Find the distance between C(2,4) and D (5. 7). Round to the nearest tenth, if necessary?

Answers

Answer 1

Answer:

The answer 4.2 units

Step-by-step explanation:

The distance between two points can be found by using the formula

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

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

C(2,4) and D (5. 7)

We have

\( |CD| = \sqrt{ ({2 - 5})^{2} + ({4 - 7})^{2} } \\ = \sqrt{ ({ - 3})^{2} + ( { - 3})^{2} } \\ = \sqrt{9 + 9} \\ = \sqrt{18} \: \: \: \: \: \\ = 3 \sqrt{2} \: \: \: \: \: \\ = 4.242640687...\)

We have the final answer as

4.2 units to the nearest tenth

Hope this helps you


Related Questions

What is the percent of decrease from 100 to 24?

Answers

Answer:

To calculate a percentage decrease, first, work out the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100. The result expresses the change as a percentage—i.e., the percentage change.

A store is instructed by corporate headquarters to put a markup of ​25% on all items. An item costing 8​$ is displayed by the store manager at a selling price of ​2$. As an​ employee, you notice that this selling price is incorrect. Find the correct selling price. What was the​ manager's likely​ error?

Answers

Answer:

the correct selling price is $10

And, the error is that the manager put the markup percentage as a selling price instead of adding up the markup to the cost price

Step-by-step explanation:

The computation is shown below:

Given that

Markup = 25%

Cost of an item = $8

Selling price of an item = $2

Based on the above information

The amount of markup would be

= 25% × 8%

= $2

Now amount after markup is

= $2 + $8

= $10

Hence, the correct selling price is $10

And, the error is that the manager put the markup percentage as a selling price instead of adding up the markup to the cost price

Answer:

part A:The correct selling price is $10

Part B:And, the error is that the manager put the markup percentage as a selling price instead of adding up the markup to the cost price

Step-by-step explanation:

Step-by-step explanation:

Select al expressions that can be subtracted from 9x to result in the experssion 3x + 5

Answers

"6x - 5" is the expressions that can be subtracted from 9x to give the result in expression 3x+5.

To find the expression that can be subtracted from 9x to result in the expression 3x+5.

Let the expression be (a - b = c),

Here a = 9x

and the result, c = 3x + 5

We have to find out b = ?

Substitute the values of a and b in the above equation then we get;

9x - b = 3x + 5

9x - (3x + 5) = b

b = 6x - 5

Hence the expressions that can be subtracted from 9x to result in the expression 3x+5 is 6x - 5

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Find the length of segment VS. (Enter the just the value,
without any units.)
R
5
3
T
12
S
х

Find the length of segment VS. (Enter the just the value,without any units.)R53T12S

Answers

Answer:  20

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

Explanation:

The triangles are similar, allowing us to form a proportion

The vertical sides pair up on one side, the horizontal sides pair up on the other side. Divide in the same order.

QV/RT = VS/TS

5/3 = x/12

12*5 = 3x ... cross multiply

60 = 3x

3x = 60

x = 60/3

x = 20

VS = 20

The graph below describes the journey of a train between two cities.
a) Work out the
acceleration, in km/h²,
in the first 15 mins
b) Work out the distance
between the two cities.
c) Work out the average
speed of the train during
the journey.

The graph below describes the journey of a train between two cities.a) Work out theacceleration, in km/h,in

Answers

The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

According to the given question:

Each block of horizontal  is 1/8 hr = 7.5 min

Each block of vertical is 10 km/hr

Time                     Velocity  (km/hr)

0 Min  ( 0 hr)               0

15 Min (1/4 hr)           50

45 Min (3/4 hr)           50

60 MIn  ( 1 hr)           100

90 Min  ( 3/2 hr)        100

120 Min ( 2hr)             0

The acceleration in first 15 minutes = (1/4 hr)  =  (50 - 0)/(1/4 - 0)  = 50/(1/4)

= 200  km/h²

The distance between the two cities =

= (1/2)(0 + 50)(1/4 - 0)  + 50 * (3/4 - 1/4)  + (1/2)(50 + 100)(1 - 3/4)  + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

=  25/4  + 25 + 75/4   + 50 + 25

= 125

Distance between two cities = 125 km

Average Speed of train during the journey = 125/2  = 62.5  km/hr

Therefore,

The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

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+
II
alu
What is the value of x in the equation
x-2
3
1) 4
2) 6
3) 8
4) 11

+IIaluWhat is the value of x in the equationx-231) 42) 63) 84) 11

Answers

\(\dfrac{x-2}3 +\dfrac 16 = \dfrac 56 \\\\\implies \dfrac{x-2}3 = \dfrac 56 - \dfrac 16\\\\\implies \dfrac{x-2}3= \dfrac 46\\ \\\implies \dfrac{x-2}3 = \dfrac 23\\\\\implies x -2=2\\\\\implies x =2+2 = 4\\\\\text{Hence, the value of x is 4.}\)

Instructions: Read each statement below carefully. Place a T on the line if you think a statement it TRUE. Place an F on the line if you think the statement is FALSE
1. The rate of exchange between certain future dollars and certain current dollars is known as the pure rate of interest.___
2. An investment is the current commitment of dollars over time to derive future payments to compensate the investor for the time funds are committed, the expected rate of inflation and the uncertainty of future payments.___
3. A dollar received today is worth less than the same dollar received in the future ___.
4. The three components of the required rate of return are the nominal interest rate, an inflation premium, and a risk premium___.
5. Participants in primary capital markets that gather funds and channel them to borrowers are called financial intermediaries.___
6. Diversification with foreign securities can help reduce portfolio risk.___
7. The total domestic return on German bonds is the return that would be experienced by a U.S. investor who owned German bonds.___
8. If the exchange rate effect for Japanese bonds is negative, it means that the domestic rate of return will be greater than the U.S. dollar return___
9. The gifting phase is similar to and may be concurrent with, the spending phase.___
10. Long-term, high-priority goals include some form of financial independence.___

Answers

F; T; T; T; F; T; F; F;T; T. The rate of exchange between certain future dollars and current dollars is known as the forward exchange rate, not the pure rate of interest.

This statement accurately describes the concept of an investment, including the factors that compensate the investor. A dollar received today is worth more than the same dollar received in the future due to the time value of money. The three components mentioned (nominal interest rate, inflation premium, and risk premium) are indeed the components of the required rate of return. Financial intermediaries are not specifically related to primary capital markets. They facilitate transactions between savers and borrowers but may operate in various markets. Diversification with foreign securities can indeed help reduce portfolio risk by spreading exposure to different markets.

The total domestic return on German bonds is not the return experienced by a U.S. investor, as it would include exchange rate effects. A negative exchange rate effect for Japanese bonds would mean that the domestic rate of return is lower than the U.S. dollar return, not greater. The gifting phase and the spending phase can indeed be concurrent, such as when gifts are given for specific expenses. Long-term, high-priority goals often include working towards financial independence as a key objective.

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Solve the following quadratic equation 5x^2+18x+9=0

Answers

Answer:

\(x = -3~\text{and}~ x = -\dfrac 35\)

Step-by-step explanation:

\(~~~~~~5x^2 +18x +9=0\\\\\implies 5x^2 +15x +3x +9 = 0\\\\\implies 5x(x+3) +3(x+3) = 0\\\\\implies (x+3)(5x+3) = 0\\\\\implies x = -3,~ x = -\dfrac 35\)

Answer:

x = -3

OR

x = -(3/5)

Step by step explanation:

Given:

5x^2+18x+9=0

To Find:

x

Soln:

Use quadratic formulae:

Here I typed Quadratic formula as x

\( \rm x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2}\)

According to the question,on the formula,

a = 5b = 18c = 9

So substitute them on the formula:

THEN solve for x.

\( \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{18 {}^{2} - 4(5 \times 9) }}{2 \times 5} \)

\( \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 20 \times 9) }}{10} \)

\(\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 180}}{10} \)

\( \rm \implies \: x = \cfrac{ - 18 \pm \sqrt{144} }{10} \)

\( \rm \implies \: x = \cfrac{ - 18 \pm12}{10}\)

\( \rm \implies \: x = \cfrac{9 \pm 6}{5} \)

Final solution will after adding first(9+6),then secondly subtracting both 9-6

\( \rm \implies \boxed{x = - \cfrac{3 }{5} }\)

\( \implies \boxed{\rm x = - 3}\)

So there'll be two possible answers.

Parallel line of y=-1/2x-2

Answers

anything that has a slope of -1/2 is parallel to your equation. parallel lines are determined by the slope- if it’s the same slope. the “b” doesn’t matter.

The parallel line of y=-1/2x-2 is y=-1/2x

Slope-intercept form y=mx+b of linear equations the slope-m and the y-intercept -b of a line,

here y=-1/2x-2 slope of the linear equation is m=-1/2,

whereas the y-intercept is b=-2,

Parallel lines are those lines that are equidistant from each other, the condition for representing two lines is parallel their slopes should be equal or the same.

here slope of the line is -1/2, and the fundamental equation of a line in slope intercept form is y=mx+b, taking the assumption the parallel line is passing through the origin hence the y-intercept of the parallel line is 0, b=0.

therefore, the parallel line of y=-1/2x-2 is y=-1/2x

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What is the equation of the line?

A: y = -4/5x + 3/2
B: y = -5/4x + 5/4
C: y = -4/5x + 5/4
D: y = -5/4x + 3/2

What is the equation of the line?A: y = -4/5x + 3/2B: y = -5/4x + 5/4C: y = -4/5x + 5/4D: y = -5/4x +

Answers

Answer:

A: y = -4/5x + 3/2 i believe is the correct answer

Step-by-step explanation:

PLEASE HELP
Mrs.Galicia dropped a ball from the top of a tower. At the same time, her son, Antonio, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-4t+22.
The height of Antonio's rocket after t seconds can be represented by the linear function: p(t)=-2t+12.
(A) What are the two solutions to this system? Show your work algebraically.
(B) Explain which solution is not reasonable in this situation.
(C) After how many seconds do the rocket and the ball reach the same height.

Answers

A) The two solutions for the system are

tennis ball, t = 3.099 OR t = -7.099

rocket launch, t = 6

B) The solution that is not reasonable is the height of Antonio's rocket, The path traced is not a linear function

C) The rocket and the tennis ball reach same height at 2.32 s

How to solve the two systems

The system of equation of the two motions are

b(t) = -t^2 - 4t + 22.

p(t) = -2t + 12

Solving the quadratic equation gives

b(t) = -t^2 - 4t + 22.

t = 3.099 OR t = -7.099

solution for the linear equation gives

t = 6

The solution that is  not reasonable in this situation is the linear equation

The linear equation because projectile motion do not follow linear part.

time to reach same height

-2t + 12 = -t^2 - 4t + 22.

-t^2 - 2t + 10

solving the equation gives

t = 2.3166 OR -4.3166

take the positive value

t = 2.32 s

time to reach same height is 2.32 s

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A factory makes two products, puzzle cubes and puzzle spheres. Unfortunately, 1.5% of the cubes are defective and 2% of the spheres are defective. They make four times as many cubes as spheres. What percent of their products are defective?

Answers

The percentage of their product is defective is 16%.

What is the percentage?

Let's assume that the factory makes 4x puzzle cubes and x puzzle spheres.

Then the number of defective cubes is 1.5% of 4x, or 0.015(4x) = 0.06x.

Similarly, the number of defective spheres is 2% of x, or 0.02x.

The total number of defective products is the sum of defective cubes and defective spheres, or 0.06x + 0.02x = 0.08x.

The total number of products is the sum of puzzle cubes and puzzle spheres, or 4x + x = 5x.

Therefore, the percentage of defective products is:

(0.08x / 5x) x 100% = 1.6%

Therefore, 1.6% of their products are defective.

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Please help with part a b and c, C says “compre the functions algebraically by rewriting them using a common denominator”

Please help with part a b and c, C says compre the functions algebraically by rewriting them using a

Answers

Given:

\(\begin{gathered} f(x)=\frac{x+2}{x+3} \\ g(x)=\frac{x+5}{x} \end{gathered}\)

Required:

To find the values of the given functions at the given values of x.

Explanation:

At x = 0.5, Put x=0.5 in f(x) and g(x).

\(\begin{gathered} f(0.5)=\frac{0.5+2}{0.5+3} \\ f(0.5)=\frac{2.5}{3.5} \\ f(0.5)=0.714 \\ g(0.5)=\frac{0.5+5}{0.5} \\ g(0.5)=11 \end{gathered}\)

Now put x=1 in f(x) and g(x)

\(\begin{gathered} f(1)=\frac{1+2}{1+3} \\ f(1)=\frac{3}{4} \\ f(1)=0.75 \\ g(1)=\frac{1+5}{1} \\ g(1)=6 \end{gathered}\)

Now put x=2 in f(x) and g(x).

\(\begin{gathered} f(2)=\frac{2+2}{2+3} \\ f(2)=\frac{4}{5} \\ f(2)=0.8 \\ g(2)=\frac{1+5}{2} \\ f(2)=\frac{6}{2} \\ f(2)=3 \end{gathered}\)

Similarly, we will put the other values of x in f(x) and g(x), and then make the table by putting the values.

Given the system:
(3x - 2y +z = -4
-x + y - 2 = 2
2x -y + 2z = 2
The determinant of the coefficient matrix is equal
to:

Given the system:(3x - 2y +z = -4-x + y - 2 = 22x -y + 2z = 2The determinant of the coefficient matrix

Answers

Answer:

it's 2 and one unique solution

Step-by-step explanation:

The determinant of the coefficient matrix is equal to 2.

What is determinant of a matrix?

The determinant of a matrix is the scalar value computed for a given square matrix. Linear algebra deals with the determinant, it is computed using the elements of a square matrix.

According to question,

3x - 2y +z = -4

-x + y - 2 = 2

2x -y + 2z = 2

\(\left[\begin{array}{ccc}3&-2&1\\-1&1&-1\\2&-1&2\end{array}\right]\)

Expanding the matrix,

3(2-1) + 2(-2+2) + 1(1-2)

=3+0-1

=3-1

=2.

Hence the determinant of the coefficient matrix = 2.

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Simplify this expression.

2(x - 3) + 4x

Answers

Answer:

Step-by-step explanation:

2x-6+4x=6x-6

Hope this helps!

6x-6 i think is the anwer

What is the sum of the polynomials x2 9 +- 3x2 11x 4?.

Answers

The sum of the polynomials  (-x² + 9) and (-3x² - 11x + 4) is -4x² - 11x - 5.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

What is the sum of the polynomials  (-x² + 9) and (-3x² - 11x + 4)?

On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 34 m long and the shadow is 24 m, how tall is the building

Answers

Answer:

Step-by-step explanation:

h=√[34²-24²]=√[(34-24)(34+24)]=√[10×58]=√(5×29)=√145 ≈12 m

The height of the building is 10 meters.

What is the Pythagorean theorem?

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's call the height of the building "h".

We can use the Pythagorean theorem to relate the height, shadow, and hypotenuse of the right triangle:

h² + 24² = 34²

Simplifying and solving for h.

h² = 34² - 24²

h² = 676 - 576

h² = 100

h = 10

Therefore,

The height of the building is 10 meters.

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Question 4 of 25
True or false: f(x) is a function.
8
12
0
f(x)
A. True
Ο Ο
B. False

Question 4 of 25True or false: f(x) is a function.8120f(x)A. True B. False

Answers

Answer:

true

Step-by-step explanation:

Solve each of the following equations. Show its solution set on a number line. |5-4r|=17

Answers

Answer:

Step-by-step explanation:

To solve the equation |5-4r| = 17, we need to consider two cases:Case 1: 5 - 4r is positiveIf 5 - 4r is positive, then we have:5 - 4r = 17Subtracting 5 from both sides, we get:-4r = 12Dividing both sides by -4, we get:r = -3So if 5 - 4r is positive, then the solution to the equation is r = -3.Case 2: 5 - 4r is negativeIf 5 - 4r is negative, then we have:-(5 - 4r) = 17Simplifying the left side by distributing the negative sign, we get:-5 + 4r = 17Adding 5 to both sides, we get:4r = 22Dividing both sides by 4, we get:r = 5.5So if 5 - 4r is negative, then the solution to the equation is r = 5.5.Therefore, the solution set of the equation |5-4r| = 17 is {-3, 5.5}.To show this solution set on a number line, we can draw a number line and mark the points -3 and 5.5 with open circles, since these values are not included in the solution set. Then, we shade the part of the number line between -3 and 5.5, since any value of r in this interval satisfies the equation. The resulting number line looks like this:

So the solution set of the equation is the interval (-3, 5.5).

Answer:

w

Step-by-step explanation:

What is the measure of the unknown angle?
A. 60°
B. 63°
C. 64°
D. 70°

What is the measure of the unknown angle? A. 60B. 63C. 64D. 70

Answers

Answer:

B. 63°

Step-by-step explanation:

The distance around a circle is 360°

This means that 297° + n = 360°

Equation:

297 + n = 360

We can find the value of n by subtracting:

297 + n = 360

-297        -297

n = 63

Therefore, the value of n is 63 degrees.

-2.5(e + 17.4) = -50

Answers

To solve the equation -2.5(e + 17.4) = -50, we can use algebraic techniques to isolate the variable e on one side of the equation.

First, we can simplify the left-hand side of the equation by distributing the -2.5 to the expression inside the parentheses:

-2.5e - 2.5(17.4) = -50

Next, we can simplify the expression on the left-hand side by multiplying:

-2.5e - 43.5 = -50

To isolate the variable e, we can add 43.5 to both sides of the equation:

-2.5e = -6.5

Finally, we can solve for e by dividing both sides of the equation by -2.5:

e = 2.6

Therefore, the solution to the equation -2.5(e + 17.4) = -50 is e = 2.6.

4,237 white game consoles and 952

Answers

Answer:

what

Step-by-step explanation:

Answer: funny question

Step-by-step explanation:

4,237 white game consoles and 952

A small radio transmitter broadcasts in a 61 mile radius. If you drive along a straight line from a city 68 miles north of the transmitter to a second city 81 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answers

To solve this problem, we need to find the intersection of the circle with a 61-mile radius centered at the transmitter and the straight line connecting the two cities.

First, let's draw a diagram of the situation:

r

Copy code

T (transmitter)

|\

| \

|  \

|   \

|    \

|     \

|      \

|       \

C1      C2

Here, T represents the transmitter, C1 represents the city 68 miles north of the transmitter, and C2 represents the city 81 miles east of the transmitter. We want to find out how much of the straight line from C1 to C2 is within the range of the transmitter.

To solve this problem, we need to use the Pythagorean theorem to find the distance between the transmitter and the straight line connecting C1 and C2. Then we can compare this distance to the radius of the transmitter's range.

Let's call the distance between the transmitter and the straight line "d". We can find d using the formula for the distance between a point and a line:

scss

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d = |(y2-y1)x0 - (x2-x1)y0 + x2y1 - y2x1| / sqrt((y2-y1)^2 + (x2-x1)^2)

where (x1,y1) and (x2,y2) are the coordinates of C1 and C2, and (x0,y0) is the coordinate of the transmitter.

Plugging in the values, we get:

scss

Copy code

d = |(81-0)*(-68) - (0-61)*(-68) + 0*0 - 61*81| / sqrt((81-0)^2 + (0-61)^2)

 = 3324 / sqrt(6562)

 ≈ 41.09 miles

Therefore, the portion of the straight line from C1 to C2 that is within the range of the transmitter is the portion of the line that is within 61 miles of the transmitter, which is a circle centered at the transmitter with a radius of 61 miles. To find the length of this portion, we need to find the intersection points of the circle and the line and then calculate the distance between them.

To find the intersection points, we can solve the system of equations:

scss

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(x-0)^2 + (y-0)^2 = 61^2

y = (-61/68)x + 68

Substituting the second equation into the first equation, we get:

scss

Copy code

(x-0)^2 + (-61/68)x^2 + 68(-61/68)x + 68^2 = 61^2

Simplifying, we get:

scss

Copy code

(1 + (-61/68)^2)x^2 + (68*(-61/68))(x-0) + 68^2 - 61^2 = 0

Solving this quadratic equation, we get:

makefile

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x = 12.58 or -79.23

Substituting these values into the equation for the line, we get:

scss

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y = (-61/68)(12.58) + 68 ≈ 5.36

y = (-61/68)(-79.23) + 68 ≈ 148.17

Therefore, the intersection points are approximately (12.58, 5.36) and (-79.23, 148.17). The distance between these points is:

scss

Copy code

sqrt((12.58-(-79.23))^2 + (5.36-148.17)^2)

A basketball player scored 8 points in the 1st quarter 5 points during 2nd quarter 2 points in the 3rd quarter and 20 in the 4th quarter

Answers

Answer: 25

Step-by-step explanation: He scored 25 in the game

choose the correct answers. which equation models the relationship? is there a viable solution when time is 30 minutes?

Answers

When t=30, w=0, hence there is no workable solution. It implies that there is no longer any water after 20 minutes. So it is illogical for t=30 minutes.

what is equation ?

Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship.

calculation

A linear relationship exists here. The linear equation's slope-intercept form is as follows: where m is the rate of change (positive if increasing rate and negative if decreasing rate)

2.5 quarts per minute are changed (it is decreasing so m is -2.5)

C is 50 since the initial value is 50 quarts.

incorporating the results' values. y = -2.5x +50

We get y = -2.5x +50 by swapping the variables w and t for y and x, respectively. Where w is the remaining water in the bathtub and t is the passing time in minutes.

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Find the exact length of the curve. y = In(sec(x)), 0≤x≤ Need Help? Read It π 4 Watch It

Answers

The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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help me please!!

Solve the system of equations using the substitution method.
-2x - 5y = 2
x = -47 +9y

help me please!! Solve the system of equations using the substitution method.-2x - 5y = 2x = -47 +9y

Answers

Answer:

y = -4.174    (aprox)

x = 9.435    (aprox)

Step-by-step explanation:

-2x - 5y = 2        Eq. 1

x = -47 + 9y        Eq. 2

substituying the  Eq. 2 in the Eq. 1:

-2(-47+9y)  - 5y = 2

(-2*-47 -2*9y) - 5y = 2

-94 -18y - 5y = 2

-23y = 2 + 94

-23y = 96

y = 96/-23

y = -4.174      (aprox)

from the Eq. 2

x = -47 + 9y

x = 47 + 9*-4.174

x = 47 - 37.565

x = 9.435      (aprox)

Check:

from the Eq. 1

-2x - 5y = 2

-2*9.345 -5*-4.174 = 2

-18.87 + 20.87 = 2

A
4 yards
B
C
15 yards
Find the area of ABC.

Answers

Answer:

what is this supposed to mean

it is not specified

1. 232 is 8 times the sum of Mark's and his sister's ages. His sister is 21. Find Mark's age.

2. George went to the store for a sale on designer socks. Each pair was $3 off. She bought 6 pairs for $31.20. How much was the original price of the socks?

Answers

Answer:

a. 8 years

b. $49.20

Step-by-step explanation:

The computation is shown below:

a. The mark age is

Given that

232 is 8 times of the sum of mark and his sister ages

And, his sister is 21

So,

Let us assume the mark age be x

now

8(x + 21) = 232

x + 21 = 29

x = 29 -21

x = 8

b. The original price of the socks is

As each pair get $3 off

And she bought 6 pairs for $31.20

= $31.20 + 6 × $3

= $31.20 + 18

= $49.20

Work out m and c for the line: y = 8 x

Answers

Answer:

m = 8 and c = 0

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 8x ← is in slope- intercept form, that is y = 8x + 0

with m = 8 and c = 0

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