PLEASE HELP WILL MARK BRANIEST

Answer:

See Below.

Step-by-step explanation:

We want to show that the normal line to the parabola:

[tex]y^2=8x[/tex]

At the point (2, 4) meets the parabola again at (18, -12).

First, find the tangent line to the parabola at the point (2, 4). We can take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[ y^2\right]=\frac{d}{dx}\left[8x\right][/tex]

Implicit differentiation:

[tex]\displaystyle 2y\frac{dy}{dx}=8[/tex]

Therefore:

[tex]\displaystyle \frac{dy}{dx}=\frac{8}{2y}=\frac{4}{y}[/tex]

Then the slope of the tangent line to the point (2, 4) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{y=4}=\frac{4}{(4)}=1[/tex]

Thus, the slope of the normal line is -1.

And since it passes through the point (2, 4), by the point-slope form:

[tex]y-(4)=-1(x-2)[/tex]

Simplify:

[tex]y=-(x-2)+4[/tex]

By letting x = 18:

[tex]y=-(18-2)+4=-16+4=-12[/tex]

So, the normal line indeed passes through (18, -12).

Answer:

answer is in the picture.

Answer:

cscθ = 5/4, secθ = 5/3

Step-by-step explanation:

First, let's view the drawing that I have attached, with the dot in the bottom left representing the origin. We know that cosecant and secant are the reciprocals of sin and cos respectively, and in order to find sin and cos, we must find the opposite, adjacent, and hypotenuse sides. The hypotenuse is opposite the right angle, equal to √(8²+6²) = 10

Next, we can find sin and cos of θ . sinθ = 8/10=4/5, making cscθ the reciprocal of 4/5, or 5/4

Similarly, cosθ = 6/10=3/5, and secθ = 5/3

Answer:

The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]

Step-by-step explanation:

Horizontally stretching a function:

Horizontally stretching a function f(x), by a factor of a, means that:

[tex]g(x) = f(\frac{x}{a})[/tex]

In this question:

[tex]f(x) = x[/tex], horizontally stretched by a factor of 3, so [tex]a = 3[/tex], and:

[tex]g(x) = f(\frac{x}{3}) = \frac{x}{3}[/tex]

The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]

Answer:

I would identify the proportions of the corresponding sides, because that would allow you to identify whether or not the triangles are similar. You could also identify if two triangles are similar using

-SSS (side-side-side) which would tell you if all three corresponding sides are congruent

-SAS (side-angle-side) which would tell you if two sides and the angle between them are congruent

-ASA (angle-side-angle) which would tell you the two angles and the side between them are congruent

-AAS (angle-angle-side) which would tell you if two angles and a non-included side are congruent. You triangles may have all of these, or just one, but it will help you identify the similarity between triangles

Step-by-step explanation:

base = 11

height = 8

so are is 11 x 8 /2

= 44

Answer:

ans: 4

Step-by-step explanation:

corresponding sides are proportional since given triangle are similar triangle, I.e

(4/5.5) = { (2x+8)/(6x-2)}

8/11 = ( x+ 4 ) / ( 3x - 1 )

8( 3x - 1 )= 11( x + 4 )

24x - 8 = 11x + 44

13x = 52

x = 4

Step-by-step explanation:

the answer is in the above image

Answer: Choice B

Game A is not fair, and game B is fair.

==============================================================

We'll start with game A.

The sides of the dice are {1,2,3,4,5,6}

There are 6*6 = 36 ways to roll two dice.

If we roll two odd numbers, say 3 and 5, the product is odd because 3*5 = 15.

If any of the numbers are even, then the product is even. Eg: 4*5 = 20 or 2*6 = 12.

To be an even number, 2 must be a factor.

So you can probably see that it's more likely to get an even number product considering that in order to get an odd product, both values must be odd (which narrows the selection pool). We can say that game A is not fair. It favors player 1 more. If you're sure about this, then I recommend looking at a multiplication table but only focus on the first 6 rows and 6 columns. Ignore the row and column that has 0s in it.

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

Now onto game B

The rules are nearly the same, except now instead of multiplying the dice values, we add them up.

We still have 6*6 = 36 outcomes.

Here are some handy rules we'll take into account

If the first dice rolls to '1', then there are 3 ways to get an even number (rolling either 1,3,or 5 on the second dice) and there are 3 ways to get an odd number (rolling either 2,4,or 6 on the second dice). We can see that there are the same number of ways to get an even sum or an odd sum. Apply this in general to any result that the first dice shows, and this basically leads to the conclusion that half of the 36 sums are even, and the other half are odd. We have a fair game now. Refer to a sum of dice chart if you need more convincing.

Answer:

Game A is not fair, and game B is fair.

Step-by-step explanation:

test on iready

Answer:

12

Step-by-step explanation:

Answer:

H0 : p = 0.5

H1 : p ≠ 0.5

Two tailed test

Step-by-step explanation:

The test if the true proportion of heads is different from 50%; this means the initial truth, that is the true proportion is 50% ; which is the null ;

H0 : p = 0.5

The researcher intends to test if the true proportion is not 50% ; that is the researcher is n spwcudfic about if the proportion is lower or higher, he just wants to test that the proportion is different, hence the test could go either way ;

Alternative hypothesis ;

H1 : p ≠ 0.5

Since the sign in the alternative hypothesis could be in either direction, then we have a two tailed test

Step-by-step explanation:

[tex] \tan(67) = \frac{x}{7} \\ 2.355852366 = \frac{x}{7} \\ x = 16.49 = 16.5[/tex]

9514 1404 393

Answer:

  15

Step-by-step explanation:

(2 loaves)(5/2 cups/loaf)/(1/3 cup/scoop) = (2)(5/2)(3/1) scoops = 15 scoops

The baker will need 15 scoops of flour.

Answer:

C.

Step-by-step explanation:

ASA stands for angle-side-angle.

one side and the 2 angles at the end points of this side are known. only one triangle can be created with that information.

and that is our situation here.

the sides PQ and respectively ST are known (the fact that they are of equal length qualifies for that).

and the angles at the end points of PQ are known (again, the fact that they have the same size as the angles for ST qualifies for that too).

so, ASA applies to prove that both triangles are congruent.

Answer:

Daniel traveled further by 2.73 miles

Step-by-step explanation:

To find the total distance traveled simply multiply average speed times time

For Wendy

She traveled for 3.9 hours at a speed of 68.3 mph

So total distance traveled = 3.9 * 68.3 = 266.37 miles

For Daniel

He traveled for 4.5 hours at a speed of 59.8 mph

So total distance traveled = 4.5 * 59.8 = 269.1 miles

As you can see Wendy traveled 266.37 miles and Daniel traveled 269.1 miles

Daniel traveled further

To find how much further we simply subtract distance Daniel traveled (269.1) from distance Wendy traveled (266.37)

269.1 - 266.37 = 2.73

So Daniel traveled further by 2.73 miles

Answer:

One leg: 3

So, the hypo: 2*3 = 6

And the third is according to the formula for right angle triangles: a^2 + b^ = c^2

So: √9+36= c

6.7 to get an exact number round it: 7

Answer:

sides are √3 ft,2√3 ft,3 ft

Step-by-step explanation:

let one leg=x

length of hypotenuse=2x

third side=3 ft

(2x)²=x²+3²

4x²-x²=9

3x²=9

x²=9/3=3

x=√3 ft

hypotenuse=2√3 ft

Answer:

75

Step-by-step explanation:

∠K and ∠ R are congruent (equal)

Triangle Sum Theory - angles of all triangles add to 180

180 - 79 - 26 = 75

Answer:

Step-by-step explanation:

y=3√x

domain : all real values≥0

1. [tex] \: {7}^{1} [/tex]

➺ [tex]\boxed{\: 7 }[/tex]

2. [tex] \: {4}^{0} [/tex]

➺ [tex]\boxed{ \: 1 }[/tex]

( ∵ any number to the power of 0 is 1. )

3. [tex] \: {6}^{ - 1} [/tex]

➺ [tex] \: \frac{1}{6} [/tex]

[tex]( \: ∵ {a}^{ - 1} = \frac{1}{a} )[/tex]

➺ [tex]\boxed{ \: 0.1667 }[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

it could only accomplish it's goal on Friday

Step-by-step explanation:

all you had to do was multiply 8 with the number of people and 2 with the number of tickets on each day and add them together to see if it was more than 1650. it was only more on Friday

Answer:

72

72

96

120

Step-by-step explanation:

The arcs are in the ratio:

3 : 3 : 4 : 5

Add all numbers in the ratio:

3 + 3 + 4 + 5 = 15

In the ratio, the sum of all numbers is 15.

In the real circle, the sum of the measures of all the arcs is 360.

360/15 = 24

Multiply all numbers in the ratio by 24.

72 : 72 : 96 : 120

Answer:

72

72

96

120

Part 1: Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)

Part 2:

H0:  

Ha:  

Part 3: The test statistic is given as 3.0081.

Part 4: The p-value is given as  0.39037

Step-by-step explanation:

As per the data

Part 2

H0:  

Ha:  

Part 3

As per the sample is of 300 homes, the expected values are given as

ABC=p(ABC)*300=0.30*300=90

CBS=p(CBS)*300=0.27*300=81

NBC=p(NBC)*300=0.26*300=78

IND=p(IND)*300=0.17*300=51

Now the values actually are given as

ABC=94

CBS=71

NBC=88

IND=47

So the test static is given as

So the test statistic is given as 3.0081.

Part 4

Now the degree of freedoms are given as 4-1=3

and chi square  is given as 3.0081 so for α = 0.05 , the p-value is given as  0.39037

Part 1.

As the value of p in part 4 is greater than the value of α = 0.05, thus Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)

Answer:

121.857

Step-by-step explanation:

6×7r = 5118

42r = 5118

r = 121.857

Answer:

121.8571428571429

Step-by-step explanation:

r=  5118/42

Answer:

All values that satisfy [tex]y[/tex] ≤ [tex]\frac{1}{3} x-3[/tex] are solutions

Step-by-step explanation:

The reason why the other equations solutions aren't solutions are because it doesn't satisfy the second equation, but the second equation satisfy both equations because the solutions of the second equations will be in both equations.

Hope this helps

Answer:

A and E

Step-by-step explanation:

x²+3x-28=0

x²+7x-4x-28=0

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

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

x=4, x= -7

Please give brainliest if it helps

Answer:

30 hour

Step-by-step explanation:

girls time

12 20 hour

8 x(let)

now,

12/8=x/20

12×20=8×x

240=8x

x=240/8

x=30,,

Answer:

PRT%

Step-by-step explanation:

PRT

[tex] = 320 \times 2.3 \times 20 \div 100 = 1472[/tex]

Answer:

v = -6       v = -4/5

Step-by-step explanation:

(6+v) ( 5v+4) = 0

Using the zero product property

6+v =0  5v+4 =0

v = -6      5v = -4

v = -6       v = -4/5

Answer:

8.5 miles an hour.

Step-by-step explanation:

There are many ways to do this, but I am going to do it the way I think is the most simple.

First, divide 748 yards by 3 minutes to get the amount of yards per minute. 748 / 3 = 249.33333

Second, divide the previously gotten number (249.33333, [3's go on forever]) by the amount of yards in a mile (which is 1760 yards per mile). This turns into 249.33333 / 1760 = 0.1416666 (6's go on forever). This is miles per minute so you must make it per hour.

You then multiply that infinite number by the amount of minutes in an hour (60 minutes per hour). 0.14166666 * 60 = 8.5 miles per hour.

Answer:

The exchange rate for Dollars to Euros is of 1.33.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

Exchange rate for Dollars to Euros.

We want to find the number of dollars in a euro.

In 375 euros, there are 500 dollars, so how many dollars in 1 euro?

375 euros - 500 dollars

1 euro - x dollars

Applying cross multiplication:

[tex]375x = 500[/tex]

[tex]x = \frac{500}{375}[/tex]

[tex]x = 1.33[/tex]

The exchange rate for Dollars to Euros is of 1.33.