log3 55=x
Use the base of formula to solve for x in logaritm experssion

Answer: 10 dimes and 6 quarters, see below for the equations.

Step-by-step explanation:

    We know how much a dime is worth and how much a quarter is worth, and they give us the total number of coins and the total number of change.

    This equation shows the total number of coins:

d + q = 16

    This equation shows the worth of these coins:

0.10d + 0.25q = 2.5

    Now, we can graph these equations. See attached. The point of intersection, where the lines cross, is our solution. In the graph, d = x and q = y.

This point is (10, 6) meaning he has 10 dimes and 6 quarters in his pocket.

We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.

We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.

We can see here that it shows that a is an element of the subgroup of H.

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The measure of <1 is 31°.

Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.

In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;

<2 = 31° (given)

So that;

<1 = <2 = 31°

Thus,

<1 = 31°

Therefore, it can be concluded that the measure of <1 is 31°.

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The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = -2x² - 4x + 12, we have:

Axis of symmetry, Xmax = -(-4)/2(-2)

Axis of symmetry, Xmax = 4/-4 = -1.

For the vertex of f(x) = -2x² - 4x + 12, we have:

f(-1) = -2(-1)² - 4(-1) + 12 = 14.

For the given quadratic function f(x) = x²-4x+3, we have:

Axis of symmetry, Xmax = -(-4)/2(1)

Axis of symmetry, Xmax = 4/2 = 2.

For the vertex of f(x) = x²-4x+3, we have:

f(2) = (2)²-4(2) +3 = -1.

Therefore, 2 is greater than -1.

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The requried area of the larger wallet is 194.4 square centimeters.

Since the two wallets are similar, their corresponding sides are proportional. Let x be the width of the smaller wallet, then the width of the larger wallet is 18/10 times x, or 9/5 times x. Therefore, the dimensions of the larger wallet are 9/5 times the dimensions of the smaller wallet.

The area of the smaller wallet is x times 10 (length times width), or 10x square centimeters. We are given that this area is 60 square centimeters, so:

10x = 60

x = 6

Therefore, the width of the smaller wallet is 6 centimeters. The width of the larger wallet is 9/5 times 6, or 10.8 centimeters. The length of the larger wallet is 18 centimeters.

The area of the larger wallet is 10.8 times 18, or 194.4 square centimeters. Therefore, the area of the larger wallet is 194.4 square centimeters.

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Financial aid letters display aid and attendance costs for one year only. Some schools offer a financial aid letter for four years of undergrad, aiding in budget planning for the program.

A few schools may give a budgetary help letter that ventures aid and costs for all four a long time of an undergrad program. This could offer assistance understudies arrange and budget for their whole undergrad instruction.

In a few cases, Financial aid letters  may show aid and costs for a single semester, instead of the complete scholarly year. This could be valuable for understudies who are as it were going to part-time or who got to take a semester off.

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Answer:correct answers 1.69

4.59

Step-by-step explanation:

We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

2u^2 - 8u - 1 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 2, b = -8, and c = -1. Substituting these values, we get:

u = (8 ± sqrt(8^2 - 4(2)(-1))) / 2(2)

u = (8 ± sqrt(72)) / 4

u = 2 ± sqrt(18)

Therefore, either:

(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.

To determine which option is not an exponential function, we will apply general equation of an exponential function.

f(x) = aⁿ

where;

So from the given options;

(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.

4ˣ  is an exponential function, because 4 is the base while x is the exponent.

(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.

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The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).

Given that,

We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.

We know that any point on the unit circle can be defined as,

(cos θ, sin θ)

where θ is the angle formed with the X axis.

-5π/4 will be the point the corresponds to -225°.

Cos(-5π/4) = cos (5π/4)

                  = cos (π + π/4)

                  = -cos (π/4)

                  = -1/√2

sin (-5π/4) = -sin (5π/4)

                  = -sin (π + π/4)

                  = sin (π/4)

                  = 1/√2

Hence the coordinate of the unit circle is (-1/√2, 1/√2).

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Answer: √35/6

Step-by-step explanation:

see image for explanation

Answer: 24 minutes and 30 seconds after the meeting as started

Step-by-step explanation:

110 minutes into 2 equal parts = 55 minutes in each section.

In the middle of 55 minutes = subtract the 10 minutes for a break from the 55 minutes that leaves you with 45 minutes. 24 minutes and 30 seconds before and after the 10 minute break.

Total session minutes - 110

Two equal parts of session: 55 minutes in each session

10 minute break in each session: 55-10 =45.

24 minutes and 30 seconds + 10 min break (in middle) + 24 minutes and 30 seconds

After 50 minutes the break will start.

The metting is 110 minutes long. According to the Question the metting have 'a'(only one) break of 10 minutes in between of two equal parts of metting.

so, duration of metting without the break=100 minutes

                                 duration of each part=50 minutes

Now, the break should be after First part which is of 50 minutes.

=> The break should 50 minutes after the starting of metting.

[tex]\large \boxed{\mathrm{10}}[/tex]

The constant function p has a fixed output of one billion, while the exponential function q has a base of two and an output of 10. As the input increases by one, the output of q doubles. For example, q(3) = 20 and q(4) = 40. The rate of growth of q is much faster than p. In fact, q will eventually surpass p for large enough inputs. This demonstrates the power of exponential growth and highlights the importance of understanding the functions used in equations and models.

Answer:

10 or 1b

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

Firstly, G and J cannot be the answers because the beginning numbers are too big. If you look at the fractions, you can see 2 and 7/8 because 2 is the smallest of all of them. Now the answer is between F and H.

In F, the second number is 3 and 1/2.

In H, the second number is 3 and 1/4.

If you want to make it an improper fraction to visualize better, it would be 7/2 and 12/4=6/2. Or you can just compare to see which is smaller, 1/2 or 1/4. In this case, 3 and 1/4 is smaller. Therefore the answer is H.

Answer:

The number 15/10 is a fraction, specifically a rational number. It can be expressed as the quotient of two integers, where 15 is the numerator and 10 is the denominator. In this case, the fraction is equivalent to 1.5, which is a decimal representation of the rational number.

Step-by-step explanation:

Answer:

Fraction, 15/10 is written out as 15 Over 10

Answer:

t⁴+5t³-3t²-2

Step-by-step explanation:

You can't subtract a variable with a different exponent:

Example:

CAN'T BE SUBTRACTED - 3x²-3x⁴

CAN BE SUBTRACTED - 4x²-2x²=2x²

[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]

[tex]\sf (5t^{3} -9)-(t^{4}-3t^{2} +7 )[/tex]

Beware of the terms of the right hand side parenthesis, as we'll have to change the symbol of all of them because of the minus (-) symbol infront of the parenthesis.

[tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]

Like terms are terms that contain the same variables and can be added and subtracted simply. For example, 7x and 2x are like terms, because they are both expressed in terms of x. However, 7x and x² are not like terms, because one os expressed in terms of x and the ither in terms of x².

• Note: All natural numbers not being multiplied by any variables are like terms.

So now let's identify those like terms:

From this expression: [tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]

Only -9 and -7 are like terms. And, since -9-7= -16, the resulting expression should be the following:

[tex]\sf 5t^{3} -t^{4}+3t^{2} -16[/tex]

So even though the last expression is the answer to this problem, we can polish it a little bit by ordering the terms. In math and other exact sciences, terms are normally ordered alphabetically and from greatest to least of it's the same variable with different exponents. Therefore, the final answer is:

[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]

Answer: Option B, the outcomes of a fair die rolled 100 times, is likely to be normally distributed.

Step-by-step explanation:

Answer: Option B, The outcomes of a fair die rolled 100 times

Step-by-step explanation:

that would most likely be normally distributed.

hope it helped! Good luck!!! :)

The relationship in the previous question involves the difference of squares pattern, which applies to polynomials of the form:

a^2 - b^2

where a and b are any real numbers.

If we replace a with x and b with 2, the equation would look like:

x^2 - 2^2 = (x + 2)(x - 2)

This means that any polynomial of the form x^2 - 4 can be factored using the difference of squares pattern.

As for creating our own replacement of a and b, let's say we replace a with y and b with 3. Then the equation would look like:

y^2 - 3^2 = (y + 3)(y - 3)

This means that any polynomial of the form y^2 - 9 can be factored using the difference of squares pattern.

A graph of triangle CAT is shown below.

A graph of triangle C'A'T, the image of ΔCAT after a reflection in the x-axis is shown below.

ΔC'A'T represents a rigid motion because the pre-image and the image are congruent.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

Next, we would apply a reflection over or across the x-axis;

(x, y)                →      (x, -y)

C (-1, 2)       →      (-1, -(2)) = C' (-1, -2)

A (-1, 4)       →      (-1, -(4)) = A' (-1, -4)

T (3, 2)       →      (3, -(2)) = T' (3, -2)

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Answer:

-13

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.

If you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...

  C = πd

so the total circumference is ...

  C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units

The perimeter of the figure is about 47.12 units.

The area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...

  A = (π/4)d²

The total area of the circles of diameters 4 and 11 is ...

  A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)

The area of the central rectangle is added to the areas of the semicircles. Its area is ...

  A = LW

  A = (11)(4)

The area of the entire figure is the sum of the circle areas and the rectangle area:

  total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units

The area of the figure is about 151.60 square units.

__

Additional comment

You usually see the formula for the area of a circle as ...

  A = πr²

Since r = d/2, we can express this using d as ...

  A = π(d/2)² = π(d²)/(2²) = (π/4)d²

You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.

Answer:

Based on the information provided, there seems to be a discrepancy between the given information about the quantity shrinking at a continuous rate and the requested information about its effective growth rate. If a quantity is shrinking continuously, it is not experiencing growth, and therefore there is no effective growth rate. Nonetheless, assuming that the requested information was about the effective shrinkage rate of the quantity per year, this information can be extracted from the given information that "A quantity shrinks at a continuous rate of 33% per year." The effective shrinkage rate of the quantity can be calculated as follows:

Let r be the continuous shrinkage rate of the quantity

The effective shrinkage rate of the quantity is given by the expression (1 - r).

From the given information , r = 33% = 0.33.

Therefore, the effective shrinkage rate of the quantity is (1 - r) = (1 - 0.33) = 0.67 or 67% per year.

Note that if the phrase "effective growth rate" was a mistake, and the original intent was to ask for the shrinkage rate, then the above calculation gives the answer. Otherwise, further clarification is needed.

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Step-by-step explanation:

The question refers to the concept of continuous growth or shrinkage, and the effective growth rate in a financial context. Despite missing figures, assuming a quantity shrinks at a continuous rate of 3% and its effective growth rate is 2%, it implies a net shrinkage is 1% annually.

The question pertains to the subject of compound interest in finance, but it appears that some of the figures and percentages are missing. However, generally speaking, continuous growth or shrinkage refers to the rate at which a quantity increases or decreases for a specific period of time. The effective growth rate is a term in finance that is used to compare the annual interest rates between financial products that have different compounding terms. For instance, if a quantity shrinks at a continuous rate of 3% per year, and its effective growth rate is 2% per year, it means that net shrinkage is 1% per year.

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Answer:

The equation is y=-3

Step-by-step explanation:

The line is horizontal, cutting across the y-axis, which means it will be a y= line. The point it hits the y-axis is -3, so it is y=-3.

Answer:

The equation that represents a direct variation is y = 5x - 2.

In a direct variation, one variable is proportional to the other variable, which means that as one variable increases or decreases, the other variable also increases or decreases in direct proportion. The general form of an equation that represents direct variation is y = kx, where k is a constant of proportionality.

In this case, the equation y = 5x - 2 is in the form of y = kx, where k = 5. This means that as x increases or decreases, y will also increase or decrease proportionally, with a constant rate of change of 5. Therefore, this equation represents a direct variation.

Answer:

The amount of fabric needed to create one quilting square is 8 inches.

Answer:

The amount of fabric needed to create one quilting square is 8 inches.

Step-by-step explanation:

The percentage of the questions she got wrong is 15%

What is a Percentage?

Percentage is a number or ratio by dividing the value by the total value and then multiplying the result by 100.

How to determine this

Out of 20 questions, Claire got 17 questions

i.e the questions she got right = 17

The questions she got wrong = 20 - 17 = 3

To get the percentage she got wrong

= 3/20 *100%

= 300/20%

= 15%

Therefore, the percentage she got wrong is 15%

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2) The way the coordinates show the given scale factor is that the ratio of both x and y coordinates to the mapped coordinate before dilation are all equal.

3) The coordinates after dilation are: (5.4, 27)

2) The coordinates transformed points after dilation are completed as:

B(2, 4) → B'(3, 6)

K(4, -4) → K'(6, -6)

N(-6, 0) →N'(-9, 0)

The scale factor is same because using the ratio of the x coordinates gives:

3/2 = 1.5

6/4 = 1.5

-9/-6 = 1.5

3) The point W of the vertex of the polygon has coordinates as (2, 10)

Thus, if dilated by a scale factor of 2.7, we have the new coordinates as:

(2*2.7, 10*2.7) = (5.4, 27)

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