How do we solve the formula for the indicated variable

Answer:

x = 12

Step-by-step explanation:

First, distribute the 3 into the parentheses:

3(x-2) = 2x+6 ----> 3x-6 = 2x+6

Next, combine like terms by adding 6 to both sides of the equation:

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

Then, subtract 2x from both sides:

3x = 2x+12 ----> 1x = 12

Finally, divide both sides by 1 to get x by itself:

x = 12

(4,5) i'm pretty sure I can't explain why but just go with it

Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.

To solve an algebraic word problem:

Define a variable.

Write an equation using the variable.

Solve the equation.

If the variable is not the answer to the word problem, use the variable to calculate the answer.

To know about algebra you have to know about your Arithmetic.

Remember PEMDAS.

Get Positively Comfortable with Negative Numbers.

Show Your Work.

Don't Let the Letters Scare You.

Formulas Are Your Friends.

Be Sure to Answer the Right Question.

Work Practice Problems.

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Answer:

Step-by-step explanation:

180-degree rotation

I explained previously, but I will explain again.

A 180-degree rotation is just a switch of signs on the numbers

Explanation:

The distance that Nathan can ride his bike is 2 miles.

The rate is the total distance per time. Rate is determined by dividing the total distance travelled by the total time travelled.

Rate = total distance / total time.

Distance = rate x time

The rate is in miles per hour while the time given is in minutes. Thus, minutes has to be changed to hour. To do this, divide 24 minutes by 60.

60 minutes = 1 hour

24/ 60 = 2/5

Distance = 2/5 x 5= 2 miles

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We need to know about asymptotes to answer this question. The vertical asymptote is x=4/3 and the horizontal asymptote is y=2/3

When the graph of a function lies very close to the axis and extends to infinity it is called an asymptote. Vertical asymptote is a vertical line that directs but does not form a part of the graph of a function. Horizontal asymptote is a horizontal line that shows how the function behaves at extreme edges. Horizontal asymptote exists for functions whose numerator and denominator have same degree or degree of numerator is less than numerator of denominator.

f(x)=2x-7/3x-4

The horizontal asymptote of the function can be given by dividing the leading coefficients.

HA=2/3

The vertical asymptote can be found by equating the denominator to zero.

3x-4=0

x=4/3

Therefore the horizontal asymptote is y=2/3 and the vertical asymptote is x=4/3.

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The equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.

Given that

10^4 = 10000 - - - - - -( 1 )

We have [tex]a^{y}[/tex] = x - - - - - ( 2 )

Comparing ( 1 ) and ( 2 ) we get

a = 10, y = 4, x = 10000

The logarithmic form is written as logₐ (x) = y .It is rearrangement of the exponential form [tex]a^{y}[/tex] = x.

By logarithmic definition

y = logₐ (x)

so we got 4 = log₁₀ (10000)

Therefore, the equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.

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Answer:

16<24

Step-by-step explanation:

4+(4×3)<(12×2)

4+12<24

=16<24

Answer:

65-72

Step-by-step explanation:

The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.

The value that approaches the output for the given input value. Limits are a very important tool in calculus.

The graph of the function is shown below.

The function is a piecewise function. The function is continuous between o to a, a to b, and b to till ∞.

The value of the function at b will be 1 which can be shown as,

[tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex]

The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.

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The annual premium of Tom Harris is $29.05

Annual premium is the amount of money that policyholder has to pay in a policy year.

Annual formula = (face value of policy per $1000)* (rate of insurance)

Given that Tom Harris is twenty four years old man want to purchase a $7000 for a ten year term insurance.

From the given table we can say that the rate of insurance for a 24 year old man per $1000 for a 10 year terms is 4.15

Face value of insurance = $7000

Face value of insurance per $1000 = 7000/1000 =$7

Then the annual premium = $7 * 4.15 =$ 29.05

Therefore, the annul premium paid by Tom Harris is $29.05

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Answer:

Step-by-step explanation:

Martha spent 1/6 of her pocket money on magazines.

The correct option regarding the bank amount as a function of time is:

This is an exponential function because there is a common ratio in the balance between the weeks.

For this problem, the differences are given as follows:

The ratios are given as follows:

Due to the same ratios, an exponential function should be used, and the correct option is given by:

This is an exponential function because there is a common ratio in the balance between the weeks.

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Answer:c

Step-by-step explanation:

At an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.

The exponential constant, denoted by the symbol e, is an essential mathematical constant. Its value is approximately equal to 2.718. This value occurs very frequently in mathematics when it is used to model physical and economic phenomena.

Here, we are given an exponential function- p = 101.3[tex]e^{-0.001h}[/tex]

where p = atmospheric pressure in pascals

h = altitude in meters.

If the altitude is 500m

h = 500

Then,

p = 101.3 [tex]e^{-0.001 * 500}[/tex]p

=  101.3 [tex]e^{-0.5}[/tex]p

=  101.3/ [tex]e^{-0.5}[/tex]p

= 101.3/ 1.648p

= 61.46

Thus, at an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.

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Based on the height that the bean plant grew after a certain number of days, the ratio of feet to days is equivalent.

The bean plant was able to grow 15 feet in 8 days and then doubled to 30 feet when the number of days doubled to 16 days.

The ratio of feet to days can be found as:

(Number of feet after 16 days / Number of feet after 8 days) : 16 days / 8 days

Solving for the ratio of feet to days gives:

30 / 15 : 16 / 8

2 : 2

The ratio of feet to days is the same which means that it is equivalent.

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The difference is 5ab + 7a + 13

An arithmetic operation is specified by combining operands with one arithmetic operator. Arithmetic operations can also be specified by the ADD, SUBTRACT, DIVIDE, and MULTIPLY

given:

(9ab+7a-7) (4ab-5)

So, the difference is

(9ab+7a-7) - (4ab-5)

=9ab + 7a - 7 -4ab + 20

=9ab - 4ab +7a -7 +20

=5ab + 7a + 13

Hence, the difference is 5ab + 7a + 13.

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If B is collinear and between points A and C, then the value of x is 5 and the value of AC is 50.

Collinear points refers to the points that lies on the same straight line.

If B is collinear with points A and C, and lies between them, then the sum of the distance from A to B and the distance from B to C is equal to the distance from A to C.

AB + BC = AC

Given:

AB = 12

BC = 8x - 2

AC = 10x

Substitute the expressions given to the equation and solve for x.

AB + BC = AC

12 + 8x - 2 = 10x

8x - 10x = 2 - 12

-2x = -10

x = 5

Substitute the value of x in the expression for AC.

AC = 10x

AC = 10(5)

AC = 50

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Answer: $3.15

Step-by-step explanation: 9% of 34.90 is 3.15

Answer: 50,000 pennies

Step-by-step explanation: there are 100,000 centimeters in a kilometer, since a penny is 2 centimeters in length, divide 100,000 by 2 t get 50,000

The distance of both the planes from the starting point will be  1029 miles.

This is a question of time, speed and distance.

Given that:-

Speed of jet plane = 480 mph

Speed of propeller plane = 200 mph

Also, the propeller plane has a 3 hour head start.

We have to find the distance of both the planes from the starting point.

When the jet plane overtakes the propeller plane both of them would have covered the same distance.

Let the time taken by the jet plane to overtake the propeller plane be t hours.

Hence, the propeller plane would have travelled for (t+3) hours.

Hence, we can write,

480*t = 200*(t+3)

480t = 200t + 600

280t = 600

t = 600/280 = 15/7 hours.

Hence, distance from both the planes from the starting point = (15/7)*480 = 1028.57 miles = 1029 miles.

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The number of vans and buses conveying the students to the field trip is 3 and 19 respectively

let

x + y = 19

7x + 25y = 421

From (1)

x = 19 - y

Substitute x = 19 - y into (2)

7x + 25y = 421

7(19 - y) + 25y = 421

133 - 7y + 25y = 421

- 7y + 25y = 421 - 133

18y = 288

y = 288/18

y = 16

Substitute y = 16 into (1)

x + y = 19

x + 16 = 19

x = 19 - 16

x = 3

Therefore, there are 3 vans and 16 buses conveying the be students to the field trip.

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The fraction -1 2/5 is modeled on the number line by: graph A.

A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

In this scenario, we can reasonably infer and logically deduce that the fraction -1 2/5 is modeled on the number line by graph A because each interval increases by 2/5 or 0.4.

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The slope of a line is y=mx+c, where m is the slope. The lines is perpendicular to y = 1/4x -3 is Y=-4x+6.

The slope of a line is y=mx+c, where m is the slope.

The given line is y = 1/4x -3.

slope m1=1/4.

slope of second line=-(1/m)

=-(1/1/4)

=-4

point slope intercept form is y-y1=m(x-x1)

Equation of the perpendicular line passing through point (0,6) is

y-6=-4(x)

y=-4x+6

Therefore the line perpendicular to y = 1/4x -3 is Y=-4x+6.

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The length of the rectangle = 21 cm

and the width of the rectangle = 19 cm

In this question, the length and width of a rectangle are consecutive odd integers.

Let n, n + 2 be the width and the length of a rectangle.

The perimeter of the rectangle is 80 centimeters.

Using the formula of the perimeter of the rectangle ,

P = 2 × [n + (n + 2)]

80 =  2(2n + 2)

40 = 2(n + 1)

20 = n + 1

n = 19

This means, the width of the rectangle is 19 centimeters.

And the length = n + 2

                         = 19 + 2

                         = 21 cm

Therefore, the length of the rectangle = 21 cm

and the width of the rectangle = 19 cm

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Answer:

Step-by-step explanation:

The reason why you should save money because if you spend all of your money you won't able to take care of yourself, your house, or have nothing to do

Answer:

65 + |-5| = 70, 65 is the farthest away from 0

Step-by-step explanation:

The equation of the parabola in discuss such that the parabola has a vertex at (2, 3) and passes through (0, 2) is; y = (-1/4) (x - 2)² + 3.

It follows from the task content that the equation of the parabola whose vertex is at (2, 3) and passes through (0, 2) is to be determined.

Since, the vertex form equation of a parabola is;

y = a (x-h)² + k

where the vertex is; (h, k) which is (2, 3) in this scenario.

Therefore, we have;

y = a (x - 2)² + 3

Ultimately, to find the value of a; substitute; x = 0 and y = 2 from the point (0,2) into the equation;

2 = a (0-2)² +3

-1 = 4a

a = -1/4.

Ultimately, the equation of the parabola as required in the task content is;

y = (-1/4) (x - 2)² + 3

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points of discontinuity for each rational function. y=x+5 / x²+9 x+20 is x = -4

Given,

y=x+5 / x²+9 x+20

It can be expressed in the form of -

⇒ y = (x+5) / (x+5) (x+4)

⇒ y = 1 / (x+4)

The function will be undefined if the denominator will be 0

⇒ x+4 = 0

⇒ x = -4

So, we can conclude that the given function will be having points of discontinuity as x = -4

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