You can model time t , in seconds, an object takes to reach the ground falling from height H , in meters, by t(H)=√2H/g . The value of g is 9.81 m/s². If an object takes 7 seconds to fall to the ground, what was its initial height?

Answer:

Step-by-step explanation:

Let,

One of the siblings age be = x

So, the other siblings ages are = x+2, x+4 and x+6

Since,

Ashley is the oldest sibling so his age is x + 6

∴ By the problem,

=> x + (x+2) + (x+4) + (x+6) = 100

=> 4x + 12 = 100

=> 4x = 100 - 12

=> 4x = 88

=> x = 22

Now,

We got the age of the youngest one that is 22 years

As,

Ashley is the oldest sibling so his age is

= 22 + 6 = 28 years

Hence,

The age of Ashley is 28 years (Ans)

Answer:

28 years old

Step-by-step explanation:

100/4 = 25

The ages are consecutive even numbers,

so add 1 to and subtract 1 from 25.

Add 3 to and subtract 3 from 25.

Ages: 22, 24, 26, 28

Ashley is the oldest: 28 years old

Step-by-step explanation:

first question:

1/7 - 3/4 LCM : 28

4/28 - 21/28

= -17/28

second equation:

1/6 - 4/9 LCM : 36

6/36 - 16/36

= -10/36

= -5/14

( I believe these are the answers )

The amount invested in the growth fund, income fund and money market fund is 20000, 20000 and 10000 respectively

Let the amount invested in the growth fund, income fund and money market fund be x, y and z respectively

As per the question, the company invested twice as much in the income market as in the money market

Therefore,

y = 2z

Equations will be:

x + 2z + z = 50000

12/100x + (8/100)*2z + 5/100z = 4500

Solving the equations

x + 3z = 50000

12x + 21z = 450000

Multiplying the first equation by 7 for equating

7x + 21z = 350000

12x + 21z = 450000

Equating these two we get

5x = 100000

x = 20000

Putting x = 20000 in 7x + 21z = 350000

z = 10000

2z = 20000

So, the amount invested in the growth fund, income fund and money market fund is 20000, 20000 and 10000 respectively

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Answer:  The three medians of the triangle are concurrent. The point of concurrency is called the centroid. Point A is the centroid of the triangle.

Step-by-step explanation:

Answer:

Centroid.

Step-by-step explanation:

This point is where the three medians of a triangle meet. The median in a triangle is the line between a vertex and the opposite side.

we have constructed the given quadrilateral.

The dimensions of the quadrilateral are:

WX = 4 cm

XY = 3.5 cm

YZ = 5 cm
WZ = 5.5 cm

∠ x = 75°

First draw a line segment  WX = 4 cm.

Now from the point X, construct an angle of 75°.

Now, on the ray of that angle, mark an arc that is 3.5 came long and mark the intersection point as Y

Now, from point Y, draw an arc of 5 cm and from point W draw an arc of 5.5 cm.

Mark their intersecting point as Z

Join WZ and YZ

The quadrilateral is formed.

Therefore, we have constructed the given quadrilateral.

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Answer:

2:14

Step-by-step explanation:

[tex]\frac{1 \times 2}{7 \times 2} = \frac{2}{14}/2:14[/tex]

Answer:

Step-by-step explanation:

if you're using Del Math (yk what i'm talking about) it requires you to have a specific way of putting it.

The equation is going to be:

4.25x + 167 = 655.75

your x is going to be:

115

I hope this helps!

For the explanation hopefully, this will make sense (english isn't my first language)

So you know the number of hours: 4.25

cost of the parts: 167

total cost: 655.75

then finally the cost per hour: x

----

so now when you write your equation you're going to end up with the total number of hours (times the cost per hour) added to the cost of the parts, then the remaining will be your total cost. This is how I pictured the equation portion in my head.

for the actual solving part you subtract the cost of the parts from itself as well as the total which should leave you with: 4.25x = 488.75

then you're going to divide 4.25 from each side, as you do.

Then you have the cost of labour per hour: 115

The equation to find the cost of the labor per hour is:

167 + 4.25C = 655.75

The cost of the labor per hour is $115.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Number of hours worked = 4.25

Cost of the parts used = $167

Total cost = $655.75

Now,

We can write an equation to find the C = cost per hour.

167 + 4.25C = 655.75

Solve for C.

167 + 4.25C = 655.75

4.25C = 655.75 - 167

4.25C = 488.75

C = 115

Thus,

The cost of the labor per hour is $115.

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Answer:

0<x<4

Step-by-step explanation:

Ok, so the question is basically asking where balls height goes up, then down. So the x has to be in the middle of a bounce. That means that x has to be 0, 4, 6, or 8. So the number on the left side must be one of the numbers I just listed. And then the number on the right must be the end of the bounce, so it would be either 4, 6, 8, or 10. So then your answer after looking must be 0<x<4

The expression for the total number of baseball cards he has now is

b + 11.

It is given that Carlos had " b " baseball cards.

Then, he got 11 more baseball then the number of baseballs will be

         [tex]b+11[/tex]

Hence , the total number of baseballs are b + 11

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Answer:

1111/2500

Step-by-step explanation:

For item a, the linear functions are given as follows:

1. y = 1.5x.

2. y = 0.5x - 1.

3. y = -0.5x + 1.

4. y = -1.5x - 1.

For item B, we have that:

1. The functions are:

a. y = 2x + 3.

b. y = 0.5x - 1.

2. The unit rates(slopes) are:

a. 2

b. 0.5.

A linear function is modeled by:

y = mx + b

In which:

In graph 1, the function goes through (0,0), hence b = 0, and through point (2,3), hence the slope is:

m = (3 - 0)/(2 - 0) = 3/2 = 1.5.

Hence the function is:

y = 1.5x.

In graph 2, the function goes through (0,-1), hence b = -1, and through point (2,0), hence the slope is:

m = (0 - (-1))/(2 - 0) = 1/2 = 0.5.

Hence the function is:

y = 0.5x - 1.

In graph 3, the function goes through (0,1), hence b = 1, and through point (2,0), hence the slope is:

m = (0 - 1)/(2 - 0) = -1/2 = -0.5.

Hence the function is:

y = -0.5x + 1.

In graph 4, the function goes through (0,-1), hence b = -1, and through point (2,-4), hence the slope is:

m = (-1 - (-4))/(0 - 2) = -3/2 = -1.5.

Hence the function is:

y = -1.5x - 1.

In table a, the function goes through (0,3), hence b = 3, and through point (1,5), hence the slope is:

m = (5 - 3)/(1 - 0) = 2.

Hence:

y = 2x + 3.

The unit rate, which is the slope, is of 2.

For table b, the function goes through (2,0) and (6,2), hence the slope is:

m = (2 - 0)/(6 - 2) = 1/2 = 0.5.

Hence:

y = 0.5x + b.

When x = 2, y = 0, hence we can find b as follows.

0 = 0.5(2) + b

b = -1.

Thus:

y = 0.5x - 1.

The unit rate is of 0.5.

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Answer:

x = 8

Step-by-step explanation:

3 + 10(9X + 4) = 763  Distribute the 10

3 + 10(9x) + 10(4) = 763

3 + 90x + 40 = 763  Combine like terms

90x + 43 = 763  Subtract 43 from both sides

90x = 720  Divide both sides by 90

x = 8

Answer:

x=8

Step-by-step explanation:

If you are emphasizing on the fact that these are its only real roots, then maybe the function has any other 2 imaginary roots, so there wouldn't be any specific equation that you're looking for.

However if you mean that these real roots are the only roots of this function, meaning that they are double roots, we can argue that:

[tex]f(x) = (x + 4) {}^{2} (x + 1) {}^{2} \\ f(x) = (x {}^{2} + 8x + 16)(x {}^{2} + 2x + 1) \\ expand \: by \: multiplying \: each \: term \: by \: the \: other \: 3 \\ f(x) = x {}^{4} + 10x {}^{3} + 33x {}^{2} + 40x + 16[/tex]

In the given statement is:

The Personal identification numbers (pins) for automatic teller machines (atms) usually consist of four digits. suppose pins are assigned at random so that all 4-digit numbers are equally likely.

To find probability that a pin assigned at random has at least one 0

To create a PIN that doesn't include any zeroes means choosing each digit from among the 9 non - zero digits. The number of such PINs is

[tex]9^{4}[/tex] = 6,561

The rest of the PINs must then include one or more zeroes, and the number of is

10,000 - 6,561 = 3, 439

If a PIN is chosen at random, the probability that it does include at least one zero is then the ratio

Hence, The final answer is : [tex]\frac{3,439}{10,00} = 0.3439[/tex]  

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Answer:

[tex]y = \dfrac{1}{4} x - 4[/tex]

Step-by-step explanation:

Slope intercept form of line equation is y = mx + b, m = slope, b = y-intercept

Slope of line perpendicular to y =m x + b will have slope   - (1/m)

4x+y=3 can be re-written as
y = -4x + 3

Slope = -4

Slope of line perpendicular to this line is - (1/-4)  = 1/4

Line equation: y = (1/4) x + b

Plug in x, y values from given point into this line equation to find b
-3 = 1/4 x 4 + b

-3 = 1 + b

-3 -1 = b

b = -4

So equation of perpendicular line is y = (1/4)x - 4

Answer:

there is no mode

Step-by-step explanation:

The inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.

We are given the function:

f (x) = 15 - 3 x

Now, we need to find the inverse of the function.

For this, first we write the function as:

y = 15 - 3 x

Now, we will find the function in terms of x

3 x + y = 15

3 x = 15 - y

x = 5 - y/3

So, the inverse will become:

f ⁻¹ (x) = 5 - x/3

g (x) = 5 - x/3

Now, for one one function:

g (x₁) = g (x₂)

5 - x₁/3 = 5 - x₂/3

- x₁ / 3  = - x₂ / 3

x₁ = x₂

So, it is one - one.

So, the inverse is also a function as every element of x only has one image in y.

Therefore, the inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.

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The intensity level of the earthquake was compared to the intensity level of each earthquake below

1) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.

2) The earthquake at New Madrid was of lesser intensity than earthquake at Valdivia.

3) The earthquake at New Madrid was of greater intensity than earthquake at  Charlottesville.

4) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.

In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values.

The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle.

A typical use of the greater than sign is to compare two values, where the first  is greater than the second, or one is greater than the other.

The greater than sign is an approximation of a closing square bracket.

Hence, The magnitude of the earthquake was compared to each earthquake's magnitude above.

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The question is incomplete. The complete question is

In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.

1. magnitude 7.7 in San Francisco, California, in 1906

2. magnitude 9.5 in Valdivia, Chile, in 1960

3. magnitude 3.2 in Charlottesville, in 2001

4. magnitude 6.9 in Kobe, Japan, in 1995

Answer:

Rs 140

Step-by-step explanation:

Rs 25 is the amount of money she bought the apples

Rs 32 is the amount of money she sold the apples

32 - 25 = $7 profit per apple

7 Rs multiplied by 20 apples is equal to Rs 140 in profit.

Hope this helps!

Answer:

27^4

2.74*10^2

4.27*10^2

Step-by-step explanation:

in exponential notation the number is expressed like this.

The number of chair being set up for a round table in a party is 6.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is called as probability.

Given that,

Banquet table rentals are often suited for less formal gatherings as opposed to round tables for formal ones.

Banquet tables are typically 4 feet, 6 feet, or 8 feet long and 30 inches wide. 8-foot tables

The most widely utilized dimension for guest seats. 4 chairs are present.

Eight people can sit comfortably at an 8-foot table.

Although seating can be provided at 4 and 6 foot tables

These sizes are often employed for different objectives.

4 guests may fit comfortably at a 4 foot banquet table, and 6 guests can

Banquet table can comfortably sit 6.

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The relative change in weekly sales is  mathematically given as

relative change= -12.857%

This is further explained below.

This Sale per week after the price decreases

=350-45  

=305

Generally, the equation for relative change is  mathematically given as

[tex]\left(\frac{\text { final Value - Intial value }}{\text { Intial value }}\right) \times 100 \%$[/tex]

Hore final value =305 week

Initial Value =350 week

Relative Change[tex]=\left(\frac{305-350}{350}\right) \times 100[/tex]

[tex]&=\frac{-45}{350} \times 100[/tex] \\

=-12.857%

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It should be noted that writing 6300kg in grams, and giving your answer in standard form is 6.3 × 10^6.

From the information, a bricklayer needs to order 6300kg of building sand. Write 6300kg in grams, giving your answer in standard form.

1 kilogram = 1000 grams

6300 kilograms = x grams

6300 × 1000 = x

x = 6,300,000 grams

Therefore, writing 6300kg in grams, and giving your answer in standard form is 6.3 × 10^6.

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Answer:

3 7/10

Step-by-step explanation:

8 4/5 - 5 1/10

8 8/10 - 5 1/10

8 - 5 = 3       8/10 - 1/10 = 7/ 10

3 7/10

Answer:

[tex] \sf \: 12x−1[/tex]

Step-by-step explanation:

Let's simplify step-by-step.

4(3x+2)−9

Distribute:

=(4)(3x)+(4)(2)+−9

=12x+8+−9

Combine Like Terms:

=12x+8+−9

=(12x)+(8+−9)

=12x+−1

=12x−1

Answer:

Figure Y is not a rotation of figure X because the length of individual side is different.

Step-by-step explanation:

Figure Y is not a rotation of figure X because the length of individual side is different.

If the variation is direct, then the value of y decreases with a decrease in x and increases when x increases.

On the other hand side, if we are following inverse variation then the value of y will decrease if x increases and increase if x decreases.

If there is a constant k that is nonzero and such that y = kx, then the variable y fluctuates directly as x. The expression y = kx is referred to as a direct variation equation, and the variable constant is denoted by the number k.

A function with the following equation as its definition is known as an inverse variation: xy = k , where k is a constant real integer that is not zero. There are several instances when one quantity changes as another does so indirectly.

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Answer:

8.5

Step-by-step explanation:

11-3/2-1

11-1.5-1

9.5-1

8.5

Using the above exponent rule,  the value of t in the given equality [tex]5^3/ 5^9 = 5^t[/tex] will be t = -6.

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

Exponentiation(the process of raising some number to some power) have some basic rules as:

[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]

WE need to find the value of t in the given equality 5^3/ 5^9 = 5^t

Using the above exponent rule, we get

[tex]5^{3 -9 }= 5^t\\\\5^{-6}= 5^t[/tex]

Therefore, compairing both the side we get;

t = -6.

Hence the value of t in the given equality[tex]5^3/ 5^9 = 5^t[/tex]will be t = -6.

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