5. A rock is thrown straight up from a 224-foot tall cliff. The height of the rock as a
function of time is given by the equation h(t) = -16t² + 80t+224. How many
seconds until the rock hits the ground?

Answer:

x = -6.8

Step-by-step explanation:

2.4x - 9.1x + 12.5x = -39.44

combine all like terms

5.8x = -39.44

÷5.8     ÷5.8

x = -6.8

I hope this helps!

Answer: 339.07

Step-by-step explanation:

Answer:

339.07.

Step-by-step explanation:

I've attached an image to help break down this problem. (credit to cymath.com)

Hope this helps! :)

Answer:

Solutions below

Step-by-step explanation:

This question requires the concept of substitution and order of operations (Bracket > Multiplication / Division > Addition / Subtraction).

Given x = - 2, y = - 3 and z = 4,

a) 2 x + 3 y = 2 (- 2) + 3 (- 3) = - 4 + (- 9) = - 4 - 9

= - 13

b) 2(y - z) = 2 (- 3 - 4) = 2 (- 7) = - 14

c)

[tex] \frac{6x}{2y} \\ = \frac{6( - 2)}{2( - 3)} \\ = \frac{ - 12}{ - 6} \\ = 2[/tex]

Answer:

4

Step-by-step explanation:

when you add a positive number to a negative number you subtract the two instead!

so, rephrase your math problem to

10-6=?

well 4

using the image you go back 6 places and you get 4

The inequality that describes the constraints is f + 6t ≤ 18

If Ty has 4 field goals and 3 touchdowns, he cannot remain on the team.

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤ because Ty's score has to be at most 18 points.

The from of the inequality that describes the constraints is:

(point of a touchdown x number of touchdowns) + (point of field goals x number of field goals) ≤ maximum points

(1 x f) + (6 x t) ≤ 18

f + 6t ≤ 18

Ty's total score when he has 3 touch downs and 4 field goals

(1 x 4) + (6 x 3) ≤ 18

4 + 18 ≤ 18

22 ≤ 18

Ty cannot remain on the team because his score exceeds 18. (i.e. 22 > 18).

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If the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.

Given that the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.

We are required to find the cost of 1 kg of mushrooms and the cost of 1 kg of turnips.

Cost is basically the expenditure that we do in order to buy or produce a product.

Suppose the cost of 1 kg of mushrooms be x and the cost of 1 kg of turnips be y. The equations will be as under:

2x+2.5y=8.55------1

3x+4y=13.10-------2

Equation1 *3 and Equation2 *2.

6x+7.5y=25.65-----3

6x+8y=26.20-------4

Subtract 4 from 3.

6x+7.5y-6x-8y=25.65-26.20

-0.5y=-0.55

y=1.1

Put the value of y in 1.

2x+2.5*1.1=8.55

2x+2.75=8.55

2x=8.55-2.75

2x=5.80

x=2.9

Hence if the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.

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The best method to solve a problem is Brainstorming.

According to the statement

We have to find that the which method is the best for solving the problem.

So, For this purpose, we know that the

A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem.

From the given information:

There are different methods to solving this problem.

Then

we know that the to solve a problem there are lot of the method, but the some method are the best to solve the problem.

The method is called a brainstorming session.

It is the Brainstorming is a problem-solving activity where students build on or develop higher order thinking skills. Encourages creative thought. Brainstorming encourages students to think creatively.

And due to their special capability it is the best method.

So, The best method to solve a problem is Brainstorming.

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The value of x so that the equation based on a and b has a solution is x = -4/3

 An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

   Equations can be graphed, just like a function.

     As we can see, we have the following equation:

a + 8 = -4(xb)

  and we have the values of the coefficients a and b, and these are:

   We substitute these values in the equation:

(8) + 8 = -4 [x(3)] We solve the equation

16 = -4(3x)

16 = -12x

x = 16-/12

x = 8/-6

x = 4/-3

x = -4/3

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The Cookie Shop's profit at the end of January will be $12000.

The profit earned by the shop at the end of December = $15000

The profit decreased by 20% at the end of January

Therefore decrease percentage, which is used to determine the percentage decrease of two values ​​(final value and initial value)

[tex]Decrease percentage = \frac{Final value - Initial Value}{Final Value} * 100[/tex]

According to the formula, the initial value is subtracted from the final value. The resulting value is divided by the initial value and multiplied by 100 to obtain the decreased percentage

Decrease Percentage  20%

Final value = $15000

[tex]20 = \frac{15000 - Initial Value}{15000} * 100[/tex]

[tex]\frac{20}{100} = \frac{15000 - Initial Value}{15000}[/tex]

[tex]\frac{20}{100} * 15000 ={15000 - Initial Value}[/tex]

20 * 150 = 15000 - Initial Value

3000 = 15000 - Initial Value

Initial value = 15000 - 3000

Initial value = $12000

The profit earned by the Cookie Shop at the end of January will be $12000.

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Answer:

a = 71°

Step-by-step explanation:

This looks like a supplementary angle

109 + a = 180

-109        -109

a = 71°

I hope this helps!

Answer:

a = 71°

Step-by-step explanation:

Hello!

The sum of angles on a line is 180°. That means, 109° and a have to add up to 180°.

Angles that add up to 180° are called supplementary angles.

a is 71°.

The number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840

The digits are given as:

2, 3, 4, 6, 7, 8 and 9

There are 7 digits represented in the above list

If each of those digits is only allowed to be used once, then we have the following possibilities

First character: Any of the 7 digits

Second character: Any of the remaining 6 digits

Third character: Any of the remaining 5 digits

Fourth character: Any of the remaining 4 digits

The number of 4-digit PIN codes is

Number = 7 * 6 * 5 * 4

Evaluate

Number = 840

Hence, the number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840

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A group of products are averaged to determine central tendency using the geometric mean. The geometric mean of 8 and 36 is 6√8.

The geometric mean in mathematics is a mean or average that, by using the product of the values of the numbers, shows the center tendency or usual value of a set of numbers.

The geometric mean, sometimes known as the compounded annual growth rate, is a tool used in finance to determine average growth rates.

The Geometric Mean (GM) is the average value or mean that reveals the central tendency of a group of numbers by adding up the values of those numbers.

Formula to calculate G.M is

x = √(a × b)

Where, a = 8 and b = 36

x = √(8 × 36)

x = 6√8

Therefore, the value of x = 6√8.

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Answer:

C.

Step-by-step explanation:

c^2-a^2

will give you b

Answer:

The Answer is C

Step-by-step explanation:

Hope this helps!!!

Answer:

60

Step-by-step explanation:

Since both bags of sugar were 120 kg, there is a total of 240 kg of sugar to be distributed into the packs. Let x represent the number of 2 kg packets and y represent the number of 3 kg packets. We know that all the sugar was packed into these two kinds of packets, so:

[tex]2x+3y=240[/tex]

And we know that there were half as many 2 kg packets as 3 kg packets, so:

[tex]x=\frac{1}{2} y[/tex]

Now, we have a system of equations!

[tex]\left \{ {{2x+3y=240} \atop {x=\frac{1}{2}y }} \right.[/tex]

Let's put the second equation equal to y, since that removes the fraction:

[tex]x=\frac{1}{2}y\\ 2x=y[/tex]

Now substitute y into the first equation:

[tex]2x+3y=240\\2x+3(2x)=240[/tex]

Now simplify to find x:

[tex]2x+3(2x)=240\\2x+6x=240\\8x=240\\x=30\\[/tex]

There are 30 of the 2 kg packets! Now, we can use x to find y, the number of 3 kg packets!

[tex]2x=y\\2(30)=y\\60=y[/tex]

There are 60 of the 3 kg packets!

8.06 is  the distance between the two points  .

What is distance in math?

distance d = [tex]\sqrt{( 5 + 3)^{2} + ( -2 + 1)^{2} }[/tex]

              d = [tex]\sqrt{8^{2} + (-1)^{2} }[/tex]

                d = [tex]\sqrt{64 + 1}[/tex]

                d = √ 65

                d = 8.06225  ≈ 8.06

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Answer:

d = 380 units

Step-by-step explanation:

Find the absolute value of the difference of the 2 numbers, that is

d = | - 235 - 145 | = | - 380 | = | 380 | = 380

or

d = | 145 - (- 235) | = | 145 + 235 | = | 380 | = 380

The 1250 represents option B in the situation, George is correct, the solution to the linear equation is h = 80$.

What is a linear equation?

A linear equation has only one or two variables. No variable in a linear equation is raised to a power greater than one or used as the denominator of a fraction. When two values satisfying a linear equation are found and shown, all of the points on a coordinate grid fall on the same line.

Given that,

Jennifer was paid $15 per hour.

Given equation is 50+15h=1250

1)Here 1250 represent B.

Her financial situation towards the end of the summer.

Because as mentioned in the equation 50+15h=1250

Here, 50 is the money already there with her, and 15h was the amount paid to her,

So, by adding those both the amount 1250 will be the amount with Jennifer at the end of the summer.

2)Given equation is 50+15h=1250

By putting 10 in place of h (h=10)

50+15(10)=1250,

50+150=1250,

200=1250$.

Since, LHS is not equal to RHS.

Therefore, George is correct, 10 could not be the solution to the linear equation.

3) Given equation 50+15h=1250

15h=1250-50,

15h=1200,

h=1200/15,

h=80$.

Therefore, the solution for the equation h is 80$.

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IfIf you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.

First step is to calculate the different in speed between first and fourth length

Using this formula

Speed =-First length time in seconds +(- Fourth length time in seconds)

Let plug in the formula

Speed=-0.23+(-0.42)

Speed=-0.65

Second step is to calculate the third length

Speed=-0.65+0.11

Speed=-0.54 seconds

Therefore If you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.

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Answer: 4.95

Step-by-step explanation:

54.25÷6.2−3.8=

54.25/6.2−3.8=

8.75-3.8=

8.75-3.80=

8-3+0.75-0.80=

5-0.05=4.95

Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624 the amount paid as tax is $ 3,765.

Given details in the question are as follows:

Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624,

By using the given tax table on the screenshot we are calculating the tax paid by Jim.

if your taxable income is greater than the $23,600 but lesser than the $23,624 and you fill separate tax return, the amount will be paid as tax is

$ 3,765.

Married filing separately is a tax status for married couples who choose to record their respective incomes, exemptions, and deductions on separate tax returns.

The alternative to married filing separately is married filing jointly. Usually, it makes sense financially for married couples to file jointly. However, when one spouse has significant medical expenses or miscellaneous itemized deductions, or when both spouses have about the same amount of income, it might be wiser to file separately.

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If JM ≅KM then M is the midpoint of ΔJKL then LM is the median of

JM  ≅ KM.

A perpendicular bisector is a 90° angle line that intersects and passes through the midpoint of a given segment.

The median of a triangle is a line segment that connects a vertex to the midpoint of the opposing side. Each triangle has three medians, one from each vertex, which all intersect at the triangle's centroid.

The altitude of a triangle is a line segment that runs through a vertex and is perpendicular to the baseline.

We know that JM ≅ KM then M is the midpoint of ΔJKL. Therefore, LM is the median of JM ≅ KM.

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The required no . is ( - 10. 4 ) .

According to ques .

10 * [ ( 1 / 2 ) x + 6 ] = 8

Solving linear equation in one variable above ,

( 1 / 2 ) x = ( 8 / 10 ) - 6

( 1 / 2 ) x = - 52 / 10

x = (  - 52 / 10 ) * 2

x = - 10 . 4

Hence , the no . is ( - 10 . 4 ) .

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The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term. The sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.

The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.

The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Let the finite geometric series be

3 + 6 + 12 + 24 + 48 +. . . + 768

Where, the first term, a = 3

common difference, r = 6/3 = 2

n = 9

The equation be Sn = a(1 - [tex]$$r^{n}[/tex])/(1 - r)

substitute the values in the above equation, we get

S9 = 3(1 - [tex]$$2^{9}[/tex]))/(1 - 2)    

simplifying the above equation, we get

= 3(1- 512)/(-1)    

= 3(-511))/(-1)

= 3(511) = 1533

Therefore, the sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.

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Answer:

radius: 3.66 Diameter: 7.32

Step-by-step explanation:

Radius =  C/2π  3.6605636911136

Diameter = C/2π7.3211273822272

Answer:

(y+4)²

Step-by-step explanation:

[tex](a+b)^2=a^2 + 2ab+b^2[/tex]

Here, a=y and b=4.

the required area of shaded part is 549.3807mm^2

Four quarter circles are cut out from a 16 cm square

that is we have given that square has each side 16 cm

we know that

area of square = (side) ^2

                      = 16*16 cm^2

                       = 256 cm^2

four quarter circles are cut out from a 16 cm square

we know that

area of sector = N/360 ( pi *r^2)

                       = 90/360( pi* 8^2)   it makes angle 90 degree and r=8cm

                       = 1/4( pi* 64)

therefore area of four quarter circles is given by

=4*(1/4)*(64*pi)

=64pi

now the required area of the shaded part is equal to

=area of square - area of four quarter circles

=       256 -  64pi

= 256 - 201.06193

= 54.93807 cm^2

we know that 1cm is equal to 10mm

54.93807*10 =549.3807mm^2

Hence the required area of shaded part is 549.3807mm^2

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The price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000

Let the price of the cycle be x

Then the price of the scooter will become X + 4200

As the price of a scooter and the price of a cycle are in the ratio of 5:2

So, it can be written as

 x+4200: x:: 5:2

which implies

x= 2a and x+4200= 5a

a= x/2 and x+4200/5

equating both the equations, we get

x/2=(x+4200)/5

in order to solve this linear equation, we need to move 2 from the left-hand side to the right-hand side which would result in the change of sign from division to multiplication and we need to move 5 from the right-hand side to the left-hand side which would result in the change of sign from division to multiplication

5x=2x+8400

3x= 8400

X= 8400/3

X= 2800

So, the price of the cycle is 2800 and the price of the scooter is 2800+ 4200=7000

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4.313

Step-by-step explanation:

Answer:Ill try my best.

The answer is

3rd one

Step-by-step explanation:

subtract 70 from both sides of the equation