What is 4 3 in expanded form?

Answer: 55

Step-by-step explanation:

Congruent angles intercept congruent chords, so since the circumference of a circle is 360 degrees, the arc angle 1 is inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

Congruent angles exist as two or more angles that exist identical to each other. Therefore, the measure of these angles exists equivalent to each other. The kind of angles does not create any distinction in the congruence of angles, which implies they can be acute, obtuse, exterior, or interior angles.

The Inscribed Angle Theorem states that the measure of an inscribed angle exists half the measure of its intercepted arc. Inscribed angles that intercept the exact arc exist congruent. This exists named the Congruent Inscribed Angles Theorem and exists shown below.

∠ A D B and ∠ A C B intercept, so m ∠ A D B = m ∠ A C B.

Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

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The perimeter of the figure with side length of 5 units is 50 units

From the question, we have the following parameters that can be used in our computation:

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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a) For this question we set h=59 and solve for t, in order to do so we use the general formula for second-degree equations:

The height of the object will be 59 feet at t=7.41 seconds and t=0.34 seconds.

b) When the object reaches the ground, h=0 therefore:

Solving for t we get:

Therefore, since t cannot be negative the solution is t=7.9 seconds.

Answer:

Step-by-step explanation:

21.019=d

21.019+4=25.019 ft of rope

25.019x.45=11.26

He willpay $11.26 for the rope

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

mean = 24

Step-by-step explanation:

the mean is calculated as

mean = \(\frac{sum}{count}\)

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = \(\frac{168}{7}\) = 24

Answer:

2√73 or 17.09 inches

Step-by-step explanation:

The small red square at the corner of the triangle symbolizes that the triangle is a right triangle. Therefore, to find the hypotenuse of the triangle, we can use the Pythagorean Theorem: a² + b² = c²

a = 6

b = 16

c = ?

Plug these values into the equation.

(6)² + (16)² = c²

Evaluate the exponents.

36 + 256 = c²

292 = c²

Take the square root of both sides to find c.

√292 = √c²

17.09 ≈ c

This is your answer.

You can also simplify the radical without using decimals.

4 • 73 = 292

Therefore,

√4 • √73 = √292

Which also means,

2•√73 = √292

So your answer is: 2√73

Hope this helps!

Answer:

We use the pythagorean theorem a²+b²=c² and in this question

a = 6

and

b = 16

so

36 + 256 = c²

so

c² = 292 so now we take the square root of it to get \(\sqrt{292}\)

Hope this helps!

2. line PQ || line SR

3. line PS || line QR

4. < P and < S are supp. angles

5.

6. < Q congruent to

7. 8. < P is congruent to

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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The unknown angle in the cyclic quadrilateral is as follows:

m∠CML = 109 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's find m∠CML as follows:

Using the arc angle and opposite angle of a quadrilateral theorem,

6x + 25 = 1 / 2 (7x + 14 + 106)

6x + 25 = 1 / 2(7x + 120)

6x + 25 = 7 / 2 x + 60

6x - 7 / 2 x  = 60 - 25

6x - 3.5x = 35

2.5x = 35

divide both sides by 2.5

x = 35 / 2.5

x = 14

Therefore,

m∠CML = 6x + 25 = 6(14) + 25 = 84 + 25 = 109 degrees

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The equivalent of (12)⁻³=1/(12)³

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,

⇒(12)⁻³

⇒1/(12)³

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a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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Answer:

\(\left[\begin{array}{cc}weeks&height(in.)\\1&12\\2&14\\3&16\\4&18\\5&20\end{array}\right]\)

Step-by-step explanation:

Every week, you add 2 inches the height.

This is why the answer should be:

\(\left[\begin{array}{cc}weeks&height(in.)\\1&12\\2&14\\3&16\\4&18\\5&20\end{array}\right]\)

Hope this helps :)

Have a spectacular day!

Step-by-step explanation:

The formula to find the interior angle of a polygon is 180(n - 2) over n.

So, we know that the interior angle of the polygon which is 120, therefore we can produce this equation, 180(n - 2) over 2 n, equals to 120.

Now we use algebric method to solve for n.

180n − 360 = 120n

60n = 360

n = 6

Note that as x gets larger, y gets smaller, but the product xy remains constant at 192.

In mathematics, a function is a relationship between two sets, called the domain and the range, such that each element of the domain corresponds to exactly one element of the range. A function takes an input value (or values) and produces an output value (or values) according to a specific rule or formula. The input values are the domain of the function, and the output values are the range of the function. Functions can be represented using equations, graphs, tables, or verbal descriptions. They are used to model relationships between variables in various fields of mathematics, science, engineering, economics, and many other areas.

Here,

If x and y vary inversely, this means that their product is a constant. We can use this fact to find the constant of proportionality k as follows:

k = xy

If we know that y is 24 when x is 8, we can substitute these values into the equation above to solve for k:

k = xy

= 8(24)

= 192

Now we can use this value of k to write the inverse variation function:

xy = 192

or

y = 192/x

To sketch a graph of this function for x > 0, we can plot a few points and connect them with a smooth curve. Here are some points we can use:

(x, y)

(1, 192)

(2, 96)

(4, 48)

(8, 24)

(16, 12)

(24, 8)

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Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

It will take 18.9 years for your investment to reach $1,500

From the question, we have the following parameters that can be used in our computation:

Initial deposit = 500 dollars

Rate of growth = 6% per year

The above implies that the growth follows an exponential path

An exponential function that represents a growth function is represented as

A(n) = a * (1 + r)ⁿ

Where

A(n) = value of investment after nth year

a = Initial deposit = 500

r = rate of growth = 6%

Substitute the known values in the above equation, so, we have the following representation

A(n) = 500 * (1 + 6%)ⁿ

Evaluate the sum

A(n) = 500 * 1.06ⁿ

When the investment is 1500 grams, we have

500 * 1.06ⁿ = 1500

Divide both sides by 500

1.06ⁿ = 3

So, we have

n = log(3)/log(1.06)

Evaluate

n = 18.9

Hence, the number of years is 18.9

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Answer:

The answer is actually 18.3 Years

Step-by-step explanation:

I got it correct on the test :D

Answer:

I don't know, maybe someone can solve the rest

Step-by-step explanation:

0.5(\(x^{4}\) - 7)12 = 4

12 * 0.5 = 6

6(\(x^{4}\) - 7) = 4

6\(x^{4}\) - 42 = 4

6\(x^{4}\) = 46

\(x^{4}\) = 46 / 6

Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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Answer:

I think its j

Step-by-step explanation:

Answer: Choice F) \(x \le -5\)

====================================================

Explanation:

One long rectangle represents x. Four of them represent 4x

One tiny unshaded square represents a unit 1. Specifically this value is positive. We have 2 columns and 6 rows, so there are 2*6 = 12 tiny squares.

So the stuff in the first box (the four long rectangles and the 12 tiny unshaded squares) represent the expression 4x+12

The stuff in the second box is -8 since we have 8 shaded squares each shaded square being -1.

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

The inequality we need to solve is \(4x+12 \le -8\)

We'll subtract 12 from both sides, then divide both sides by 4 to fully isolate x

This is what the steps would look like:

\(4x+12 \le -8\\\\\\4x+12-12 \le -8-12 \ \text{ subtract 12 from both sides}\\\\\\4x \le -20\\\\\\\frac{4x}{4} \le \frac{-20}{4} \ \text{ Divide both sides by 4}\\\\\\x \le -5\\\\\\\)

The inequality sign does not flip since we did not divide both sides by a negative number.

Answer:

7/15 is the probability of selecting a boy and a girl.

Step-by-step explanation:

Combination = nCr = n!/((n-r)!r!)

((7C1)(3C1))/(10C2)

= (7*3)/45

=21/45 = 7/15 the probability of selecting a boy and a girl.  

Answer:

x = -15

Step-by-step explanation:

In fractional equations we cross multiply the expressions:

In cross multiplying the denominator of the first fraction is multiplied with the numerator of the second fraction and vice versa:

-2x = 30 divide both sides by -2

x = -15

(a) The greatest number of boxes she can use so that each box contains the same number of pencils and pens is 48.

(b) There will be 48 pencils and pens in each box.

We have given that Tamika has 48 pencils and 80 pens.

So, the greatest number of boxes is 48, because the total number of pencils is 48, in order to share the same number of pencils and pens, the greatest number of boxes would be 48.

And,

Based on above answer and according to question's statement (each box contains the same number of pencils and each box contains the same number of pens), so, there will be one pencil and one pen in each box.

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Answer:

Step-by-step explanation:

The correlation coefficient is -0.4124

From the question, we have the following parameters that can be used in our computation:

The table of values

Next, we enter these values in a graphing tool, where we have the following summary

X Values

∑ = 52

Mean = 6.5

∑(X - Mx)2 = SSx = 42

Y Values

∑ = 93

Mean = 11.625

∑(Y - My)2 = SSy = 7567.875

X and Y Combined

N = 8

∑(X - Mx)(Y - My) = -232.5

For the coefficient, we have

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -232.5 / √((42)(7567.875)) = -0.4124

Hence, the value is -0.4124

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The total amount of money that you can deposit in the account would be = $ 8,000

Interest is defined as the amount of money that an individual earns from an investment made after a particular period of time.

The formula for calculating simple interest;

simple interest (SI) = Principal×time ×rate/100

The principal amount = $x

time = 5 years

Rate = 5%

simple interest = $2000

From the formula, make principal the subject of formula:

Principal= SI × 100/T ×R

Principal= 2000×100/5 × 5

principal= 200000/25

Principal=$ 8,000.

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Answer:

To solve m^2 - 6m = 3 using the quadratic formula, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.

m^2 - 6m - 3 = 0

Now we can identify a, b, and c:

a = 1, b = -6, c = -3

Next, we can plug these values into the quadratic formula:

m = (-b ± sqrt(b^2 - 4ac)) / 2a

m = (-(-6) ± sqrt((-6)^2 - 4(1)(-3))) / 2(1)

m = (6 ± sqrt(48)) / 2

Simplifying the square root of 48, we get:

m = (6 ± 4sqrt(3)) / 2

Now we can simplify by factoring out a 2 from the numerator:

m = 3 ± 2sqrt(3)

So the solutions to the equation are:

m = 3 + 2sqrt(3) or m = 3 - 2sqrt(3)

Step-by-step explanation:

Answer: 3±2√3

Step-by-step explanation:

see image for explanation

Let me know if you more explanation with simplifying the root.  That is a whole lesson in itself.

Answer:

Add 3 and then multiply by 5.

Step-by-step explanation:

The problem looks like this to me:

\( \dfrac{m}{5} - 3 = 8 \)

If this is correct, then the operations are:

Add 3 to both sides.

Multiply both sides by 5.

I don't see that answer. The picture is not very clear to me. What is the denominator of the fraction?