Travis wrote a $53 check for a new pair of shoes. Then, he withdrew $40 from his bank account. What integer represents the change to his bank account balance after the two transactions?

Answer:step 2

Step-by-step explanation:

The evaluated the integral of the product of tangent and secant functions  is -(1/6) ln| sin(6x)| + C, where C is the constant of integration.

Integration is an important topic in calculus that deals with finding the antiderivative or indefinite integral of a given function. In this problem, we are required to evaluate the integral of the product of tangent and secant functions.

To evaluate the given integral, we need to use the substitution method. Let u = 6x, then du/dx = 6, and dx = du/6. Substituting these values, we get:

∫tan(6x) sec(6x) dx = ∫tan(u) sec(u) (du/6)

Now, we need to simplify the integrand by using trigonometric identities. Recall that secant is the reciprocal of cosine, so we can write sec(u) = 1/cos(u). Similarly, we know that tangent is the quotient of sine and cosine, so we can write tan(u) = sin(u)/cos(u). Substituting these values, we get:

∫tan(u) sec(u) (du/6) = ∫(sin(u)/cos(u)) (1/cos(u)) (du/6)

Simplifying the expression further, we get:

∫tan(6x) sec(6x) dx = (1/6) ∫sin(u)/cos^2(u) du

We can now integrate this expression by using another substitution. Let v = cos(u), then dv/dx = -sin(u) du/dx = -sin(u) * 6. Rearranging this equation, we get du = dv/(-6sin(u)) = -dv/(6v * √(1 - v^2)). Substituting these values, we get:

∫sin(u)/cos^2(u) du = -∫(1/v^2) (-dv/(6v * √(1 - v^2)))

Simplifying the expression further, we get:

∫tan(6x) sec(6x) dx = (1/6) ∫(1/v^2) (dv/√(1 - v^2)))

This expression can be integrated by using the substitution v = sin(x), then dv/dx = cos(x), and dx = dv/cos(x). Substituting these values, we get:

∫(1/v^2) (dv/√(1 - v^2))) = -∫(1/(1 - v^2)) (-dv/v)

Integrating this expression, we get:

∫tan(6x) sec(6x) dx = -(1/6) ln|v| + C

Substituting back the value of v, we get:

∫tan(6x) sec(6x) dx = -(1/6) ln| sin(u)| + C

Finally, substituting back the value of u, we get:

∫tan(6x) sec(6x) dx = -(1/6) ln |sin(6x)| + C

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Complete Question:

Evaluate ∫tan(6x) sec(6x) dx.

Answer:

A is the corect answer

Step-by-step explanation:

when solved it will equal 0=4 which is a contridition.

Answer:

B,C And D have no solution

A has infinit solutions

The result is 16, which matches the information given in the problem. Thus, our solution is correct. Thao originally had 30 coins.

Let's solve this problem step by step.

Let's assume the number of coins Thao originally had is x.

According to the problem, Thao gives two fifths of her coins to her sister. Two fifths of x can be represented as (2/5)x.

After giving away two fifths of her coins, Thao receives 4 coins for her birthday. So, the number of coins she has now is (2/5)x + 4.

The problem states that she now has 16 coins. Therefore, we can set up the following equation:

(2/5)x + 4 = 16

To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 4 from both sides:

(2/5)x = 16 - 4

(2/5)x = 12

To get rid of the fraction, we can multiply both sides of the equation by 5:

5 * (2/5)x = 5 * 12

2x = 60

Next, divide both sides of the equation by 2 to solve for x:

(2x)/2 = 60/2

x = 30

Therefore, Thao originally had 30 coins.

To verify our answer, we can substitute x = 30 back into the equation (2/5)x + 4 and see if it equals 16:

(2/5) * 30 + 4 = 12 + 4 = 16

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The value of x in the statement negative 3 less than 4.9 times a number x is the same as 12.8 is 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given a statement negative 3 less than 4.9 times a number, x, is the same as 12.8 this can be numerically expressed as,

4.9x - (- 3) = 12.8.

4.9x + 3 = 12.8

4.9x = 12.8 - 3.

4.9x = 9.8.

x = 9.8/4.9.

x = 2.

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Answer:

D

Step-by-step explanation:

Recall that a⟌b means b/a. So, we want to find the expression: 20⟌4 and 4 ÷ 20. By examining, we see that D has those two expressions.

So, the answer is \(\boxed{D}\) and we're done!

Answer:

Answer:

D

Step-by-step explanation:

Recall that a⟌b means b/a. So, we want to find the expression: 20⟌4 and 4 ÷ 20. By examining, we see that D has those two expressions.

So, the answer is  and we're done!

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

Answer:

1/4 gallon of yellow of paint and none of the blue paint

Step-by-step explanation:

Answer:

the fifth number is 11

Step-by-step explanation:

8,11,13 and 17, x

the mean is =12  ( which means the sum of the terms divided by the numbers of terms )

to find the mean :

(8+11+13+17+x)/5 =12

5*12=49+x

60-49=x

x=11

Step-by-step explanation:

Componets of a vector are

\(x = r \cos(x) \)

\(y =r \sin(x) \)

The vector of F1 has a angle of 30 and radius of 30 n so the component are

\(x = 30( \cos(30) ) = {15 \sqrt{3} }\)

\(y = 30 \sin(30) = 15\)

F2 is a 90 degree so

\(x = 20 \cos(90) = 0\)

\(y = 20\sin(90) = 20\)

F3 is a 240 degree so we have

\(x = 35( \cos(240) ) = - 17.5\)

\(y = 35 \sin(240) = - 17.5 \sqrt{3} \)

F4 is 310 angle so we have

\(x = 40 \cos(310) = - 21.01\)

\(y = 40 \sin(310) = 34.04\)

Answer:

\(9\frac{41}{51}\)

Step-by-step explanation:

Given the expression:

\(41 \frac{2}{3} \div4\frac{1}{4}\)

Convert the mixed numbers into improper fractions and then use KCF (Keep, Change, Flip) to solve the problem. Simplify if needed and then convert the improper fraction back into the mixed number.

\(41\frac{2}{3} \div4\frac{1}{4}\)

\(41\frac{2}{3} =3\times41=123+2=125=\frac{125}{3}\)

\(4\frac{1}{4} =4\times4=16+1=17=\frac{17}{4}\)

\(\frac{125}{3} \div\frac{17}{4}\)

\(\frac{125}{3} \div\frac{17}{4} =\frac{125}{3} \times\frac{4}{17}\)

\(125\times4=500\)

\(3\times17=51\)

\(=\frac{500}{51}\)

\(\frac{500}{51} =500\div51=9\frac{41}{51}\)

\(=9\frac{41}{51}\)

Hope this helps.

Step-by-step explanation:      

Step 1: Convert mixed numbers to improper fractions

\(=\frac{125}{3}\div \:4\frac{1}{4}\)

Step 2: Apply fraction rule

\(\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\)

\(=\frac{125}{3}\times \frac{4}{17}\)

Step 3: Multiply Fractions

\(=\frac{125\times \:4}{3\times \:17}\)

Step 4: Multiply the numbers

\(125\times \:4=500\)

\(=\frac{500}{3\times \:17}\)

Step 5: Multiply the numbers

\(\:3\times \:17=51\)

\(=\frac{500}{51}\)

Step 6: Convert Improper fraction to mixed numbers

\(=9\frac{41}{51}\)

Answer:     

\(=9\frac{41}{51}\)

Hope this helps.

Answer: 3 * -4 = -12

Answer:

four less than three times a number

Step-by-step explanation:

Answer:

0.67

Step-by-step explanation:

The probability that the event will not happen is 1 - 0.33 and that is 0.67

A quadrilateral is a parallelogram if its adjacent angles are supplementary.

We are expected to demonstrate that a quadrilateral is a parallelogram if its adjacent angles are supplementary. Writing down what is given and needs to be supported will be our first step.

1) An ABCD quadrilateral is a given.

2) ∡A supplements ∡B, ∡B supplements ∡C, ∡C supplements ∡D and ∡D supplements ∡A.

To demonstrate: Parallelogram ABCD is a quadrilateral.

Consider AC and BD as evidence. The intersection of AC and BD is AB.

Two angles on the same side of the transversal AB are ∡A and ∡B.

A property states that two lines are parallel if a transversal cuts them and the interior angles on the same side of the transversal are additional.

Here, it is given that ∡A supplements ∡B.

⇒∡A+∡B=180∘

The lines AC and BD are therefore parallel to one another.

Now think about AB and CD. The intersection of AB and CD is AC.

Two angles on the same side of the transversal AB are ∡A and ∡D .

A property states that two lines are parallel if a transversal cuts them and the interior angles on the same side of the transversal are additional.

Here, it is given that ∡D supplements ∡A.

⇒∡A+∡D=180∘

The lines AB and CD are therefore parallel to one another.

Now, since both the pairs of opposite sides are parallel, ABCD is a parallelogram.

Hence proved.

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The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.

To find the probability that a randomly selected student will like pizza but not chicken nuggets.

Let P = the number of students who like pizza but not chicken nuggets

Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets

P = 28n - 8

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students)

We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:

Total number of students = 28n + 15 - 8 = 28n + 7

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)

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The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.

Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure

A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.

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Answer:

3 sqrt(10)

Step-by-step explanation:

To find the distance, we use the formula

d = sqrt( ( x2-x1)^2 + (y2-y1)^2)

  = sqrt( ( 2- -1)^2 + ( -4-5)^2)

  = sqrt( (2+1)^2 +(-4-5)^2)

  = sqrt( 3^2 +(-9)^2)

  = sqrt( 9+81)

 = sqrt(90)

= sqrt ( 9*10)

  3 sqrt(10)

Answer:

We can conclude that if two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

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Answer:

-273c

Step-by-step explanation:

Answer:

72%

Step-by-step explanation:

As the T-shirts have 20% off and Juanita would get an extra 10% off the sale price, the additional discount would be over the price with the 20% off included. This means that the sale price is the 80% of the normal price and an additional 10% over that 80% would be:

80*10%= 8

80%-8%= 72%

This means that Juanita would have to pay the 72% percent of the regular price of the T-shirt as the total discount would be 28% off.

The volume of the cone will be 21 cubic units.

Volume is defined as the space occupied by any object in the three dimensions. All three parameters are required for the volume like length, width, and height of the cube.

The formula for the volume of a cone is ⅓ r²h cubic units, where r is the radius of the circular base and h is the height of the cone.

Volume = ⅓ r²h

Volume = ⅓ x x 2² x  5

Volume = 21 cubic units

Therefore, the volume for the given shape of the cone will be 21 cubic units.

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The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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Answer:

width : 21ft

length : 63ft

Step-by-step explanation:

(42ft + w) + (42ft + w) + w + w = 168ft

42ft + w + 42ft + w + w + w = 168ft

w + w + w + w = 168ft - 42ft - 42ft

4w = 84ft

w = 84ft ÷ 4

w = 21ft

so,

width : 21ft

length : 21ft + 42ft = 63ft

Brand B contains 3% saline solution by volume. Then, C is the right answer.

Percentage of saline solution in brand B, let x be.

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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Triangle 1

A = 64

B = 51

C = ?

C = 180 - 64 -51

C = 65

Triangle 2

F = 65

D = 64

E ?

E = 180- 65 -64

E = 51

Procedure

Yes they are similar

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

Answer:

both elements will be negative in rot.180°

It should be close to 7m at around 5pm. In fact, this is the time of day when the water rises the fastest, so perhaps 8m

The interval between successive peaks in the sinusoidal signal graph, or period, is only the number of seconds needed for one cycle of the sinusoid.

Depending on the values of angular frequency (), discrete-time sinusoidal sequences may or may not be periodic. A discrete-time sinusoidal signal must have an angular frequency () that is a multiple of 2 to be considered periodic.

It takes roughly 6 hours from low tide to high tide, or 12 hours for the entire tide cycle. Since low tide was at 2 a.m., low tide will be at around 2 p.m. as well. Three hours later, or at around 5 p.m., the water should be at the average level, which should be at (12.4+1.2)/2=6.8 m. Therefore, it should be close to 7m around 5:45. Actually, this is when the water rises the fastest, so it's probably close to 8m. Your 5.5m is obviously too low, regardless of where it is.

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Answer:

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

Given two similar triangles:

We know similar figures have same ratio of corresponding sides.

Apply this to the given triangles to get:

Substitute values:

The matching choice is B.

The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

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Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

Which triangle is ​△abc​ similar to and why? responses △abc is similar to △ghi by ​aa similarity postulate. triangle a b c, is similar to , triangle g h i, by , ​, a a similarity postulate, ., △abc is similar to △jkl by ​aa similarity postulate​. triangle a b c, is similar to , triangle j k l, by , ​, a a similarity postulate, ​, . △abc is similar to △def by ​aa similarity postulate​. triangle a b c, is similar to , triangle d e f, by , ​, a a similarity postulate, ​, . ​△abc​ is not similar to any of the triangles given.