The velocity in feet per second, V, a skydiver is moving at after falling for t seconds is given by the following function. \(V=\frac{900t}{6t+7}\)
Write an equation that expresses the amount of time, t, that the skydiver has been falling for as a function of his velocity, V.

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Answer:

AAAAAAAAAAAA answer is A

Step-by-step explanation:

Answer:

looks good to me

Step-by-step explanation:

The inequality statement 7.745966… < √59 is true.

The symbol √59 represents the square root of 59, which is approximately 7.681146. The value 7.745966… is a decimal representation of the square root of 59 that has been rounded to three decimal places. Because 7.681146 is less than 7.745966, the inequality statement 7.745966… < √59 is true.

The dimensions of the aquarium that minimize the cost of the materials are x = y = ∛-(2V/3) and z = ∛(3V/4).

To find the dimensions of the aquarium that minimize the cost of the materials, we need to find an equation that expresses the total cost of the materials in terms of the dimensions. Let's assume that the height of the aquarium is z, and the base has dimensions x and y.

Since the base is made of slate and the sides are made of glass, the cost C can be expressed as:

C = 3A₁ + A₂

where A₁ is the area of the base covered by slate, A₂ is the area of the sides covered by glass, and the factor of 3 in front of A₁ reflects the fact that slate costs three times as much as glass per unit area.

The volume V of the aquarium is given as V = xyz, so we can express one of the dimensions in terms of the other two, say z = V/(xy). Substituting this expression into the equation for C and simplifying, we get:

C = 3xy + 2xz + 2yz

To minimize C, we need to take the partial derivatives of C with respect to x and y, set them equal to zero, and solve for x and y. Doing so, we get:

∂C/∂x = 3y + 2z = 0

∂C/∂y = 3x + 2z = 0

Solving these equations for x and y in terms of z, we get:

x = -(2/3)z

y = -(2/3)z

Substituting these expressions into the equation for z in terms of V, we get:

z = V/((2/3)z * (2/3)z)

Simplifying this expression, we get:

z = ∛(3V/4)

Substituting this value of z into the expressions for x and y, we get:

x =∛ -(2/3)(3V/4) = ∛-(2V/3)

y = ∛-(2/3)(3V/4) = ∛-(2V/3)

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Answer:

Step-by-step explanation:

A: Kilogram

B: Milliliters

C: 100 Kilometers

Answer:

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

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer:

2 hours 11 minutes

Step-by-step explanation:

Each hour Sally can paint 1/3 rooms, Steve can paint 1/8 rooms.

If they work together, each hour they can paint 1/3 + 1/8 = 11/24 rooms.

So They will take 1/(11/24) = 24/11 = 2.18 hours to paint a whole room.

2.18 hours = 2 hours 0.18*60 minutes

0.18 * 60 = 11

Answer: 2 hours 11 minutes

Answer:

True

Step-by-step explanation:

3x5=15

15+8=23

23=23

Answer:

True

Step-by-step explanation:

3 x 5 = 15

15 + 8 = 23

Answer:

\(\Huge \boxed{\boxed{ x = 1}}\)

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

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

Step1: Subtract \(\bold{2x}\) from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation \(\bold{8x + 3 = 2x + 9}\) is \(\bold{x = 1}\).

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Answer:

^ you need to feel more confident my brother or sister and say I know its 16 and don't make people worried about getting the question wrong by saying I'm pretty sure beacuse that dosn't seem like a 50%50 percent

Step-by-step explanation:

But yes it is 16

The value of x in the given expression is 16.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression -5x/6 = -40/3, we will have to find the value of x,

-5x/6 = -40/3

Minus sign will be cancelled,

5x/6 = 40/3

5x/2 = 40

5x = 80

x = 16

Hence, the value of x in the given expression is 16.

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Answer:

A:The equation y=54x describes the relationship

B: y as 216 and x being 4

If a car travels for 0​ hours, it will travel 0 ​mile(s). This means it will pass through the point (0,0)

.Use the slope to move 3 units to the right of the origin and

162 ​unit(s) up to find the point

(3,162) that can be used to graph the relationship. Step-by-step explanation:

Based on the set of transformations for trapezoid ABCD, the location of point A after the transformations are complete is: D. (−5, 1).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)                           →               (-x, -y)

Points A = (-5, 1)        →     Points A' = (-(-5), -(1)) = (5, -1).

Next, we would reflect the given point over the x-axis as follows;

(x, y)                           →              (x, -y)

Points A' = (5, -1)        →     Points A' = (5, -(-1)) = (5, 1)

Lastly, we would reflect the given point over the y-axis as follows;

(x, y)                           →              (-x, y)

Points A' = (5, 1)        →     Points A' = (-(5), 1) = (-5, 1)

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The number of cereal bars each student got is 2.5.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, five cereal bars are shared equally by 2 students.

Now, number of cereal bars each student got

= 5/2

= 2.5

Therefore, the number of cereal bars each student got is 2.5.

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Answer: While a child could have the same blood type as one of his/her parents, it doesn’t always happen that way.

Step-by-step explanation:

For example, parents with AB and O blood types can either have children with blood type A or blood type B. These two types are definitely different than parents’ blood types!

Answer:

A. 0.2734 = 27.34% probability that there are an equal number of boys and girls

B. 0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

Step-by-step explanation:

In each of these questions, the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A.The Murray family has produced 8 children.

What is the probability that there are an equal number of boys and girls?

8 children means that \(n = 8\)

Each children is equally as likely to be a boy or a girl, which means that \(p = 0.5\)

This probability is P(X = 4). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734\)

0.2734 = 27.34% probability that there are an equal number of boys and girls

B.Margie has the uncanny ability of being able to guess the correct answer to TRUE/FALSE questions with an 80% accuracy rate. Tomorrow’s test has 7 questions on it and she needs to answer 5 questions correctly in order to make the Honor Roll. If she guesses on every question, what is the probability that she’ll answer exactly 5 questions correctly?

80% accurracy rate means that \(p = 0.8\)

7 questions means that \(n = 7\)

The probability is P(X = 5). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{7,5}.(0.8)^{5}.(0.2)^{2} = 0.2753\)

0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

Answer:

8019 possible 5 digit numbers

Step-by-step explanation:

Available number to pick from are a total of 10 which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

>> Now, let's consider when the first digit is 6 since we are told that 6 can appear only once.

For the first digit, it's only 1 way.

For the 2nd, 3rd, and 4th digit, we have 9 digits to pick from. Which is 9 ways each.

While for the 5th digit, it can't be 6 or 7. And it has to be even and so, we can pick only 0, 2, 4. Thus, we have 3 ways to choose.

So total number of ways here = 1 × 9 × 9 × 9 × 3 = 3 × 9³ ways

>> Now, let's consider when the 2nd digit is 6 since we are told that 6 can appear only once.

For the 1st digit, since 6 is not possible, and also 0 is not possible because a 5 digit number can't start with zero as it would no longer be a 5 digit number.

Thus, there are 8 ways to choose here.

For the second, third and fourth digits, there will be 9 ways each to chops.

While for the fifth digit, there will be 3 ways to choose.

Total number of ways here = 8 × 1 × 9 × 9 × 3 = 24 × 9² ways

>> When the third digit is 6, number of ways to choose will be same as above = 24 × 9² ways

>> When the fourth digit is 6, number of ways to choose will be same as above = 24 × 9² ways

We can't say none of the digits is 6 because we are told it appears exactly once.

Thus, total possible 5 digit numbers are;

(3 × 9³) + 3(24 × 9²) = 8019 possible 5 digit numbers

Therefore, we have found that measure of angle WXY is 45 - 16x.

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are often denoted as "legs" or "sides" of the angle. The measure of an angle is usually given in degrees or radians and represents the amount of rotation needed to move one of the rays to align with the other.

Here,

To solve this problem, we'll need to use some basic properties of angles in a triangle.

First, we know that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of angle WXY by subtracting the measures of angles WVX and WXZ from 180:

m(WXY) = 180 - m(WVX) - m(WXZ)

m(WXY) = 180 - (13x + 9) - (5x + 36)

m(WXY) = 135 - 18x

Next, we can use the fact that the sum of the angles in a quadrilateral is 360 degrees to find the measure of angle 2WXY:

m(2WXY) = 360 - m(WXY) - m(WXY) - m(WXY)

m(2WXY) = 360 - (135 - 18x) - (135 - 18x) - m(WXY)

m(2WXY) = 90 + 2x - m(WXY)

Finally, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle WXY:

m(WXY) = 180 - m(WXY) - m(XYa)

m(WXY) = 180 - (135 - 18x) - 90

m(WXY) = 45 + 18x

Now we can substitute these values into our expression for m(2WXY):

m(2WXY) = 90 + 2x - (45 + 18x)

m(2WXY) = 45 - 16x

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To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Answer:

x intercept- (8,0)

y intercept-(0,-4)

Step-by-step explanation:

hope this helps!

The amount of change that the customer will be given when payment is made with a $20 bill would be = $7.15. That is option G.

The total number of items purchased by the customer = 10

The cost for 5 items = $1.60× 5 = $8

The cost of 3 items = $1.25×3 = $3.75

The cost of 2 items = $0.55×2 = $1.1

The total cost = 8+3.75+1.1 = $12.85

Therefore, the change of the customer when $20 bill is used = 20-12.85

= $7.15.

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Answer:

x=1.2 and y= -2.8

Step-by-step explanation:

x-4=6x-10

-4=5x-10

6=5x

x=6/5 or 1.2

y=x-4

y=1.2-4

y= -2.8

Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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Answer: Total number person using bus = 16 + 2 = 18

Hence, Total number person using bus to get to town is 18  .

Step-by-step explanation:

Given :

Total number of people = 80

Total number of male = 24

Number of male who use bicycle = 11

Number of female who use bus = 16

Number of people use car = 28

Number of female who use car = 17 out of 28

To find :

The number of people use bus to get to town

Solution :

Number of female who use bus = 16          ..........1

Number of female who use car = 17

Number of female use bicycle =

Number of male uses bicycle = 11

As Total number of male = 24

So, rest of male use either bus or car = 24 - 11 = 13

Since

number of people use car = 28

And number of female use car = 17

So, Number of male use car = 28 - 17 = 11

Again

As 11 male using car, so from 13 male using either car or bus

Number of male using bus = 13 - 11 = 2

Answer: Hello: ) ✨Total number person using bus = 16 + 2 = 18

Hence, Total number person using bus to get to town is 18  .

Step-by-step explanation:

Given :

Total number of people = 80

Total number of male = 24

Number of male who use bicycle = 11

Number of female who use bus = 16

Number of people use car = 28

Number of female who use car = 17 out of 28

To find :

The number of people use bus to get to town

Solution :

Number of female who use bus = 16          ..........1

Number of female who use car = 17

Number of female use bicycle =

Number of male uses bicycle = 11

As Total number of male = 24

So, rest of male use either bus or car = 24 - 11 = 13

Since

number of people use car = 28

And number of female use car = 1

So, Number of male use car = 28 - 17 = 1

Again

As 11 male using car, so from 13 male using either car or bus

Number of male using bus = 13 - 11 = 2

Answer: The ladder reaches 14.46 feet up of the building.

Step-by-step explanation:

According to Pythagorean theorem,

In a right triangle,

(Hypotenuse)²= (Base)²+(perpendicular)^2

Using given information, we have

\((15)^2=(4)^2+(height)^2\\\\225=16+(height)^2\\\\(height)^2=209\\\\ (height)^2=\sqrt{209}\approx14.46\ feet\)

Hence, the ladder reaches 14.46 feet up of the building.

Answer:

120 cups

Step-by-step explanation:

120 cups

Answer:

120

Step-by-step explanation:

u multiply 24 × 5 and get 120 :D

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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Answer:

nx2=3-(n/4)

Step-by-step explanation:

Im pretty confused bu6t hoped this helped