Find the length indicated.
7) Find FG
E
2x+1
F
16
2x+3
G

The solutions to the quadratic equations are as follows

4a. The rocket was launched from an initial height of 10 meters.

b. The maximum height of the rocket was 55 meters.

c. The rocket reaches its maximum height at 3 seconds

d. the rocket is in the air for t = 6.316 seconds

5. when the horizontal distance is 1 foot, the height of the balloon is 8.875 feet

b. when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet.

The function is a quadratic equation, and here is how we solve each problem;

a. The initial height of the rocket is the value of h when t=0. So we substitute t=0 into the equation to find:

h = -5(0)² + 30(0) + 10 = 10 meters

b. & c. The maximum height of a projectile launched upward occurs at the vertex of the parabola represented by the quadratic function. For a quadratic function in the form y = ax² + bx + c, the time at which the maximum (or minimum) occurs is -b/2a. In this case, a = -5 and b = 30. So:

t = -b/2a = -30 / (2×-5) = 3 seconds

So, the rocket reaches its maximum height at t=3 seconds. We can find this maximum height by substituting t=3 into the equation:

h = -5(3)² + 30(3) + 10 = -5×9 + 90 + 10 = 45 meters

The rocket is in the air from the time it was launched until it hits the ground. The time when it hits the ground is when h = 0. So we can set the equation to 0 and solve for t:

0 = -5t² + 30t + 10

This is a quadratic equation and can be solved using the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a)

Let's calculate the roots:

t = [-30 ± √((30)² - 4×-5×10)] / (2×-5)

= [-30 ± √(900 + 200)] / -10

= [-30 ± √(1100)] / -10

= 6.316 or -0.32

5. a. To find the height of the balloon when d=1, we substitute d=1 into the equation:

h = -1/8(1)²+ 4(1) + 5 = -1/8 + 4 + 5 = 8.875 feet

b. To determine whether the balloon hits your enemy, we need to see if the balloon's height (h) is above ground level (h > 0) when d=33. So, we substitute d=33 into the equation:

h = -1/8(33)² + 4(33) + 5

h = -1/8×1089 + 132 + 5

h = -136.125 + 132 + 5

h = 0.875 feet

when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet. This means the balloon is above ground level and therefore would indeed hit your nemesis standing 33 feet away.

Find more exercises on quadratic equations;

https://brainly.com/question/26090334

#SPJ1

Answer:

Step-by-step explanation:
The standard equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, we have:

(x - (-3))^2 + (y - 5)^2 = 2^2

Simplifying:

(x + 3)^2 + (y - 5)^2 = 4

Therefore, the standard equation of the circle is (x + 3)^2 + (y - 5)^2 = 4.

Answer:

[tex] (x + 3)^2 + (y - 5)^2 = 4 [/tex]

Step-by-step explanation:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

[tex] (x - (-3))^2 + (y - 5)^2 = 2^2 [/tex]

[tex] (x + 3)^2 + (y - 5)^2 = 4 [/tex]

Answer:

4

Step-by-step explanation:

To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4.  Therefore the missing value will be 4.

Hope this helped :)

Answer: the answer is 4

Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4

Answer:

To find the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces, and then add them together.

First, let's find the length of one side of the base of the pyramid:

Perimeter of the square base = 4 x side length

48 inches = 4 x side length

Side length = 12 inches

Now we can find the area of the base:

Area of the base = side length squared

Area of the base = 12 inches x 12 inches

Area of the base = 144 square inches

Next, we need to find the area of each triangular face. To do this, we need to find the length of the slant height of the pyramid. We can use the Pythagorean theorem to do this:

Slant height squared = height squared + (1/2 base length) squared

Slant height squared = 8 inches squared + (6 inches) squared

Slant height squared = 64 inches squared + 36 inches squared

Slant height = square root of (64 + 36) inches

Slant height = 10 inches

Now we can find the area of each triangular face:

Area of a triangular face = (1/2 base length) x slant height

Area of a triangular face = (1/2 x 12 inches) x 10 inches

Area of a triangular face = 60 square inches

Finally, we can add the area of the base and the area of the four triangular faces together to find the total surface area of the pyramid:

Total surface area = Area of the base + (4 x Area of a triangular face)

Total surface area = 144 square inches + (4 x 60 square inches)

Total surface area = 384 square inches

Therefore, the surface area of the pyramid is 384 square inches.

Answer:

Step-by-step explanation:

The surface area of a sphere is given by the formula:

S = 4πr^2

where S is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 60 square feet. Using the formula above, we can solve for the radius:

60 = 4πr^2

Dividing both sides by 4π, we get:

15/π = r^2

Taking the square root of both sides, we get:

r = sqrt(15/π)

Using 3.14 as an approximation for π, we can evaluate this expression:

r ≈ sqrt(15/3.14)

r ≈ 2.20

Therefore, the best approximation for the radius of the sphere is 2.20 feet.

Answer:

Radius is 2.18

Step-by-step explanation:

;)

The answer to the crossnumber is 25.

Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics and is used to describe sets, groups, and other mathematical objects. Numbers are used to measure quantities, such as length, area, time, and weight. They are also used to represent relationships between objects, and to describe the properties of those objects. Numbers can be represented in various forms, such as integers, fractions, and decimals.

This can be determined by examining the clues and their corresponding digits. Across, the clue is "A square", so the digit in the corresponding cell must be a perfect square, in this case 1. The next clue is "An odd square", so the digit must be an odd perfect square, which is 3. Down, the first clue is "A square", so the digit must be a perfect square, which is 5. The last clue is "A square", so the digit must be a perfect square, which is 7. When all the digits are put together, the resulting two-digit number is 25.

To know more about number click-
https://brainly.com/question/24644930
#SPJ1

The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²

Factoring polynomials simply means separating a polynomial into its component polynomials.

Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.

We have the equation:

(3y - 2)² - (3y - 2)⁻²

Let 3y - 2 be denoted by S and as such we have:

S² - S⁻²

= S² - 1/S²

Using the denominator as factor, we have:

= (S⁴ - 1)/S²

Plugging 3y - 2 for S gives us:

((3y - 2)⁴ - 1)/(3y - 2)²

Read more about Polynomial at: https://brainly.com/question/17517586

#SPJ1

the point that would not be found on the line is option A, (-7,19).

How to calculate the line?

We can use the equation of the line that passes through these three points to determine which of the given points would not be on the line.

First, we can find the slope of the line using the first two points:

slope = (y₂ - y₁)/(x₂- x₁) = (4 - 9)/(-1 - (-3)) = 5/2

Now, we can use the point-slope form of the equation of a line with the slope we just found and the first point (-3,9):

y - y₁= m(x - x₁)

y - 9 = (5/2)(x + 3)

Simplifying this equation gives us:

y = (5/2)x + (27/2)

We can check that the third point (1,-1) also lies on this line by plugging in the values of x and y into the equation above.

Now, we can check which of the given points would not be on this line by plugging in the values of x and y into the equation above.

A. (-7,19): y = (5/2)(-7) + (27/2) = 5.5, which does not equal 19, so this point is not on the line.

B. (7,-16): y = (5/2)(7) + (27/2) = 22.5, which does not equal -16, so this point is not on the line.

C. (-8,20.5): y = (5/2)(-8) + (27/2) = 4.5, which does not equal 20.5, so this point is not on the line.

D. (8,-18.5): y = (5/2)(8) + (27/2) = 25.5, which does not equal -18.5, so this point is not on the line.

Therefore, the point that would not be found on the line is option A, (-7,19).

To know more about line visit :-

https://brainly.com/question/24644930

#SPJ1

The probability of both gumballs not being red is 11/21.

What is the probability?

The probability of the first gumball not being red is:

P(first gumball not red) = P(blue) + P(yellow)

= (6/15) + (5/15)

= 11/15

After removing the first gumball, there are 14 gumballs left in the bag. The probability of the second gumball not being red depends on what color the first gumball was.

Case 1: The first gumball was blue

If the first gumball was blue, there are 5 blue, 4 red, and 5 yellow gumballs left in the bag. The probability of the second gumball not being red is:

P(second gumball not red | first gumball was blue) = P(blue or yellow)

= P(blue) + P(yellow)

= (5/14) + (5/14)

= 5/7

Case 2: The first gumball was yellow

If the first gumball was yellow, there are 6 blue, 4 red, and 4 yellow gumballs left in the bag. The probability of the second gumball not being red is:

P(second gumball not red | first gumball was yellow) = P(blue or yellow)

= P(blue) + P(yellow)

= (6/14) + (4/14)

= 5/7

The probability of both gumballs not being red is the product of the probabilities of each event:

P(both gumballs not red) = P(first gumball not red) * P(second gumball not red | first gumball not red)

P(both gumballs not red) = (11/15) * (5/7)

P(both gumballs not red) = 55/105

P(both gumballs not red) = 11/21

Therefore, the probability of both gumballs not being red is 11/21.

To know more about probability, visit:

https://brainly.com/question/11234923

#SPJ1

The equation is now in the standard shape of a hyperbola, as per the provided assertion. [(x - h)² / a²] - [(y - k)² / b²] = 1

A curve formed by the junction of a double right-angled cone and a plane that slices one half of the cone. a plane curve produced by a point so mobile that the difference between its distance from two fixed locations is a constant.

To complete the square for the given equation, we will group the x and y terms and complete the square separately for each.

4x² + 24x - 9y² + 18y - 9 = 0

4(x² + 6x) - 9(y² - 2y) = 9

4(x² + 6x + 9 - 9) - 9(y² - 2y + 1 - 1) = 9

4(x + 3)² - 9(y - 1)² = 36

Dividing by 36, we get:

(x + 3)² / 9 - (y - 1)² / 4 = 1

So, the equation is now in the standard form of a hyperbola:

[(x - h)² / a²] - [(y - k)² / b²] = 1

where h and k are the coordinates of the center, a is the distance from the center to the vertices along the x-axis, b is the distance from the center to the vertices along the y-axis, and the slope of the asymptotes is b/a.

Comparing with the standard form, we can see that:

h = -3, k = 1, a = 3, b = 2, and the slope of the asymptotes is b/a = 2/3.

The center is (-3, 1). The hyperbola opens horizontally, and its vertices are located at (-3 + a, 1) and (-3 - a, 1). So, the vertices are (-6, 1) and (0, 1).

The asymptotes are two straight lines passing through the center with a slope of ±(b/a) = ±2/3. So, the equations of the asymptotes are y - 1 = (2/3)(x + 3) and y - 1 = -(2/3)(x + 3), which simplify to y = (2/3)x + 5/3 and y = -(2/3)x + 1/3.

The distance between the center and the foci is c = sqrt(a² + b²) = √(13). The foci are located at (-3 + c, 1) and (-3 - c, 1). So, the foci are approximately (-0.16, 1) and (-5.84, 1).

The graph of the hyperbola looks like two mirrored U-shaped curves, with the vertices being the endpoints of the transverse axis.

The asymptotes intersect at the center and divide the hyperbola into four parts, called branches. The foci are located on the transverse axis, inside the branches.

To know more about Hyperbola visit:

brainly.com/question/28989785

#SPJ1

4 number was not used in the statement. we can use -3 as the other value.

A simple statement is a single assertion that can be classified as true or false, while a compound statement is formed by combining two or more simple statements using logical operators such as "and", "or", and "not".

To explain the statement mathematically:

First, we evaluate N/N:

N/N = 1

Next, we simplify the inequality using this value:

1•N < N - 1 < N - N

Simplifying further, we get:

N < N - 1 < 0

We can then substitute the values of -4 to 4 for N and see which value(s) satisfy the inequality.

If N = -4, then we have:

-4 < -5 < 0

This is true, so we can use -4 as one of the values.

If N = -3, then we have:

-3 < -4 < 0

This is also true, so we can use -3 as the other value.

Therefore, the completed statement is:

-4/-4 • -4 < -4 - (-4/-4) < -4 + 4/-4 <br>

which simplifies to:

1 < -3 < 5/2

Note that one number, 4, was not used in the statement.

To know more about statement visit:

https://brainly.com/question/11823039

#SPJ1

23/200

Hope it helped

1) y = -3x and y = -3x + 2: inconsistent system of equations.

2) y = x - 5 and -2x + 2y = - 10: consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.

The given equation are:

The graph for each system of equations is plotted.

1) y = -3x and y = -3x + 2

From the graph 1 it is shown that the lines for the each equation form the parallel lines.

Thus, system of equations are inconsistent.

2) y = x - 5 and -2x + 2y = - 10

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

Know more about the inconsistent system of equations

https://brainly.com/question/19282045

#SPJ1

Answer:

1.3

Step-by-step explanation:

look at the hundredths place to decide how to round (1.2541).

when a digit is greater than or equal to 5, we round up

in this number, the hundredths place is 5, meaning we round up to get 1.3

i hope this helps :D

Statement B is true: The population will increase by 9%.

Various Functions:

A single function (Injective function) Many – one function. From onto function (Surjective Function) Function is into. polynomial operation.

P(t)=18,751(1.09)t is the population function, where t is the time in years.

The function's growth factor or multiplier, which is bigger than 1, is represented by the expression (1.09t). In other words, the population is growing over time.

Finding the difference between the final and starting values, dividing by the initial value, and then multiplying by 100% will give us the percentage growth in the population.

Let's contrast the population at t=0 and t=1 to see how they differ:

P(0) = 18,751(1.09)^0 = 18,751

P(1) = 18,751(1.09)^1 = 20,436.59

In the last year, the population has grown from 18,751 to 20,436.59.

The population has grown by the following amount:

[(20,436.59 - 18,751)/18,751] × 100% ≈ 9.0%

Thus, the population will grow by 9%, as stated in statement B.

To know more about Function visit:

https://brainly.com/question/14996337

#SPJ1

Answer:

1.5

Step-by-step explanation:

-18/3 = -6

-6/-4 = 3/2 or 1.5

Answer: 24

Step-by-step explanation:

Answer:

9 minutes and 25 seconds to 9 in the evening in analogue time is represented as:

8:50:35 PM

Using proportions we can find,

6. The weight of the adult bear = 750 pounds.

7. The measure of each angles are: 10°, 75° and 95°

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

Here in the question,

The weight is in the ratio = 3:1000

The average birth weight = 12 ounces = 3/4 pounds.

Now the weigh of adult bear = 1000 × 3/4 = 750 pounds.

In the second part the angles are in the ratio, 2:15:19.

So, 2x+ 15x + 19x = 180

x = 180/36

x = 5

Hence, the measure of each angles are: 10°, 75° and 95°

To know more about proportions, visit:

https://brainly.com/question/30675547

#SPJ1

Answer:

question where is the question?

Answer: D. 2/3

Step-by-step explanation:

If it is 1/5 of an hour, we times it by 5, to get full hour, right?

So, we also do ×5 for the acre of land, so we can get the amount of acres in a full 1 hour.

5 is the same as 5/1 as a fraction

1/5 × 5 = 5/5 ......1 hour

2/15 × 5/1 = 10/15

So we get, 10/15 acre of land cleared in 1 hour

We simplify 10/15,

Which becomes,

2/3.

In conclusion, this is the working out =

2/15 × 5 = 10/15 = 2/3

The value of x in the figure such that Ray YU is an angle bisector is 18 degrees

Given

The figure

Such that Ray YU is an angle bisector

An angle bisector is a line or a ray that divides an angle into two equal parts or halves.

In other words, an angle bisector divides an angle into two smaller angles with equal measures.

The point where the angle bisector intersects the opposite side is the angle bisector point

This means that

2x = 36

So, we have

x = 18

Hence, the value of x in the figure is 18

Read more about angle bisector at

https://brainly.com/question/24334771

#SPJ1

Answer:

8x - 58 ≤ 500

8x ≤ 500 + 58

8x ≤ 558

x ≤ 69.74

The values of x such that f(x) = x + 2 and g(x) = 2^x + 1 if f(x = g(x) are x =0 and x = 1

Given that

f(x) = x + 2

g(x) = 2^x + 1

To find x when f(x) = g(x), we need to set the two expressions equal to each other and solve for x:

f(x) = g(x)

x + 2 = 2^x + 1

Subtracting 1 from both sides:

x + 1 = 2^x

We can solve for x by using trial and error or by using numerical methods.

One solution to this equation is x = 1.

To see why, we can plug x = 1 into both sides of the equation:

x + 1 = 2^x

1 + 1 = 2^1

2 = 2

Another solution is x = 0

0 + 1 = 2^0

0 + 1 = 1

1 = 1

Hence, the solutions are x = 0 and x = 1

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

As given:

The side of the Square= (2x+

As we know:

The area of a square = Side × side

Putting the values of side in above formula we get:

 Area = (2x+4) ×(2x+4)

on solving we get:

Area= 2x×2x + 2x×4 +4×2x + 4×4

Area= 4x^2 + 8x + 8x + 16

Area= 4x^2 + 16x + 16

Hence,The Area of the Square is (4x^2+ 16x +16)

The answer to the all questions was solved by the methods of factoring:

Factoring is the process of breaking down a mathematical expression or equation into simpler components, such as factors that when multiplied together give the original expression.

In the given questions,

1.Factoring 2x² + 9x + 18:

2.Factoring x² - 20x + 36:

3.Factoring 2x² - 5x - 3:

4.Finding the greatest common factor of 8x² + 18x + 4:

5.Factoring 8x² + 18x + 4:

To know more about factoring expression, visit:

https://brainly.com/question/11994048

#SPJ1

Answer:

Using the distributive property, we can multiply -5m by each term inside the parentheses:

-5m(-2m + m^2 - 4m^3 + 9) = (-5m)(-2m) + (-5m)(m^2) + (-5m)(-4m^3) + (-5m)(9)

Simplifying each term:

= 10m^2 - 5m^3 + 20m^4 - 45m

The terms are arranged in descending powers of m, so this is already in standard form. Therefore, the final answer is:

20m^4 - 5m^3 + 10m^2 - 45m.

Thus, the area of the pentagon formed by the given coordinates is:

A = 28.5 sq. units.

A pentagon is just a five-sided polygon in geometry having five straight sides and five inner angles totaling 540 degrees. A pentagon is a five-sided, flat (two-dimensional), plane geometric form.

The coordinates of polygon are:

A(1,3), B(2,8), C(8, 8), D(10,3), and E(5,-2).

Plot the points on the graph as shown.

The area of a pentagon calculation is used to determine the area of a pentagon with apothem, a, but one side length, s:

A = 1/2 * a * (5s)

a = apothem, of perpendicular distance from the centre.

s = length of side.

From graph:

s = 6 units.

a is calculated using the tan function.

each interior angle of pentagon  = 54 degrees.

So,

tan (54/2) = a/ (s/2)

tan (36) = a/3

a = 3*tan (36)

a = 1.90 units

A = 1/2 * 1.90 * (5*6)

A = 28.5 sq. units.

Thus, the area of the pentagon formed by the given coordinates is:

A = 28.5 sq. units.

Know more about the pentagon

https://brainly.com/question/11759904

#SPJ1

Answer:7

Step-by-step explanation:

6.7 to the 10 is 7

Answer:

0 (-72522)

Step-by-step explanation:

ahora tienes negativo manzanas