Select the correct answer.
Which exponential equation is equivalent to this logarithmic equation?
log_2 x = 24
A. x^24 = 2
B. x^2 = 24
C. 2^24 = x
D. 2^x= 24

Answer:

[tex]x = \frac{4}{3}- 1[/tex]

x=4/3 , -1

Answer:

Its C: 12 units × 8 units are the dimensions of the rectangle

Step-by-step explanation:

Answer: 27090 is invested. part at 13% part at 10% the interest earned at 13% exceeds the interest earned at 10% by 440.16 how much is invested at each rate.

Answer:

204

Step-by-step explanation:

Answer:

204

Step-by-step explanation:

Given the following question:

[tex]10\frac{2}{3} \times3\times6\frac{3}{8}[/tex]

In order to solve we will convert the mixed numbers into improper fractions and then solve by multiplying the numerators by the numerators and multiplying the denominators by the denominators.

[tex]10\frac{2}{3} \times3\times6\frac{3}{8}[/tex]
[tex]10\frac{2}{3} \times3[/tex]
[tex]10\frac{2}{3} =3\times10=30+2=32=\frac{32}{3}[/tex]

[tex]3=\frac{3}{1}[/tex]

[tex]\frac{32}{3} \times\frac{3}{1}[/tex]
[tex]32\times3=96[/tex]
[tex]3\times1=3[/tex]
[tex]=\frac{96}{3}[/tex]

[tex]\frac{96}{3}\times6\frac{3}{8}[/tex]
[tex]6\frac{3}{8} =8\times6=48+3=51=\frac{51}{8}[/tex]
[tex]\frac{96}{3}\times\frac{51}{8}[/tex]
[tex]96\times51=4896[/tex]
[tex]3\times8=24[/tex]
[tex]=\frac{4986}{24}[/tex]

Simplify by reducing:
[tex]=\frac{4986}{24}\div2=\frac{2493}{12}[/tex]
[tex]=\frac{2493}{12}[/tex]
[tex]\frac{2493}{12}[/tex]
[tex]=\frac{2493}{12}=2493\div12=204[/tex]
[tex]=204[/tex]

Your answer is indeed "204."

Hope this helps.

Answer: (1,4) (2,7) (3,10)

HOpE iT hElpS

plS mArK As bRaiNlieSt -wiggly

Step-by-step explanation:

Answer:

5

4x^11*y^6

In words:

5 over 4x to the 11th power times y to the 6 power.

Step-by-step explanation:

simplify from original to this:

5x^9*y^6

4x^20*y^12

=

5y^6

4x^11*y^12

=

5

4x^11*y^6

Answer:

[tex]46\frac{1}{8}[/tex]

Step-by-step explanation:

Formulate

[tex]1845\div40[/tex]

Calculate

[tex]\frac{1845}{40}[/tex]

Cross out the common factor

[tex]\frac{369}{8}[/tex]

Write [tex]\frac{369}{8}[/tex] as a mixed fraction

[tex]46\frac{1}{8}[/tex]

I hope this helps you

:)

Solution:

Step-1: Use point slope form.

Step-2: Identify the equation of the line.

Option B is correct.

Equation in point slope form

[tex]\\ \rm\Rrightarrow y-4=3(x-2)[/tex]

[tex]\\ \rm\Rrightarrow y-4=3x-6[/tex]

[tex]\\ \rm\Rrightarrow 3x-y-6+4=0[/tex]

[tex]\\ \rm\Rrightarrow 3x-y-2=0[/tex]

Answer:

(3/2, -1/2)

Step-by-step explanation:

add the 2 inequalities together.

you get 2X<3 so x<3/2. plug X back in and solve for y and you get y= -1/2

Answer:

16+ 2x

Step-by-step explanation:

2(10) +2(x-4)

20 + 2x -8

16+ 2x

Answer:

divide it into smaller shapes and find the area then find the sum

Answer:

180 cm³

Step-by-step explanation:

A rectangular prism with length, L, width, W, and Height, H, has a volume, V, given by the formula below.

V = LWH

Think of this solid as being a rectangular prism with a smaller rectangular prism taken out of the top right corner.

V = 6 cm × 5 cm × 8 cm - 3 cm × 5 cm × 4 cm

V = 240 cm³ - 60 cm³

V = 180 cm³

Answer:

220.35

Step-by-step explanation:

Think of this rectangle of as two horizontal rectangles. The area of the bottom one is expressed by 17.4*12

The area of the top rectangle can be expressed by 3.3*3.5, as 17.4-14.1=3.3 and 15.5-12=3.5.

Add the products for the whole area.

Answer:

the answer send me a 100dollar gift card

Answer:

y=2x+3

Step-by-step explanation:

y=mx+b

Answer:

y=$3 + $2x.

Step-by-step explanation:

y=3+2x. Make a table, at week 1 Nate has $2 + the $3 he started with. At week 2, Nate has $4 plus the $3 he started with.  And so on.  Plug the number of weeks in for x and solve for y for the total at any number of weeks given.

Answer:

r = 7

Step-by-step explanation:

Calculate the slope using the slope formula then equate to - [tex]\frac{1}{4}[/tex]

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, r ) and (x₂, y₂ ) = (2, 5 )

m = [tex]\frac{5-r}{2-(-6)}[/tex] = [tex]\frac{5-r}{2+6}[/tex] = [tex]\frac{5-r}{8}[/tex] , then

[tex]\frac{5-r}{8}[/tex] = - [tex]\frac{1}{4}[/tex] ( multiply both sides by 8 to clear the fractions )

5 - r = - 2 ( subtract 5 from both sides )

- r = - 7 ( multiply both sides by - 1 )

r = 7

Answer:

[tex]\displaystyle 7[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m\\ \\ \frac{-r + 5}{6 + 2} = m \Rightarrow \frac{-r + 5}{8} \hookrightarrow -\frac{2}{8} = -\frac{1}{4} \\ \\ \boxed{7 = r}[/tex]

I am joyous to assist you at any time.

Answer:

see explanation

Step-by-step explanation:

a represents adults and c represents children , then the system of equations is

a + c = 35 → (1)

12a + 7c = 315 → (2)

Answer:

a + c = 35 → (1)

12a + 7c = 315 → (2)

Step-by-step explanation:

a + c = 35 → (1)

12a + 7c = 315 → (2)

Relative error = absolute error / measured speed

Relative error = 1/52 = 0.01923

Percent = 0.01923 x 100 = 1.923%

Rounded to nearest tenth = 1.9%

Answer:

x-intercept is 5

y-intercept is -6

Step-by-step explanation:

To find x-intercept put y=0

since 6x-5y=30 then 6x=30

x=30/6 = 5

To find y-intercept put x=0

since 6x-5y=30 then -5y=30

y=30/-5 = -6

Answer:

[tex]\boxed{a=2,\:b=4}[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}3a+5b=26\\ a+5b=22\end{bmatrix}[/tex]

Isolate a from 3a + 5b = 26,

[tex]a=\cfrac{26-5b}{3}[/tex]

[tex]\begin{bmatrix}\cfrac{26-5b}{3}+5b=22\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\cfrac{26+10b}{3}=22\end{bmatrix}[/tex]

Now, Isolate b for  

[tex]\cfrac{26+10b}{3}=22\:\:\boxed{b=4}[/tex]

Now, Substitute b=4

[tex]a=\cfrac{26-5\times \:4}{3}[/tex]

[tex]\cfrac{26-5\times \:4}{3}\:\:\boxed{a=2}[/tex]

[tex]\boxed{a=2,\:b=4}[/tex]

~

Answer:

It's asking what 3^k+2 is in terms of m. That is where the 2 comes from.

Please let me know if this helped <3

Answer:

Answer is A

Step-by-step explanation:

X is below -3

Answer:

x>3=2>3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x + 10 = 20\\x = 20 - 10\\x = 10[/tex]

Answer:

10

Step-by-step explanation:

x+10=20

x=20-10

=10

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

- I have used different colours for indicating different process

- I used brown colour to indicate steps

- I used green colour for explaining solution

- Pink colour for known properties of integration

- Purple colour for the middle steps that are optional.

[Note :- For solving such questions it is mandatory that you should know all the functions and it's derivatives ]

[tex]\sf{=}{\sf{\dfrac{ x^{2}}{2}}}{\sf{ + 7x + 67x .In| x - 4 | - 30.In| x - 3 | + c }}[/tex]

Answer:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}[/tex]

Step-by-step explanation:

To find an integration of this function, first, you must know these integration methods and differences of them.

These methods above are common when it comes to integrating fractional functions, except there are differences when to use these methods.

Examples (of these integrands that require partial fraction technique)

[tex]\displaystyle \large{\int \frac{3}{x^2-5x+6} \ dx}\\\displaystyle \large{\int \frac{x+2}{x^2-4} \ dx}[/tex]

Examples (of these integrands that require long division)

[tex]\displaystyle \large{\int \frac{x^2+5x+6}{x+2} \ dx}\\\displaystyle \large{\int \frac{x^4+3}{x} \ dx }[/tex]

Therefore, from the given integral, the integrand requires long division method. (See attachment for long division.)

After long division, we should get:

[tex]\displaystyle \large{\int x+7+\frac{37x-81}{x^2-7x+12} \ dx}[/tex]

Recall important properties of integral such as:

[tex]\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}[/tex]

Hence:

[tex]\displaystyle \large{\int x \ dx + \int 7 \ dx + \int \frac{37x-81}{x^2-7x+12} \ dx}[/tex]

Recall important integration formula for polynomial and constant:

[tex]\displaystyle \large{\int x^n \ dx = \frac{x^{n+1}}{n+1} + C}\\\displaystyle \large{\int x \ dx = \frac{x^2}{2} + C}\\\displaystyle \large{\int k \ dx = kx + C \ \ \tt{(k \ \ is \ \ a \ \ constant.)}[/tex]

Therefore:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}[/tex]

From the boxed integral above, we cannot evaluate it by default. From what I said, if the degree of numerator is less than the degree of denominator, we’ll use partial fraction technique.

Therefore, factor the denominator:

[tex]\displaystyle \large{\frac{37x-81}{(x-4)(x-3)}}[/tex]

Set to A/x-4 and B/x-3

[tex]\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} = \frac{A}{x-4} + \frac{B}{x-3}}[/tex]

Multiply both sides by (x-4)(x-3).

[tex]\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} \cdot (x-4)(x-3)= \frac{A}{x-4} \cdot (x-4)(x-3) + \frac{B}{x-3} \cdot (x-4)(x-3)}\\\displaystyle \large{37x-81= A(x-3) + B(x-4)}\\\displaystyle \large{37x-81= Ax-3A+Bx-4B}\\\displaystyle \large{37x-81= (A+B)x-(3A+4B)}[/tex]

Then compare the coefficients:

[tex]\displaystyle \large{\left \{ {{A+B=37} \atop {3A+4B=81}} \right}[/tex]

Solve the simultaneous equation for A and B.

[tex]\displaystyle \large{\left \{ {{A=37-B} \atop {3A+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {3(37-B)+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111-3B+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111+B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=81-111}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=-30}} \right}\\\displaystyle \large{\left \{ {{A=67} \atop {B=-30}} \right}\\[/tex]

Therefore, A = 67 and B = -30. Substitute the values in:

[tex]\displaystyle \large{\int \frac{67}{x-4}-\frac{30}{x-3} \ dx}\\\displaystyle \large{\int \frac{67}{x-4} \ dx -\int \frac{30}{x-3} \ dx}[/tex]

Recall the integration formula for above:

[tex]\displaystyle \large{\int \frac{k}{x-a} \ dx = \int k \cdot \frac{1}{x-a} \ dx = k\ln |x-a| + C}[/tex]

Therefore:

[tex]\displaystyle \large{\int \frac{37x-81}{x^2-7x+12} \ dx = \int \frac{67}{x-4}-\frac{30}{x-3} \ dx = 67\ln |x-4| - 30\ln |x-3|}[/tex]

Back from this:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}[/tex]

Substitute in:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}[/tex]

Therefore the solution is:

[tex]\displaystyle \large \boxed{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}[/tex]

Answer:

58.45

Step-by-step explanation:

Use BIDMAS

14.5 X 3.1 = 44.95

44.95 + 13.5 = 58.45

Answer:

58.45

Step-by-step explanation:

step 1

[tex]\begin{matrix}\:\:\:\:\emptyspace0.\:\:\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace3.0}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\emptyspace3\emptyspace0\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

step 2

[tex]\begin{matrix}\:\:\:\:\emptyspace0.\emptyspace3\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace3.0\cdot \:0}\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\emptyspace3\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\end{matrix}[/tex]

step 3

[tex]\begin{matrix}\:\:\:\:\emptyspace.\emptyspace3\emptyspace7\:\:\:\:\:\:\:\\ 8\overline{|\smallspace 3 0\ \ \:}\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\emptyspace3\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace5\emptyspace6}\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace4\emptyspace0\:\:\:\:\:\:\end{matrix}[/tex]

step 4

[tex]\begin{matrix}\:\:\:\:\epe0.\ece3\empt7\e5\:\:\:\:\:\\ 8\overline{|\sm30 \ \ \ \ }\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\em3\e0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\eme6\ece0\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\empte5\ee6}\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\ee4\ece0\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\ee4\epace0}\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\e0\:\:\:\:\:\:\end{matrix}[/tex]

Answer:

3.75

Step-by-step explanation:

[tex]\mathrm{Write\:the\:problem\:in\:long\:division\:format}[/tex]

[tex]\begin{matrix}8\overline{|\smallspace3.0}\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{Divide\;30\;by\;8\;to\;get\;3}[/tex]

[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace3.\:\:\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace30.0}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{Divide\;60\;by\;8\;to\;get\;7}[/tex]

[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace3.\emptyspace7\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace30.0\cdot \:0}\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace5\emptyspace6}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace4\emptyspace0\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{Divide\;40\;by\;8\;to\;get\;5}[/tex]

[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace3.\emptyspace7\emptyspace5\:\:\:\:\:\:\:\\ 8\overline{|\smallspace30.0\cdot \:0}\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \underline{\emptyspace5\emptyspace6}\:\:\:\:\:\:\:\:\:\:\\ \emptyspace4\emptyspace0\:\:\:\:\:\:\:\:\\ \underline{\emptyspace4\emptyspace0}\:\:\:\:\:\:\:\:\\ \emptyspace0\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{3}{0.8}\:\mathrm{is}\:3.75[/tex]

~lenvy~

The Given Polynomial has three different parameters scattered, first we have to rearrange and then solve for the missing numbers the answer is gotten as 2x^2+7x+4

Given Data

2x−6+4x^2+5x−2x^2+10

We begin by collecting like terms

4x^2-2x^2+2x+5x-6+10

Carrying out addition and subtraction operation on like terms

2x^2+7x+4

The Simplified polynomial is

2x^2+7x+4

Learn more about polynomial here:

https://brainly.com/question/2833285

Answer:

c-9>23.

Step-by-step explanation:

The difference in an equation is c-9. Greator is >. So c-9>23.