100 Points! Algebra question, only looking for an answer to B. Photo attached. Please show as much work as possible. Thank you!

The equivalent expression of log4 ( 1/4x²) is log4(1/4) + log4(x²) ( option D)

The logarithm is the inverse function to exponentiation. For example log2 (8) = 3 and 2³ = 8

The following are math logarithm rules:

loga (MN) = loga M + loga N.

loga (M/N) = loga M - loga N.

IogaMn = n Ioga M.

For example Log5 (5²) = Log5 (5) + Log5 (5)

= 1+1 = 2

this means Log5 ( 5²) = log5 ( 25) = 2

Therefore if loga (MN) = loga M + loga N.,

we can say that,

log4( 1/4x²) can also be written as ;

log4 (1/4) + log4 (x²) .

therefore the equivalent expressions for

log4 ( 1/4x²) is log4 (1/4) + log4 (x²) .

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A circle-based model is highly suitable for the design and construction of roundabouts, which present themselves as practical solutions to tackle traffic-related issues.

Roundabout intersections involve vehicles circulating around a central island in a counterclockwise direction. The circular form guarantees fluidity in traffic movements and significantly reduces the requirement for traffic lights and stops signs while enhancing security.

This model entails using a circle, ascertaining that the diameter corresponds with the width of the roadway, with its center accommodating the location of the island at equidistant distances from all contact points on the circle's periphery, thus ensuring optimal functionality.

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Answer:

the other two sides of the rectangle is 147

Step-by-step explanation:

because since u told us that there is a side with a length of 6 cm and u also gave us the preimeter which can help us do this so what I did is 6 x 2 why because if one side is 6cm then the other side will also be 6cm and then 6 x 2 = 12 and this is what I did 306 - 12 = which equalls 294 and then divide that by 2 = 147 please mark as brainliest bye have a great day :D

Answer: #1

Step-by-step explanation:

In situation number one, the equation for the garden's area would be [tex]x^2[/tex] which is nonlinear. The other questions map to linear equations in the form [tex]y = mx + b[/tex]

Answer:

Linear relationship always produces a straight line and are without exponential.

2.the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

3.the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

Step-by-step explanation:

Hope this helps! =D

Answer:

Therefore, Frank's monthly credit card payment will be $454.31.

Step-by-step explanation:

Monthly payment = (PV * r) / (1 - (1 + r)^-n)

PV = $2,500 + $1,000 + $3,000 + $1,500

= $8,000

r = 0.18 / 12

= 0.015

Monthly payment = ($8,000 * 0.015) / (1 - (1 + 0.015)^-24)

= $454.31

Answer:

x = 360°/8 = 45°

y = 2 × 45° = 90°

The arc length generated by a radius r is S = 11πr

The formula for arc length is given by:

S = θr

where θ is the central angle in radians and r is the radius of the circle.

For a full revolution, a radius r revolves around the center of the circle at an angle of 2 radians. Therefore, the central angle for 5 1/2 revolutions would be:

θ = (5 1/2) * 2π radians

θ = 11π radians

So, the arc length generated by a radius r rotating 5 1/2 revolutions is:

S = θr

S = 11πr

Note that if the radius is not given, then the arc length cannot be determined.

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Using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.

When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.

The angle from the horizontal downward to an item is referred to as the "angle of depression."

The line of sight of an observer would be below the horizontal.

So, in the given situation:
We will find the base which is the distance of the boat from the land.

Which means:
hypotenuse/Base

Which is represented by Cosx.

The angle is 24°.

Then, the equation for a solution would be:

cos(24) = x/45

Therefore, using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

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The answer on shape of house is , (1) A rectangle for the main structure of the house. (2) A triangle for the roof. (3) A rectangle for the front porch. (4) Two trapezoids for the roof of the front porch. (5) A rectangular door.

A trapezoid is a four-sided geometric shape with two parallel sides, called the bases, that are of different lengths, and two non-parallel sides that connect the bases. The non-parallel sides are also called legs, and they may or may not be equal in length.

Trapezoids are often encountered in geometry and in real-life situations, such as in construction and architecture. They can be classified as either right trapezoids or oblique trapezoids depending on whether one of the angles formed by the bases and a leg is a right angle or not.

Based on the image provided, the shapes that make up the front of the house are:

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Answer: 6,450 words per minute

Step-by-step explanation:

Each hour is 60minutes long, making your total number of minutes 150.

The last step would be to multiply 150 by the wpm (43) and making the total number typed 6,450

The dimensions of the strongest beam are 27 inches x 13.5 inches.

In general, dimension refers to a measurable extent of a physical quantity, such as length, width, height, depth, or time. These dimensions provide a framework for describing and measuring objects and events in the physical world. In geometry, dimension are refers to the number of coordinates needed to specify a point in a space. In physics, the concept of dimension is used to describe the properties of space and time.

We know that the strength of the beam is directly proportional to its width multiplied with the square of its height. Let's call the width of the beam "w" and the height "h". Then we can write the strength of the beam as:

S = kwh², where "k" is the constant of proportionality.

We want to find the dimensions of the strongest beam, which means we want to find the values of "w" and "h" that will maximize the strength "S". To do this, we need to find the maximum value of the function S = kwh² subject to the constraint that the diameter of the log is 18 inches.

The diameter of the log is equal to the width of the beam plus twice the height of the beam:

d = w + 2h

Since the diameter of the log is 18 inches, we can write:

w + 2h = 18

or

w = 18 - 2h

Substituting this expression for "w" into the equation for the strength of the beam, we get:

S = k × w(18-2h) × h²

Expanding and simplifying this expression, we get:

S = 36kh³ - 2kh⁴

To find the maximum value of S, we take the derivative of S with respect to h and set it equal to zero:

dS/dh = 108kh² - 8kh³ = 0

Simplifying this expression, we get:

h²(108 - 8h) = 0

This equation has two solutions: h = 0 and h = 13.5.

Since a beam with height equal to zero would have zero strength, we reject the solution h = 0. Therefore, the maximum strength is achieved when h = 13.5 inches.

To find the corresponding width, we can use the equation we derived earlier:

w = 18 - 2h = 18 - 27 = -9

Since the width of the beam cannot be negative, we reject this solution as well.

Therefore, the required dimensions of the strongest beam are:

Width = 2h = 2(13.5) = 27 inches

Height = h = 13.5 inches

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Since this is about the angle theorem and the angle theorem is a theorem that helps us know the relationship between angles. Being a corresponding angle, x = 105°. Hence option A is correct.

A corresponding angle is an angle that occupies the same relative position as another angle elsewhere in the diagram. The corresponding angle in planar geometry occurs when a transverse line crosses his two straight lines. Two angles correspond or relate to each other by being on the same side of the horizontal line. One is the exterior angle (outside the parallel lines) and the other is the interior angle (inside the parallel lines).

You can see that the transversal line intersects two parallel lines DE and XY. From the transversal theorem of angles in mathematics, we know that when a transversal line intersects two parallel lines, the corresponding angles formed are congruent and therefore equal to each other.

In this question we see that one of the angles is 105°. Therefore x° is congruent to it, x = 105°.

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The complete question is as follows:

We can see here that the best representation of the possible range of values for the third side, s is: 2 < s < 18.

An acute triangle is a type of triangle where all three angles are acute angles, meaning they are less than 90 degrees. In other words, an acute triangle is a triangle with all three angles being sharp or narrow.

The best representation of the possible range of values for the third side, s, can be determined using the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have two sides measuring 8 cm and 10 cm. Let's call the third side "s". Using the Triangle Inequality Theorem, we can write:

8 + 10 > s

18 > s and

8 + s > 10

s > 2

and

10 + s > 8

s > -2 (since a length cannot be negative)

Therefore, we know that s must be greater than 2 and less than 18.

The best representation of the possible range of values for s is: 2 < s < 18

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Answer:

Step-by-step explanation:

1,2,3,4,6,8,12,16,24,48

hope i helped

Mathematical statement  μ = 18000 where μ is the mean, Null hypothesis H₀ : μ = 18000, Alternate hypothesis Hₐ : μ ≠ 18000.

A mathematical statement is a meaningful string of words that can be either true or false.

For instance , 3+4=7 is always true. Consequently, it is a true statement.

Similar to this ,  3+4=8 is never true  Therefore,  it is a false statement.

Here the amusement park makes the claim that the mean daily attendence at the park is 18000 people

∴ μ = 18000 is the statement .

A null hypothesis is known as statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the "null," it is represented as H₀.

∴  Here the null hypothesis is μ = 18000

The alternative hypothesis is an assertion used in statistical inference experiment. It is contradictory to the null hypothesis and indicated by Ha or H₁ . We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing.

For instance :  A school principal claims that students in her school score an average of seven out of 10 in exams. The alternate hypothesis is μ ≠ 7.0.

Similarly here in this question alternate hypotesis will be μ ≠ 18000.

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The required value of z such that 0.6318 of the area lies between −z and z is 0.89.

If 0.6318 of the area lies between −z and z, then the area outside of this range is (1-0.6318) = 0.3682.

Since the normal distribution is symmetric, the area to the left of −z is equal to the area to the right of z. So, the area to the right of z is (0.3682 / 2) = 0.1841.

Using a standard normal distribution table, we can find the z-score corresponding to an area of 0.1841 to the right of z:

z = invNorm(0.1841) ≈ 0.89

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Answer: i. y = 60÷5

Step-by-step explanation: If he has 60 sheets of paper and 5 notebooks, it would only make sense to divide the number of sheets by the number of notebooks to get the sum. Which is 12 btw! <33

Answer:

The student's claim is incorrect. While it is true that √x^2 = x for all non-negative values of x, this property does not apply to expressions with multiple terms, such as 4√x^2.

Step-by-step explanation:

consider the case where x = -1. Then, √x^2 = √(-1)^2 = 1, but 4√x^2 = 4√1 = 4. On the other hand, √x = √(-1) is undefined, so the equation 4√x^2 = √x is not true for this value of x.

Therefore, the student's claim is not true for all values of x, and it is important to be careful when applying algebraic properties to expressions with multiple terms.

The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points .

A circle is a closed shape made up of all elements in a plane that are indistinguishable from a predetermined point known as the centre. The radius (r) of a circle is the separation between the circle's centre and any other point on the circumference.

given

These procedures can be used to graph the circle :

Determine the circle's centre. The point in this instance serves as the centre (5, 6).

Determine the circle's radius. The circle's diameter is 4/2, or two.

Place the circle's centre on the coordinate plane.

Plot points that are 2 units distant from the centre in all directions to form the circle.

The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points, and the points (5, 4) and (5, 8) are two points on the circle's y-axis.

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You would need to purchase 720 different tickets to guarantee a win.

You must pick the first three finishers in the correct order to win a trifecta race with 10 entries.

Since there are ten participants in the race, there are ten ways to select the winner of the first place prize. In the wake of choosing the primary spot finisher, there are just 9 passages remaining, so the quantity of ways of choosing the second-place finisher is 9.

Finally, since there are only eight entries left after selecting the first two, there are 8 ways to select the third-place finisher.

Therefore, the total number of possible winning trifecta combinations is:

10 x 9 x 8 = 720

This indicates that in order to guarantee a win, you would need to purchase 720 distinct tickets. However, it is essential to keep in mind that betting on a race in this manner may not always be the most profitable or efficient option, and that purchasing each and every possible combination can be very costly. It's vital to painstakingly think about the chances, payouts, and your financial plan prior to putting down any wagers.

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Answer:

C.

Step-by-step explanation:

C. is an impossible equation.

The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. The input values are often called the independent variable, while the output values are called the dependent variable. Functions are commonly denoted using functional notation, such as f(x), where x is the input and f(x) is the output. Functions are used to describe relationships between variables, such as in algebraic expressions or equations. They can take many forms, including linear, quadratic, polynomial, exponential, trigonometric, and logarithmic functions. Functions are fundamental to many areas of mathematics, science, engineering, and economics, and have many applications in real-world situations.

Here,

A. The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. In other words, the function is not a straight line, because y is not directly proportional to x. Instead, it is a linear equation in two variables x and y, where the graph of the equation is a straight line.

B. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change. In a linear function, the rate of change of the function (slope) is always constant, meaning that for any two points on the line, the change in y over the change in x is always the same. However, in this case, the rate of change of the function depends on the value of x, and thus the graph of the function is not a straight line. Instead, it is a quadratic function, where the graph is a parabola.

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The incorrect statement regarding the dilation is given as follows:

2. The transformation can be represented by (7x/3, 7y/3).

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, we have that:

Hence the scale factor is given as follows:

k = 3/7.

And the rule is then given as follows:

(3x/7, 3y/7).

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Answer: So, what are you asking?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 7 and h = 4 , then

A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 cm²

The requried,  3025 bacteria are present after 12 hours.

To find the number of bacteria present after 12 hours, we simply need to substitute t=12 in the given equation:

[tex]n(12) = 500e^{(0.15*12)}[/tex]

[tex]n(12) = 500e^{1.8}[/tex]

n(12) ≈ 3024.82

Rounding this to the nearest whole number, we get:

n(12) ≈ 47,416 ≈ 3025

Therefore, there are approximately 3025 bacteria present after 12 hours.

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The amount she charges for each necklace is $7.50 (option B).

Profit is the total difference between total revenue and total cost. Total cost is the sum of fixed cost and variable cost.

Profit = total revenue - total cost

Profit = (price x quantity sold) - (fixed cost + total variable cost)

Profit = (price x quantity sold) - (fixed cost +(variable cost per unit x quantity sold)

P = 7.5n - (2.25n + 15)

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Answer:

We can use trigonometry to find AB.

First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:

A + B + C = 180°

A + 90° + 30° = 180°

A = 60°

Now, we can use the sine function to find AB:

sin A = opposite/hypotenuse

sin 60° = AB/96

AB = 96 * sin 60°

AB = 96 * √3/2

AB = 48√3

Therefore, AB is approximately 83.14 cm (rounded to two decimal places).

You rented the car for 10 days.

Let's begin by setting up the equation to solve for the number of days:

Total rental cost = (daily rental cost + CDW fee) x number of days + gasoline cost

We know that the daily rental cost is 37.45, and the CDW fee is 19.40, so we can substitute those values into the equation:

646.50 = (37.45 + 19.40) x number of days + 78

Simplifying the equation:

646.50 = 56.85 x number of days + 78

Subtracting 78 from both sides:

568.50 = 56.85 x number of days

Dividing both sides by 56.85:

number of days = 10

Therefore, You rented the car for 10 days.

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The two lines are parallel because they have thesame slope and different y intercept

If two non-vertical lines that are in the same plane has the same slope. However the lines will have different y intercept.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Therefore putting the equations 15x−6y=−5 and 5x−2y=5 into that form.

15x-6y = -5

-6y = -15x-5

y = 5x/2 +5/6

for the second equation,

5x-2y =5

-2y = -5x-5

y = 5x/2 +5/2

therefore , the two lines are parallel because they have the same slope( 5/2) and different y intercept.

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