Rewrite in simplest terms: (-6x+2)+(x-3)

Answer:

  (a) ∠4 = 115°

  (b) ∠7 = 65°

  (c) ∠3 = 65°

Step-by-step explanation:

There are several applicable relationships in this figure. Perhaps the simplest is to take advantage of the relationships wherever any lines cross:

When two parallel lines are crossed by a transversal, the Corresponding Angle Theorem comes into play. It tells you ...

The rule for vertical angles gives you ...

The rule for corresponding angles tells you ...

Angles 2 and 4 are a linear pair, so are supplementary.

There are many other relationships that can be derived from these, but these are sufficient to provide a basis for answering the questions.

__

Angle 4 is supplementary to angle 2 so measures ...

  ∠4 = 180° -65° = 115°

__

Angle 7 is a vertical angle to angle 6, which is a corresponding angle with angle 2. Vertical and corresponding angles are congruent, so ...

  ∠7 ≅ ∠6 ≅ ∠2 = 65°

(See also the comment below.)

__

Angle 3 is a vertical angle to angle 2, so is congruent to it.

  ∠3 ≅ ∠2 = 65°

(Angle 3 is also "corresponding" to angle 7, which we just showed was 65°.)

_____

Additional comment

When the transversal crosses parallel lines at other than 90°, all obtuse angles are congruent, and all acute angles are congruent. The obtuse and acute angles are supplementary. Once you know one acute angle is 65°, you know all acute angles are 65°, and all obtuse angles are 115°.

Various theorems relate different angles pairs. For example, angles 2 and 7 are called "alternate exterior angles" (as are angles 1 and 8). There is a theorem that says alternate exterior angles are congruent. We arrived at the same fact using the congruence of corresponding and vertical angles.

The associated radius of convergence, R is infinity, or R = ∞.

To obtain the Maclaurin series for f(x) = xe^8x, we can use the known Maclaurin series for e^x, which is:

e^x = 1 + x + x^2/2! + x^3/3! + ...

Substituting 8x for x, we get:

e^(8x) = 1 + 8x + (8x)^2/2! + (8x)^3/3! + ...

Multiplying both sides by x, we get:

xe^(8x) = x + 8x^2 + (8x)^3/2! + (8x)^4/3! + ...

Therefore, the Maclaurin series for f(x) = xe^8x is:

f(x) = x + 8x^2 + (8x)^3/2! + (8x)^4/3! + ...

To find the radius of convergence, we can use the ratio test:

lim_n→∞ |(8x)^(n+1)/(n+1)!| / |(8x)^n/n!| = 8|x|/(n+1)

This limit approaches zero for all values of x, so the series converges for all x. Therefore, the radius of convergence is infinity, or R = ∞.

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Answer:

A

Step-by-step explanation:

I think

Answer:

\(j=qn\)

Step-by-step explanation:

\(q=\frac{j}{n}\)

Switch sides:

\(\frac{j}{n} =q\)

Multiply n to both sides:

\(\frac{j}{n} *n=q*n\)

\(j=qn\)

Answer:

\(23 L= 23 000ml\\750ml\\50L = 50 000ml\\\\50000=x+23000+750\\x=50000-23000-750\\x=26250ml\\x=26.250L\)

Step-by-step explanation:

Change all the values given to one unit. (Litres to millilitres to avoid working with decimals)

Let x represent the amount of water left to be poured.

Since all will be equal to the volume of the tank, equate all values to the total capacity of the tank.

Change the subject and solve.

Hope you understood.

Have a nice day. :)

The value of the expression 7₂ + 3₃ is 10₅.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

An expression is 7₂ + 3₃.

To find the value of the expression, first, add 7 and 3.

That means, 7 + 3 = 10.

Now add 2 and 3,

2 +3 = 5

So, the value of the expression is 10₅.

Therefore, the result is 10₅.

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Answer:

6.45

Step-by-step explanation:

29.95+7.75%=32.27

32.27/5

6.45

Answer: The answer to this math question about solving for the value of k with the given full of the angles is k = 6.

Step-by-step explanation: As always to remember, all of the forming angles to a straight line with a sum of 180 degrees, so anyways, here are 6 steps in order to solve for the value of k:

Step 1. First, let's find the measures of the value of all 3 angles, the measures of all 3 angles are, 8°, 90°, and 40° that looks in the equation form like this: \(7k + 8 + 90 + 40 = 180.\)

Step 2. Next, after finding the measures of the value of all 3 angles, it's time to add all 3 angles up together that looks in the equation form like this: \(7k + 138 = 180.\)

Step 3. Then, let's move positive 138 to the right side so you got negative 138, and keep the positive 180 the same when moving to the left side that looks in the equation form like this: \(7k = 180 - 138.\)

Step 4. In addition to that, after moving positive 138 to the right side so you got negative 138, and keep the positive 180 the same when moving to the left side, it's time to subtract 138 degrees and 180 degrees that looks in the equation form like this: \(7k = 42.\)

Step 5. Now last but not least is finally, after subtracting 138 degrees and 180 degrees, it's time to divide the both sides by 7 that looks in the equation form like this: \(\frac{7k}{7}=\frac{42}{7}.\)

Step 6. Hence the value of k is 6.

I hope that my full given answer with my full given step-by-step explanation is very helpful to your own math question about solving for the value of k with the given full of the angles, please mark me as Brainliest, take care, always be safe, and have a great rest of the day and a great weekend! :D

Sincerely,

Jason Ta,

The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.

Answer:

it can consist of translations, reflections, and rotations

Step-by-step explanation:

i would say reflection, then slide right, then slide down

if there is 2 pizza and 5 children then 1/5 (fraction) of a pizza, or two slices, must be given to each child.

Start with two pizzas of equal size. Cut each pizza into 5 equal slices, so you have a total of 10 slices. Give each child 2 slices of pizza. Each child receives 2 slices of pizza, which is:

2/10 = 1/5 of a pizza

Each child now has 1/5 of a pizza.

Since there are 5 children, the total amount of pizza shared is:

5 × (1/5) = 1 pizza

Therefore, each child has 1/5 of a pizza, or 0.2 of a pizza.

To get the total amount of pizza that was shared, we can add up the amount of pizza each child received:

5 × (2/10) = 1 pizza

So, each child receives 2 slices of pizza, which is 1/5 of a pizza, and the total amount of pizza shared is 2 pizzas, or 1 whole pizza per 2 children.

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Answer:

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Step-by-step explanation:

The general form of the straight line equation is, y = m·x + c

Where;

m = The slope

c = The y-intercept

The parent function is, f(x) = x

The slope of the parent function, m₁ = 1

The y-intercept of the parent function, c₁ = 0

The x-intercept of the parent function = 0

The equation of the given function g(x) is derived as follows;

Two points on the line g(x) are (-2, 5) and (1, -4)

The slope of g(x), m₂ = (-4 - 5)/(1 - (-2)) = -3

The equation of g(x) is therefore;

y - 5 = -3 × (x - (-2)) = -3·x - 6

∴ y = -3·x - 6 + 5 = -3·x - 1

y = -3·x - 1

The slope of the given function, m₂ = -3

The y-intercept of the given function, c₂ = -1

The x-intercept of the function = -1

We have that a reflection of (x, y) across the y-axis gives (-x, y)

Therefore, the function g(x) is a reflection of f(x) across the y-axis

The slope of g(x) = -3 × The slope of f(x), therefore, g(x) is obtained by a vertical stretch of of f(x) by a factor of 3

The y-intercept of g(x) is lower than the y-intercept of g(x) by -1, therefore, f(x) is shifted down vertically by 1 unit to obtain g(x)

Therefore, the sequence of transformation that can be used to obtain g(x) from the parent function f(x) are;

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

The root test is Divergent, for given [infinity] 1 nn n = 1.

The foundation take a look at to research the restrict of the nth root of the nth time period of your collection. Like with the ratio check, if the restrict is less than 1, the series converges; if it is extra than 1 (together with infinity), the series diverges; and if the restrict equals 1, you analyze not anything.

The root check this collection is divergent. again, there is not too much to this series. therefore, with the aid of the root take a look at this collection converges clearly and hence converges. notice that we needed to maintain the absolute cost bars at the fraction until we would taken the limit to get the sign accurate

Root test requires you to calculate the value of R the usage of the components under. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent.

explanation:

If tan is series

if Lim n root (1) = l

if l =<1 than it is convergent

if l = > 1 than it is divergent

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Answer:

radius = 2

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( where r is the radius )

x² + y² = 4 ← is in this form

with r² = 4 ⇒ r = \(\sqrt{4}\) = 2

centre (0, 0 ) and radius = 2

The sum of the two given polynomials is 2x⁴+5x³+2x-6.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given polynomials are (2x⁴-3x³-x-1) and (8x³+3x-5).

To add polynomials we simply add any like terms together.

(2x⁴-3x³-x-1)+(8x³+3x-5)

= 2x⁴-3x³+8x³-x+3x-1-5 (Group like terms and add them)

Arrange each polynomial with the term with the highest degree first then in decreasing order of degree.

2x⁴+5x³+2x-6

Therefore, the sum of the polynomials is 2x⁴+5x³+2x-6.

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After solving,  41.67 Hz wing beats the dragonfly performs per second.

In the given question, if the video is shot at 190 frames per second, then we have to find how many wing beats the dragonfly performs per second.

From the given question,

Frames per one wing beat = 6 frames

Video shot at = 250 frames per second

We firstly find the time period

So, Time period (T) = 6/250

T= 0.024 s

Snce we have to find how many wing beats the dragonfly performs per second.

Per second number of wing beats = 1/T

Per second number of wing beats = 1/0.024

Per second number of wing beats = 41.67 Hz

Hence, 41.67 Hz wing beats the dragonfly performs per second.

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The right question is;

A frame by frame analysis of a slowmotion video shows that a hovering dragonfly takes 6 frames to complete one wing beat.

If the video is shot at 190 frames per second, how many wing beats does the dragonfly perform per second?

The distance of the football on hitting the ground is D = 196.152 feet

Given data ,

A football player punts a ball at an angle of 43° at 1.5 feet off the ground

And , the initial velocity is 79 feet per second

On simplifying , we get

The distance D is given by the range

where Range = u² sin ( 2θ ) / g

And , g = 32.17 feet/sec²

So , D = ( 79 )² sin ( 86° ) / 32.17

On further simplification , we get

D = 6225.79723767 / 32.17

D = 196.152 feet

Hence , the distance is D = 193.5 feet

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The complete question is attached below :

A football player punts a ball at an angle of 43 at 1.5 feet off the ground, with an initial velocity of 79 feet per second. How far away does the ball land, in feet, when hitting the ground?

A dependency diagram of the given data is given below:Dependency diagram for given dataFormula for the Chain Rule is given below:$$\frac{dy}{dt} = \frac{dy}{dx} \cdot \frac{dx}{dt}$$For dt
dw.

From the diagram, we see that there are two independent variables, r and s, which are used to calculate the dependent variable w. Both r and s are functions of the independent variable t. Therefore, we can use the Chain Rule formula to find the derivative of w with respect to t.The Chain Rule formula states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In summary, the Chain Rule formula is used to find the derivative of a composite function. To apply it to the given problem, we created a dependency diagram to show the relationship between the variables. Then, we used the formula to find the derivative of w with respect to t by taking the derivative of w with respect to r and s, respectively, and then multiplying by the derivative of r and s with respect to t.

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Answer:

16 cards were left in the stack.

Step-by-step explanation:

27 to begin with + 6 that Cate added - 10 that Elena took - 7 that Cate took.

27 + 6 - 10 - 7 = 16

I recommend that Ronald Lau build the pilot plant first to maximize his expected payoff. The expected payoff for this decision is $55,000.

To help Ronald Lau maximize his expected payoff, we can use decision analysis to evaluate the potential outcomes and probabilities of each decision.

The first decision is whether to build the new facility directly or to build the pilot plant first and then decide whether to build the complete facility.

If the new facility is built directly, the expected payoff is $200,000 × 0.5 + (-$190,000) × 0.5 = $5,000.

If the pilot plant is built first, the expected payoff is:

$5,000 + $200,000 × 0.75 × 0.6 + (-$190,000) × 0.25 × 0.6 = $55,000

or

$5,000 + (-$190,000) × 0.75 × 0.4 + $200,000 × 0.25 × 0.4 = -$45,000

The best decision is to build the pilot plant first since this decision has a higher expected payoff of $55,000 compared to the expected payoff of $5,000 for building the new facility directly.

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Problem

1 1/3 divided by 40 by using the algorithm method

Solution

For this case we can do this first:

And then we can divide this number by 40 like this:

Answer:

I only want free points

Step-by-step explanation:

Thank you for the free points.

Let us make the line from the picture, pointing the given equations:

From the draw and the given equations, we note that:

Therefore, we can solve the equation for y as follows

Where in the last line, we add the similar terms, for example 3y+4y=7y. Let us continue the calculations

where in the second line of the equation above, we pass the 12 from the right to the left with opposite sign. We discover y as follows

That is, we have y=6.

Let us now calculate the value of RD an RT. We know from the question that

as we discover that y=6, substituting this value in the equations above we find:

We conclude that RS=27 and ST =27 .

The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

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Answer: Where is the triangle?

Step-by-step explanation: Brainliest pls:)

The central angle of the reverse curve is 0.6 radians.

The central angle of a reverse curve can be determined by using the length of the intermediate tangent and the radius of the curve. In this case, the intermediate tangent is given as 600 m and the common radius is 1000 m.

To find the central angle, we can use the formula:

Central angle = (Intermediate tangent length) / (Radius)

Plugging in the given values, we get:

Central angle = 600 m / 1000 m

Simplifying the expression, we find that the central angle is 0.6 radians.

Therefore, the central angle of the reverse curve is 0.6 radians.

It's important to  that the units of the central angle are in radians, which is a standard unit for measuring angles in mathematics.

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Answer:

Height 15 feet

Base 12 Feet

Step-by-step explanation:

The formula to find the area of a triangle is A= (0.5) x base x height, so if the area is 90 then before it was halved it must be 180 so the base x height must equal 180 and the only number that equal 180 when multiplied with a difference of 3 between them is (15,12) so thats are answer. I know this is right because if I put it through the area formula I get 90.

A=(.5) x 12 x 15

A=(.5) x 180

A= 90

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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Answer:

Answer is A

Step-by-step explanation:

Hope it helps