What is an equation of the line that passes through the point (4, 5) and is parallel to the line whose equation is y= 2/3x-4?

Answer:

Step-by-step explanation:

We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.

  (x^2 +4x) +(y^2 -10y) = 7

  (x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25

  (x +2)^2 +(y -5)^2 = 6^2

Compare to ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle

We see that the center is ...

  (h, k) = (-2, 5)

and the radius is ...

  r = 6

Answer:

  (13, 11)

Step-by-step explanation:

The vertex of g(x) = |x| is (0, 0).

When the function is transformed to ...

  f(x) = g(x -h) +k

the vertex is moved to (h, k).

Here, we have (h, k) = (13, 11), translating the function to ...

  f(x) = |x -13| +11

and moving the vertex to (13, 11).

Answer:

D. (13, 11)

Step-by-step explanation:

EDGE 2020 :)

Answer:

A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]

Step-by-step explanation:

The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.

Answer:

  5.7

Step-by-step explanation:

The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...

  AD/BD = BD/CD

Cross multiplying gives ...

  AD·CD = BD²

  (x+3)(2x+3) = 5²

  2x² +9x = 16 . . . . . perform the multiplication, subtract 9

  2(x² +4.5x) = 16

  2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square

  2(x +2.25)² = 26.125 . . . . . write as a square

  x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root

  x = -2.25 +√13.0625 . . . . subtract 2.25 to find x

We want the value of CD, so ...

  CD = 2x +3 = 2(-2.25 +√13.0625) +3

  CD = -1.5 +2√13.0625 ≈ 5.7284

The length of CD is about 5.7 units.

Answer: 2sqrt(33)

Step-by-step explanation:

We want to find the length of the line y = 4 in the circle x^2+y^2=49.

Substitute y = 4 to get x^2 = 33, so x = sqrt(33) or -sqrt(33).

That means the total length is sqrt(33) * 2 = 2sqrt(33).

Hope that helped,

-sirswagger21

The approximate length of the portion of the line is 11.49.

Circle centered at (h,k) with radius r is  [tex](x-h)^{2} + (y-k)^{2}=r^{2}[/tex]

A circle of a radius 7 centered at the origin:

[tex]x^{2} +y^{2}=49[/tex]   ......... (i)

[tex]y=4[/tex]               ..........(ii)

We have a circle and a line.  We need to find the points of

intersection and find the distance between those two points.

Replace y with 4 in the 1st equation and solve for x.

[tex]x^{2} +4^{2} =49\\x^{2} =49-16\\x^{2} =33\\[/tex]

[tex]x=[/tex] ±[tex]\sqrt{33}[/tex]

We have the 2 values of x where the line intersects the circle.

Plug those into one of the original equations to find the associated

y values.

[tex]\sqrt{33} ^{2} +y^{2} =49\\y^{2}=49-33\\y=4[/tex]

Two points on the circle are [tex](\sqrt{33} , 4)[/tex] and [tex](-\sqrt{33} , 4)[/tex]

Using the distance formula:-

[tex]=\sqrt{(4-4)^{2}+(-\sqrt{33}-\sqrt{33)} ^{2} } \\=\sqrt{(2\sqrt{33}) ^{2} } \\=2\sqrt{33}\\[/tex]

≈ 11.49

Therefore, the length of the portion of the line is approximately 11.49.

For more information:

https://brainly.com/question/24214108

Answer:

$5759.12

Step-by-step explanation:

$5759.12

At the end of the year, the compound interest on her loan is: $5000(1+0.1212)12=$5000(1.01)12≈$5634.12. To pay off the loan at the end of the year, she pays 5634.12+125=$5759.12.

Answer:

8 pieces

Step-by-step explanation:

Take 6 yds and divide by the length of each piece

6 ÷ 3/4

Copy dot flip

6 * 4/3

24/3

8

We can get 8 peices

Answer:

Step-by-step explanation:

Here,

H_o: The way of reservation is independent of gender.

H_a: The way of reservation is not independent of gender.

We use a chi square test because we can calculate the expected frequencies for this chart.

Doing an Expected Value Chart,          

33.7625   9.7125   30.525  

39.2375   11.2875   35.475

Using chi^2 = Sum[(O - E)^2/E],          

chi^2 =    4.482385929

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,

a =    3      

b =    2

df =    2

Thus, the critical value is

significance level =    0.05

chi^2(critical) =    5.991464547

Also, the p value is

P =    0.106331579

Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]

Rotating the graph of [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] with [tex]B\ne0[/tex] counterclockwise by [tex]\theta[/tex] eliminates the [tex]xy[/tex] term, where [tex]\cot2\theta=\frac{A-C}{B}.[/tex] Plugging in, we have [tex]\cot2\theta=\frac{7}{24},[/tex] since [tex]C=0.[/tex] Solving, we have [tex]\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.[/tex]

Answer:

the standard error of the proportion is 0.0272

Step-by-step explanation:

We have that if the sample size is greater than 5% of the entire population, a finite population correction factor (fpc) is multiplied with the standard error :

fpc = [tex]\sqrt{\frac{N -n}{N -1} }[/tex]

We know that N = 250 n = 91, replacing:

fpc = [tex]\sqrt{\frac{250 - 91}{250 -1} }[/tex]

fpc = 0.799

Now, the formula would then be:

SE  = [tex]\sqrt{\frac{p * (1 -p)}{n} }[/tex]*fpc

Now replacing, knowing that p = 0.12

SE= [tex]\sqrt{\frac{0.12 * (1 - 0.12)}{91} }[/tex]*0.799

SE = 0.0272

So the standard error of the proportion is 0.0272

Answer:

56 out of 224 times

Step-by-step explanation:

8 out of 32 = 1 out of 4

56 out of 224 = 1/4

Answer:56

Step-by-step explanation:

Answer:

63 cubic inches

Step-by-step explanation:

You have to first find the volume of each mold:

6 × 4 × 2= 48 cubic inches

3 × 5 × 1= 15 cubic inches

Add these two volumes together to find the overall volume of the whole sand castle.

48+15= 63 cubic inches

Answer:

The whole castle can hold 63 in² of sand.

Step-by-step explanation:

First, find the volume of the first mold.

V = whl          Substitute

V = (6)(2)(4)    Multiply

V = 48 in²

Now, find the volume of the second mold.

V = whl          Substitute

V = (5)(1)(3)    Multiply

V = 15 in²

Add together both volumes to find the volume of the whole castle.

48 + 15 = 63 in²

Answer:

Step-by-step explanation:

Answer:

raising a number to the 34th power

Step-by-step explanation:

Answer:

[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]

And we can find this probability to find the answer:

[tex] P(z<-0.903)[/tex]

And using the normal standar table or excel we got:

[tex]  P(z<-0.903)=0.1833 [/tex]

Step-by-step explanation:

Let X the random variable that represent the amounts of nocatine of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0.917,0.303)[/tex]  

Where [tex]\mu=0.917[/tex] and [tex]\sigma=0.303[/tex]

We have the following info from a sample of n =37:

[tex] \bar X= 0.872[/tex] the sample mean

And we want to find the following probability:

[tex] P(\bar X \leq 0.872)[/tex]

And we can use the z score formula given by;

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

And if we find the z score for the value of 0.872 we got:

[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]

And we can find this probability to find the answer:

[tex] P(z<-0.903)[/tex]

And using the normal standar table or excel we got:

[tex]  P(z<-0.903)=0.1833 [/tex]

Answer: answer is D

Step-by-step explanation:

Answer: The correct answer is 6,4,2

Step-by-step explanation: Doing a 100 point giveaway stay tuned!

Answer:

Given:

Sample size, n = 350

Sample proportion, P' = 0.21

H0 : p = 0.16

Ha : p ≠ 0.16

a) A 90% confidence interval for P.

Significance level = 1 - confidence interval = 1 - 0.90 = 0.10

For Z critical, we have:

Z critical = [tex] Z_0_._1_/_2 = Z_0_._0_5 = 1.645 [/tex] (using z table)

Standard error, S.E = [tex] \sqrt{\frac{P'(1 - P')}{n}} = \sqrt{\frac{0.21(1 - 0.21)}{350}} = 0.02177 [/tex]

Margin of error, E = 1.645 * 0.02177 =0.03581

The 90% confidence interval =

0.21 ± 0.03581

The lower limit: 0.21 - 0.03581 = 0.17419

The upper limit: 0.21+0.03581 =0.24581

b) Based on the confidence interval at significance level = 0.10,

We reject null hypothesis, H0, since 0.16 is not cointained in the confidence interval. We conclude that p ≠ 0.16.

c) Standard error is based on sample proportion p^ while standard deviation is based on hypothesized proportion Po.

d) Standard error is used to compute the confidence interval.

Answer:

Error interval is [tex]35\leq x< 45[/tex]

Step-by-step explanation:

Given: A number x becomes 40 if it is rounded to 1 significant figure

To find: error interval for x

Solution:

In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.

As a number x becomes 40 if it is rounded to 1 significant figure, error interval is [tex]35\leq x< 45[/tex].

A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.

Answer:

2500

Step-by-step explanation:

Monthly total cost, C(x) = 400 + 200x dollars

Monthly total revenue, R(x) = [tex]350x -\dfrac{1}{100}x^2[/tex] dollars

Profit = Revenue - Cost

[tex]=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400[/tex]

To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.

[tex]P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500[/tex]

Next, we check if the point x=7500 is a maxima or a minima.

To do this, we find the second derivative of P(x).

[tex]P''(x)=-\dfrac{1}{50} $ which is negative[/tex]

Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.

Therefore, the company needs to produce 2500 units to maximize profit.

Answer:

1/2 hour

Step-by-step explanation:

I am assuming you meant "lives 5km"

The first km would take 1/4 an hour because she is going 4km/h for one hour. One hour she would go 4km but we only need 1 mile so it would be cut to a fraction.

The same fraction goes for the bus. 4 is 1/4 of 16 so you would have to add them together and have 1/2 and hour to get home.

Answer:

8

Step-by-step explanation:

(290-25)/30

265/30

8 and 5/6

so how many full 30 cm lengths?

8

Answer:

7

Step-by-step explanation:

3 × 25 = 75cm

He cuts 75cm of 290cm so the remaining length is 290 - 75 = 215 cm

→ He then cuts the rest of the wire into as many 30 cm lengths as possible.

215 ÷ 30 = 7.17

Answer:

d=2

Step-by-step explanation:

Shape: Circle

Solved for diameter

Radius: 1

Formula: d=2r

Formula: Radius

Answer: 2

Hope this helps.

Answer:

[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]

Step-by-step explanation:

Given system of equations are

2x-6y-2z = 1

3y - 2z = -5

2y + 2z = -3

given

2 x - 6 y - 2 z = 1

0 x + 3 y - 2z = -5

0 x +2y + 2 z = - 3

The Matrix form of the given system of equations

A X = B

[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]

Answer:

x =42

Step-by-step explanation:

(3x+12)+x=180

Combine like terms

4x +12 = 180

Subtract 12 from each side

4x +12-12=180-12

4x = 168

Divide by 4

4x/4 =168/4

x =42

Answer:

x=42

Step-by-step explanation:

180-12=168

168 divided by 4 = 42

x=42

Answer:

A) 2

B) 33

C) 13

Step-by-step explanation:

Baseball =26

Football = 23

Basketball = 22

Baseball and Football (BF) = 12

Baseball and basketball (BK) = 13

Football and basketball (FK) = 14

All three (BFK) = 7

A) The total number of cities that have basketball teams is given by the cities with basketball only, added to the cities with basketball and football and cities with basketball and baseball, minus the cities with all three sports:

[tex]22=K+BK+FK-BFK\\22=K+13+14-7\\K=2[/tex]

B) The total number of cities with baseball of football is given by sum of the cities with either sport, minus the number of cities with both sports:

[tex]B\ or\ F = 23+22-12\\B\ or\ F =33[/tex]

C) If 22 cities have basketball and only 2 have basketball only, 20 cities have basketball and either baseball, football or all three sports. The number of cities with baseball or football, but not basketball is:

[tex](B\ or\ F)\cap (not\ K) = 33-20=13[/tex]

Answer:

13 2/3 cm

Step-by-step explanation:

To find the perimeter, add up all the sides

2 1/2 + 3 1/3+ 4 1/2 + 3 1/3

Add up the whole numbers

2+3+4+3 = 12

Add up the fractions

1/2+1/3+1/2+1/3

2/2 + 2/3

1 +2/3

Put them together

12+1+2/3

13 2/3

Answer: 13 2/3 cm

Step-by-step explanation:

1. Turn mixed fractions into improper fractions:

2 1/2 = 5/2

3 1/3 = 10/3

3 1/3 = 10/3

4 1/2 = 9/2

2. Formula for perimeter: left side + right side + upper base + lower base

3. Put your numbers in replace: 10/3 + 10/3 + 5/2 + 9/2

4. Solve: 41/3

5. Simplify into mixed fraction: 41/3 = 13 2/3

6. Don't forget to add the unit!

Answer:

[tex]i[/tex]

Step-by-step explanation:

[tex]\sqrt{-1} =i[/tex]

[tex]i[/tex]  is an imaginary number that represents the square root of -1.

Answer:

[tex] \frac{11}{24} [/tex]

Answer:

D. 11/24

Step-by-step explanation:

Total students' reading preferences = 240

Using electronic device = 110

Probability of having electronic device = 110/240

= 11/24

Answer:

the answer is Point G