What is the rule/output?

[tex]\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ e^{\ln(1)}=e^{\ln(5x)}\implies e^{\log_e(1)}=e^{\log_e(5x)}\implies 1=5x\implies \cfrac{1}{5}=x[/tex]

Answer: it’s 1 and 5x on edg

Step-by-step explanation:

Answer:

=3/4

Step-by-step explanation:

A bus arrives at a bus stop every 40 minutes.

You arrive at a bus stop at a random time.

So, probability that you will wait at most 10 minutes = 10/40

So, The probability that you will wait at least 10 minutes= 1-10/40

=1- 10/40

By taking L.C.M we get;

=40-10/40

=30/40

=3/4

Thus the probability that you will have to wait at least 20 minutes for the bus is 3/4....

Answer:

3/4

Step-by-step explanation:

hahahaha to you asell

Answer:

30/3x

Step-by-step explanation:

Let

x ----> a number

we know that

The algebraic expression of the phrase" thirty" is equal to the number 30

The algebraic expression of the phrase"three times a number" is equal to multiply the number by 3 ----> 3x

therefore

"The quotient of thirty and three times a number" is equal to divide the number 30 by 3x

30/3x

Answer:  The correct option is (B) [tex]\dfrac{30}{3x}.[/tex]

Step-by-step explanation:  We are given to translate the following phrase into an algebraic expression :

"the quotient of thirty and three times a number."

Let the unknown number be represented by x.

Then, according to the given phrase, the algebraic expression can be written as :

[tex]E=\dfrac{30}{3\times x}\\\\\\\Rightarrow E=\dfrac{30}{3x}.[/tex]

Thus, the required algebraic expression is [tex]\dfrac{30}{3x}.[/tex]

Option (B) is CORRECT.

9.3 points. Look at the tenths place, whatever number is between 2 and 4 (3) is your answer.

Answer:

Yes. In between both of those would be 9.3. Best of luck to you! :)

-mark as brainliest please!- XD

The answer is " D. Graph D"

Answer:

9

Step-by-step explanation:

To find the common difference, take the second term and subtract the first term

13-4 =9

Lets check:

Take the third term and subtract the second term

22-13 =9

The common difference is 9

Answer:

9

Step-by-step explanation:

9 is the common difference between the numbers in this sequence

4 +9 = 13

13 +9 = 22

22 +9 = 31

31 +9 = 40

Therefore the common difference is 9

PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL ;)

Answer:

Option D. x=15°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

see the attached figure to better understand the problem

∠x=(1/2)[arc AB-arc CD]

arc AB=40°

Remember that the diameter divide the circle into two equal parts

arc CD=180°-(130+40)°=10°

substitute

∠x=(1/2)[40°-10°]=15°

Answer:

x = 15!

Step-by-step explanation:

I got it right on my in class exercise!

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+3y+2z=8&(1)\\3x+y+3z=-10&(2)\\-2x-2y-z=10&(3)\end{array}\right\qquad\text{subtract both sides of the equations (1) from (2)}\\\\\underline{-\left\{\begin{array}{ccc}3x+y+3z=-10\\x+3y+2z=8\end{array}\right }\\.\qquad2x-2y+z=-18\qquad(4)\qquad\text{add both sides of the equations (3) and (4)}\\\\\underline{+\left\{\begin{array}{ccc}-2x-2y-z=10\\2x-2y+z=-18\end{array}\right}\\.\qquad-4y=-8\qquad\text{divide both sides by (-4)}\\.\qquad\qquad y=2\qquad\text{put the value of y to (1) and (3)}[/tex]

[tex]\left\{\begin{array}{ccc}x+3(2)+2z=8\\-2x-2(2)-z=10\end{array}\right\\\left\{\begin{array}{ccc}x+6+2z=8&\text{subtract 6 from both sides}\\-2x-4-z=10&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+2z=2&\text{multiply both sides by 2}\\-2x-z=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+4z=4\\-2x-z=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad3z=18\qquad\text{divide both sides by 3}\\.\qquad\qquad z=6\qquad\text{put the value of z to the first equation}[/tex]

[tex]x+2(6)=2\\x+12=2\qquad\text{subtract 10 from both sides}\\x=-10[/tex]

Answer:

The distance from the midpoint of the interval to  either endpoint is 6 units

Step-by-step explanation:

step 1

Find the midpoint of the interval

The formula to calculate the midpoint between two numbers is equal to

[tex]M=(\frac{x1+x2}{2})[/tex]

substitute

[tex]M=(\frac{2+14}{2})[/tex]

[tex]M=8[/tex]

step 2

Find the distance from the midpoint of the interval to  either endpoint.

14-8=6 units

or

8-2=6 units

therefore

The distance from the midpoint of the interval to  either endpoint is 6 units

To find the distance from the midpoint of the interval (2,14) to either endpoint, first find the midpoint, which is 8, then calculate the distance to either endpoint by subtracting the lower endpoint from the midpoint, resulting in a distance of 6 units.

The question asks to find the distance from the midpoint of the interval (2,14) to either endpoint. To start, we find the midpoint of the interval by adding the two endpoints together and dividing by 2:

Midpoint = \((2 + 14) / 2\) = \(16 / 2\) = 8

Next, we calculate the distance from the midpoint to one of the endpoints. The distance can be found by subtracting the lower endpoint from the midpoint:

Distance = \(8 - 2\) = 6

Therefore, the distance from the midpoint of the interval to either endpoint is 6 units.

Answer:

[tex]-2y^{b-1}[/tex]

Step-by-step explanation:

[tex]\frac{12x^ay^b}{-6x^ay}[/tex]

In multiplication of fractions you can do this:

[tex]\frac{a}{c} \cdot \frac{b}{d}=\frac{a \cdot b}{c \dot d} \text{ or the other way around } \frac{a \cdot b}{c \dot d}=\frac{a}{c} \cdot \frac{b}{d}[/tex].

So that is exactly what we are going to do here:

[tex]\frac{12x^ay^b}{-6x^ay}[/tex]

[tex]\frac{12}{-6} \cdot \frac{x^a}{x^a} \cdot \frac{y^b}{y}[/tex]

We know that 12 divided by -6=12/-6 =-2.

We also know assuming x isn't 0 that x^a/x^a=1.

On the last fraction, the only thing you can do there to simplify is use the following law of exponents: [tex]\frac{v^m}{v^n}=v^{m-n}[/tex].

So we have

[tex]\frac{12x^ay^b}{-6x^ay}[/tex]

[tex]\frac{12}{-6} \cdot \frac{x^a}{x^a} \cdot \frac{y^b}{y}[/tex]

[tex](-2) \cdot (1) \cdot (y^{b-1})[/tex]

Simplifying a bit and leaving out the ( ).

[tex]-2y^{b-1}[/tex]

Answer:

11/15

Step-by-step explanation:

First, get a common denominator of 30. 2/5 becomes 12/30. 4/6 becomes 20/30. 1/3 becomes 10/30.

Now we can add and subtract accordingly.

12/30 + 20/30 = 32/30.

32/30 - 10/30 = 22/30.

Finally, simplify the fraction.

22/30 becomes 11/15 when each number is divided by 2.

Answer: [tex]\frac{11}{15}[/tex]

Step-by-step explanation:

The first step is to find the Least Common Denominator of  the fractions. Descompose each denominator into its prime factors and muliply the commons and non-commons with the least exponent. Then:

[tex]5=5\\6=2*3\\3=3\\\\LCD=2*5*3=30[/tex]

Divide each denominator by the LCD and multiply this quotient by the corresponding numerator, add the products and then reduce the fraction.

Therefore you get:

[tex]=\frac{(2*6)+(4*5)-(1*10)}{30}=\frac{12+20-10}{30}=\frac{22}{30}=\frac{11}{15}[/tex]

Answer:

[tex]\large\boxed{h(x)=x^3}[/tex]

Step-by-step explanation:

[tex]f(x)=(6x^3-7)^3\\\\(h\circ g)(x)=h\bigg(g(x)\bigg)\to\text{exchange x to}\ g(x)=6x^3-7\\\\f(x)=(\underbrace{6x^3-7}_{g(x)})^3=\bigg(g(x)\bigg)^3=h\bigg(g(x)\bigg)\\\\\text{Therefore}\ h(x)=x^3[/tex]

Answer:

option a

Step-by-step explanation:

To find the slope 'm' we use 2 points from the line, those are given in the statement:

[tex]x_{1} =3\\y_{1} =6\\\\x_{2} =5\\y_{2} =3\\m=\frac{y_{2} -y_{1} }{x_{2}-x_{1}}\\m=\frac{3 -6 }{5-3}}\\m=\frac{-3 }{2}}[/tex]

Answer: [tex]0.96\ m^2[/tex]

Step-by-step explanation:

We can make the conversion from milimeters to meters (Remember that [tex]1m=1,000\ mm[/tex]). Then:

[tex]1,200\ mm[/tex] to [tex]m[/tex]:

[tex](1,200\ mm)(\frac{1\ m}{1,000\ mm})=1.2\ m[/tex]

[tex]800\ mm[/tex] to [tex]m[/tex]:

[tex](800\ mm)(\frac{1\ m}{1,000\ mm})=0.8\ m[/tex]

Now, we need to use this formula for calculate the area of a rectangle:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width.

Knowing that:

[tex]l=1.2\ m\\w=0.8\ m[/tex]

We can substitute values into the formula. Then we get:

[tex]A=(1.2\ m)(0.8\ m)\\\\A=0.96\ m^2[/tex]

Final answer:

The area of the rectangular shape is 0.96 square meters.

Explanation:

To find the area of a rectangle, we multiply its length by its width. Given that the length is 1200 mm and the width is 800 mm, we can convert these measurements to meters by dividing each measurement by 1000. So, the length in meters is 1.2 m and the width in meters is 0.8 m. To find the area in square meters, we multiply the length and width in meters: Area = 1.2 m × 0.8 m = 0.96 m².

Answer:

D

Step-by-step explanation:

Matrices are equal when they are of the same order and their corresponding entries are equal.

This is the case with the given matrix and matrix D

Answer:

reciprocal

Step-by-step explanation:

Final answer:

To divide two fractions, rewrite the operation as the first fraction multiplied by the reciprocal of the second. Multiplication of fractions involves simply multiplying the numerators and denominators, then simplifying by any common factors.

Explanation:

To divide two fractions, first rewrite the problem as the dividend times the reciprocal of the divisor. When dividing by a fraction, it is equivalent to multiplying by the reciprocal of that fraction. For example, dividing by ⅓ is the same as multiplying by 3 (the reciprocal of ⅓). Similarly, multiplying by ½ is the same as dividing by 2 because ½ is the reciprocal of 2. To multiply fractions, simply multiply the numerators together and the denominators together, simplifying by any common factors as necessary.

Demonstrating this concept through an example, let’s consider the division of 4 by ⅓. First, we find the reciprocal of ⅓, which is 3, and then we multiply 4 by 3 to get 12. Through the multiplication of fractions, if we have ⅛ multiplied by ⅓, we would multiply the numerators (2 and 1) and the denominators (8 and 3), and then simplify the resulting fraction by canceling out any common factors.

Answer:

[tex]x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\[/tex]

Step-by-step explanation:

the quadratic formula is:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a= -2, b = -1 and c =-3

Putting values in the formula

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(-3)(-3)}}{2(-3)}\\x=\frac{1\pm\sqrt{-35}}{-6}\\x=\frac{1+\sqrt{-35}}{-6}\,\, and\,\, x=\frac{1-\sqrt{-35}}{-6}\\We\,\, know \,\,that \,\,\sqrt{-1} = i  \\x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\[/tex]

So, [tex]x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\[/tex]

Answer:

Using quadratic formula, the solution to this equation is  the roots of the equations given are ;   x = 1+√35i /  -6   or                x = 1-√35i /  -6

Step-by-step explanation:

-3x²  -  x   - 3=0

To solve this using quadratic formula, we will first of all write down the quadratic formula

x = -b ±√b²- 4ac   /   2a

From the above question;

a = -3    b = -1  and c=-3

So we can now proceed to plug-in our variable

x = -(-1) ± √(-1)² - 4(-3)(-3)    /      2(-3)

x=  1±√1-36   /   -6

x = 1 ±√-35    /  -6

x=1 ± √35  ·  √-1    /-6

x = 1±√35 i    /     -6

Note the square root of negative 1 is i

Either x = 1+√35i /  -6   or   x = 1-√35i /  -6

Therefore the roots of the equations given are ;   x = 1+√35i / -6   or   x = 1-√35i /  -6

Answer: A. M=2, y int=3

Step-by-step explanation:

In slope intercept form the equation is y=2x+3, in the formula y=mx+b m=slope and b=y intercept.

The slope and y-intercept of the equation 6x - 1 = 3y - 10 is Option(A) m=2, b = 3 .

The slope of a straight line is the measure of its inclination or tangent to the point of the straight line.

The y-intercept gives the value of the y-coordinate where the straight line intercepts with the y-axis.

For general representation of a straight line y = mx + c , the slope is the value of m and its y-intercept is c.

The given equation is 6x - 1 = 3y - 10 .

⇒ 3y = 6x + 10 - 1

⇒ 3y = 6x + 9

∴  y = 2x + 3

Comparing with the general equation of straight line, y = mx + c we get slope = 2 and y-intercept = 3.

Thus, the slope and y-intercept of the equation 6x - 1 = 3y - 10 is Option(A) m=2, b = 3 .

To learn more about slope refer -

https://brainly.com/question/3493733

#SPJ2

Answer:

2

Step-by-step explanation:

1) Take the natural log of both sides, obtaining:

   -0.20x + ln 3.80 = ln 2

2)  Group the ln terms on the right side:  -0.20x = ln 2 - ln 3.80

3)  Find the natural logs of 2 and 3.80 and combine them:  -0.408, so that we have 0.20x = 0.408.

4) Solving for x, we get 2.03, or approx 2 (Answer C)

Answer:

a. 3 is the closest choice.

Step-by-step explanation:

2 = 3.80 e^-0.20x

e^-0.20x = 2/3.8

Taking logs:

-0.20x = ln(2/3.8) = -0.64185

x =  3.2.

Step-by-step explanation:

If x is the amount the eldest receives, y is the amount the middle receives, and z is the amount the youngest receives, then:

x + y + z = 656000

x = 6z

y = z + 15000

Substituting the last two equations into the first:

(6z) + (z + 15000) + z = 656000

8z + 15000 = 656000

8z = 641000

z = 80125

Solving for the remaining variables:

x = 6z = 480750

y = z + 15000 = 95125

The eldest receives $480,750, the middle receives $95,125 and the youngest receives $80,125.

The youngest sibling receives $80,125, the middle sibling gets $95,125, and the eldest receives $480,750 from the $656,000 estate. The distribution complies with the stipulation that the eldest receives 6 times what the youngest does, and the middle sibling receives $15,000 more than the youngest.

The distribution of an estate of $656,000 among three siblings with specific conditions. Let's designate the amount the youngest sibling receives as y. According to the provided information, the eldest sibling receives 6 times as much as the youngest, meaning they receive 6y. The middle sibling receives y + $15,000. To find out how much each sibling receives, we need to solve the equation: y + 6y + (y + $15,000) = $656,000.

Add up the terms containing y: 8y + $15,000 = $656,000. Subtract $15,000 from both sides: 8y = $641,000. Divide both sides by 8 to find y:
y = $80,125.

Now, calculate each sibling's share:

The youngest receives y, which is $80,125.

The middle sibling receives y + $15,000, which is $95,125.

The eldest receives 6y, which is $480,750.

These calculations ensure that the total is $656,000, distributed according to the stipulated conditions.

Answer:

f(x) = (-4/5)*x + 4

Step-by-step explanation:

The line which passes through these points will decrease y by 12 for every x increase of 15. This is the same as decreasing y by 4 for every x increase of 5. This means the slope (rise over run) is -4/5. If this is applied to the first point to find what y is at 0, then the point (0, 4) is on the line.

This means that f(x) = (-4/5)*x + 4

Answer:

[tex]\large\boxed{y=-\dfrac{4}{5}x+4}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-5, 8) and (10, -4). Substitute:

[tex]m=\dfrac{-4-8}{10-(-5)}=\dfrac{-12}{15}=-\dfrac{12:3}{15:3}=-\dfrac{4}{5}[/tex]

Put it to the equation of a line:

[tex]y=-\dfrac{4}{5}x+b[/tex]

Put the coordinates of the point (-5, 8) to the equation, and solveit for b:

[tex]8=-\dfrac{4}{5\!\!\!\!\diagup_1}(-5\!\!\!\!\diagup^1)+b[/tex]

[tex]8=4+b[/tex]           subtract 4 from both sides

[tex]4=b\to b=4[/tex]

Finally we have:

[tex]y=-\dfrac{4}{5}x+4[/tex]

Answer:

it's A

Step-by-step explanation:

The domain is all the input values which is x|x=-5,-3,1,2,6

Answer:

The solution of kx-2=7 is x = 9/k

Step-by-step explanation:

Given:

kx-2 = 7

In order to get the solution of the given equation, we have to isolate x so that we can determine its value.

Adding 2 on both sides

kx-2+2 = 7+2

kx = 9

Dividing both sides by k

kx/k = 9/k

x = 9/k

Therefore, the solution of kx-2=7 is x = 9/k ..

Answer:

X=9/k

Step-by-step explanation:

^^^ person is right

Answer:

B) 4

Step-by-step explanation:

Tan is opposite/adjacent. That means that 3 is the opposite side while 4 is the adjacent side.

Answer:

The value is 14/9.

Step-by-step explanation:

xy/9

Put the value of x= -7 and y= -2 in the expression.

=(-7) (-2)/9

=14/9

[tex]\bf \underset{\textit{same denominator}}{\cfrac{4x+2}{x+5}+\cfrac{3x-1}{x+5}}\implies \cfrac{(4x+2)+(3x-1)}{x+5}\implies \cfrac{7x+1}{x+5}[/tex]

Answer:

(7x+1)/(x+5)

Step-by-step explanation:

4x+2       3x-1

--------  +  ----------

x+5           x+5

Since the denominator is the same, we can add the numerators

4x+2   +    3x-1

-----------------------

x+5    

Combine like terms

7x+1  

-----------------------

x+5      

Hi !

625 - (625 ÷ 25) - 25 = 575

Answer:

575

Step-by-step explanation:

Following the order of operations, division is performed before subtraction

Given

625 - 625 ÷ 25 - 25 ← perform the division

= 625 - 25 - 25 ← now perform the subtraction

= 600 - 25

= 575

Step-by-step explanation:

Cavalieri's Principle. A method, with formula given below, of finding the volume of any solid for which cross-sections by parallel planes have equal areas. This includes, but is not limited to, cylinders and prisms.

Answer:

the answer is B

Step-by-step explanation:

the sum of both angles is 90 degree.

By definition if the sum of two angles is 180 is supplementary

If the sum of two angles is 90 is complementary

Then, 70 + 20 =90 degree

So, They are complementary angles

Answer:

Option B.

Step-by-step explanation:

Measure of ∠ABC = 20°

and measure of ∠NML = 70°

Then ∠ABC + ∠NML = 20 + 70

                                  = 90°

Therefore, ∠ABC and ∠NML are complementary angles because sum of complementary angles is 90°.