Solve system of equations using substitution method

2x-3y=6
x + y = -12

Rearranging the equation to solve for the variables gives;

v = d - at^2/t

a = 2d - 2vt/t^2

Given the equation;

d = vt + 1/2 at^2

Let's solve for v

First, collect like terms

vt = d - 1/2 at^2

Now, divide both sides by the coefficient of v which is 't', we have;

vt/t = d - at^2/t

v =

[tex] \frac{d - a {t}^{2} }{t} [/tex]

Let's solve for a

d - vt = at^2/2

cross multiply

2( d - vt) = at^2

expand the bracket

2d - 2vt = at^2

divide both sides by the coefficient of a which is t^2, we have;

2d - 2vt /t^2 = a

a = 2d - 2vt/t^2

Thus, rearranging the equation to solve for the variables gives v = d - at^2/t and a = 2d - 2vt/t^2 respectively.

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Answer:

|x + 1| < 27

-27 < x + 1 < 27

-28 < x < 26

The conjecture of the pattern - 3, 6, - 9, 12 is all the set of series generated by the expression s = (- 1)ⁿ · 3 · n.

In this problem we have a sequence with a pattern, which has to be translated into mathematical expressions. We notice two features of this sequence:

Then, the pattern can be generated by using the following expression:

s = (- 1)ⁿ · 3 · n

Now we check if the pattern is the same as the shown in the question:

n = 1

s = (- 1)¹ · 3 · 1

s = - 3

n = 2

s = (- 1)² · 3 · 2

s = 6

n = 3

s = (- 1)³ · 3 · 3

s = - 9

n = 4

s = (- 1)⁴ · 3 · 4

s = 12

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The logarithm expression as a single logarithm is log 4 70.

Logarithm expression of Log 4 7 + log 4 10 =  log 4 70.

Log 4 7 + log 4 10

The properties of logarithm is product rule.

Log 4 7 + log 4 10 = Log 4 7 * 10

= log 4 70

It should be noted that logarithm, is the exponent or power to which a base must be raised to get a given number.

We can apply the quotient rule to find the differentiation of a function.

In this case, the quotient rule for logarithms states that the log of the logarithm of a quotient is the difference of the logarithms.

Hence, the quotient rule for logarithms states that the log of the logarithm of a quotient is the difference of the logarithms.

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Answer:

The answer is 1000

Step-by-step explanation:

10x10=100

100x10=1000

1000+1=1001

1001-2=999

999+1=1000

Answer:

1000

Step-by-step explanation:

10x10=100

100x10=1000

1000+1=1001

1001+1=1002

1002-2=1000.

therefore the answer is 1000

The velocity of the car at t = 2 seconds is 0 ft/second.

We know that the position equation (in feet) of the race car is:

s(t) = t^2 - 4t + 4

To get the velocity equation we need to find the first derivative of the position equation, we will get:

v(t) = 2t - 4

Now we just need to evaluate this in t = 2 seconds, we will get:

v(2) = 2*2 - 4 = 4 - 4 = 0

The velocity of the car at t = 2 seconds is 0 ft/second.

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Answer:

the shoes

Step-by-step explanation:

the shoes never changed, and the amount money sarah has remaining will depend on the shoes.

Answer:46.08

Step-by-step explanation the only thing you has to do was multiply  your keyword was per  I hope this helps

The equation of the line perpendicular to y = 2x + 2 and passes through (4, 3) is y = - 1 / 2 x + 5

The equation of the line is perpendicular to y = 2x + 2 and passing through the points (4, 3).

Perpendicular lines follows the principle below:

m₁ m₂ = -1

where

Therefore,

2m₂ = -1

m₂ = - 1 / 2

Let's find the y-intercept of the line using (4, 3).

y = - 1 / 2 x + b

3 = - 1 / 2 (4) + b

3 = - 2 + b

b = 3 + 2

b = 5

Therefore, the equation of the line perpendicular to y = 2x + 2 and passes through (4, 3) is y = - 1 / 2 x + 5

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In San Francisco, the tax on a property with a $860,000 assessed value is $12900.

In Tacoma, the tax on a property assessed at $330,000 is $4,950.

The tax rates are proportional to this city.

Now, to find the tax on a property assessed at $860,000.

So, we need to determine the tax rate of Tacoma first.

Tax Rate = Tax / Property assessed × 100.

[tex]Tax {~}rate = \frac{4950}{330000} \times 100[/tex]

Tax rate = 0.015 × 100

Tax rate = 1.5%

From the question, the tax rates are proportional.

Now, we apply the same tax rate as Tacoma in this city:

Tax = tax rate of property assessed.

Tax = 1.5% of $860,000

[tex]Tax=\frac{1.5}{100} \times 860000[/tex]

Tax = 1.5 × 8600

Tax = $12900

Therefore, the tax on property in San Francisco assessed at $860,000 is $12900.

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Answer:

Step-by-step explanation:

3,000 divided by the 500 is 6. It would take 6 days.

When you come across problems like this usually the best way to answer them is d (distance) divided by s (speed, miles per day, miles per hour, miles per second, etc.).

Answer: 3.14

Step-by-step explanation:

Use the algorithm method.

3 . 1 4

6 0 | 1 8 8 . 4

1 8 0 .  

8 . 4

6 . 0

2 . 4 0

2 . 4 0

2 Therefore, 188.4\div 60=3.14188.4÷60=3.14.

3.14

The logarithm is used to define compressed scales, resulting in a decompression of the data is a true statement.

A logarithmic scale is a nonlinear scale often used when analyzing a large range of quantities. Instead of increasing in equal increments, each interval is increased by a factor of the base of the logarithm. Typically, a base ten and base e scale are used.

Data compression is the art of reducing the number of bits needed to store or transmit data. Compression can be either lossless or lossy. Losslessly compressed data can be decompressed to exactly its original value.

Information theory places hard limits on what can and cannot be compressed losslessly, and by how much:

There is no such thing as a "universal" compression algorithm that is guaranteed to compress any input, or even any input above a certain size. In particular, it is not possible to compress random data or compress recursively.

Given a model (probability distribution) of your input data, the best you can do is code symbols with probability p using log2 1/p bits. Efficient and optimal codes are known.

Data has a universal but uncomputable probability distribution. Specifically, any string x has probability (about) 2-|M| where M is the shortest possible description of x, and |M| is the length of M in bits, almost independent of the language in which M is written. However there is no general procedure for finding M or even estimating |M| in any language. There is no algorithm that tests for randomness or tells you whether a string can be compressed any further.

Thus , It is true to say that the logarithm is employed to establish compressed scales, leading to a decompression of the data.

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The solution to the given equation 19= y/5 + 16 is y = 15.

Given the equation in the question;

First reorder the equation by moving all terms not containing y to the right side of the equation.

19 = y/5 + 16

19 - 16 = y/5

y/5 = 19 - 16

Subtract 16 from 19

y/5 = 19 - 16

y/5 = 3

Multiply both sides of the equation by 5

5( y/5 ) = 3 × 5

5y/5 = 15

y = 15

Therefore, the solution to the given equation 19= y/5 + 16 is y = 15.

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Answer:

the mean mark for girls is 86

Step-by-step explanation:

62x20+10xX=70*(10+20)

Answer:

-7390

Step-by-step explanation:

Parenthesis

Exponents

Multiply

Divide

Addition

Subtraction

5-2x924x4-3

First do multiplication or division what ever comes first and then addition or subtraction what ever comes first from left to right.

5-1848x4-3

5-7392-3

-7390

A. The consumers interviewed in this manner can be considered a random sample of the population as a whole.

B. The sample is a random sample of people who go to malls.

C. It should be noted that the sample applies for just for people who go to that mall.

It should be noted that in a random sample, everyone has an equal chance of being selected.

In this case, the consumers interviewed in this manner can be considered a random sample of the population as a whole. Here, everyone had an equal chance of being picked.

In this case, the sample is a random sample of people who go to malls.

It should be noted that 95% of American households shop at malls at least once a year and that two-thirds shop at malls at least once every 2 weeks. This will give the random sample of the people.

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Answer: 5.8%

Step-by-step explanation: .

The rate of acceleration of the skateboarder is 2m/s²

Acceleration can be described as the speed of an object during a period of time

The formula is

v= u + at

v= 40m/s

u= 10m/s

time= 15 seconds

40 = 10 + 15a

40-10= 15a

30= 15a

a= 30/15

a= 2

Hence the rate of acceleration of the skateboarder is 2m/s²

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Answer:

30/5

15/5

-15/5

-10/5

Step-by-step explanation:

The measure of the ∠6 which is interior to 144° measures 36°

An equation is an expression that shows the relationship between two or more numbers and variables.

An angle is formed at a point where two or more lines intersect. We have acute angles, right angle and obtuse angle depending on the angle measure.

From the diagram:

∠6 + 144 = 180° (interior angles are supplementary)

∠6 = 36°

The measure of the ∠6 which is interior to 144° measures 36°

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Answer: [tex]y=\frac{3}{4}x+5.8[/tex]

Step-by-step explanation:

We can think of this as a linear function with the slope being the 3/10 of a mile and the y intercept being the initial amount you can run.

So, using the information about 24 weeks, we get that:

[tex]13=\frac{3}{10}(24)+b\\\\b=5.8[/tex]

So, the equation is [tex]y=\frac{3}{4}x+5.8[/tex]

The surface area of a cylinder = 527.52 feet

A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

The total surface area of the cylinder formula is simply the sum of the base surface area and the lateral surface area:

total area = base area + lateral area ,

or

total area = 2πr² + (2πrh ),

or

total area = 2πr (r + h)

where h= Height

r= Radius

given that

height = 8 feet

base radius = 6 feet

Find the lateral surface area of a cylinder with a base radius of 6 feet and a height of 8 feet.

L.S.A.=2π(6)(8)=96π feet

for the total surface area of a cylinder is T.S.A.=2πrh+2πr².

T.S.A. = 96π + 2π (6²)

T.S.A. = 96π + 72π

T.S.A. =168π

where π= 3.14

T.S.A. = 168×3.14

T.S.A. = 527.52 feet

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The required number of general admissions is 76 and the number of admission with student id is 108.

Here,
let the number of general admissions be x and the number of the admission with student id be y
Using arithmetic operations
According to the question,
x + y = 184  
x = 184 - y  - - -  -(1)
5x + 4y = 812  - - - - (2)
From equation (1)
5 (184 - y) + 4y = 812
920 - 5y + 4y = 812
-y = 812 - 920
-y = 108
y = 108
Put y in equation 1
x = 184 - 108
x = 76

Thus, the required number of general admission is 76, and the number of admission with student id is 108.

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Answer: D 28

Step-by-step explanation:

use the formuls x= -b/2a

the maximum is 28 and the minimum is 2

Answer:

The value of w = 4/5

Step-by-step explanation:

=> -4/5w = -1

=> -4 = -5w

=> 4 = 5w

=> w = 4/5

Answer:

5/4

Step-by-step explanation:

1st and 5th tables represent the same function

To find the two equal functions we will formulate their equations, using the formula [tex]\frac{y-y1}{x-x1} = \frac{y2-y1}{x2-x1}[/tex] where (x1,y1) and (x2,y2) are the endpoints of the equation.

Now finding the equation for each table we get:

Table 1:

(x1,y1) = (4,8) and (x2, y2) = (6,7)

Putting this in the formula we get:

= [tex]\frac{y-8}{x-4} = \frac{7-8}{6-4}[/tex]

So, the equation will be x + 2y = 20

Table 2:

(x1,y1) = (4,5) and (x2, y2) = (6,4)

Putting this in the formula we get:

= [tex]\frac{y-5}{x-4} = \frac{4-5}{6-4}[/tex]

So, the equation will be x + 2y = 14

Table 3:

(x1,y1) = (2,8) and (x2, y2) = (8,5)

Putting this in the formula we get:

= [tex]\frac{y-8}{x-2}=\frac{5-8}{8-2}[/tex]

So, the equation will be x+2y=18

Table 4:

(x1,y1) = (2,10) and (x2, y2) = (6,14)

Putting this in the formula we get:

= [tex]\frac{y-10}{x-2} =\frac{14-10}{6-2}[/tex]

So, the equation will be x-y=-8

Table 5:

(x1,y1) = (2,9) and (x2, y2) = (8,6)

Putting this in the formula we get:

= [tex]\frac{y-9}{x-2}=\frac{6-9}{8-2}[/tex]

So, the equation will be x+2y=20

Hence, table 1 and table 5 represent the same function

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