Complete the equation of the line through (–6,5) and (-3, -3).
Use exact numbers.

a. The length of the rectangular wing is 14.16 ft.

b.  The plane needs to fly at a speed of 462 ft/s at an altitude of 35,000 ft to generate the same lift as at sea level.

The lift generated by a wing can be calculated using the formula below

L = 1/2 * ρ *\(V^2\) * S * CL

where

L is the lift,

ρ is the density of air,

V is the airspeed,

S is the wing area, and

CL is the lift coefficient.

Given that the lift generated is 3,000 lbf, the airspeed is 250 ft/s, and the lift coefficient is 1.0

3000 lbf = \(1/2 * 0.002378 slugs/ft^3 * (250 ft/s)^2 * S * 1.0\)

\(S = 28.14 ft^2\)

The aspect ratio of the wing is defined as the ratio of the wing span (b) to the wing chord (c). For a rectangular wing

b = AR * c

where AR is the aspect ratio.

Substitute the given aspect ratio of 6 and the wing area calculated above

\(b * c = 28.14 ft^2\\6c^2 = 28.14 ft^2\)

c = 2.36 ft

Therefore, the length of the wing is b = AR * c = 6 * 2.36 ft = 14.16 ft

To find the airspeed required to generate the same lift at an altitude of 35,000 ft

solve for the airspeed required at 35,000 ft:

3000 lbf = \(1/2 * 0.00052 slugs/ft^3 * V^2 * 28.14 ft^2 * 1.0\)

V = 462 ft/s

Hence, the plane needs to fly at a speed of 462 ft/s at an altitude of 35,000 ft to generate the same lift as at sea level.

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Answer:

Lacey could afford 4.25lb of cherries

Step-by-step explanation:

Cost of onions= 3 lb x 0.98/1=2.94

21.45-2.94=18.48$

1 lb=4.35

18.48 x 1lb of cherries/4.35=4.25lb of cherries.

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The trigonometric ratios with respect to angle A are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The hypotenuse is of 37, and the sides relative to angle A are given as follows:

Hence the trigonometric ratios are given as follows:

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Answer:

Convert fraction (ratio) 7 / 10 Answer: 70%

Answer:

70%

Step-by-step explanation:

To find percentage = fraction * 100

                                = 7/10 * 100

                                = 0.7 * 100

                                = 70%

Answer:

Independent: The number of Tickets

Dependent: The number of Josiah's friends

Step-by-step explanation:

The number of tickets is Independent because the number of tickets is something that is final. The number of Josiah's friends could change depending on if the friend come or not.

the answer is 17.5

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here we have,

4/7 = 10/x

2x=35

x=17.5

That the answer.

hence, the answer is 17.5 .

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Answer:i think it is 7/3

Step-by-step explanation:

In the given figure,

In triangle DEF,

The length of DF is

Now in triangle DFG,

The length of FG is

Now apply Pythagoras theorem to determine DG,

The length of DG is 24.

Answer:

169 sq m

Step-by-step explanation:

= 13 × 13 = 169 sq m.

Answer:

y=2/3x+4

Step-by-step explanation:

4 is y-intercept

2/3 is  the slope (rise/run)

Answer: y = \(\frac{2}{3}\)x + 4

Step-by-step explanation:

    This is in slope-intercept form. We are missing the m and the b value. See attached for more information.

[m aka the slope]

   Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of \(\frac{2}{3}\) via rise-over-run

[b aka the y-intercept]

   The line intersects the y-axis at positive 4.

-> This value is "4"

Answer:

4s = g

s + 5 = p

s + g +p = 35

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Answer:

YO THE PICTURE DIFFRENT

Step-by-step explanation:

The compound interest calculated for 10 years annually, semi-annually, quarterly, monthly, and daily are (a) $2195.05,  (b) $2206.18  (c) $2211.88 (d) $2215.75, and, (e) $2217.63

The formula for Compound Interest is

Amount = Principal X (1 + r/n100)ⁿˣ

where,

Principal = original mount

n = no. of times the interest is applied

t = time period

Here,

Principal = $1400

x = 10

r = 4.6

a)

Since it is compounded annually, the interest will be given 10 times in 10 years. therefore, once a year

Hence,

n = 1

Amount = 1400 X (1 + 4.6/100)¹⁰

= 1400 X (104.6/100)¹⁰

= 1400 X (1.046)¹⁰

= $2195.05

b)

Since the interest is compounded semi-annually here, it will be calculated twice a year.

Hence, n = 2

Therefore we get

Amount = 1400 X (1 + 4.6/200)²⁰

= 1400 X (204.6/200)²⁰

= 1400 X (1.023)²⁰

= $2206.18

c)

Since it is compounded 4 times a year now,

n = 4

Hence we get

Amount = 1400 X (1 + 4.6/400)⁴⁰

= 1400 X (1.0115)⁴⁰

= $2211.88

d)

Here, the interest is calculated 12 times a year

Hence we get

Amount = 1400 X (1 + 4.6/1200)¹²⁰

= 1400 X (10038)¹²⁰

= $2215.75

e)

Here we are told to ignore leap years, hence we are only going to consider a year to have 365 days.

Hence,

n = 365

Therefore, we get

Amount = 1400 X (1 + 4.6/36500)³⁶⁵⁰

= 1400 X (1 + 4.6/36500)³⁶⁵⁰

= 1400 X (1.00012)³⁶⁵⁰

= $2217.63

Correct Question

If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:

(a) 4.6% compounded annually

(b) 4.6% compounded semiannually

(c) 4.6% compounded quarterly

(d) 4.6% compounded monthly

(e) 4.6% compounded daily (ignore leap years)

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The scale factor of the dilation is 0.8 and the coordinates of point B are (-5, -7.5)

From the question, we have the following parameters that can be used in our computation:

A' = (3.2, 6.4)

B' = (-4, -6)

A = (4, 8)

The scale factor of the dilation is calculated as

Scale factor = A'/A

So, we have

Scale factor = (3.2, 6.4)/(4, 8)

Evaluate

Scale factor = 0.8

The coordinates of point B are

B = B'/Scale factor

So, we have

B = (-4, -6)/0.8

Evaluate

B = (-5, -7.5)

So, the coordinates of point B are (-5, -7.5)

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The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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Answer:

Total Number of students taking Math and History and not music are 68.

Number of students who took both math and history at the same time is 6.

Step-by-step explanation:

History = 30

Math = 32

Music= 33

Math and Music= 9

History and Music= 13

History and Music and Math = 2

History but not math = 14

We have to find students taking history and math but not music.

Total number of students = 125

From the figure  number of students taking Math and History and not music are

=30+6+32= 68

Number of students who took both math and history at the same time is 6.

Answer: 15/17

Step-by-step explanation: I took the K12 Math test!

Based on the trigonometric calculations, the value of cosC is equal to: C. 15/17.

In Mathematics, there are six (6) types of trigonometry graph that are used to graphically represent a trigonometric function and these include:

Based on the right-angled triangle attached, we can deduce the following parameters:

Opposite side (BA) = 8 units.

Adjacent side (BC) = 15 units.

Hypotenuse (AC) = 17 units.

In trigonometry, cosine (cos) is given by this mathematical expression:

cosC = BC/AC

cosC = 15/17.

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The completed table using the function f(x) = 2x + 5 is:

x          y

-2        1

-1         7

0         5

1          7

2         9

What is the function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

To complete the table using the function f(x) = 2x + 5, we need to substitute the given values of x into the function and evaluate to find the corresponding values of y.

x        y

⇒ f(-2) = 2(-2) + 5

= 1

-2      1  

⇒ f(-1) = 2(-1) + 5

= 3

-1       7  

⇒ f(0) = 2(0) + 5

= 5

0       5  

⇒ f(1) = 2(1) + 5

= 7

1        7  

⇒ f(2) = 2(2) + 5

= 9

2       9  

Therefore, the completed table is:

x          y

-2        1

-1         7

0         5

1          7

2         9

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Answer:

4(x+2)-6=14

or,4x+8=14

or,4x=14-8

or,4x=6

therefore,x=3/2

The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Answer:

x = 23

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan ? = 3/7

Taking the inverse tan of each side

tan ^-1 ( tan ?) = tan ^-1 (3/7)

?=23.19859

To the nearest degree

x = 23

Answer:

$0.09 or nine cents!

Step-by-step explanation:

Divide 6.75 by 75

Answer:0.09 cents

Step-by-step explanation:

because if you trying find cost per text you divide 6.75/75 =0.09.

The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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Answer:

Elias Nebiyu gives seven breads for his eight friends and he continues this give away for three days.

Step-by-step explanation:

3x 7/8 result is attached above.

Answer:

B.) The graph of g(x) is shifted 4 units up

Step-by-step explanation:

In a linear function in slope-intercept form, b, or 4 in this case, represents the y-intercept which technically acts as a vertical shift

The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.

Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.

A hypothesis in a study is a statement that is made to explain a given observation without prior testing to prove or disprove the statement.

The two types of hypothesis are:

The null hypothesis states that there is no significant difference between two variables while the alternative hypothesis states that there is a significant difference between the variables.

For the given observation:

Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.

Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.

In conclusion, the null hypothesis is the hypothesis of no significant difference.

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Answer:

2100

Step-by-step explanation:

6300/3

Answer:

x = 94°

Step-by-step explanation:

ABCD is a cyclic quadrilateral , its 4 vertices lie on the circle.

the opposite angles of a cyclic quadrilateral sum to 180° , that is

x + 86° = 180° ( subtract 86° from both sides )

x = 94°

Answer:

3.

11² + 11² = x²

121 + 121 = x²

242 = x²

x = √242

x = 11√2

4.

tan(60°) = y/36

√3 = y/36

y = 36√3

tan(30°) = x/36

√3/3 = x /36

x = 36√3/3

x = 12√3

Answer:

Step-by-step explanation:

3) Using the Pythagorean Theorem (A^2+B^2=C^2) We can tell that x^2=11^2+CB^2. If you can find what CB is then you can find x by doing 11^2+CB^2=x^2 and if you square root x^2 you get x.

4) Same thing, y^2+x^2=36^2.