The steps Thomas used to solve an equation are shown.
Which statement about the steps Thomas used is true?

Solution

Final answer

Randomization

Answer:

x   y

0   -2

4   -1

8   0

Step-by-step explanation:

y + 2 = 1/4 x

Subtract 2 from both sides.

y = 1/4 x - 2

Now let x equal each value of x in the table and solve for y.

x = 0

y = 1/4 * 0 - 2

y = -2

x = 4

y = 1/4 * 4 - 2

y = 1 - 2 = -1

x = 8

y = 1/4 * 8 - 2

y = 2 - 2

y = 0

If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.

An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.

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The second derivative of y with respect to x at t=2 is 31/42.

To find the second derivative of y with respect to x at the given point, we need to compute d²y/dx². Given the parametric equations x = 21t² and y = 31t³, we can express t in terms of x and substitute it into the equation for y to eliminate the parameter.

Let's start by finding the first derivative of y with respect to t:

dy/dt = d/dt (31t³) = 93t².

Now, we can find the derivative of x with respect to t:

dx/dt = d/dt (21t²) = 42t.

To find dt/dx, we can take the reciprocal of dx/dt:

dt/dx = 1 / (42t).

Next, we can find the second derivative of y with respect to x:

d²y/dx² = d/dx (dy/dx) = d/dx (dy/dt * dt/dx).

Now, substituting the expressions we derived earlier:

d²y/dx² = d/dx (93t² * 1 / (42t)) = d/dx (93t / 42) = 93/42 * dt/dx.

Now, we can evaluate this at t = 2:

d²y/dx² = 93/42 * dt/dx = 93/42 * (1 / (42 * 2)) = 93/42 * 1/84 = 31/42.

Therefore, the second derivative of y with respect to x at the point where t = 2 is 31/42.

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Answer:

the price is 4 dollars

Step-by-step explanation:

Answer:

$0.63 per unit

Step-by-step explanation:

you divide 3.78 by 6 and you get 0.63 if rounded 0.60

srry if it's incorrect

Answer:

Convert the percentage to a fraction by placing the expression over 100. Percentage means 'out of 100'.

5/100 Cancel the common factor of 5 and 100.  1/20

Convert the fraction to a decimal by dividing the numerator by the denominator. 0.05 => 0.05 raise

Step-by-step explanation:

If two polygons are similar, then they have the same shape but not necessarily the same size.

They can be either enlarged or reduced in size or reflected. Hence, even though the polygons are similar, they do not have to be drawn to scale.

The term scale refers to the ratio of any two corresponding lengths in two geometric figures, so if two figures are drawn to scale, the ratio of their corresponding lengths in the drawing is the same as the ratio of their corresponding lengths in the actual figures.

Therefore, if two polygons are similar but not drawn to scale, the drawing may not be an accurate representation of the actual figures, as the scaling information may not be consistent.

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Answer:

10/16

5 can be divided into ten, and 8 can be divided into 16. They are both divided by two, thus creating a proportional ratio.

katie, stop deleting my answer =_=

Answer:

10/16

Step-by-step explanation:

The other person is right!

I hope this helps! Have a great day!

Lilac~

The volume of the right pyramid with the given properties is 80√3 cubic volume

The given parameters are:

Start by calculating the base area using:

Base area = 6 * Area of equilateral triangle

So, we have:

Base area = 6 * 4√3

Evaluate

Base area = 24√3

The volume of the pyramid is:

Volume = 1/3 * Base area * Height

So, we have:

Volume = 1/3 * 24√3 * 10

Evaluate

Volume = 80√3

Hence, the volume of the right pyramid is 80√3 cubic volume

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Answer:

WY represents the height.

If the area of an equilateral triangle with sides of 4 ft is 4StartRoot 3 EndRoot square feet, then the area of the regular hexagon base is 24 StartRoot 3 EndRoot square feet.

The volume is 80 StartRoot 3 cubic feet. :D

The size of a matrix is ​​its dimension,

AB and BA are of size 4 x 4 and 2 x 2 respectively

Matrix A has dimension 4 x 2 and matrix B has dimension 2 x 4

Matrix:

In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or formulas, arranged in rows and columns, used to represent mathematical objects or properties of such objects .

Product of Matrix:

Multiplication of two matrices is defined only if the number of columns in the left matrix equals the number of rows in the right matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then its matrix product AB is an m-by-p matrix whose entries correspond to the corresponding rows of A in the matrices.

A column of B whenever a product of different sizes is such that it is defined.  The product AB can be defined without BA being defined. That is, if A and B are m-by-n and n-by-k matrices, respectively, and m ≠ k. In general, even if both products are defined, they need not be the same. So, AB ≠ BA,

Product AB:

The dimensions of AB are the rows of matrix A multiplied by the columns of matrix B.

Matrix A has 4 rows and Matrix B has 4 columns.

Therefore, the dimension of the matrix AB is 4 x 4.

Product BA:

The dimensions of matrix BA are the rows of matrix B multiplied by the columns of matrix A.

Matrix B has 2 rows and Matrix A has 2 columns.

Therefore the dimension of the matrix BA is 2 x 2.

Therefore, the sizes of AB and BA are 4 x 4 and 2 x 2 respectively.

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Answer:

11.1

Step-by-step explanation:

Recall the three trig functions remember SOH CAH TOA

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Here we are given an angle as well as the hypotenuse(longest side) and we want to find h which is opposite of the given angle.
When dealing with opposite and hypotenuse we use the trig function sine

Knowing this we create an equation and plug in what we are given

Sin = Opposite / Hypotenuse

Sin(48) = h / 15

==> multiply both sides by 15

15sin(48) = h

==> simplify

11.1 = h

Zeros of the given polynomial are -2, 2, -3/2, 3/2

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

Given a polynomial 1/4(4\(x^{4}\) - 25\(x^{2}\) + 36)

1/4(4\(x^{4}\) - 25\(x^{2}\) + 36) = 0

(4\(x^{4}\) - 25\(x^{2}\) + 36) = 0

4\(x^{4}\) - 16\(x^{2}\) - 9\(x^{2}\) + 36= 0

4\(x^{4}\)(\(x^{2}\) - 4) - 9(\(x^{2}\) - 4) = 0

(4\(x^{4}\)-9)(\(x^{2}\) - 4) = 0

(x+2)(x-2)(2x+3)(2x-3) = 0

x = -2, 2, -3/2, 3/2

Hence, Zeros of the given polynomial are -2, 2, -3/2, 3/2

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The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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Answer:

16

Step-by-step explanation:

by using pythagorean theorem we know that the equal sides of the isosceles triangle are 5 units in length while the bottom side appears to be 6 units in length.

so we the perimeter is 16

The elementary matrix E = [1 0 0; 0 1 0; 5/3 -2 1] such that EC = A.

To find an elementary matrix E such that EC = A, we need to perform row operations on the matrix C such that it becomes A.

We can achieve this by performing the following row operations on C:

R3 ← R3 + R1

R1 ← R1/3

R2 ← R2 - 3R1

R3 ← R3 + 5R2

The resulting matrix after these row operations is:

1 0 0

0 1 0

5/3 -2 1

Therefore, the elementary matrix E that corresponds to these row operations is:

1 0 0

0 1 0

5/3 -2 1

We can verify that EC = A by multiplying EC:

[0 3 -5 0 1 2-1 2 0 0 0 0-1 2 0 0 0 0] x [0 3 -5 0 1 2                      

0 1 2 0 0 0                      -1 2 0 0 0 0]

= [0 3 -5 1 -1 2   -1 2 0 0 0 0   0 3 -5 0 1 2]

= A

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Answer and Step-by-step explanation:

These four tangents are all equal in length. By definition, you can draw two tangent lines from a point outside a circle that will touch the circle. These two tangent lines are always congruent. Looking at the two leftmost lines, they are tangents of the nickel, so we can say that they're congruent. Looking at the middle two lines, we see that they must be equal, as well, since they're tangent lines to the dime, but we notice that the second leftmost line is shared by the nickel and the dime. So, these three must all be congruent. By similar reasoning, the rightmost line is congruent to the other three. Thus, all four tangent lines have the same length.

Answer:

Tangents drawn from the same point are equal in length.

Since the middle coin share tangents with the coins on either sides, all tangents are equal in length.

Explanation:

We are asked to get the slope of the graph

To do so, we have to make use of the relationship:

From the graph given

We have the following points:

So we can obtain the slope as follow

Thus, the slope

Answer:

x=60

Step-by-step explanation:

x+2x=3x

180/3=60(interior angles add up to 180)

Answer:

The next sequence is 243

The pattern is x 3

3 x 3 = 9

9 x 3 = 27

27 x 3 = 81

81 x 3 = 243

Step-by-step explanation:

You're welcome.

Answer:

\(\sin(x)=-\dfrac{1}{2}\)

Step-by-step explanation:

The tangent function, tan(x), can be expressed as the ratio of sin(x) to cos(x):

\(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)

We are told that tan(x) = -1/√3.

There are two ways that tan(x) can be negative:

As we have been told that cos(x) is positive, then sin(x) must be negative.

To find the value of sin(x), equating the tan(x) ratio to the given value of tan(x), and rearrange to isolate cos(x):

\(\tan(x) = -\dfrac{1}{\sqrt{3}}\)

\(\dfrac{\sin(x)}{\cos(x)}=-\dfrac{1}{\sqrt{3}}\)

\(\cos (x)=-\sqrt{3}\sin(x)\)

Substitute the found expression for cos(x) into the trigonometric identity sin²(x) + cos²(x) = 1 and solve for sin(x):

\(\begin{aligned}\sin^2(x)+\left(-\sqrt{3} \sin(x)\right)^2&=1\\\\\sin^2(x)+3\sin^2(x)&=1\\\\4\sin^2(x)&=1\\\\\sin^2(x)&=\dfrac{1}{4}\\\\\sin(x)&=\sqrt{\dfrac{1}{4}}\\\\\sin(x)&=\pm \dfrac{1}{2}\end{aligned}\)

As we have already determined that sin(x) is negative, this means that the value of sin(x) is:

\(\boxed{\sin(x)=-\dfrac{1}{2}}\)

Answer:

the formula is

base^2+height^2=hypotenuse^2

I hope it helps

have a nice day

if you still can't understand feel free to ask me

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Answer:

21

Step-by-step explanation:

Kindly check the image below to see a visual of how the question is set up.

( my apologies for the terrible handwriting lol )

Now lets look back at the question.

The question is asking us to find the total length of Jayleen and Walter's entire walk.  

Essentially it's asking for the perimeter.

In order to find the perimeter we must find the length of the hypotenuse.

Notice that the image created forms a triangle with a right angle.

That being said we can use the Pythagorean Theorem to solve for the missing side length ( or the "shortcut" ) ( also note that the Pythagorean theorem only works with right triangles )

The Pythagorean theorem = \(a^2+b^2=c^2\) where a and b = legs and c = hypotenuse

The two legs = 5 and 7 and the hypotenuse = the shortcut

That being said, we plug in the given values ( a and b ) and solve for "c"

\(5^2+7^2=c^2\)

step 1: Simplify

\(5^2=25\\7^2=49\\25+49=74\)

now we have 74 = c²

step 2 take the square root of each side

\(\sqrt{74} =8.60232\\\sqrt{c^2} =c\)

we're left with c = 8.60232

This means that the shortcut that Jayleen and Walter took had a distance of 8.6

Finally we find the perimeter of the triangle

Perimeter = sum of side lengths

8.6 + 7 + 5 = 20.6

* round to the nearest whole number *

The answer would be 21

To compare fractions with like numerators always compare denominators.

We can calculate the LCM of the numerators and then multiply the numerators by the corresponding values to make the numerators of two or more fractions the same or similar. If the numerators are similar or the same, comparisons become simple. Verify the denominators of fractions with comparable or identical numerators. The fraction decreases as the denominator increases. They are referred to as having like or the same numerators when two or more fractions have the same numerators but distinct denominators. While they are referred to as having like or the same denominators when the denominators of two or more fractions are the same.

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The sum of all the possible values of the hypotenuse is 128.4.

According to the statement

we have given that the Three relatively prime integers are the sides of a right triangle and the smallest leg has length 28.

And we have to Find the sum of all the possible values of the hypotenuse.

So, For this purpose, we know that the

Let us consider a three relatively prime integers which are 29,31,37.

we choose these numbers because we have given that the

the smallest leg has length 28.

And according to the Pythagoras theorem.

we know that the

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

And let the smallest length be a base.

So , Put the values of the perpendicular in this one by one then

so,

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

Here Put perpendicular = 29 and base = 28.

Then

(Hypotenuse)^2 = (29)^2 + (28)^2

(Hypotenuse)^2 = 1625

(Hypotenuse) = 40.31

And then

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

Here Put perpendicular = 31 and base = 28.

Then

(Hypotenuse)^2 = (31)^2 + (28)^2

(Hypotenuse)^2 = 1745

(Hypotenuse) = 41.77

And then

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

Here Put perpendicular = 37 and base = 28.

Then

(Hypotenuse)^2 = (37)^2 + (28)^2

(Hypotenuse)^2 = 2153

(Hypotenuse) = 46.40

And then

The all possible values of the hypotenuse are 40.31, 41.77, 46.40.

And the sum become is 128.4

So, The sum of all the possible values of the hypotenuse is 128.4.

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If the angles are ∠1 = 2x + 4 and ∠2 = 3x - 3, then m∠TRS =  36°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of ∠1 = 2x + 4

The measure of ∠2 = 3x - 3

The measure of ∠TRS is -

∠TRS = ∠1 + ∠2

Since, PR is a bisector then ∠1 = ∠2.

The equation is -

2x + 4 = 3x - 3

2x - 3x = - 3 - 4

-x = -7

x = 7

Substitute the value of x in the angles -

∠1 = 2(7) + 4

∠1 = 14 + 4

∠1 = 18°

∠2 = 3(7) - 3

∠2 = 21 - 3

∠2 = 18°

So, the value of ∠TRS is -

∠1 + ∠2

18° + 18°

36°

Therefore, the measure of ∠TRS is 36°.

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The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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By eliminating values from the given the given set , it will reduce the mean and median value. Mean = 23.5 and Median = 5

According to the question, the given set of values for the calculation of mean and median is as follows:

Values: = (-6, 3, 3, 3, 3, 5, 6, 6, 8, 10)

After eliminating -6 from the given set of values:

Values: = (3, 3, 3, 3, 5, 6, 6, 8, 10)

Now the median is the middle tern from the given set of the values:

Median = 5

And mean is : 3 + 3 + 3 + 3 + 5 + 6 + 6 + 8 + 10 / 2 = 47/2 = 23.5

Hence, the correct answer is median = 5 and mean = 23.5

What is mean and median?

The mean is the average value of the given set of the data. It is the addition of all the values and later divide it by two. Similarly, median is the middle value from the set of values provided it should be arranges in the order ascending to descending.

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Answer:

The corresponding sides:

\(NO\)≅\(ZW\)

\(PM\)≅\(XY\)

\(MN\)≅\(YZ\)

\(OP\)≅\(WX\)

The corresponding angles:

\(< M\)≅\(< Y\)

\(< P\)≅\(< X\)

\(< O\)≅\(< W\)

\(< N\)≅\(< Z\)

?????????????????????

The slope is positive and equal to 3, there is a positive relationship between X and Y. The remaining statements regarding a horizontal relation, a negative slope, or a vertical relation between X and Y are incorrect.

Based on the given information, we can conclude the following:

1. The slope is positive, and it is equal to 3: The coefficient of X in the equation Y = 390 * 3X is 3, indicating a positive relationship between X and Y. For every unit increase in X, Y increases by 3 units.

2. When X = 0, Y = 390: When X is zero, the equation becomes Y = 390 * 3 * 0 = 0. Therefore, when X is zero, Y is also zero.

3. The relation between X and Y is horizontal: The statement "the relation between X and Y is horizontal" is incorrect. The given equation Y = 390 * 3X implies a linear relationship between X and Y with a positive slope, meaning that as X increases, Y also increases.

4. When Y = 0, X = 130: To find the value of X when Y is zero, we can rearrange the equation Y = 390 * 3X as 3X = 0. Dividing both sides by 3, we get X = 0. Therefore, when Y is zero, X is also zero, not 130 as stated.

5. The slope is -3: The statement "the slope is -3" is incorrect. In the given equation Y = 390 * 3X, the slope is positive and equal to 3, as mentioned earlier.

6. The relation between X and Y is vertical: The statement "the relation between X and Y is vertical" is incorrect. A vertical relationship between X and Y would imply that there is no change in Y with respect to changes in X, which contradicts the given equation that shows a positive slope of 3.

7. As X goes up, Y goes down (downward sloping or negative relationship between X and Y): This statement is incorrect. The equation Y = 390 * 3X indicates a positive relationship between X and Y, meaning that as X increases, Y also increases.

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