Solve the system. 0.2x + 0.5y = 4 -0.1x + 0.3y = -2 A) (20, 0) B) (-2, 5) C) (-5, 10) D) (50, 10)

The angle of elevation from Jonathan to Mina is approximately 43.81 degrees.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
We can use the tangent function to find the angle of elevation from Jonathan to Mina.

Let θ be the angle of elevation, then we have:

tan(θ) = opposite / adjacent

Where the opposite is the height of the tower (389 feet) and adjacent is the distance between Jonathan and the base of the tower (412 feet).

So, we have:

tan(θ) = 389 / 412

θ ≈ 43.81 degrees

Therefore, the angle of elevation from Jonathan to Mina is approximately 43.81 degrees.

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Answer:

2u + v - 4w = <40 , -4>

6u - 8v = <-78 , 58>

4v - 7w = <101 , -36>

11u + 3w = <-88 , 89>

Step-by-step explanation:

* Lets find the value of each operation to find its resultant vector

# 2u + v - 4w

∵ u = <-5 , 7>

∴ 2u = <-10 , 14>

∵ v = <6 , -2>

∵ w = <-11 , 4>

∴ 4w = <-44 , 16>

∴ 2u + v - 4w = <-10 + 6 - -44 , 14 + -2 - 16>

∴ 2u + v - 4w = <40 , -4>

# 6u - 8v

∵ u = <-5 , 7>

∴ 6u = <-30 , 42>

∵ v = <6 , -2>

∵8v = <48 , -16>

∴ 6u - 8v = <-30 - 48 , 42 - -16>

∴ 6u - 8v = <-78 , 58>

# 4v - 7w

∵ v = <6 , -2>

∴ 4v = <24 , -8>

∵ w = <-11 , 4>

∴ 7w = <-77 , 28>

∴ 4v - 7w = <24 - -77 , -8 - 28>

∴ 4v - 7w = <101 , -36>

# 11u + 3w

∵ u = <-5 , 7>

∴ 11u = <-55 , 77>

∵ w = <-11 , 4>

∴ 3w = <-33 , 12>

∴ 11u + 3w = <-55 + -33 , 77 + 12>

∴ 11u + 3w = <-88 , 89>

Answer:

Step-by-step explanation:

Let x represent the amount invested at the higher rate (6%). Then the amount invested at the lower rate is (2400-x) and the total interest earned is ...

  6%·x + 4%·(2400-x) = 5.5%·2400

Dividing by % and rearranging, we have ...

  x(6 -4) = 2400(5.5 -4)

  x = 2400·(5.5 -4)/(6 -4) = 2400(1.5/2) = 2400·0.75

  x = 1800 . . . . . . . . amount invested at 6%

  2400-x = 600 . . . amount invested at 4%

Maria put $1800 in the 6% account and $600 in the 4% account.

_____

Comment on the solution

You will note that the proportion of the investment that went to the higher interest rate account is (5.5-4)/(6-4). This is the ratio of the mixed interest rate less the lower rate to the difference of account rates. This will be the generic solution to mixture problems, so is worthy of note for that reason.

Answer:  

For 4% interest, investment $600

For 6% interest, investment $1,800  

Explanation:  

Maria invested $2,400 into two accounts. One account paid 4% interest and the other paid 6% interest. She earned 5.5% interest on the total investment.

It is a system of linear equations in two variables. Variables are x and y. Solve for x and y using substitution method.

In substitution method: First solve for one variable in terms of another variable and then substitute into another equation.

Further explanation:  

Let $x invested in account which paying 4% interest.

Let $y invested in another account which paying 6% interest.  

Therefore,  x + y = 2400   --------------(1)

                                                                                        = 132

Therefore,  0.04x + 0.06y = 132 -----------(2)

Solve system of equations for x and y , using substitution method.

                     x + y = 2400  

solve for y in terms of x and we get,

                         y = 2400 - x ------------ (3)  

Substitute the value of y into equation (2) and we get,  

                   0.04x + 0.06(2400-x) = 132

                      0.04x + 144 - 0.06x = 132

                                            -0.02x = 132 - 144

                                                     [tex]x=\dfrac{-12}{-0.02}[/tex]  

                                                     [tex]x=600[/tex]

Substitute the value of x into eq(3)  

                                                y = 2400 - 600

                                                y = 1800

In account paying 4% interest, invest $600 and paying 6% interest invest $1,800

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Keywords:

System of equation, Two variable equations, solve for x and y, substitution method, elimination method, cross multiplication method.

Answer:

The range of width is 10 ≤ W ≤ 28

Step-by-step explanation:

* lets study the meaning of compound inequality

- If x is greater than a and x is smaller than b, then x is between a and b

∵ x > a and x < b

∴ The compound inequality is ⇒ a < x < b

# Ex: ∵ x > -2 and x < 10

∴ The compound inequality is ⇒ -2 < x < 10

- If x is greater than or equal a and x is smaller than or equal b, then

 x is from a and b

∵ x ≥ a and x ≤ b

∴ The compound inequality is ⇒ a ≤ x ≤ b

# Ex: ∵ x ≥ -2 and x ≤ 10

∴ The compound inequality is ⇒ -2 ≤ x ≤ 10

* Now lets solve the problem

- The garden in the shape of a rectangle with dimensions length (L)

 and width (W)

- The length of the garden is 10 feet

- The perimeter (P) of the garden is at least 40 feet and not more than

  76 feet

∵ L = 10 feet

∵ P = 2L + 2W

- At least means greater than or equal (≥) and not more than means

 smaller than or equal (≤)

∴ P ≥ 40 feet

∴ P ≤ 76 feet

- lets use the rule of the perimeter

∴ 2(10) + 2(W) ≥ 40 ⇒ simplify

∴ 20 + 2W ≥ 40 ⇒ subtract 20 from both sides

∴ 2W ≥ 20 ⇒ divide both sides by 2

∴ W ≥ 10 ⇒ (1)

- Do similar with P ≤ 76

∴ 2(10) + 2(W) ≤ 76 ⇒ simplify

∴ 20 + 2W ≤ 76 ⇒ subtract 20 from both sides

∴ 2W ≤ 56 ⇒ divide both sides by 2

∴ W ≤ 28 ⇒ (2)

- From (1) and (2)

∴ 10 ≤ W ≤ 28 ⇒ compound inequality

* The range of the width is from 10 feet to 28 feet

Answer:

Betty's boss use the MEAN to describe the average tip.

Betty use the MEDIAN.

Step-by-step explanation:

The MEAN is 50+45+48+125+85= 353

353/5=70 or 70.6

The MEDIAN is the middle which is 50.

45,48,50,85,125

Hope this helps

Final answer:

The mean tip amount Betty made was $70.60, and the median was $50. Betty's boss used the mean to describe her average nightly tips, whereas Betty used the median.

Explanation:

To calculate the mean and median tip amount for Betty's nightly tips, we list her tips from last week: $50, $45, $48, $125, and $85. To find the mean, we add all the tip amounts together and divide by the number of days she worked. Betty worked 5 days, so the mean is calculated as: (50 + 45 + 48 + 125 + 85) / 5 = $70.60. The median is the middle number when the tips are arranged in order, which are $45, $48, $50, $85, and $125. Thus, the median tip amount is $50.

Based on this information, Betty's boss used the mean to describe her average tip, while Betty herself used the median to describe her average tip.

Answer:

An outlier is the number that is much smaller or larger than the other numbers.

In this case it is 29 :)

Answer:

D:  29

Step-by-step explanation:

D:  29 is your outlier.  It's quite different from the commonest values (which are in the range 8 - 17).

the answer is 10. just use the distance formula which is the square root of (x2-x1)^2+(y2-y1)^2

Answer: 10 units

Step-by-step explanation:

The distance  from point (a,b) and (c,d) is given by formula below:-

[tex]D=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Therefore, the distance between the points (5, 1) and (-3, -5) will be :

[tex]D=\sqrt{(-3-5)^2+(-5-1)^2}\\\\\Rightarrow\ D=\sqrt{(-8)^2+(-6)^2}\\\\\Rightarrow\ D=\sqrt{64+36}\\\\\Rightarrow\ D\sqrt{100}\\\\\Rightarrow\ D=10\text{ units}[/tex]

Hence, the distance between the points (5, 1) and (-3, -5) = 10 units

The owner wants people to believe that dance classes are popular so that they sign up for classes. Therefore, option C is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

The most likely reason the owner of the dance studio chain releases the report is to demonstrate the success of their business. By highlighting the fact that participation in dance classes has increased by 5% in each of the past three years, the owner is showing the public that the business is doing well and that they are providing a valuable service. This report may also be used to encourage potential customers to join the studio's classes, which would further increase their profits.

Therefore, option C is the correct answer.

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Answer:

60

Step-by-step explanation:

Angles AKB and EKD are vertical angles and congruent.

The measure of angle AKB is the sum of the measures of arcs AB and ED divided by 2.

m<AKB = (110 + 130)/2 = 120

Angles AKB and AKE are supplementary angles, so their measures add to 180 deg.

m<AKE + m<AKB = 180

m<AKE + 120 = 180

m<AKE = 60

To find the tension in each cable, we need to consider the forces acting on the weight. Using Newton's second law and trigonometry, we can set up equations to solve for the tension in each cable. The tension in each cable is (OPTION C) 50 lb.

To find the tension in each cable, we need to consider the forces acting on the weight. In this case, there are two cables pulling upward and the weight pulling downward. Since the weight is in equilibrium, the sum of the upward forces must equal the downward force. Let's label the tension in the first cable as T1 and the tension in the second cable as T2.

Using Newton's second law, we can set up the following equation: T1 + T2 = 100 lb. We also know that the angle between each cable and the vertical is the same, so the horizontal components of tension in both cables are equal. Let's call this component T.

Since the weight is in equilibrium, the vertical components of tension in the cables must also balance the weight's weight. The vertical component of tension in each cable can be found using trigonometry. Let's call this component V.

Now, we can set up two equations for the horizontal and vertical components:

T + T = 100 lb (Equation 1)

V + V = weight of the weight = 100 lb (Equation 2)

Since T1 + T2 = 2T, Equation 1 becomes:

2T = 100 lb

T = 50 lb

Substituting T = 50 lb into Equation 2, we can find V:

2V = 100 lb

V = 50 lb

Therefore, the tension in each cable is 50 lb.

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Answer:

Correct answer on ed is C.

Step-by-step explanation:

Just did the exam and it was correct.

The solution is A = ( x - 14 ) / ( x + 4 )

The value of the equation ( h * f * g ) ( x ) = ( x - 14 ) / ( x + 4 )

What is Composition of functions?

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the function f ( x ) be represented as

f ( x ) = ( x - 6 ) / x

Let the function g ( x ) be represented as

g ( x ) = x + 4

Let the function h ( x ) be represented as

h ( x ) = 3x - 2

Now , the equation is ( h * f * g ) ( x )

The equation of composition of functions can be simplified as

h * ( f ( g ( x ) ) ) = h * ( f ( x + 4 ) )

On simplifying the equation , we get

h * ( f ( x + 4 ) ) = h * [ ( x + 4 - 6 ) / ( x + 4 ) ]

h * ( f ( x + 4 ) ) = h * [ ( x - 2 ) / ( x + 4 ) ]

Now , the composition of h * ( f ( g ( x ) ) ) is given by

h ( x ) = 3x - 2

Substitute the value of x as ( x - 2 ) / ( x + 4 ) , we get

( h * f * g ) ( x ) = 3 [ ( x - 2 ) / ( x + 4 ) ] - 2

( h * f * g ) ( x ) = ( 3x - 6 ) / ( x + 4 ) - 2

( h * f * g ) ( x ) = ( 3x - 6 - 2x - 8 ) / ( x + 4 )

( h * f * g ) ( x )  = ( x - 14 ) / ( x + 4 )

Therefore , the value of A is ( x - 14 ) / ( x + 4 )

Hence , the value of ( h * f * g ) ( x )  is ( x - 14 ) / ( x + 4 )

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Answer:

y=4x+7

Slope m=4 with the equation y2-y1/x2-x1 with any points

y-intercept (0,7)

Answer: Third option.

Step-by-step explanation:

You need to find the surface area with the formula for calculate the surface area of a rectangular prism:

[tex]SA=2(wl + lh + hw)[/tex]

Where w is the width, l is the length, and h is the height.

You can observe in the figure that:

[tex]l=5cm\\w=4cm\\h=2cm[/tex]

Then, substituting the values into the formula  [tex]SA=2(wl + lh + hw)[/tex], you get that  minimum amount of cardboard used for the wrapper is:

[tex]SA=2[(4cm)(5cm)+(5cm)(2cm)+(2cm)(4cm)]\\SA=76cm^2[/tex]

Answer:

third option

Step-by-step explanation:

Answer:

It has no special appearance.

Step-by-step explanation:

Any angle of measure 180° or less is supplementary to some angle. A supplementary angle is one that is the difference between 180° and the angle you have. That is, two supplementary angles total 180°.

__

Supplementary angles are readily identifiable in a number of geometries. Adjacent angles of a parallelogram are supplementary; linear angles are supplementary. Same-side interior angles where a transversal crosses parallel lines are supplementary.

The value 1.8 represents the growth factor in the expression, indicating the monthly growth rate of club members after advertising.

The value 1.8 in the given expression that models the number of club members, in hundreds, after advertising for t months represents the growth factor, which is the rate at which the total number of members at the club increases each month. This is not the initial number of members, nor the monthly percentage increase, nor the number of new members joining per month, but rather the multiplier applied to the previous month's total to find the next month's projected total.

Answer: A'=(1, 3); B'=(-3, 4);C'=(3, 0); D'=(-2, 5)

You can check the PNG attached as well.

Step-by-step explanation:

You need to represent the symmetry of every given points respet to the line

[tex]y = 2[/tex]

In that case, the line beeing paralell to the x- axis, x- value of the symmetry is the same of the given point and y = 2 is the middle between both points.

Point A(1, 1)

[tex]x_{A} = 1\\ x_{A'} = 1 \\\\\frac{y_{A} +y_{A'} }{2} =2\\y_{A'} = 4 - y_{A} = 4 - 1 = 3[/tex]

Point B(-3, 0)

[tex]x_{B} = 1\\ x_{B'} = 1 \\\\\frac{y_{B} +y_{B'} }{2} =2\\y_{B'} = 4 - y_{B} = 4 - 0 = 4[/tex]

Point C(3, 4)

[tex]x_{C} = 1\\ x_{C'} = 1 \\\\\frac{y_{C} +y_{C'} }{2} =2\\y_{C'} = 4 - y_{C} = 4 - 4 = 0[/tex]

Point D(-2, -1)

[tex]x_{D} = 1\\ x_{D'} = 1 \\\\\frac{y_{D} +y_{D'} }{2} =2\\y_{D'} = 4 - y_{D} = 4 - (-1) = 4 + 1 = 5[/tex]

Answer:

0.91.

Step-by-step explanation:

We use the formula:

P(a U b) = p(a) + p(b) - p (a ∩ b)     where P(a U b) is p(a or b) and p (a ∩ b) is p  (a and b).

So p(a or b) = 0.78 + 0.66 - 0.53

= 0.91.

The surface area of a sphere is given by

[tex]S = 4\pi r^2[/tex]

We deduce

[tex]r = \sqrt{\dfrac{S}{4\pi}}[/tex]

So, in your case, the radius is

[tex]r = \sqrt{\dfrac{100\pi}{4\pi}}=\sqrt{25}=5[/tex]

The volume of a sphere is given by

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

So, we have

[tex]V = \dfrac{4}{3} \pi 5^3 = \dfrac{500}{3}\pi[/tex]

Answer:

[tex]\large\boxed{x=\dfrac{1}{a}}[/tex]

Step-by-step explanation:

[tex]2-4(ax-3)=10\qquad\text{subtract 2 from both sides}\\\\-4(ax-3)=8\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4(ax-3)}{-4}=\dfrac{8}{-4}\\\\ax-3=-2\qquad\text{add 3 to both sides}\\\\ax-3+3=-2+3\\\\ax=1\qquad\text{divide both sides by}\ a\neq0\\\\x=\dfrac{1}{a}[/tex]

Answer:

an = 6 (1/4)^(n-1)

Step-by-step explanation:

We're given the first term, a₁ = 6.

The common ratio is a term aₓ divided by the previous term aₓ₋₁.

aₓ = 1/4 aₓ₋₁

aₓ / aₓ₋₁ = 1/4

r = 1/4

Therefore:

an = 6 (1/4)^(n-1)

Your answer is correct, good job!

The recursive rule for a geometric sequence is given a₁ = 6, aₓ = 1/4 aₓ₋₁. The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

[tex]a, ar, ar^2, ar^3, \cdots[/tex]

Thus, the nth term of such sequence would be  

[tex]T_n = ar^{n-1}[/tex]

We have been given the first term,

a₁ = 6.

The common ratio is the term aₓ divided by the previous term aₓ₋₁.

aₓ = 1/4 aₓ₋₁

aₓ / aₓ₋₁ = 1/4

r = 1/4

Therefore:

[tex]a_n = 6 (1/4)^{n-1}[/tex]

Hence, The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].

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For this case we have the following system of equations:

[tex]-2x + 5y = -3\\y-15 = 3x[/tex]

We multiply the second equation by -5:

[tex]-5y + 75 = -15x[/tex]

Now we add the equations:

[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]

We find the value of the variable "y":

[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]

THE solution is: (-6, -3)

Answer:

(-6, -3)

I just took the test!

Answer:

16.2 m²

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

In this problem Triangles BAE and DAE are congruent by SAS postulate

so

BE=DE

substitute the given values

[tex]3x-24=x+10[/tex]

solve for x

[tex]3x-x=24+10[/tex]

[tex]2x=34[/tex]

[tex]x=17[/tex]

Answer:

B. 17

Step-by-step explanation:

Answer:

Surface area increases by a factor of 4

Step-by-step explanation:

Given the linear ratio = a : b, then

the area ratio = a² : b²

Here the linear ratio = 1 : 2, hence

area ratio = 1² : 2² = 1 : 4 ← increase by factor of 4

Answer:

It is c = kt.

Step-by-step explanation:

This is direct variation . As the time increases the number of cranes increases.

The equation is c = kt  where k is the constant  of variation.  In this case it will be a positive value because c is increasing with time.

If they make 20 cranes in 10 minutes then we can find the value of k by plugging in these values;

20 = k * 10

g = 20/10

k = 2.

So they make 2 cranes per minute.

Answer:x = -2

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

25=5x+35

25-35=5x

-10=5x/:5

-2=x

x=-2

Answer:

Yes

Step-by-step explanation:

0.4 = 4/10 = 2/5

0.4 converted into a fraction is 4/10, 4/10 simplified is 2/5

Answer:

  see below

Step-by-step explanation:

Since there are fewer sequences than functions, we'll identify the matchup according to the sequence.

11, 33, 55, 77, ...

The first term is 11. The terms have a common difference of 33 -11 = 22. That is, each term is 22 more than the previous one. The appropriate recursive function is ...

__

-18, -108, -648, -3888, ...

The first term is -18. The terms obviously do not have a common difference, but their common ratio is -648/-108 = -108/-18 = 6. That is, each term is 6 times the previous one. Then the appropriate recursive function is ...

__

-18, 3, 24, 45, ...

The first term is -18. The terms have a common difference of 3-(-18) = 21. That is, each term is 21 more than the previous one. The appropriate recursive function is ...

Answer:

11, 33, 55, 77, ...=f(n) = f(n - 1) + 22 for n = 2, 3, 4, ...

-18, -108, -648, -3,888, ...=f(n) = 6 · f(n - 1) for n = 2, 3, 4, ...

-18, 3, 24, 45, ...=f(n) = f(n - 1) + 21 for n = 2, 3, 4, ...

Step-by-step explanation:

Answer:

Step-by-step explanation:

Set up a ratio in the form of pages/minute:

[tex]\frac{pages}{minute} :[/tex]

then fill in next to that how many pages per minute George can read:

[tex]\frac{pages}{minute}:\frac{15}{12}[/tex]

Now we want to figure out how long (time is our unknown, so we call that x) it will take him to read 85 pages.  The 85 goes in a ratio on the same line as the other number of pages:

[tex]\frac{pages}{minute}:\frac{15}{12}=\frac{85}{x}[/tex]

Cross multiply to get 15x = 1020

Now divide both sides by 15 to get x = 68 minutes, which is an hour and 8 minutes.

Answer:

68 minutes

Step-by-step explanation:

Given that George read 15 pages in a book in 12 minutes, and we need to find out how long it will take him to finish the book if it has 85 pages, we must first find how much minutes it takes to read per page because we need to find the amount of time.

Write an equation (In this case p=pages and t= minutes or time):

(Remember! We are trying to find the minutes per page, not how many pages per minute.)

15p=12t

p=12/15t

p=0.8t

We now know he reads 1 page in 0.8 minutes. Given that we need to find the amount of time to read 85 pages, multiply 0.8 by 85 because 0.8 minutes=1 page.

85*0.8=68

Therefore, it takes him 68 minutes to read 85 pages

Answer:

[tex]\displaystyle x=\frac{-8\pm\sqrt{(8)^2-4(4)(-221)}}{2(4)}\ \text{; x = 6.5 and x = -8.5}[/tex]

Step-by-step explanation:

Subtract the right side of the given equation to put it into standard form:

  4x² +8x -221 = 0

Then the coefficients used in the quadratic formula are ...

When these are filled into the form ...

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

the result is as shown above.