The sample is unusual if claim is false. Therefore there is sufficient evidence to support the claim.

The correct option is C.

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Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:

a-) -√2 / 2.

Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.

In this problem, the function is:

xcos(y) = 2.

The derivative is relative to t, applying the product rule, as follows:

[tex]\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0[/tex]

[tex]\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}[/tex]

Since dx/dt=−2, we have that:

[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]

When y = π/4, x is given by:

xcos(y) = 2.

[tex]x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}[/tex]

Hence:

[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]

[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}[/tex]

Since cot(pi/4) = 1, we have that:

[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}[/tex]

Which means that option a is correct.

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Answer: She started with 28 pieces of candy.

Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.

Answer:

She started with 28 candies.

Explanation:

Let the total amount of candies be c

Build equation:

→ remaining: c - 8

→ each gets: (c - 8)/5

Here given each gets 4 candies

So,

(c - 8)/5 = 4

c - 8 = 5(4)

c - 8 = 20

c = 20 + 8

c = 28

When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).

We are required to divide the first expression by second expression.

Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.

Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.

We know that  relationship between quotient, divisor, divident and remainder is as under:

Dividend=Divisor*Quotient+Remainder

[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39

Quotient=[tex]x^{2} +8x+19[/tex]

Remainder=39

Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

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Answer:

show the image because we cant answer it if there's no picture or image

Step-by-step explanation:

The probability that the value of p(x) is greater than 315 is 0.063754

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (315 - 283)/21

Evaluate the difference of 315 and 283

z = 32/21

Evaluate the quotient of 32 and 21

z = 1.524

The probability that the value of p(x) is greater than 315 is then calculated as:

P(x > 315) = P(z > 1.524)

From the z table of probabilities, we have;

P(x > 315) = 0.063754

Hence, the probability that the value of p(x) is greater than 315 is 0.063754

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Answer:

9x3 - 6x2 + 3x

Step-by-step explanation:

(27x 4 - 18x 3 + 9x 2) ÷ 3x

Dividing each term between 3x we have:

9x3 - 6x2 + 3x

We can check the result:

(9x3 - 6x2 + 3x) * (3x)

= (27x4 - 18x3 + 9x2)

The time taken for the smaller pipe to fill the pool by itself is 15.71 hours

1/6 = 1/x + 1/(x+6)

1/6 = (x+6)+(x) / (x)(x+6)

1/6 = (x+6+x) / x²+6x

1/6 = (2x+6)(x² + 6x)

1(x² + 6x) = 6(2x+6)

x² + 6x = 12x + 36

x² + 6x - 12x - 36 = 0

x² - 6x - 36 = 0

x = 9.71 or -3.71

The value of x cannot be negative

Therefore, the

Time taken for long pipe = x

= 9.71 hours

Time taken for small pipe = x + 6

= 9.71 + 6

= 15.71 hours

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Answer:

45

Step-by-step explanation:

Assuming this is a trapezoid,

[tex]\frac{29+WZ}{2}=37 \\ \\ 29+WZ=74 \\ \\ WZ=45[/tex]

Answer:

Your answer is - 28

Step-by-step explanation:

Given,

          a = 2

          b = - 3

          c = - 1

          d = 4

Now,

       - 2 ( b²  -  5 c )

= - 2 ( -3²  -  5 ( - 1 ) )

= - 2 ( 9 + 5 )

= - 2 × 14

= - 28   ans….

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