write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind only 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step

Answer:

n=16 kg

c=44 kg

Step-by-step explanation:

Let

n=nuts at $2.50 per kg

c=cereal at $1 per kg

n+c=60 (1)

2.5n + c=1.40(60) (2)

From (1)

n=60-c

Substitute n=60-c into (2)

2.5n + c=1.40(60)

2.5(60-c) +c=84

150-2.5c+c=84

-1.5c=84-150

-1.5c= -66

Divide both sides by -1.5

c=44 kg

Substitute c=44 into (1)

n+c=60

n+44=60

n=60-44

=16

n=16 kg

The amount of nuts is 16 kg and cereal mixture is 44 kg to obtain 60 kg of a mix that will sell for $1.40 per kg.

Answer:

The length of the diagonal of the trunk is 56.356011 inches

Step-by-step explanation:

According to the given data we have the following:

height of the trunk= 26 inches

length of the trunk= 50 inches

According to the Pythagorean theorem, to calculate the length of the diagonal of the trunk we would have to calculate the following formula:

length of the diagonal of the trunk=√(height of the trunk∧2+length of the trunk∧2)

Therefore, length of the diagonal of the trunk=√(26∧2+50∧2)

length of the diagonal of the trunk=√3176

length of the diagonal of the trunk=56.356011

The length of the diagonal of the trunk is 56.356011 inches

Answer:

19.6 ft

Step-by-step explanation:

4²+x²=20²

16+x²=400

384 = x²

x = 19.6 ft

Answer:

19.6 feet

Step-by-step explanation:

We know that

The hypotenuse is 20 feet, and the bottom leg is 4 feet.

We also know that Pythagorean theorem is used when there is one missing side to a triangle.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

Substitute in a for 4 and c for 20. The hypotenuse is always the variable c.

4^2 + b^2 = 20^2

16 + b^2 = 400

b^2=384

[tex]\sqrt{384}[/tex] = 19.6

Answer:

a = (15-11b)/7

Step-by-step explanation:

19a + 11b = 12a + 15

Subtract 12a from each side

19a-12a + 11b = 12a-12a + 15

7a +11b = 15

Subtract 11b from each side

7a+11b-11b = 15 -11b

7a = 15-11b

Divide by 7

7a/7 = (15-11b)/7

a = (15-11b)/7

Answer:

A = (15-11b)/7

Step-by-step explanation:

Steps to solve:

6/3x = 3

~Multiply 3/6 to both sides

x = 3/2

Best of Luck!

Answer:

x = 3/2

Step-by-step explanation:

Hey there!

To solve this equation, let's rewrite it for cohesive purposes. This would result in (6/3)(x) = 3.

Now, we can simplify the fraction because it reduces to a whole number. Three will go into six two times, so 6/3 is equivalent to 2.

This leaves us with 2x = 3.

Now, we need to isolate the x. Because there is a coefficient leading the variable, we can divide the entire term (2x) by 2 as well as dividing the 3 on the righthand side of the equation by 2.

Remember the mathematical rule of thumb: what you do to one side of the equation, you must perform to the other side. Therefore, if we divide by 2 on the left side of the equation, we must also divide the righthand side of the equation by 2.

By performing this step, it leaves us with x = 1.5.

[tex]{\frac{2x}{2}=\frac{3}{2}}\\\\\bold{x = \frac{3}{2}}[/tex]

We can reduce [tex]\frac{3}{2}[/tex] to a decimal, which transfers to 1.5. However, it's best to leave the answer in fractional form. This leaves our final answer as [tex]\bold{x=\frac{3}{2}}[/tex].

Answer:

Which numbers go to each bakery

Answer:

D.  Median for both bakeries because the data is not symmetric.

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

To create a dot plot:

We need to draw/put dots with the given data.

You'll find your answer in the attached file.

Let me know if it's not clear!

Answer:

x = $34.45

Step-by-step explanation:

Solution:-

The company makes a profit of $y by selling widgets at a price of $x. The profit model is represented by a parabola ( quadratic ) equation as follows:

                       [tex]y = -10x^2 + 689x -6775[/tex]

We are to determine the profit maximizing selling price ( x )

From the properties of a parabola equation of the form:

                      [tex]y = ax^2 + bx + c[/tex]

The vertex ( turning point ) or maximum/minimum point is given as:

                     [tex]x = -\frac{b}{2a} \\\\x = - \frac{689}{2*(-10)} = \frac{689}{20}\\\\x = 34.45[/tex]

The profit maximizing selling price of widgets would be x = $34.45.

Answer:

Option B is the correct answer.

Step-by-step explanation:

Finding the distance between the points A and B

A ( 3 , - 1 ) → ( x1 , y1 )

B ( 9 , - 5 )→ ( x2 , y2 )

Distance = [tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

[tex] = \sqrt{ {(9 - 3)}^{2} + {( - 5 - ( - 1)}^{2} } [/tex]

[tex] = \sqrt{ {(9 - 3)}^{2} + {( - 5 + 1))}^{2} } [/tex]

[tex] = \sqrt{ {6}^{2} +( - 4) ^{2} } [/tex]

[tex] = \sqrt{36 + 16} [/tex]

[tex] = \sqrt{52} [/tex]

[tex] = 2 \sqrt{13} [/tex]

Finding the distance between the points B and C

B ( 9 , - 5 ) → ( x1 , y1 )

C ( 16 , - 2 )→ ( x2 , y2 )

Distance = [tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

[tex] = \sqrt{ {(16 - 9)}^{2} + { (- 2 - ( - 5))}^{2} } [/tex]

[tex] = \sqrt{ {(16 - 9)}^{2} + { ( - 2 + 5)}^{2} } [/tex]

[tex] = \sqrt{ {7}^{2} + {(3)}^{2} } [/tex]

[tex] = \sqrt{49 + 9} [/tex]

[tex] = \sqrt{58} [/tex] units

Finding the distance between the points A and C

A ( 3 , - 1 )→ ( x1 , y1 )

C ( 16 , - 2 )→ ( x2 , y2 )

Distance = [tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

[tex] = \sqrt{ {(16 - 3)}^{2} + {( - 2 - ( - 1))}^{2} } [/tex]

[tex] = \sqrt{ {(16 - 3)}^{2} + ( - 2 + 1) ^{2} } [/tex]

[tex] = \sqrt{ {13}^{2} + ( { - 1)}^{2} } [/tex]

[tex] = \sqrt{169 + 1} [/tex]

[tex] = \sqrt{170} [/tex] units

Now, let's find the perimeter:

Perimeter = AB + BC + AC

plug the values

[tex] = 2 \sqrt{13} + \sqrt{58} + \sqrt{170} [/tex]

Calculate

[tex] = 27.9[/tex] units

Hope this helps..

Best regards!!

Answer:

(20, 800) and (27, 1080)

Step-by-step explanation:

The chart shows that it costs 40 per person, so you need to identify which bills costs 40 times the number of people.

12x40=460 No

20x40=800 Yes

24x40=1020 No

27x40=1080 Yes

28x40=1110 No

Answer:

blank 1: 2xy(4x-5y)+3(4x-5y)

blank 2: (2xy+3)(4x-5y)

Step-by-step explanation:

Using factoring group to factor the polynomial 8x²y−10xy²+12x−15y

Step 1: Group the polynomial function

(8x²y−10xy²)+(12x−15y)

Step 2: Factor the common value and variables from the functions in parentheses.

= (2xy*4x - 2xy(5y)) + (3(4x) - 3(5y))

= 2xy(4x-5y)+3(4x-5y)

Step 3: Rearrange the expression by selecting one of the function in parentheses and combine those not in parenthesis.

(2xy+3)(4x-5y)

The final expression gives the factor form of the polynomial.

Hence the statement for each blank that correctly completes Lana's work are;

blank 1: 2xy(4x-5y)+3(4x-5y)

blank 2: (2xy+3)(4x-5y)

Answer:

190 possibilities.

Step-by-step explanation:

The problem is called 20 choose 2, given by the formula for combinations

C(20,2) = 20! / (2! (20-2)!) = 190

alternatively, we can reason it this way:

there are 20 choices to choose a captain and 19 choices for an alternate captain for a total of 380 ways.

However, there are 20 choices to choose an alternate captain and 19 choices for a captain for a total of 380 ways.

Since we are essentially double counting every choice of the posts, we need to divide 380 by 2 to get 190 ways.

Answer:

The area covered by it is "95%".

Step-by-step explanation:

Consequently, because the shaded region encompasses the range of two standard deviations, the portion protected is 95%.

Answer:

is 1

step by step explanation:

Answer:

graph c is 2x> 50 and graph b is x+6<32

Step-by-step explanation:

For 2x>50 you first divide 50 by2 leaving you with x>25 therefore x is all numbers greater than 25.

For x+6<32 you first subtract 6 from 32 leaving you with x<26 therefore x is  all numbers less than 26.

Hope this helps, please mark brainliest if it does!!! Thank you!!

Answer:

graph c is 2x> 50 and graph b is x+6<32

Step-by-step explanation:

For 2x>50 you first divide 50 by2 leaving you with x>25 therefore x is all numbers greater than 25.

For x+6<32 you first subtract 6 from 32 leaving you with x<26 therefore x is  all numbers less than 26.

Hope this helps, please mark brainliest if it does!!! Thank you!!

Answer:

4. F '(3, 2.5), G '(5, 0.5), H '(1, 0.5)

Step-by-step explanation:

The formula for dilations are

[tex]\left(x_{1}\cdot t_{1},\ y_{1}\cdot t_{1}\right)[/tex] where t1 is the scale factor

F has coordinates (6,5) so you can write

[tex](6*0.5,5*0.5)[/tex]

Multiply 6 by 0.5 and 5 by 0.5 to get

[tex](3,2.5)[/tex]

Next, do G. It has coordinates (10, 1) so you can write

[tex](10*0.5, 1*0.5)[/tex]

Multiply 10 by 0.5 and 1 by 0.5 to get

[tex](5, 0.5)[/tex]

Finally, point H has coordinates (2, 1) so you can write

[tex](2*0.5, 1*0.5)[/tex]

Multiply 2 by 0.5 and 1 by 0.5 to get

[tex](1, 0.5)[/tex]

Hope this helps. Feel free to ask any follow-up questions.

Have a great day! :)

Answer:  F '(3, 2.5), G '(5, 0.5), H '(1, 0.5).

From the image the vertices are F(6, 5), G(10, 1), H(2, 1).

We have to dilate the figure by a scale factor of 0.5 with the origin as the center of dilation.

We will multiply the vertices by 0.5.

So the new vertices will be: F '(3, 2.5), G '(5, 0.5), H '(1, 0.5).

Learn more: https://brainly.com/question/20521181

Answer:

(- 5, 0 ), (7, 0 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, - 108 ), thus

y = a(x - 1)² - 108

To find a substitute (0, - 105 ) into the equation

- 105 = a(- 1)² - 108 ( add 108 to both sides )

3 = a

y = 3(x - 1)² - 108 ← equation in vertex form

To find the x- intercepts, let y = 0, that is

3(x - 1)² - 108 = 0 ( add 108 to both sides )

3(x - 1)² = 108 ( divide both sides by 3 )

(x - 1)² = 36 ( take the square root of both sides )

x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6  ( add 1 to both sides )

x = 1 ± 6, so

x = 1 - 6 = - 5

x = 1 + 6 = 7

x- intercepts are (- 5, 0), (7, 0)

Answer: x=19

Step-by-step explanation:

We know that 2x is equal to w. We also know that the angle of the triangle is 90 degrees. We also know the 90 plus 3x-5 plus w will equal 180 degrees since it is a triangle. So, by substituting the w from w+ 3x-5+90=180 with 2x, we can solve for x by moving all the numbers around. So it goes from 2x+3x-5+90=180 to 2x+3x-5=90 and then to 5x-5=90 and finally to 5×=95 and divide 95 by 5 to get x. And you're done! Hope this helps!

Answer:

  BC/BE = FG/FI

Step-by-step explanation:

Corresponding segments are proportional:

  BC/BE = FG/FI

Answer:

Your answer is A

Step-by-step explanation:

By using substitution method, we obtained the solution of equations (3, 3).

The given linear system of equations are 6x+3y=27 and 5x+2y=21.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Using substitution method we can solve given equations

6x+3y=27 can be written as 2x+y=9 ----------(I)

5x+2y=21 ----------(II)

From equation (I), we have y=9-2x

Substitute y=9-2x in equation (II), we get

5x+2(9-2x)=21

⇒ 5x+18-4x=21

⇒ x=21-18

⇒ x=3

Substitute x=3 in equation (I), we get

2(3)+y=9

⇒ y=3

Therefore, by using substitution method, we obtained the solution of equations (3, 3).

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ6

Answer:

Total number of pages in book = 570 pages

Step-by-step explanation:

Given:

Rate of reading = 55  page per hour

Number of hour = 4 hour

Total pages remain = 350 pages

Find:

Total number of pages in book

Computation:

Number of pages read = Number of hour × Rate of reading

Number of pages read = 4 × 55

Number of pages read = 220

Total number of pages in book = Number of pages read + Total pages remain

Total number of pages in book = 220 + 350

Total number of pages in book = 570 pages

Answer:

Step-by-step explanation:

The function represented by the yellow graph has exactly one y-intercept and one x-intercept.  The y-intercept is (0, 4) and the x-intercept is (2, 0).

Answer:

Its the one shown

Step-by-step explanation:

Answer: x=12

Step-by-step explanation:

OQ is equal to NL since both contain 90 degree angles and are intersected by a radius. Since OS is 3x-2 and NL is 32, then we need to find OQ and set it equal to NL. OS is half of OQ, so multiplying OS by 2 will get you OQ. 6x-4=32

That yields x=12.

Answer:

X=12

Step-by-step explanation:

Answer:

the number [tex]6\,\,\,10^{-2}[/tex] is three million times larger than [tex]2\,\,\,10^{-8}[/tex]

Step-by-step explanation:

To answer this, just do the quotient of the first one over the second one, and use the rules for quotient of exponential expressions of the same base:

[tex]\frac{6\,\,\,10^{-2}}{2\,\,\,10^{-8}} =\frac{6}{2} \,\frac{10^{-2}}{10^{-8}} =3\,\,\,10^{-2+8}=3\,\,\,10^6=3000000[/tex]

So the answer is: the number [tex]6\,\,\,10^{-2}[/tex] is three million times larger than [tex]2\,\,\,10^{-8}[/tex]

Answer:

Linear

Step-by-step explanation:

y = 2x + 4 is linear -- any equation involving only first powers of x and y (and constants) is linear. You'll usually see linear equations in the forms y = mx + b, ax + by = c, or y - y1 = m(x - x1).

If you take any two points, find the slope of the line between them, and then plug in one point to solve for the constant term (like you did), you will get a linear equation through those points.

Answer:

it is linear pair of the variable

Answer:

I think the closest to the correct answer is choice B:

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

Step-by-step explanation:

the accurate answer is: [tex]f^{-1} (x)=-\frac{1}{1-x}[/tex]

Replace x with x+3:

f(x+3) = (x+3)²

which is x² translated 3 units left