Type the correct answer in the box. Use numerals instead of words.
Mariah's teacher tells her that this expression can be written as log k, where k is an integer.

3 log 3x- log 9x^4 + log x

What is the value of k?
The value of k is

Answer:

The slope is 3, and y-intercept is -1.

Step-by-step explanation:

All slope - intercept equations are written in the form y = mx + b.  m represents the slope and b represents the y-intercept.  Therefore, the slope is 3 and the y-intercept is -1.

the slope of the line is 3, and the y-intercept is -1

In the equation y = 3x - 1, the coefficient of x (the number multiplied by x) is 3. This coefficient represents the slope of the line.

Therefore, the slope of the line y = 3x - 1 is 3.

To find the y-intercept, we can observe that the equation is in the form y = mx + b, where b represents the y-intercept. In this case, the y-intercept is the constant term, which is -1.

Therefore, the y-intercept of the line y = 3x - 1 is -1.

In summary, the slope of the line is 3, and the y-intercept is -1. These values provide information about the steepness of the line and where it intersects the y-axis.

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Answer:

16 cm, 63 cm, 65 cm

Step-by-step explanation:

Because those side lengths are to big to make a right triangle

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Answer:

$1.50+$3=$4.5

Step-by-step explanation:

Answer: the last one in the middle

ok done. Thank to me :>

Katya initially had 192 pennies, and Mimi initially had 288 pennies. Therefore, together Katya and Mimi lost 96 + 192 = 288 pennies.

Let's assume Katya initially had "k" pennies, and Mimi initially had "m" pennies. According to the given information, we have the following equations:

k + m = 480 (Together, they have 480 pennies)

k - (1/2)k = m - (2/3)m (After losing pennies, they have an equal amount left)

Simplifying equation (2), we have:

1/2 * k = 1/3 * m

To make the equation easier to work with, let's multiply both sides by 6 to eliminate the fractions:

6 * (1/2 * k) = 6 * (1/3 * m)

3k = 2m

Now we have a system of equations:

k + m = 480

3k = 2m

Rearranging equation (2), we get:

m = (3/2)k

Substituting this value of "m" into equation (1):

k + (3/2)k = 480

(5/2)k = 480

k = (480 * 2) / 5

k = 192

Substituting the value of "k" back into equation (1):

192 + m = 480

m = 480 - 192

m = 288

So, Katya initially had 192 pennies, and Mimi initially had 288 pennies.

To calculate the number of pennies they lost altogether, we need to find the difference between their initial amounts and their final amounts.

Katya lost (1/2) * 192 = 96 pennies.

Mimi lost (2/3) * 288 = 192 pennies.

Therefore, together Katya and Mimi lost 96 + 192 = 288 pennies.

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Given:

Price of new AirPods = $199.99

Tax rate = 9%

To find:

How much will he spend?

Solution:

We have,

Price of new AirPods = $199.99

Tax rate = 9%

Tax value = 9% of $199.99

                = \(\dfrac{9}{100}\times 199.99\)

                = \(17.9991\)

Now,

Total money spend = Price of AirPods + Tax

                                = \(199.99+17.9991\)

                                = \(217.9891\)

                                \(\approx 217.99\)

Therefore, the total money spend by James is $217.99.

If the distance to a star was suddenly cut in half, it would appear four times brighter.

The brightness of a star is directly proportional to the inverse square of its distance from us. This means that if the distance to a star is halved, its brightness will increase by a factor of four.

The relationship between brightness and distance can be expressed as follows:

B = k / d^2

where B is the brightness, k is a constant of proportionality, and d is the distance.

If the distance to the star is halved, it can be expressed as:

d' = d / 2

Plugging this into the equation for brightness, we get:

B' = k / (d / 2)^2

Expanding this and simplifying, we get:

B' = 4 * k / d^2

Since k is a constant, it cancels out and we are left with:

B' = 4 * B

This means that if the distance to a star was suddenly cut in half, it would appear four times brighter. In astronomical terms, this is equivalent to an increase of 2 magnitudes on the logarithmic magnitude scale.

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According to the video game money system, copper = 1, 6, silver = 2, and silver is worth one-fourth of gold. As a result, the format is 13g, 1s, 3c.

To discover the worth of two gold and two silver split by one silver and one copper in-game money, we must convert them to the same unit. One silver equals two copper.

So, we can write the value of silver in terms of copper as follows:

1 silver = 2 copper

4 silver = 8 copper

1 gold = 4 silver = 8 * 4 copper = 32 copper

Then, the value of two gold and two silver in copper is (2 * 32 + 2 * 4) copper = 68 copper.

In copper, the value of one silver and one copper equals (1 * 2 + 1 * 1) copper = 3 Copper.

Now, we can find the value of two gold and two silver divided by one silver and one copper as follows:

(2g + 2s) ÷ (1s + 1c)= (2g + 2s) ÷ (2c + 1s)=

(2 × 32 + 2 × 4) ÷ (2 × 2 + 1)= 68 ÷ 5= 13 remainder 3

So, the value in-game currency of two gold and two silver divided by one silver and one copper is 13g, 1s, 3c. Therefore, the answer is 13g, 1s, 3c.

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Answer:

54

Step-by-step explanation:

the 2 lines are parallel and the line going through is a transversal.

because of vertical angles, the x+3 is equal to the angle diagonal to it.

that diagonal angle is equal to the top right one (57˚) by same side interior angle thereom. So intern, x+3 = 57

x = 54

Answer:

they are supplementary

Step-by-step explanation:

The angles AED and DEC are adjacent angles option (C) They are adjacent angles is correct.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that:

The diagram is shown in the picture.

As we can see in the diagram,

The angle AED and DEC are sharing a common vertex which means they are adjacent angles.

Thus, the angles AED and DEC are adjacent angles option (C) They are adjacent angles is correct.

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Answer:

C. 6(4) + 6(9)

Step-by-step explanation:

Using distributive property for the expression 6(4+9) you multiply each number by the 6.

Answer:

  j = 19.6

  k = 25.9

  J = 49°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.

The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Tan = Opposite/Adjacent   ⇒   Adjacent = Opposite/Tan

Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.

  Hypotenuse = Opposite/Sin

  IJ = 17/sin(41°) ≈ 25.9

  Adjacent = Opposite/Tan

 IK = 17/tan(41°) ≈ 19.6

  Angle J = 90° -41° = 49°

In summary, ...

  j = 19.6

  k = 25.9

  J = 49°

Answer:

(2,-3) thats where they intersect

and also that the answer

Step-by-step explanation:

Answer: rational

Step-by-step explanation:

Answer:

  11%

Step-by-step explanation:

You want to know the rate of inflation if the price of a haircut increased from $7 to $20 in 10 years.

The inflation of prices is modeled by an exponential function.

  p(t) = p₀·(1 +r)^t

where p₀ in the price at t=0, r is the annual inflation rate, and t is the number of years.

Solving for r, we find ...

  p(t)/p₀ = (1 +r)^t . . . . . . . . divide by p₀

  (p(t)/p₀)^(1/t) = 1 +r . . . . . . take the t-th root

  r = (p(t)/p₀)^(1/t) -1 . . . . . . . subtract 1

For the given numbers, we find the rate to be ...

  r = (20/7)^(1/10) -1 ≈ 0.11 = 11%

The rate of inflation is 11% per year.

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Answer:

x=9,1

Step-by-step explanation:

Take the root of both sides and solve.

x = 9 , 1

Answer:

X=9 or 1

Step-by-step explanation:

It's really complicated to explain, sorry!

(P.S, if that's you in your pfp, you are so freaking stunning, period. As you should)

Hope this helped, and please mark as brainliest :)

Answer:

\(3^{4}\)

Step-by-step explanation:

\(3^{4}\)

The equivalent expression will be;

⇒ 3⁴

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3 × 3 × 3 × 3

Now,

Since, The expression is,

⇒ 3 × 3 × 3 × 3

Hence, It can be written as;

⇒ 3 × 3 × 3 × 3 = 3 ⁴

Thus, The equivalent expression will be;

⇒ 3⁴

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Answer:

I'm going to say \(\frac{4}{1}\) and \(\frac{4}{2}\)

Step-by-step explanation:

Answer:

I think 60 s.sq m

The students that will like exactly one of the two sports out of football and baseball is 200.

These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).

Here,

F=140

B=144

F∩B=42

F-B=n(F)-n(F∩B)

=140-42

F-B=98

B-F=n(B)-n(F∩B)

=144-42

=102

So, the students that will like exactly one of the two sports,

=102+98

=200

There are 200 students who will only enjoy one of the two sports—football or baseball.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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The expansion of the logarithmic expressions are:

log(abc)⁵ = 5 (loga +  logb + log c)

log(a²c) =   2loga + logc

ln a/b = lna - lnb

log c³/b = 3logc - logb

log (√a)/c² =  (1/2)·loga - 2·log c

To expand a logarithmic expression, we will apply logarithm laws as follow:

log(abc)⁵ = 5·log(abc) = 5 (loga +  logb + log c)

log(a²c) = loga² + logc =  2loga + logc

ln a/b = lna - lnb

log c³/b = log c³ - logb = 3logc - logb

log (√a)/c² = log√a - log c² = loga^(1/2) - log c² = (1/2)·loga - 2·log c

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Answer: 8 to 12 years

Step-by-step explanation: A cluster is formed when several data points lie in a small interval. The domain of the cluster is the set of x-coordinates.

The range of the cluster in the scatter plot is between $40,000 and $60,000 when the data points are heavily clustered between the years 8 to 12.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

Given that, on scatter plot

Years of experience is represented at x-axis

Annual Salary is represented at y-axis

From the scatter plot, it is clear that from the x-axis the data points are tightly clustered between the years 8 to 12. As major portion of the data points lie between 8 to 12 years.

Similarly, from the y-axis the data points are tightly clustered between between $40,000 and $60,000. As major portion of the data points lie between $40,000 and $60,000.

When the certain data points in a scatter plot make distinct groups, these groups are considered as clusters. Those data points normally appear to be converged around a particular value.

Therefore, the range of the cluster in the scatter plot is between $40,000 and $60,000 for the data points between the years 8 to 12.

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Answer:

i is d i think so

Step-by-step explanation:

Answer:

it is A area of trapezoid = 1/2 × h( base1+base2) so it is 1/2× 8×(13+19)

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

For the function f(x) to be continuous at x = -4, the left-hand limit and the right-hand limit of the function must exist and be equal to f(-4).

The left-hand limit is given by:

lim f(x) = lim (x^2 + 9x + 20)/(x + 4) = (-4)^2 + 9(-4) + 20/(-4 + 4)

x→-4- x→-4-

lim f(x) = lim (x^2 + 9x + 20)/(x + 4) = (-4)^2 + 9(-4) + 20/(-4 + 4)

x→-4+ x→-4+

where we have used the fact that f(x) = a for x = -4.

Since the denominator of the function is (x + 4), which becomes zero as x approaches -4, we can't directly evaluate the limits by substitution. We can, however, factor the numerator and simplify:

lim f(x) = lim (x^2 + 9x + 20)/(x + 4) = lim (x + 4)(x + 5)/(x + 4)

x→-4- x→-4- x→-4+

lim f(x) = lim (x^2 + 9x + 20)/(x + 4) = lim (x + 4)(x + 5)/(x + 4)

x→-4+ x→-4+ x→-4+

Canceling the common factor of (x + 4), we get:

lim f(x) = lim (x + 5)

x→-4- x→-4+

lim f(x) = lim (x + 5)

x→-4+ x→-4+

which both evaluate to 1.

Therefore, we must have:

f(-4) = lim f(x) = lim (x + 5) = 1

x→-4 x→-4+

And since we know that f(-4) = a, we get:

a = 1

So the value of the constant a for which the function f(x) is continuous at -4 is 1.

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Answer:

A=4ft²

Answerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Step-by-step explanation: