An airplane with a speed of 160 knots is headed east while a 24-knot wind is blowing from 240°. Explain how you would use the result of finding the ground speed to find the course of the airplane.

[tex]10e^{2x}-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^{2x}-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=\dfrac{5}{2} > 0\ \vee\ t=-\dfrac{1}{5} < 0\\\\\text{therefore}\ e^x=\dfrac{5}{2}\to\ln e^x=\ln\left(\dfrac{5}{2}\right)\\\\\boxed{x=\ln\left(\dfrac{5}{2}\right)}[/tex]

Answer:

B is the correct option choice !

Answer:

-2-p

Step-by-step explanation:

(p-2)x=4-p^2

(4-p^2)/(p-2)

-2-p

The solution of the expression for the given condition would be, - (p + 2).

Used the concept of trigonometry formula which stated that,

[tex](a - b)^2 = a^2 - 2ab + b^2[/tex]

Let us assume that,

When we multiply by x in (p - 2) the solution is (4 - p²).

So, it can be written in mathematical form as,

[tex]x \times (p - 2) = (4 - p^2)\\[/tex]

[tex]x \times (p - 2) = (2^2 - p^2)\\[/tex]

[tex]x \times (p - 2) = (2 - p) (2 + p)[/tex]

[tex]x \times (p - 2) = - (p - 2) (2 + p)[/tex]

Divide both sides by (p - 2),

[tex]x = - (p + 2)[/tex]

So, we get;

[tex](p - 2) \times - (p + 2) = (4 - p^2)[/tex]

To learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ6

Answer:

Choice C --- It intersects the x-axis at the same angle as line m

Step-by-step explanation:

Check out the attached image below for an example. In this example, both lines form a 30 degree angle with the x-axis. These two angles are congruent due to the corresponding angle theorem. This is the idea where two parallel lines form congruent angles such that they are in the same corresponding position.

Answer:

the answer is c

Step-by-step explanation:

Answer:

$1,250

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other. If 1200 is 4% less than last year, it's 96% of what he raised last year.

[tex]\frac{96}{100}=\frac{1200}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

96(y)=100(1200)

96y=120000

y=1250

Answer: WZ

The sequence ABCD has AD as the first and last letters of that sequence, so this pattern applies to WXYZ as well to pull out WZ. Angle A pairs up with angle W because they are both the first letters of the sequences. These angles are congruent from the fact that the parallelograms are similar. The same can be said for angle D and angle Z.

note: WZ is the same as ZW. The order doesn't matter when it comes to labeling segments based on endpoints.

Answer:

Well if you are trying to find the length of each side you Divide 24 by 4 so your answer would be 6

Step-by-step explanation:

Answer:

2√6 inches

Step-by-step explanation:

Since the picture is a square the lengths of each side are equal and their measure is √24

= √4*√6

= 2√6  in simplest form

Answer:

true/ true/ false/ true

Step-by-step explanation:

4x² is a term in both the numerator and denominator → Correct

factorise numerator and denominator

4x² - 4 = 4(x² - 1) ← common factor of 4

x² - 1 ← is a difference of squares and factors as

(x - 1)(x + 1)

4x² - 3x - 1 = (4x + 1)(x - 1) ← in factored form

Hence (x - 1) is a common factor in the numerator and denominator → Correct

4 is only a common factor in the numerator not the denominator

the denominator has three terms → Correct

being 4x² , - 3x and - 1

Answer:

11.33333...(keeps repeating)

Step-by-step explanation:

8.5 ÷ 3/4 = 11.33333...(keeps repeating)

The measure of 2 yards in centimeters is 182.88 cm

Using the conversions given:

1 yard = 3 × 12 inches

1 yard = 36 inches

1 yard = 36 × 2.54 cm

1 yard = 91.44 cm

Hence,

For 2 yards : (91.44 × 2) = 182.88 cm

The measure of 2 yards in centimeters is 182.88 cm

Final answer:

The width of the rectangle is calculated using the formula for the perimeter of a rectangle, P = 2l + 2w. Given a perimeter of 66 cm and a length of 24 cm, the width is found to be 9 cm.

Explanation:

The question is asking to find the width of a rectangle given the perimeter and the length. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

To find the width, we can rearrange the formula: w = (P - 2l) / 2.

Substituting the given values into the formula:

w = (66 cm - 2 * 24 cm) / 2

w = (66 cm - 48 cm) / 2

w = 18 cm / 2

w = 9 cm

Therefore, the width of the rectangle is 9 cm.

Answer:

The answer is 823,054,658,786.

Step-by-step explanation:

Add all of them together.

Answer:

Step-by-step explanation:

Answer:

EF = 5 units

Step-by-step explanation:

If ΔABC and ΔDFE are congruent, then

AB = DF

BC = FE

CA = ED

and

angles A and D are congruent

angles B and F are congruent

angles C and E are congruent

Answer:

see explanation

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x , y) → (y , - x)

Answer:The answer is choice C. and the rotation is 180

Step-by-step explanation:i just got it right

Answer: 8 miles per hour

Step-by-step explanation:

30 + 30 = 60, 60 minuets in an hour  4 + 4 = 8. 8 miles per hour hope i helped :)

Answer:

8 miles!

Step-by-step explanation:

30 + 30 = 60, 60 minutes in an hour and  4 + 4 = 8. So the answer is 8 miles per hour

Hope this helps!

Answer:

Cost of 72 ounces of grapes is $13.5

Step-by-step explanation:

In order to solve his problem, we first need to get all the values in the same units.

  1 pound = 16 ounces

∴ 6 pounds= 16×6 = 96 ounces

Now by unitary method, we solve the question as follows:

price of 96 ounces of grapes = $ 18

price of 1 ounce of grapes = $ (18÷96)

∴ price of 72 ounces of grapes = $ [(18÷96)×72]

= (0.1875×72) =  $ 13.5

Answer:

2x + 3

Step-by-step explanation:

product means to multiply, hence

the product of 2 and a number x = 2 × x = 2x

3 more than means add on 3, thus

expression is 2x + 3

Jenny's profit per bracelet is about $1.22. If she sells all 45 bracelets, her total profit is approximately $54.77.

The subject of this question is profit, which in this case will occur when Jenny is able to sell her bracelets for more than she paid for the materials to make them. She pays $12.75 for the materials to make 45 bracelets, meaning each bracelet costs her $12.75 / 45 = $0.283 to make. If she sells each bracelet for $1.50, that means she earns $1.50 - $0.283 = $1.217 in profit for each bracelet. If she sells all 45 bracelets, her total profit would therefore be $1.217 * 45 = $54.765. However, since we typically round money to the nearest cent, her total profit will be approximately $54.77.

Learn more about Profit Calculation here:

https://brainly.com/question/32944523

#SPJ2

When the pack of 80 stickers is divided evenly among the three friends, each friend receives 26 stickers, with the remaining 2 stickers going to their teacher.

In order to find out how many stickers each friend will get from a pack of 80, we can divide the total number of stickers by the number of friends. In this case, that's 80 stickers ÷ 3 friends. This division gives us a result of 26 stickers with a remainder of 2.

However, the question states that the remainder is given to their teacher. So while the remainder division resulted in each friend getting 26 stickers with an extra 2 left over, those extra 2 stickers are given to the teacher. Therefore, each friend ends up with 26 stickers.

https://brainly.com/question/2273245

#SPJ3

Can you please provide the diagram.

[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}=-\Bigg[\left(\dfrac{1}{3}\right)^{-1}\Bigg]^x=-(3)^x\\\\f(x)<0\ \text{for any real values of x}\ (III\ and\ IV\ quadrant)\\\\a^x\ \text{is increased for}\ a>1.\ \text{Therefore}\ 3^x\ \text{is increased}.\\\\\text{We have}\ -3^x,\ \text{therefore the graph is decreased}.[/tex]

Only bottom left graph satisfy the conditions of the end behaviour and y-intercept. The bottom left option is correct.

Given:

The given function is:

[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}[/tex]

To find:

The graph of the given function.

Explanation:

The given function can be rewritten as:

[tex]f(x)=-\dfrac{1}{3^{-x}}[/tex]

[tex]f(x)=-3^{x}[/tex]

For [tex]x=0[/tex], we get

[tex]f(0)=-3^{0}[/tex]

[tex]f(0)=-1[/tex]

So, the y-intercept of the graph is [tex]-1[/tex].

End behaviour of the graph:

[tex]f(x)\to 0[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]

Only bottom left graph satisfy the above conditions.

Therefore, the bottom left option is correct.

Learn more:

https://brainly.com/question/25314114

Answer: 6 of the picks would be green

Step-by-step explanation:

[tex]f(x)=5x\\\\\text{The domain:}\ D=\{0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6\, ...\}=\text{Whole numbers}\\\\\text{The range:}\\\\f(0)=5(0)=0\\f(1)=5(1)=5\\f(2)=5(2)=10\\f(3)=5(3)=15\\f(4)=5(4)=20\\f(5)=5(5)=25\\\vdots\\R=\{0,\ 5,\ 10,\ 15,\ 20,\ 25,\ ...\}[/tex]

Answer:

(12) A

(14) A

(15) E

hope this help

Step-by-step explanation:

Answer:

ok first get each corner make a line to the dot with each point

Step-by-step explanation:

The slope-intercept form:

[tex]y=mx+b[/tex]

We have:

[tex]3x+7y=14[/tex]              subtract 3x from both sides

[tex]7y=-3x+14[/tex]             divide both sides by 7

[tex]\boxed{y=-\dfrac{3}{7}x+2\to\boxed{C.}}[/tex]

Answer:

The Rosita investment worth in 2025 is $83486.4 .

Step-by-step explanation:

The expontential increase function is given by.

[tex]y = a(1 + r)^{t}[/tex]

Where a is the initial value , r is the rate of interest in the decimal form and t is the time.

As given

Rosita invested in a precious mineral.

The value of the mineral tends to increase by about 12% per year.

She invests $24,000 in 2014.

As

a = 24000

12% is written in the decimal form.

[tex]= \frac{12}{100}[/tex]

= 0.12

r = 0.12

As Rosita invested from 2014 to 2025.

Than

t = 2025 - 2014

t = 11 years

Put in the expontential increase function.

[tex]y = 24000(1 + 0.12)^{11}[/tex]

[tex]y = 24000(1.12)^{11}[/tex]

y = 24000 × 3.4786 (Approx)

y = $83486.4

Therefore the Rosita investment worth in 2025 is $83486.4 .

Answer:

C

Step-by-step explanation:

We can find the surface area of the dumbbell by adding the surface areas of each part. We have two equal round ends of the dumbbell to count and the skinnier inside. Each is a cylinder and each can be found by finding the area of the base (times 2 for two bases) and adding it to the circumference times the height.

[tex]2(\pi r^{2} )+(\pi d)h[/tex]

Dumbbell Ends

There are two ends and so we will count this measurement twice. The diameter is 12.5. The radius is half of this and is 6.25. The height is 8.

[tex]2(\pi r^{2} )+(\pi d)h[/tex]

[tex]2(\pi (6.25)^{2} )+(\pi 12.5)8[/tex]

[tex]2(\pi 39.0625 )+(\pi 100[/tex]

245.4369+314= 559.43

But we must count is twice, so 559.43(2)=1118.87 cm squared.

Dumbbell Middle

The diameter is 2.50. Radius is 1.25. The height is 10.5. The ends actually don't show because they are attached. So we will only calculate the second part and add it to the other.

[tex](\pi 2.5)10.5[/tex]=82.47

82.47+1118.87=1201.33 cm squared.

Why is this too large? Why isn't it an answer choice? Because the ends of the middle don't show, they also take up that much area on other side. They are not part of the surface area and they make it smaller. So we will subtract that area now.

[tex]2(\pi 1.25^{2} )[/tex]=9.817

1201.33-9.817=1191.84 cm squared.

q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

[tex]2q(0.1)+q(0.25)=9\\\\0.2q+0.25q=9\\\\0.45q=9\qquad\text{divide both sides by 0.45}\\\\q=20[/tex]

Paul has 20 quarters.

To find quarters does Paul have.

The branch of mathematics dealing with the properties and manipulation of numbers.

Let the q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

2q(0.1)+q(0.25)=9

0.45q=9

q=20

So, Paul has 20 quarters.

Learn more about arithmetic here:

https://brainly.com/question/11860162

#SPJ6

Answer:

1) f(x) = -1/2x+1

I'm sorry I don't know the 2nd one...

Step-by-step explanation:

The y-intercept is always plotted first. from there, you go down one, and to the right too. and so one, and in reverse, up one, and left two.

Answer:1. f(x) = -1/2x+1