What is meant by the term formula in mathematics? Give an
example.

Answer:

The answer is in the image above

Answer:

Step-by-step explanation:

The antiderivative for b is definitely incorrect, as stated in the comments section.

[tex]\int\limits {\frac{1}{2x^2}+\sqrt{x} } \, dx \\\frac{1}{2} \int\limits{\frac{1}{x^2} } \, dx+\int\limits {x^{\frac{1}{2}} } \, dx[/tex]  That's a bit more simplified. One more important simplification and then we can integrate one term at a time:

[tex]\frac{1}{2}\int\limits{x^{-2}} \, dx +\int\limits{x^{\frac{1}{2} } \, dx[/tex]  and here we go:

[tex]\frac{1}{2}(\frac{x^{-2+1}}{-2+1})+(\frac{x^{\frac{1}{2}+\frac{2}{2}} }{\frac{1}{2}+\frac{2}{2} })+C[/tex] and

[tex]\frac{1}{2}(\frac{x^{-1}}{-1})+(\frac{x^{\frac{3}{2}} }{\frac{3}{2} })+C[/tex] and finally,

[tex]-\frac{1}{2x}+\frac{2}{3}x^{\frac{3}{2}}+C[/tex]

Answer:

Just study and pay attention in class and take good notes. I would say that you should pay more attention when they teach you the trigonometry unit.

Your answer is in the attachment .

Note: I have only done upto q.n d because you haven't clearly uploaded question of no. e. stay blessed !!!!!!

Answer:

$150.60

Step-by-step explanation:

$984.20-$381.80= $602.40

Take $602.40 and divide by 4 which equals $150.60 which is the 1/4 $ Charlie has in his savings account.

Answer:

Step-by-step explanation:

23550=15000(1+.0475t)

t=12

Answer:

h(-5) = (-2)^2 + 5 = 9

h(-1) = (2)^2 + 5  = 9

(9-9)/4 = 0

average rate of change is 0

Step-by-step explanation:

Answer:

Your final grade will be 78.67 %

Step-by-step explanation:

67% of your grade will be from your test average which is 79 (higher)

33% of your grade will be from your homework average which is 78.

Calculating:

(67×79+33×78) / (67+33) = 7867 / 100 = 78.67

Answer:

-13=5×1+5×4m-2m

-13=5+20m-2m

-13-5=18m

-18=18m

18m=-18

m=18÷18

m=1

Answer:

[tex]\frac{55}{4}[/tex]

Step-by-step explanation:

let the number be n the multiply by - 4 is - 4n and add 5 gives

- 4n + 5 = - 50 ( subtract 5 from both sides )

- 4n = - 55 ( divide both sides by - 4 )

n = [tex]\frac{-55}{-4}[/tex] = [tex]\frac{55}{4}[/tex]

The number is [tex]\frac{55}{4}[/tex] or 13.75 if you prefer

(92.50-55)/15 =2.5 hours

Step-by-step explanation:

92.5 (total) -55 (trip charge) = 37.50(hour charge)

37.50(hour charge)/15{per hour charge)=2.5(hours)

Answer:x+20

Step-by-step explanation:

Answer:

y = -1/2x + 6

Step-by-step explanation:

The slope of a parallel line will remain the same. The only thing that is different is the y-intercept but we can solve that using the point given, the slope, and the slope intercept form equation [ y = mx + b ].

0 = -1/2(12) + b

0 = -6 + b

6 = b

Now input the data we were given and solved for back into the formula.

y = -1/2x + 6

Best of Luck!

Insert grouping symbols to make each number sentence true 3+8-2*5=45

Answer:

3+2+8×5

Answer:

8x-16y

Step-by-step explanation:

Answer:

8x - 16y and a + 3b - 2c

Step-by-step explanation:

(a)

8(x - 2y) ← multiply each term in the parenthesis by 8

= 8x - 16y

(b)

[tex]\frac{6a+18b-12c}{6}[/tex] ← factor out 6 from each term in the numerator

= [tex]\frac{6(a+3b-2c)}{6}[/tex] ← cancel the 6 on numerator/ denominator

= a + 3b - 2c

Answer:

10.71

Step-by-step explanation:

0.15*71.40

Answer:

Hi, There! Leah Is Correct

Step-by-step explanation:

A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all.

____________________________________________________________

-Darkspirit-

Answer:

Both are correct.

Step-by-step explanation:

Repeating decimals are rational.

Answer:

AB= AC+CB

50 = (2x – 2 ) + 4(x+1)

50 = (2x – 2) + ( 4x+4)

50 = 6x +2

6x = 50 – 2

6x = 48

x= 48/6

x= 8

So; x=8 Q.E.D.

I hope I helped you^_^

Answer:

x = 10

Step-by-step explanation:

AC = AB + BC

Substitute the values for the line segments:

50 = (2x) + (x + 20)

50 = 2x + x + 20

Combine like terms:

50 = 3x + 20

Subtract 20 from both sides:

30 = 3x

Divide both sides by 3:

10 = x

Check your work:

50 = 2(10) + 10 + 20

50 = 20 + 30

50 = 50

Correct!

Answer:

13x + 10

Step-by-step explanation:

Rafael's hot-water tank holds:

[tex]17x + 11[/tex]

Gallons of hot water.

Rafael used:

[tex]4x + 1[/tex]

Gallons of hot water.

And we want to determine which binomial represent the amount of hot water remaining in the tank.

The amount remaining R in the tank will be the amount taken by Rafael subtracted from the total amount. Hence:

[tex]\displaystyle R = (17x+11) - (4x + 1)[/tex]

Simplify. Distribute:

[tex]\displaystyle R = (17x + 11) + (-4x - 1)[/tex]

Rearrange:

[tex]R = (17x - 4x) + (11 - 1)[/tex]

Combine like terms:

[tex]R = 13x + 10[/tex]

In conclusion, 13x + 10 gallons remain in the tank.

Hi! I'm happy to help!

This expression is an exponent, or repeated multiplication. 3^3 is three multiplied by itself (3), 3 times, or 3×3×3

So, our non-exponent expression will be 3×3×3.

I hope this was helpful, keep learning! :D

Answer:

137027.1 Rupees

Step-by-step explanation:

(125200+5302) * 0.05 = 6525.1

130502+6525.1 =  137027.1

Answer:

The forest will cover an area of approximately 2994 square kilometers after 10 years.

Step-by-step explanation:

A forest covers an area of 5000 square kilometers. Each year, the area of the forest decreases by 5%. We want to determine its area after 10 years.

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x is the time that has passed (in this case in years).

Since the original area is 5000 square kilometers, let a = 5000.

Each year, the area decreases by 5%. In other words, for each subsequent year, the forest's area will be 100% - 5% = 95% = 0.95 of its previous year. Hence, r = 0.95.

Thus, our function is:

[tex]\displaystyle f(x) = 5000(0.95)^x[/tex]

Then after 10 years (x = 10), the area will be:

[tex]\displaystyle f(10) = 5000(0.95)^{(10)}= 2993.6846...\approx 2994\text{ km}^2[/tex]

In conclusion, the forest will cover an area of approximately 2994 square kilometers after 10 years.

Answer:

3/7

Step-by-step explanation:

21w - 21 = -12

21w = -12 +21

21w = 9

w = 9/21

i.e w= 3/7

Step-by-step explanation:

21w-21= -12

21w= -12 + 21

w=9/21

Answer:

Step-by-step explanation:

Factorize both numbers:

Common factors are:

So HCF is:

[tex]\Large \red \mid \: \underline {\rm {{{\color{blue}{Explanation...}}}}} \: \red \mid[/tex]

As per Euclid Division Algorithm.

[tex] \longrightarrow \: \Large\underbrace {\rm {{{\color{red}{ \: a \: = \: bq \: + \: r \: }}}}} [/tex]

[tex]\large\bf{\purple{ \hookrightarrow \: }} \tt \: \: 900 \: = \: 270 \: \times \: 3 \: + \: 90[/tex]

[tex]\large\bf{\orange{ \implies \: }} \: \:r \: \neq \: 0[/tex]

Again Applying Euclid Division Algorithm

[tex]\large\bf{\purple{ \hookrightarrow \: }} \tt \: 270 \: = \: 90 \: \times \: 3 \: + \: 0[/tex]

[tex]\large\bf{\orange{ \implies \: }} \: \:r \: = \: 0[/tex]

As the reminder is 0 , 90 will be the greatest common divisor for the two given numbers.

[tex]{\boxed{ \Large{ \blue{ \bf{ \underline{ HCF \: = \: 90}}}}}}[/tex]

Answer:

Step-by-step explanation:

Answer:

n+2 represemts the number of sides in the polygon for the nth member of the sequence

Answer:

Step-by-step explanation:

The midpoint formula is

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] and we have the coordinates of the midpoint and the coordinates of one endpoint. Filling that in we have:

[tex](-5,-4)=(\frac{-4+x_2}{2},\frac{-7+y_2}{2})[/tex] and we will solve for the missing values one at a time. x first:

[tex]-5=\frac{-4+x_2}{2}[/tex] and

-10 = -4 + x₂ so

-6 = x₂ and do the same for y:

[tex]-4=\frac{-7+y_2}{2}[/tex] and

-8 = -7 + y₂ so

-1 = y₂

Thus, the coordinates of point g are (-6, -1)

First off, we factor out the expression:

[tex] \displaystyle \large{y = 2 {x}^{2} - 12x + 16} \\ \displaystyle \large{y = 2 ( {x}^{2} - 6x + 8) }[/tex]

In the bracket, separate 8 out of the expression.

[tex] \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}[/tex]

In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:

[tex] \displaystyle \large{ {(x - 3)}^{2} = {x}^{2} - 6x + 9}[/tex]

So we add +9 in x^2-6x.

[tex] \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}[/tex]

Convert the expression in the small bracket to perfect square.

[tex] \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}[/tex]

Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.

[tex] \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}[/tex]

Then we distribute 2 in.

[tex]\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ [/tex]

[tex]\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }[/tex]

Remember that negative multiply positive = negative.

Hence the vertex form is y = 2(x-3)^2-2 or first choice.