The height (metres) of an object is given by h(t) = -2t² + 9t + 56 where t is time is seconds. When does the object hit the ground?

Answer: 8 seconds

Answer:

36 miles

Step-by-step explanation:

speed = distance/time

distance = speed × time

distance = 12 miles/hour × 3 hours

distance = 36 miles

Answer:

[tex]x = 2 , y = 6[/tex]

Step-by-step explanation:

The substitution method suggests that you will "substitute" a portion of one given equation to another in the system of equation:

In this case, substitute 3x for y in the 2nd equation:

[tex]y = 3x\\x + y = 8\\\\x + (3x) = 8[/tex]

Simplify. Combine like terms. Like terms are terms with the same amount of the same variable.

[tex]x + 3x = 8\\4x = 8[/tex]

Next, isolate the variable, x. Divide 4 from both sides of the equation:

[tex]4x = 8\\\frac{4x}{4} = \frac{8}{4} \\x = \frac{8}{4}\\ x = 2[/tex]

Next, plug in 2 for x in one of the equations, and simplify to solve for y:

[tex]y = 3x\\y = 3(2)\\y = 6[/tex]

Check: Plug in 2 for x and 6 for y in the second equation:

[tex]x + y = 8\\(2) + (6) = 8\\8 = 8[/tex](True)

~

[tex]x = 2 , y = 6[/tex] is your answer.

~

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Answer:

I don't know

Step-by-step explanation:

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By trigonometric functions, the missing sides of the right triangles are:

Case 7: AC = 9.725, BC = 10.071

Case 8: AB = 21.301, BC = 18.807

Case 9: BC = 4.585, AC = 8.999

Case 10: AB = 10.461, BC = 7.774

In this problem we have four cases of right triangles, each of which has a known side and a known angle and we must determine all the missing lengths by trigonometric functions:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Where:

Now we proceed to determine the values of the missing lengths:

Case 7

AC = 14 · sin 44°

AC = 9.725

BC = 14 · cos 44°

BC = 10.071

Case 8

AB = 10 / cos 62°

AB = 21.301

BC = 10 · tan 62°

BC = 18.807

Case 9

BC = 10.1 · sin 27°

BC = 4.585

AC = 10.1 · cos 27°

AC = 8.999

Case 10

AB = 7 / cos 48°

AB = 10.461

BC = 7 · tan 48°

BC = 7.774

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Answer:

38 in²

Step-by-step explanation:

We can solve for the area of this trapezoid by using the area formula:

[tex]A = \dfrac{b_1 + b_2}{2} \cdot h[/tex]

First, we need to identify the trapezoid's bases ([tex]b_1[/tex] and [tex]b_2[/tex]). We know that the bases of a trapezoid are parallel. Using this information, we can identify 8 in and 11 in as the bases.

Next, we need to identify the height ([tex]h[/tex]). We know that the height of a trapezoid is the length from [tex]b_1[/tex] and [tex]b_2[/tex] that is perpendicular (at a right angle) to both of the bases. We can identify this as 4 in because we can see that it adjoins at a right angle to both of them.

Finally, we can plug these values into the area formula and solve for A.

[tex]A = \dfrac{8 + 11}{2} \cdot 4[/tex]

[tex]A = \dfrac{19}{2} \cdot 4[/tex]

[tex]A = \dfrac{76}{2}[/tex]

[tex]\boxed{A = 38 \text{ in}^2}[/tex]

Answer:

Let's assume that a serving of Cereal B contains x grams of carbohydrates.

According to the problem, a serving of Cereal A contains 4 more grams of carbohydrates than Cereal B. So, the amount of carbohydrates in Cereal A is (x + 4) grams.

The total amount of carbohydrates consumed from both cereals is 66 grams:

x + (x + 4) = 66

Simplifying the equation:

2x + 4 = 66

Subtracting 4 from both sides:

2x = 62

Dividing by 2:

x = 31

So a serving of Cereal B contains 31 grams of carbohydrates.

And a serving of Cereal A contains 4 more grams:

31 + 4 = 35

Therefore, a serving of Cereal A contains 35 grams of carbohydrates.

The statements that are true about the diagram given above = Line JL is an angle bisector and L is the midpoint of a segment in the diagram. That is option B and F.

An angle bisector is defined as the lone the

at is drawn through an angle such that it divides the angle into two equal parts.

From the diagram above, line JL divided the angle < J into two equal angles while diving the line segment KI into two equal parts such as KL and LI.

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Answer: 18x + 45y.

Step-by-step explanation:

Expanding the brackets, we get:

9(2x+5y) = 92x + 95y

Simplifying the products, we get:

9(2x+5y) = 18x + 45y

Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.

Answer:

18x+45y

Step-by-step explanation:

9(2x+5y) = 18x + 45y

Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.

The measure of line segment JK using the Secant Theorem is found as 7 units.

According to the intersecting secants theorem, the product of one whole secant segment but also its outer segment is equivalent to the product of the other whole secant segment as well as its external segment when two secants cross at an exterior point.

According to the Secant Theorem,

If two secants are drawn from an identical point through a circle, their products, A times their external segment and B times their external segment, are equal.

So, using Secant Theorem:

JK*JL = RM*RL

8* (2x + 7) = 24 * 7

Solving the equation:

x = 7

Thus, the  measure of line segment JK using the Secant Theorem is found as 7 units.

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A: (4,-2)

B: (1,-1)

C: (1,-4)

Hope this helps! Just graph it.

To complete the table, we can use the expression 10 + 4h to calculate the total cost of renting the golf clubs for different values of h.

h Total cost

1 14

2 18

3 22

4 26

5 30

For example, if the golf clubs are rented for 1 hour, the total cost is $14 (10 + 4(1) = 14). If they are rented for 2 hours, the total cost is $18 (10 + 4(2) = 18), and so on.

The expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented is 10 + 4h.

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Answer:

Assuming the ball is a perfect sphere, we can use the formula for the volume of a sphere to calculate the amount of air it can hold.

The formula for the volume of a sphere is:

V = (4/3)πr^3

where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.

To calculate the radius of the ball from its diameter of 15 inches, we divide by 2:

r = d/2 = 15/2 = 7.5 inches

Substituting this value into the formula, we get:

V = (4/3)π(7.5)^3 ≈ 1767.15 cubic inches

Therefore, the ball can hold approximately 1767.15 cubic inches of air to the nearest tenth.

Step-by-step explanation:

The length of the diagonal AG = 7.56 cm.

A cuboid is a three-dimensional shape that is bounded by six rectangular faces. It is also known as a rectangular prism. A cuboid has six faces, twelve edges, and eight vertices.  

To find the Length of the side AG, find the length of AC by using the Pythagorean formula. Now using the trigonometric ratios formulas find the length of AG.

Here we have a cuboid

Where

AD = 23 cm

DC = 18 cm

∠GAC = 75°  

From the right angle triangle, ADC

=> AC² = AD² + DC²    [ Using the Pythagorean formula ]

=> AC² = (23)² + (18)²

=> AC² = 529 + 324

=> AC = √853 = 29.20    

From the right angle triangle, AGC

=> Cos B = AC/AG

=> Cos 75° = 29.20/AG

=> AG = Cos 75° (29.20)

=> AG = (0.26)(29.20)

=> AG = 7.56

Therefore

The length of the diagonal AG = 7.56 cm.

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answer

306.87 degrees and 666.87 degrees.

steps

4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Equation with tangent function.

Title: Solving an equation involving tangent function

Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).

Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).

Numbered list:

Start with the equation 4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

Take the arctangent (or inverse tangent) of both sides to find θ.

Specify the interval [0,360) when giving the solution.

Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.

One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).

To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.

Subtracting 5 from both sides gives us: 4tanθ = -5

Dividing both sides by 4: tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Sure, here's just the math:

4tanθ + 5 = 0

Subtracting 5 from both sides:

4tanθ = -5

Dividing both sides by 4:

tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides:

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

ChatGPT

Answer:

16:24

Step-by-step explanation:

The ratio of boys to girls is 2 : 3

total of the ratio is 5

∴ fraction of the class are boys = 2/5

and  the girls=  3/5

Ratio of boys =( 2/5)×40=16

Ratio of girls=3/5  ×40 =24

Answer:

  94.3

Step-by-step explanation:

You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"

The diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.

The solution is found by multiplying both sides by 82:

  (x/82)·82 = (115/100)·82

  x = 94.3

The question can also be written as a statement:

  "what" is 115% of 82

When written as an equation, "is" means "equals", and "of" means "times":

  what = 115% × 82

Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...

  x = 115/100 × 82 = 1.15 × 82

All that remains is to evaluate this expression.

  x = 1.15 × 82 = 94.3

So, the answer to the question is ...

  94.3 is 115% of 82.

The value of t is equal to 4.

The equation of PR is y = -x + 6.

The area of the rhombus is equal to 32 square units.

Since BPCR is a rhombus and all the side lengths of a rhombus are always equal in length, we would use the distance formula to determine the length of BP as follows:

Distance BP = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance BP = √[(0 - 2)² + (6 - 0)²]

Distance BP = √[4 + 36]

Distance BP = √40 units.

Also, side length BP is equal to side length PC:

√40 = √[(t - 6)² + (6 - 0)²]

√40 = √[(t - 6)² + 36]

40 = (t - 6)² + 36

(t - 6)² = 4

t - 6 = ±2

t = 6 ± 2

t = 8 or t = 4.

Therefore, C should be located at (6, 4).

Since Q is the midpoint PR and BC, we know that B is shifted 2 units right and 6 units down from P. Therefore, point R is represented by R(8, -2).

In order to determine the equation of PR, we would use the point-slope form:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 6 = \frac{(-2-6)}{(8 - 0)}(x - 0)[/tex]

y - 6 = -1(x)

y = -x + 6

In Mathematics, the area of a rhombus is calculated by using this formula:

Area = 1/2(d₁ × d₂)

Where:

d₁ and d₂ represent the diagonals of a rhombus.

PR = 2BC

8√2 = 2BC

BC = (8√2)/2

BC = 4√2

Area of rhombus = 1/2(PR × BC)

Area of rhombus = 1/2(8√2 × 4√2)

Area of rhombus = 1/2(64)

Area of rhombus = 32 square units.

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the answer is (a) [tex]\frac{1}{6}b-\frac{5}{6}[/tex]

In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):

1/3b + 2/3b = 3/3b = 1/b

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

from the question:

In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):

1/3b + 2/3b = 3/3b = 1/b

We can now reintroduce this value into the first expression:

1/b - 5/6(b+1)

We can distribute the 5/6 term in order to further simplify this:

1/b - 5/6b - 5/6

Now that the first two terms share a common denominator of 6b, we may combine them:

6/6b - 5/6b - 5/6

Simplifying this gives us:

1/6b - 5/6

Therefore, the answer is (a) 1/6b - 5/6.

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Answer:

Step-by-step explanation:

5.5.1 cos² 19⁰ - sin² 19° = cos² 19° - (1 - cos² 19°) = 2cos² 19° - 1

5.5.2 cos² 19° + sin² 19⁰ = 1

5.5.3 2 cos² 50° -1 = cos 100° - 1

5.5.4 1-2 sin² 50° = cos² 50°

5.5.5 6cos² 2 -3 = 6cos²(180°-11°) -3 = 6cos²11° -3 = 6cos²(360°-349°) -3 = 6cos²349° - 3

Note: cos(360°-x) = cos x and cos(180°-x) = -cos x, so we can write cos169° = cos(180°-11°) = -cos11°.

The probability of the sum of 4 is 3/36

From the question, we have the following parameters that can be used in our computation:

rolling a 6-sided die twice

So, the sample space are

S1 = {1, 2, 3, 4, 5, 6}

S2 = {1, 2, 3, 4, 5, 6}

For the sum of 4, we have]

(1, 3), (2, 2) and (3, 1): Count of 3

The sample size of the event is

Size = 6 * 6

Size = 4

Using the above as a guide, we have the following:

P = Count/Size

So, we have

P = 3/36

Evaluate

P = 1/12

Hence, the probability is 1/9

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Considering the complex-conjugate root theorem, the statement is given as follows:

If a polynomial has one root in the form a - √5, it has a second root in the

form of a + √5.

The complex conjugate theorem for rational roots states that if a polynomial with real coefficients has a complex root of the form a + bi (where a and b are real numbers and i is the imaginary unit), then its complex conjugate a - bi is also a root of the polynomial.

In the case of a rational root, we have that:

If [tex]a + \sqrt{b}[/tex] is a root, then the number [tex]a - \sqrt{b}[/tex] is also a root, which justifies the answer for this problem.

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The correct formula for the slope will be:

m = (100 - 50)/(4 - 2) = 50/2 = 25 . Rafael took the reciprocal of the values.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. Δy and Δx are the net changes in the y and x coordinates, respectively.

So,

m = Δy / Δx

Using the slope-intercept form, as illustrated below, we can quickly get the slope for just a given line:

Y = mx + c can be used to represent a line.

For the stated question:

The slope calculated by Rachel is:

m = (4 - 2) / (100 - 50) = 2/50 = 1/25

Which is incorrect .

Thus, the correct formula for the slope will be:

m = (100 - 50)/(4 - 2) = 50/2 = 25

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Answer:

Rodolfo has two checks, one for $108.93 and the other for $372.47. Let's add the amounts of the checks to get the total amount of the deposit:

$108.93 + $372.47 = $481.40

Next, Rodolfo wants to receive $75 cash back from his deposit. We need to subtract $75 from the total amount of the deposit to get the net deposit:

$481.40 - $75 = $406.40

Therefore, Rodolfo's net deposit is $406.40.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find Rodolfo's net deposit, we need to add the values of his two checks and subtract the amount of cash he wants to receive back:

Net deposit = (Value of Check 1) + (Value of Check 2) - (Amount of Cash Back)

Net deposit = $108.93 + $372.47 - $75

Net deposit = $406.40 - $75

Net deposit = $331.40

Therefore, Rodolfo's net deposit is $331.40.

The multiplicatiοn οf the cοmplex number is 13+19i.

Cοmplex numbers are the numbers that are stated in the fοrm οf a+ib where, a,b are real numbers and I is an imaginary number termed "iοta".

Cοmplex numbers allοw sοlutiοns tο all pοlynοmial equatiοns, even thοse that have nο sοlutiοns in real numbers. Mοre precisely, the fundamental theοrem οf algebra asserts that every nοn-cοnstant pοlynοmial equatiοn with real οr cοmplex cοefficients has a sοlutiοn which is a cοmplex number.

Here the given cοmplex number is ,

=> (7-2i)(1+3i)

Nοw simplifying the expression then,

=> [tex]7\times1+7\times3i-2i \times1 -2i \times3i[/tex]

=> 7+21i-2i-[tex]6i^2[/tex]

=> 7+19i -6(-1) [[tex]i^2=1[/tex]]

=> 7+19i+6

=> 13+19i

Hence the multiplication of cοmplex number is 13+19i.

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The amount that would be in the account after 20 years would be $33,277.48.

The doubling time of the emissions would be  23.45 years

The total emissions will be higher in 2030 than 2010 by 100.96%

To find the amount in the account after 20 years, we can use the formula:

A(t) = P(1 + r)^t

Take the 12th root of both sides:

(1 + r) = 2^(1/12)

Now find r:

r = 2^(1/12) - 1 ≈ 0.05946

Now we can find the amount in the account after 20 years with the investment of $10,000:

A(20) = 10000(1 + 0.05946)^20

A(20) = $33,277.48

To find the doubling time for emissions, we can use the formula:

Doubling time = ln(2) / ln(1 + r)

Doubling time = ln(2) / ln(1 + 0.03)

Doubling time = 23.45 years

To find how much higher total emissions will be in 2030 than in 2010, we can use the exponential growth formula:

E(t) = E₀(1 + r)^t

We want to find the ratio of emissions in 2030 to emissions in 2010:

E(20) / E(0) = (1 + 0.03)^20

E(20) / E(0) ≈ 2.0096

Higher emissions = E(20) / E(0) - 1

Higher emissions ≈ 1.0096

So, total emissions will be approximately 100.96% higher in 2030 than in 2010.

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Step-by-step explanation:

If the LOSE 27% per year, they RETAIN 100- 27 = 73%  (.73 in decimal) per year

after ten years :

 $  1128 ( .73)^10 = $48.48

Answer:

$48.48

Step-by-step explanation:

Using compound depreciation

time

amount × percentage^

10

1128 × 0.73^ =48.477

The following table lists Telkom's rates for international calls. Number minutes needed for [tex]x[/tex] to be [tex]17[/tex]and [tex]y[/tex] to be [tex]14.85[/tex].

Many numbers have deeper symbolic connotations in addition to their spiritual significance, and it is crucial to grasp these meanings in order to comprehend how they influence other cultures' perceptions of the physical world.

According to Wilder, any sequence of consecutive threes is probably a sign of good fortune or a shift in your job, achievement, aspirations, or emphasis. According to Wilder, the number 333 is frequently a signal that you should have faith in your ability to make the next move.

Let[tex]y=k*b[/tex]

When [tex]x=3, y=4.95, x=5, y=8.25[/tex]

[tex]4.95=3k+b[/tex]

[tex]8.25=5k+b[/tex]

[tex]k=1.65[/tex]

[tex]b=0[/tex]

[tex]y=1.65x[/tex]

when [tex]x=9[/tex]

[tex]y=1.65*9 = 14.85[/tex]

when [tex]y=28.05[/tex]

[tex]x=y/1.65=28.05/1.65=17[/tex]

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The complete and the correct form of question is:

The International calls tariffs of Telkom are given in the following table:

Number of minutes         3                  5                   9                     y

Cost                               R4.95          R8.25              X                R28.05

Determine the cost of 9 minute call

Answer:

75.6%

Step-by-step explanation:

Reducing Debt: 2024's debt to equity ratio has increased from 67.6% to 75.6% over the past 5 years. Debt Coverage: 2024's operating cash flow is negative, therefore debt is not well covered.