Write the quadratic function in the form f(x)=a(x-h)^2+k
Then, give the vertex of its graph.
f(x)=2x^2-20x+51

Answer:

False

Step-by-step explanation:

we know that

In this problem the vertical distance is equal to 12 ft (the horizontal distance must be equal to the vertical distance, by angle of 45 degrees)

so

The length of the ladder is equal to

Applying Pythagoras Theorem

[tex]L=\sqrt{12^{2}+12^{2}} \\ \\L=\sqrt{288}\ ft\\ \\L=16.97\ ft[/tex]

Answer: $1980

Step-by-step explanation:

Well, based off of the question being asked, I assume that you will need to pay $11 for 90 square footage of tiling, and then the same for the other square footage of tiling. Therefore your answer will be $1980. If you are looking for the equation, it is (11x90)=990   (990)2 = 1980

you do not need to multiply 11 by 90 again because you already know the answer.

Answer:

$110

Step-by-step explanation:

We are given that

Cost of 1 square yard of floor tile =$11

We have to find the cost of 90 square feet of tile.

To find the cost of 90 square feet we will convert it into square yard.

We know that

9 square foot=1 square yard

1 square foot=[tex]\frac{1}{9}[/tex]

90 square feet=[tex]\frac{1}{9}\times 90=10[/tex] square yard

By unitary method

Cost 1 square yard=$11

Cost of 10 square yard=[tex]11\times 10=[/tex]$110

Hence, the cost of 90 square feet to tile a bathroom=$110

The probability that at least three out of five randomly picked buttons are black is approximately 0.6614.

To find the probability that at least three out of five randomly picked buttons are black, we can consider the different combinations of buttons that satisfy this condition.

There are two cases where at least three buttons are black:

1. Exactly 3 buttons are black.

2. All 5 buttons are black.

Let's calculate the probabilities for each case:

1. Exactly 3 buttons are black:

  This can happen in [tex]\( \binom{4}{3} \)[/tex] ways (choosing 3 black buttons) multiplied by [tex]\( \binom{5}{2} \)[/tex] ways (choosing 2 brown buttons).

  Probability of this case:

[tex]\[ P(\text{3 black}) = \frac{\binom{4}{3} \times \binom{5}{2}}{\binom{9}{5}} \][/tex]

2. All 5 buttons are black:

  This can happen in [tex]\( \binom{4}{5} = 0 \)[/tex] ways (because there are only 4 black buttons).

The probability that at least three buttons are black is the sum of the probabilities of these two cases.

[tex]\[ P(\text{at least 3 black}) = P(\text{3 black}) + P(\text{5 black}) \]\[ P(\text{at least 3 black}) = \frac{\binom{4}{3} \times \binom{5}{2}}{\binom{9}{5}} + 0 \][/tex]

[tex]\[ P(\text{at least 3 black}) = \frac{\frac{4!}{3!(4-3)!} \times \frac{5!}{2!(5-2)!}}{\frac{9!}{5!(9-5)!}} \]\[ P(\text{at least 3 black}) = \frac{\frac{4 \times 5}{3!} \times \frac{5 \times 4}{2!}}{\frac{9 \times 8 \times 7 \times 6 \times 5}{5!}} \][/tex]

[tex]\[ P(\text{at least 3 black}) = \frac{\frac{4 \times 5}{6} \times \frac{5 \times 4}{2}}{\frac{9 \times 8 \times 7 \times 6 \times 5}{5 \times 4 \times 3 \times 2 \times 1}} \]\[ P(\text{at least 3 black}) = \frac{\frac{20}{6} \times \frac{20}{2}}{\frac{3024}{120}} \][/tex]

[tex]\[ P(\text{at least 3 black}) = \frac{\frac{100}{6}}{\frac{3024}{120}} \]\[ P(\text{at least 3 black}) = \frac{100 \times 120}{6 \times 3024} \]\[ P(\text{at least 3 black}) = \frac{1000}{1512} \][/tex]

[tex]\[ P(\text{at least 3 black}) ≈ 0.6614 \][/tex]

Answer:

The side length of the smaller pyramid is 3/4 the side length of the larger pyramid.

Step-by-step explanation:

Answer:

(4,3)

Step-by-step explanation:

Given

x^2+y^2=25

x-y^2=-5

In order to solve the equations, from equation 2 we get

-y^2= -5-x

y^2=5+x

Putting the value of y^2 in equation 1

x^2+5+x=25

x^2+5-25+x=0

x^2+x-20=0

x^2+5x-4x-20= 0

x(x+5)-4(x+5)=0

(x+5)(x-4)=0

So

x+5=0  x-4=0

x=-5   x=4

Now for x=-5

x^2+y^2=25

(-5)^2+y^2=25

25+y^2=25

y^2=25-25

y^2=0

so Y=0  

And for x = 4

x^2+y^2=25

(4)^2+y^2=25

16+y^2=25

y^2=25-16

y^2=9

y= ±3

So the solution to the system of equations is

(-5,0) , (4,3), (4,-3)

The only solution that belongs to first quadrant is (4,3)

Answer:

(4,3)

Step-by-step explanation:

solve the simultaneous equations

x²+y²=25.........................(i)

x-y²= -5.............................(ii) ⇒make y² the subject of the equation;

y²=x+5.................................(iii)

Substitute equation (iii) in (i)

x² + x+5 =25

x²+x=25-5

x²+x-20=0..........solve for the quadratic equation

x(x-4)+5(x-4)=0

(x-4)(x+5)=0

x-4=0

x=  4 or

x+5=0

x=  -5

finding value of y

if y²=x+5 then;

when x=4, y²=4+5=9⇒y=√9 = ±3...................y= ±3

when x= -5  , y²= -5+ 5=0............... y=0

Coordinates = (4,3) and (-5,0)

Coordinates that lie in the 1st quadrant is (4,3)

Answer:

No, no, yes, no

Step-by-step explanation:

The first one is not random.  He is sampling only the earliest gym goers.

The second one is not random.  He is sampling only from one zip code.

The third one is random.  He is using a random number generator.

The fourth one is not random.  He is sampling only volunteers.

The third is completely random. He's generating numbers with a random number generator. So yes, for the third statement and No, for the first, second, and fourth statements.

Random sampling is the method of selecting the subset from the set to make a statical inference.

An employee at a gym wants to select a random sample of gym members for a survey about their exercise habits.

The first is not a fluke. He's simply tasting the first gym attendees.

The second is not a coincidence. He's just taking samples from one zip code.

The third is completely random. He's generating numbers with a random number generator.

The fourth is not a fluke. Only volunteers are being sampled.

More about the random sample link is given below.

https://brainly.com/question/15125943

#SPJ2

Answer:

the answer is 18 birds and 5 cats

Step-by-step explanation:

the easiest way i did this was that i used a calculator and kept subtracting 8.5 untill i reached a number that was completely divisable by 5, i subtracted 8.5 five times which got the total down to 90$ and since each bird is 5$ you can just divide which means there was a total of 18 bird and 5 cats on Tuesday

To find out how many birds were at the shelter on Tuesday, we set up and solved a system of linear equations involving the total daily care costs and the total number of animals. By substituting and simplifying, we found the number of birds among the 23 animals.

The question involves solving a system of linear equations to find out how many birds were at the shelter on Tuesday, given the daily care costs for birds and cats, the total cost for Tuesday, and the total number of birds and cats. We use the information that the shelter spends $5.00 per day to care for each bird and $8.50 per day to care for each cat, with a total expenditure of $132.50 for 23 birds and cats together.

Let x be the number of birds and y be the number of cats. Therefore, we have two equations:

From the second equation, we can isolate one variable, say x = 23 - y. Substituting this into the first equation gives us:

5(23 - y) + 8.5y = 132.50

After simplifying, we find the value of y, and then substitute back to find x, which represents the number of birds. This method of solving the system of equations is straightforward and efficient for this problem.

Answer:

  the distance between the points is about 9.2 units

Step-by-step explanation:

It is well you should not understand it. No question is asked.

__

The answer choices suggest you are to find the distance between the two points. There is only one choice in a reasonable range: 9.2 units.

Each point is more than 2 units from any axis, so 2 units is clearly not the answer. The size of the graph is much less than 81 units, so clearly that is not the answer.

The difference of coordinates in the x-direction is 6; in the y-direction the difference is 7 units. The distance between the points will be more than the longest of these (7) and less than about 1.5 times that (10.5). Only one choice is in this range: 9.2 units.

__

The Pythagorean theorem is used to calculate the distance between points. The distance is considered to be the hypotenuse of a right triangle with legs of lengths equal to the differences of coordinates. Here, that means the distance (d) is ...

  d² = 6² + 7² = 36 +49 = 85

  d = √85 ≈ 9.2 . . . . grid squares, or "units"

Answer:

Approximately 485 meters

Step-by-step explanation:

We can first construct a right triangle, using the 500 m length of hill as our hypotenuse. Using the fact that the cosine of an angle is the ratio of the adjacent side to the hypotenuse, we see that

[tex]\cos{15^\circ}=\frac{x}{500}[/tex]

where x is the horizontal distance covered. Solving for x, we find this horizontal distance to be

[tex]x=500\cos{15^\circ}\approx500(0.97)=485[/tex]

so our answer is approximately 485 m.

Answer:

7

5

27.5

Step-by-step explanation:

edgu 2020

Answer:first 7 then 5 and 27.5 used the other person and got it right on edge:)

Step-by-step explanation:

Answer:

6 feet

D

Step-by-step explanation:

Givens

l = 10

h = 8

w = ?

Formula

l^2 = h^2 + w^2

Solution

10^2 = 8^2 + w^2

100 = 64 + w^2

100 - 64 = 64 - 64 + w^2

w^2 = 36

sqrt(w^2) = sqrt(36)

w = 6 feet.

The answer would be the first option.

6.2 percent of 300 is 18.6,

and 1.45 percent of 300 is 4.35

It makes a total of 22.95

300 - 22.95 = 277.05

Answer:

a) 864,000,000,000      8.64E11

b) 8,640,000,000           8.64E9

c) 86,400,000,000,000     8.64E13

d) 864,000,000,000,000    8.64E14

Step-by-step explanation:

A scientific notation is a way to represent very large values into the decimal form.

Steps to write in scientific notation:

Move the decimal to left before first digit of the given number.

Find the number of times decimal is moved to left.

Put that number in the exponent of e.

So, matching:

a) 864,000,000,000      8.64E11

b) 8,640,000,000           8.64E9

c) 86,400,000,000,000     8.64E13

d) 864,000,000,000,000    8.64E14

Final answer:

To find the number of friends when 36 apples are shared with each friend getting 2 apples, divide the total apples by the number of apples each friend gets. The equation to solve for the number of friends, n, is n = 36 / 2 = 18.

Explanation:

To solve for the number of friends, n, sharing 36 apples when each friend gets 2 apples:

Identify the total number of apples = 36 and the number of apples each friend gets = 2.

Divide the total apples by the apples each friend gets: 36 ÷ 2 = 18, which represents the number of friends (n). So, the equation would be n = 36 / 2 = 18.

Answer:

7569 meters cubed

Step-by-step explanation:

first: make the improper fractions to a fraction greater than one.

11 3/5= 58/5

12 1/2 = 145/2

9=9

then you have to multiply them all together

cross multiply 58/5 and 145/2...you should get 841. Now multiply 841 and 9...you should get 7569 meters cubed.

*When VOLUME of a RECTANGLE is given, make sure to MULTIPLY the HIEGHT, WIDTH and the LEGNTH.

Answer:

7569³m

Step-by-step explanation:

Answer:

(x - 5)² + (y + 3)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (5, - 3) and r = 4, so

(x - 5)² + (y - (- 3))² = 4², that is

(x - 5)² + (y + 3)² = 16

Answer:

Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.

Step-by-step explanation:

The volume is given in terms of x as  [tex]V(x)=x^3-6x^2+8x[/tex].

We factor the GCF to get;

[tex]V(x)=x(x^2-6x+8)[/tex].

We split the middle term of the trinomial in the parenthesis.

[tex]V(x)=x(x^2-4x-2x+8)[/tex].

We now factor the expression within the parenthesis by grouping;

[tex]V(x)=x[x(x-4)-2(x-4)][/tex].

[tex]V(x)=x(x-2)(x-4)[/tex].

Since the width of the box is [tex]x-2[/tex] units, the linear expression for the height and length is [tex]x(x-4)[/tex]

Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.

Answer:

There are 38 dimes, 22 nickels and 16 quarters.

Step-by-step explanation:

Let n, d and q represent the # of nickels, dimes and quarters respectively.

Then n + d + q = 76

The value of a nickel is $0.05; that of a dime is $0.10, and that of a quarter is $0.25.

Thus, the value of n nickels is $0.05n (and so on).

The total value of the coins is $0.05n + $0.10d + $0.25q = $8.90.

d = n + q allows us to eliminate d.

First, n + d + q = 76 becomes n + (n + q) + q = 76, and second:

$0.05n + $0.10(n + q) + $0.25q = $8.90.  Here we have succeeded in eliminating d from two different equations, and now we have these two different equations in two unknowns (n and q), which is solvable.

Simplifying both equations, we get:

2n + 2q = 76 and

5n + 10n + 10q + 25q = 890, or 15n + 35q = 890

Let's use the substitution method of solving linear equations:

Rewrite 2n  + 2q = 76 as n + q = 38, or n = 38 - q.  Substituting this result into the second equation, we get:

15(38 - q) + 35 q = 890, or

  570 - 15q + 35q = 890, or

   570 + 20 q = 890.  Then 20q = 890 - 570 = 320, and q = 320/20 = 16.

There are 16 quarters.  Thus, the number of nickels is n = 38 - 16 = 22.

Finally, since n + d + q = 76, 22 + d + 16 = 76, or:

22 + d = 60, or d = 60 - 22 = 38.

There are 38 dimes, 22 nickels and 16 quarters.

Answer:

The elevation of Mt. Wilson is 16,160.10 ft

Step-by-step explanation:

Let

x-----> represent the elevation of Mt. Wilson

y ----> represent the elevation of Snow Crest

we know that

y=x+11,990.21 ----> linear equation that represent this situation

we have that

y=28,150.31 ft ----> see the attached figure

substitute in the linear equation and solve for x

28,150.31=x+11,990.21

x=28,150.31-11,990.21=16,160.10 ft

Final answer:

A triangle with sides of lengths 28, 195, and 197 satisfies the Pythagorean theorem (a² + b² = c²), which confirms it is a right triangle.

Explanation:

To determine if a triangle with sides of lengths 28, 195, and 197 is a right triangle, we can apply the Pythagorean theorem. According to this theorem, for a triangle to be a right triangle, the square of the length of the hypotenuse (the longest side) must be equal to the sum of the squares of the lengths of the other two sides.

Let us calculate:

As we can see, 784 plus 38025 indeed equals 38809. Hence, the triangle with sides 28, 195, and 197 satisfies the condition of the Pythagorean theorem and therefore is a right triangle.

Answer:

L = 10, w = 17

Step-by-step explanation:

Area of a rectangle is A = Lw.  We are told that the width is 3 less than twice the length, so we will change the width into some expression in terms of the length.

w = 2L - 3 and

length = L.

Filling in the area formula now, knowing that the area is given as 170:

170 = (2L - 3)(L) so

[tex]170=2L^2-3L[/tex]

Get everything on one side of the equals sign and throw it into the quadratic formula to factor it and solve for the values of L.  When we do this we get that L = 10 and L = -8.5

Since the 2 things in math that will NEVER EVER be negative are time and distance/length measures, it is safe to disregard the -8.5.  Therefore,

if L = 10, then

w = 2(10) - 3 and

w = 17

Final answer:

The probability of choosing all boys for the classroom responsibilities from a classroom of 11 boys and 14 girls is calculated using combinatorial probability, which is the ratio of the number of ways to choose 4 boys out of 11 to the total number of ways to choose 4 students out of 25.

Explanation:

The probability that all four students chosen at random from a classroom of 11 boys and 14 girls will be boys is a classic example of a combinatorial probability question.

First, we calculate the total number of ways to choose 4 out of 25 students, which is the combination of 25 students taken 4 at a time. This is given by the binomial coefficient 25 choose 4, which is calculated as 25! / (4! * (25-4)!).

Next, we calculate the total ways to choose 4 out of the 11 boys, which is the combination of 11 boys taken 4 at a time, given by 11 choose 4, calculated as 11! / (4! * (11-4)!).

The probability is the ratio of the number of favorable outcomes (only boys chosen) to the total number of outcomes. Therefore, the probability is (11 choose 4) / (25 choose 4).

Answer:

As long as you mistyped Rashid's work and meant that the answer was 3/36 or 1/12, the answer would be

A. Rashid solved the problem correctly

Step-by-step explanation:

When you are dividing, it is the same thing as multiplying by the reciprocal of that value. This means that

[tex]\frac{\frac{3}{4} }{9} =\frac{3}{4} *\frac{1}{9} =\frac{1}{12}[/tex]

bro this is middle school work, its B

Answer:

Option C

Step-by-step explanation:

The standard form of equation of a cirle is:

(x-h)^2+ (y-k)^2=r^2

In the given question as the point is given and the radius of circle is given:

So,

(h,k)=(2,-1)

and

r=3

Here,

h=2

k= -1

Putting the values of h,k and r in standard form

(x-2)^2+ (y-(-1))^2=(3)^2

(x-2)^2+ (y+1)^2=(3)^2

So the equation of circle is:

(x-2)^2+ (y+1)^2=9(3)^2

Option C is the correct answer ..

Answer:

16%

Step-by-step explanation:

The Empirical rule says that 68% of a normal distribution lies between -1 and +1 standard deviations.

That means that 32% lies outside of ±1 standard deviations.

Since the normal curve is symmetrical, that means 16% is less than -1 standard deviation and 16% is greater than +1 standard deviation.

So the answer is 16%.

Heather and her lab partners found that the probability of the weight of a US quarter being below one standard deviation from the mean is 16%.

Heather and her lab partners need to find the probability that the weight of a US quarter is below one standard deviation from the mean. Since the weight of a quarter follows a normal distribution, we use the property of the normal distribution to find this probability.

In a normal distribution:

Therefore, the probability of a weight being below one standard deviation from the mean is 16%. This is calculated by taking half of the remaining probability outside the 68%, which is (100% - 68%) ÷ 2 = 16%.

Answer:

x = 2[tex]\sqrt{34}[/tex]

Step-by-step explanation:

Since the triangle is right use Pythagoras' theorem to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, thus

x² = 6² + 10² = 36 + 100 = 136

Take the square root of both sides

x = [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = 2[tex]\sqrt{34}[/tex]

Answer:

2√34

Step-by-step explanation:

6² + 10² = x²

x² = 6² + 10²

x² = 36 + 100

x² = 136

x = √136

x = 2√34

Answer:

  it depends

Step-by-step explanation:

The endpoints of the hypotenuse are insufficient to specify a right triangle. The perimeter can range from twice the distance between these points, about 18.868 units, to 1+√2 times the distance between these points, about 22.776 units.

___

In the attached figure, the colored numbers are the total length of the two legs of that color. The hypotenuse and its length are in black.

_____

The distance between two points is given by the formula ...

  d = √((x2-x1)^2 +(y2 -y1)^2)

The perimeter will be the sum of the distances between pairs of points that define the vertices of the triangle. We need to know the third vertex to answer the question precisely.

Answer:

Black

Step-by-step explanation:

Black-White-Yellow-Brown

Also can you please rate this as the most brainliest because I need it to level up?

Answer:

The maximum value of g(x) = 2/3 at x = 0

Step-by-step explanation:

* Lets find the maximum value of a function using derivative of it

- The function g(x) = 2/(x² + 3)

- 1st step use the negative power to cancel the denominator

∴ g(x) = 2(x² + 3)^-1

- 2nd use derivative of g(x) to find the value of x when g'(x) = 0

* How to make the derivative of a function

# If f(x) = a(h(x))^n, then f'(x) = an[h(x)^(n-1)](h'(x))

∵ [tex]g(x)=2(x^{2}+3)^{-1}[/tex]

∴ [tex]g'(x) = 2(-1)(x^{2}+3)^{-2}(2x)=-4x(x^{2}+3)^{-2}[/tex]

# Put g'(x) = 0

∴ [tex]-4x(x^{2}+3)^{-2}=0====\frac{-4x}{(x^{2}+3)^{2}}=0[/tex]

∴ [tex]-4x=(0)(x^{2}+3)^{2}====-4x = 0[/tex]

∴ x = 0

* The maximum value of g(x) at x = 0

- Substitute the value of x in g(x)

∴ g(0) = 2/(0 + 3) = 2/3

* The maximum value of g(x) = 2/3 at x = 0

Answer:

Step-by-step explanation:

Law of Sines.

a/sin(A) = b/sin(B)

In this case, a = y and A = 26.5. b = 15 and B = 90.

y/sin(26.5) = 15/sin(90).

y/sin(26.5) = 15/1

y = sin(26.5) * 15, which is about 6.69 feet.

The answer to your question is

6.69