Solve the linear system
4x +9y = -72
4x +9y = 54

This needs to be answered in x and y

The distance between Earth and Mars in the standard form is               43, 500, 000 miles.

The correct answer is an option (C)

In this question we have been given the distance between Earth and Mars.

The distance between Earth and Mars is approximately 4.35 × 10^7 miles.

We need to write above distance between Earth and Mars in the standard form.

So, we get an expression,

4.35 × 10^7 miles

= 435 × 10^5 miles

= 435 × 100, 000 miles

= 43, 500, 000 miles

Therefore, the distance between Earth and Mars in the standard form is 43, 500, 000 miles.

The correct answer is an option (C)

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1) The time taken is 2.47 s

2) The time taken is 21.4 s

3) The time taken is 1.2 s

4) The time taken is 81 s

5) The time taken is 5.7 s

Using the equation of kinematics under gravity we knw that;

h = ut + 1/2 gt^2

h = height from which it fell

u = initial velocity

g = acceleration due to gravity

t = time taken

Given the fact that the objects were dropped from a height u = 0 m/s

h = 1/2 gt^2

t = √2h/g

1) √2 * 30/9.8

t =2.47 s

2) t = √2 * 2250/9.8

t = 21.4 s

3)  t = √2 * 7/9.8

t = 1.2 s

4) t = √2 * 32000/9.8

t = 81 s

5)  t = √2 * 160/9.8

t = 5.7 s

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Answer:13

Step-by-step explanation:

68-54=14

14-1=13

Answer:

k= 7

Step-by-step explanation:

First let's add like terms: a+b+a=c: a²+b=c

k+9+5=21

k+14=21

Subtract 14 from both sides of the equation

k+14-14=21-14

K=7

Hi!

[tex]\tt{9+k+5=21}[/tex]

Step 1: Combine like terms.

[tex]\tt{9+5+k=21}[/tex]

[tex]\tt{14+k=21}[/tex]

Step 2: Subtract 14 from both sides.

[tex]\tt{k=7}[/tex] [tex]\checkmark[/tex]

Have a great day!

Hope that helps. :)

-Stargazing & daydreaming -

Answer: B(4,-4)

Step-by-step explanation:

M(3,0)     A(2,4)     B(x,y)=?

[tex]\displaystyle\\x_M=\frac{x_A+x_B}{2} \\\\Multiply\ both\ parts\ of\ the\ equation\ by \ 2:\\2x_M=x_A+x_B\\2x_M-x_A=x_A+x_B-x_A\\2x_M-x_A=x_B\\x_M=3\ \ \ \ \ x_A=2\\Hence,\\2*3-2=x_B\\6-2=x_B\\4=x_B\\Similarly:\\2y_M-y_A=y_B\\y_m=0\ \ \ \ \ y_A=4\\Hence,\\2*0-4=y_B\\0-4=y_B\\-4=y_B\\Thus,\ B(4,-4)[/tex]

Answer:

y=2x+2

Step-by-step explanation:

y=mx+b where:

m=slope; b=y intercept

Therefore, simply plug in values for (m) and (b)

(m=2); (b=2)

and you're left with the equation (y=2x+2)

Answer:

sorry if wrong again but for a put (r+y) (a+b)

for b put (pq-[tex]r^{2}[/tex]) x (9-1)

Step-by-step explanation:

the correct value for x is -1.2, 2.2

Given 5 | 2x - 1 | + 20 = 3

Modulus of a  number

The modulus or absolute value, of a number, denoted |x+y| is calculated as

|x + y | =1

x + y   = ±1

We need to solve for the value of x

5 | 2x - 1 | = 3 - 20

5 | 2x - 1 | = -17

| 2x - 1 | = - 17 / 5

| 2x - 1 | = - 3.4

2x - 1 = ± (- 3.4)

2x - 1 = -3.4            2x -1 = 3.4

2x = - 3.4 + 1           2x = 3.4 + 1

2x = - 2.4                2x = 4.4

x = - 1.2                     x = 2.2

Therefore, the value for x is -1.2, 2.2

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Answer:

So a cube has all the same edge lengths and since the cube has an edge length of 3

you would just do:

3•3•3

Which is 27

Answer:

18, 20 and 22.

Step-by-step explanation:

Let the lowest number be n, then:

n + n + 2 + n + 4 = 60

3n + 6 = 60

3n = 54

n = 18.

So the other 2 are 20 and 22.

Answer: x=-1/7

Step-by-step explanation:

11-10x-7-4x=6

11-7-10x-4x=6

4-14x=6

-14x=2

x=-1/7

Answer:

4/8, 4/6, 3/4

Step-by-step explanation:

3/4 = 18/24

4/6 = 16/24

4/8 = 12/24

18>16>12

From the arc length given radius yielded is 22.91 cm.

What is the arc length?

The primary angle:

40°

Arc size

20 cm

Recall the arc length formula.

[tex]l=(\frac{Theta}{360} )*(2\pi r)[/tex]

Inserting the values:

20 =[tex]\frac{40}{360} *(2\pi r)[/tex]

[tex]r=\frac{36(20)}{10\pi }[/tex]

=72/π

=22.918cm the radius is.

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The current price of the item = 400 dollars

The price in 8 years from today = 543.23 dollars

Given the rate of inflation = 3.9%

The exponential function modelling the future price, p(t) in t years for a certain item is, [tex]p(t)=400(1.039^t)[/tex]

We have to find the current price of the item. This is given by substituting t = 0 in p(t).

That is, p(0) = 400 x 1 = 400 dollars

Therefore current price = 400 dollars

To find the price of the product in 8 years, substitute t = 8 in p(t).

That is, p(8) = [tex]400(1.039^8)[/tex] = 543.23 dollars

Therefore, the future price of the item in 8 years = 543.23 dollars

The question is incomplete. Find out the complete question below:

If the rate of inflation is 3.9% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)= 400(1.039^t).Find the current price of the item and the price 8 years from today.

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A = \frac{hb_{1} }{2} +  \frac{hb_{2} }{2}  is the solution of this linear equation.

What in mathematics is a linear equation?

Apply the distributive property.

A = [tex]\frac{1}{2} . ( hb_{1} + hb_{2} )[/tex]

Apply the distributive property

A = [tex]\frac{1}{2} ( hb_{1} ) + \frac{1}{2} hb_{2}[/tex]

Multiply [tex]\frac{1}{2}( hb_{1} )[/tex]

combine h and 1/2

A =[tex]\frac{h}{2} b_{1} + \frac{1}{2} ( hb_{2} )[/tex]

[tex]A = \frac{hb_{1} }{2} + \frac{hb_{2} }{2}[/tex]

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Answer:

-125z³

Step-by-step explanation:

cube each value

(-)³x(5)³x(z)³

negative sign multiplied by three is negative

- x - x - = -

5 x 5 x 5 = 125

z x z x z = z³

answer = -125z³

Answer:

10 and 1/2 for the first, and 3 and 3/4 for the second

Step-by-step explanation:

Answer:-5 1/3 is repeating and 1 1/4 is  terminal

Step-by-step explanation:

Answer: Terminal

Step-by-step explanation: yw :)

Answer:

3

Step-by-step explanation:

Rosario: (78+77+64+86+70)/5=75

Enrique: (90+61+79+73+87)/5=78

3

The percentage of error in Pansy's measurement is 14.67%

In the given statement is :

Pansy measured the height of a window frame as 5.12 feet, but the actual height was 6 feet.

We know that

Percentage error can be calculated using the formula: (what was measured - the actual measurement) / actual measurement × 100%.

Thus:

The height that was measured = 5.12 feet

Actual measurement of the height = 6 feet

Percentage error = (6 - 5.12) / 6 × 100

Percentage error = 14.67

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Answer:

D. (A U C) ∩ B

Step-by-step explanation:

12.

A = {-2, -1, 0, 1}

B = {0, 1, 2, 3}

C = {-2, 0, 2, 4}

A. A U B = {-2, 1, 0 , 1, 2, 3}

B. A U (C ∩ B} = A U {0, 2} = {2, 1, 0, 1, 2}

C. B ∩ C = {0, 2}

D. (A U C) ∩ B = {-2, -1, 0, 1, 2, 4} ∩ {0, 1, 2, 3} = {0, 1, 2}

Answer:to answer this question you have to look at what the relationship is between tones of sugar and the equation C(n) = 6,500 + 225n. The question gave you a hint in parenthesis in the form of (n) tons. This statement means that the amount of sugar is n so for question 1 the 13 tons is the n value.

Q1:

C(13) = 6,500 + 225*13

C(13) = 6,500 + 2,925

C(13) = 9,425

so what does the 9,425 mean? This is the cost to transport 13 tons of sugar.

Q2:

so this part n is unknown and we are given the C(n) number.

11,450 = 6,500 + 225n

subtract the 6500 from both sides

11,450 - 6,500 = 225n

evaluate

4,950 = 225n

I don't like the n on the right side so I am going to rewrite the equation

225n = 4,950

divide by 225

n = 4,950/225

evaluate

n = 22

So this result means that the company would transport 22 tones of sugar.

Have a great day!

Step-by-step explanation:

Answer:

f = g - an

Step-by-step explanation:

f + an = g

To isolate f, we need to do inverse (opposite) operation for an.

The opposite of +an is -an

f = g - an

Hope this helps :)

Have a great day!

Answer:

Step-by-step explanation:

During those 2 hours 24 more seagulls arrived.

Answer:

it is 12 seagulls per hour

Step-by-step explanation:

Answer:

noooo

Step-by-step explanation:

Applying the rule of modulus for given values, the expression will result to 20.

The modulus of a value for example |a|=a if a is greater than or equal to zero

and also

|a|=-a if a is less than zero

In the expression given; the modulus of -6 written as

|-6|=-(-6) this is because the value is less than zero

The modulus of 2 written as; |2|=2 this is because the value is greater than zero. and;

|The modulus of -14 written as; |-14|= -(-14) since the value is less than zero.

Hence, we can rewrite the expression as;

we deal with multiplication first following the rules of BODMAS

2×-(-6)-3×2+[-(-14)]

2×6-6+14

and thus adding values

12+14-6

and finally we subtract;

26-6

which will results to the solution of 20.

In order for f(x) to be a linear function, determine the value of k in the data set.

x = {-7, -2, 2, 5}

f(x) = {-15, k, 3, 9}

The value of k is {-5}.

Given that to find the value of k in the data set such that the data set represents a linear function.

Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.

Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}

The slope of the function,

(x, f(x)) = (2,3) and (5,9)

Slope formula is m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Slope m= [tex]\frac{9-3 }{5-2}[/tex]

Slope m=[tex]\frac{6}{3}[/tex]

Slope m=2.

Using the point slope form, determine the linear function's equation.

[tex]y-y_{1} =m(x-x_{1})[/tex]

Here, [tex](x_{1},y_{1})=(-7,-15)[/tex] and m=2

We get

y + 15 = 2 (x + 7)

y = 2x - 1

Now at x = -2 and f(x) = k

k = 2(-2) - 1

k = -4-1

k=-5

Therefore, the value of k is -5.

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The statement "the difference between cross-sectional and time series data is whether the data is evaluated at a single point in time or multiple factors in time" is true.

The distinction between cross-sectional data and time-series data is that time-series data takes into account the identical variables over a period of time, whereas cross-sectional data makes use of specific records for a specific factor in time.

A data set may be both time series and cross sectional.

When the records of go sectional records is regressed, the defined and explanatory variables are all related to the identical single length or point in time.

Time-series and cross-section (TSCS) data collectively are normally analyzed in political technology and associated disciplines.

Therefore, the statement "the difference between cross sectional and time series data is whether the data is evaluated at a single point in time or multiple factors in time" is true.

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Answer:

Step-by-step explanation: