Which is a solution to (x − 2)(x + 10) = 13?
x = 3
x = 8
x = 10
x = 11

The answer is:

The speed of the wind is 150mph.

To calculate the speed of the wind, we need to write two equations using the given information about the speed when the airplane was traveling with the wind and against the wind, considering that it travel the same length of time.

So, writing the equations, we have:

Traveling with the wind:

We know that the speed of the airplane is 325 mph and it travels 1360 miles with the wind, so, for the equation, we have:

[tex]distance=(AirplaneSpeed+WindSpeed)*t[/tex]

[tex]1360miles=(325mph+WindSpeed)*t[/tex]

[tex]t=\frac{1360miles}{325mph+WindSpeed}[/tex]

Traveling against the wind:

We know that the speed of the airplane is 325 mph and it travels 1240 miles with the wind, so, for the equation, we have:

[tex]distance=(AirplaneSpeed-WindSpeed)*t[/tex]

[tex]1240miles=(325mph-WindSpeed)*t[/tex]

[tex]t=\frac{1240miles}{325mph-WindSpeed}[/tex]

Then, making making equal the time, we have:

[tex]\frac{1360miles}{325mph+WindSpeed}=\frac{1240miles}{325mph-WindSpeed}[/tex]

[tex]\frac{1360miles}{325mph+WindSpeed}=\frac{1240miles}{325mph-WindSpeed}\\\\(1360miles)*(325mph-WindSpeed)=(1240miles)*(325mph+WindSpeed)\\\\442000miles.mph-1360miles*WindSpeed=403000miles.mph+1240miles*WindSpeed\\\\442000miles.mph-403000miles.mph=1240miles*WindSpeed+1360miles*WindSpeed\\\\39000miles.mph=2600miles*Windspeed\\\\WindSpeed=\frac{39000miles.mph}{2600miles}=150mph[/tex]

Hence, we have that the speed of the wind is 150mph.

Have a nice day!

Answer:

the second step in solving a system of nonlinear equations by substitution is usually:

solve one equation for either variable of the given equation

Answer:

substituting a value in place of one of the variables to find the remaining variable.

Step-by-step explanation:

Answer:

[tex]{x}^{3} - 4x - 12[/tex]

Step-by-step explanation:

[tex] {x}^{3} + 6 \times 2 - 4x - 24[/tex]

[tex] = {x}^{3} + 12 - 4x - 24[/tex]

[tex] = {x}^{3} - 4x + 12 - 24[/tex]

[tex] = {x}^{3} - 4x - 12[/tex]

Answer:

Step-by-step explanation:

[tex]x^2-8x-20=0\\\\x^2+2x-10x-20=0\\\\x(x+2)-10(x+2)=0\\\\(x+2)(x-10)=0\iff x+2=0\ \vee\ x-10=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\x-10=0\qquad\text{add 10 to both sides}\\\boxed{x=10}[/tex]

Answer: 1110 grams

Step-by-step explanation: see the paper attached. (:

Answer:

11.4 mixture:26 and 2/3

7.8 mixture: 53 and 1/3

Step-by-step explanation: Sorry if this is hard to underestand. This is my first answer. This is a RSM question that has been checked.

11.4+7.8=9

 x+80-x=80

Multiply

11.4x+624-7.8x=720

3.6x=96

1.2=32

0.6x=16

6x=160

x=26 2/3

80-26 2/3= 53 1.3

Answer:

53 1/3 for $7.80, and 26 2/3 for $11.40

Step-by-step explanation:

x*11.4=11.4x

(80-x)*7.8=624-7.8

9*80=720

Those three steps are because he wants to make 80 pounds out of $9, $11.40 for a pound, and then a pound for $7.80. Since the total is 80 pounds, it could be 11.4 for x pounds and 7.8 for 80-x pounds. Then the equation is:

11.4x+624-7.8x=720

Simplify:

3.6x=96

Times both times by 10:

36x=960

x=26 2/3

80-x=53 1/3

Answer:

6.70

Step-by-step explanation:

6^2 = 36

9^2 = 81

81-36 = 45

square root 45 = 6.708203932

Answer:     10.8

so formula for this is a^2 x b^2=c^2

Step-by-step explanation:

6^2 is 36

9^2 is 81

36+81 is 117

117 squared is 10.8

Answer:

y = 2x - 5

Step-by-step explanation:

The equation has to have the same slope -- in this case, it is 2 -- to be parallel to 2x - y = 4.

Now we have y = 2x - k.

Then, we plug in the coordinates to our new equation to solve for k.

-1 = 2(2)-k

-1 = 4-k

k = 5

So the final equation would be y = 2x - 5

the answer to this question is 110°

Answer:

Step-by-step explanation:

Use FOIL:  (a + b)(c + d) = ac + ad + bc + bd

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

= 8x² - 2xy - 12xy + 3y²

combine like terms

= 8x² + (-2xy - 12xy) + 3y² = 8x² - 14xy + 3y²

You must FOIL (first, outside, inside, last)

First (The first number/variable of each parentheses must be multiplied together)

(2x - 3y)(4x - y)

[tex]8x^{2}[/tex]

Outside (The outside number/variable of each parentheses must be multiplied together)

(2x - 3y)(4x - y)

-2xy

Inside (The inside number/variable of each parentheses must be multiplied together)

(2x - 3y)(4x - y)

-12xy

Last (The last number/variable of each parentheses must be multiplied together)

(2x - 3y)(4x - y)

[tex]3y^{2}[/tex]

Now add/subtract each FOIL answer according to its sign

[tex]8x^{2}[/tex] - 2xy - 12xy + [tex]3y^{2}[/tex]

Combine like terms

[tex]8x^{2}[/tex] + [tex]3y^{2}[/tex] - 14xy

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

-0.8 and 0.75.

Step-by-step explanation:

20x^4 + x^3 + 8x^2 + x – 12 = 0

by the rational roots theorem:-

The leading coefficient is 20 with factors +/-  1,2,4,5,10,20

and the constant is -12 with factors  +/- 1,2,3,4,6,12

so there are many possible roots like -1, 2, 3/4 3/5 , -4/5 .....

Drawing a graph would be the quickest way to do this,  either manually, using graphical software or a graphical calculator.

I used the latter and got 2 rational roots -0.8 and 0.75.

The rational roots of the polynomial f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12 is -0.8 and 0.75 and this can be determined by sketching the graph of the given polynomial.

Given :

f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12

The following steps can be used in order to determine the rational roots of the given polynomial:

Step 1 - Write the polynomial equation.

f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12

Step 2 - Draw the graph of the above polynomial equation.

Step 3 - The coefficient of [tex]x^4[/tex] is 20 with factors +/-  1,2,4,5,10,20

Step 4 - The constant term of the given polynomial is -12 with factors  +/- 1,2,3,4,6,12.

Step 5 - So, from the polynomial equation, the two rational roots are -0.8 and 0.75.

For more information, refer to the link given below:

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Answer:

Step-by-step explanation:

Vertex of y = |x| have the coordinates (0, 0).

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

nf(x) - stretches/shrinks vertically

f(nx) - stretches/shrinks horizontally

We have

f(x) = |8x + 8| - 3 = |8(x + 1)| - 3 = |8| · |x+1| - 3 = 8|x + 1| - 3

g(x) = |x| → f(x) = 8g(x + 1) - 3

vertically streched by 8      (0, 8 · 0) → (0, 0)

shifted 1 unit to the left    (0 - 1, 0) → (-1, 0)

shifted 3 units down       (-1, 0 - 3) → (-1, -3)

Answer: x= -7/11

Step-by-step explanation:

13x+17+5x=7x+10

collect the like terms by adding their coefficients

18x+17=7x+10

move variable to the left side and change its sign

18x-7x+17=10

move constant to the right side and change its sign

18x-7x=10-17

collect the like terms

11x=10-17

calculate the difference

11x= -7

divide both sides by 11

x= -7/11

The solution to this equation 3x +17 + 5x = 7x + 10 is x = -7

The solution to this equation 3x +17 + 5x = 7x + 10

Given equation is:

3x +17 + 5x = 7x + 10

To find the value of x, combine the like terms by adding or subtraction.

3x + 5x - 7x = 10 - 17

x = - 7

Therefore, x = -7 is the solution to this equation 3x +17 + 5x = 7x + 10

Learn more about simplification here:

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Answer: 6x^7+ 12x^6+ 3x^5

Hope that helped

Answer: 140 degree

Step-by-step explanation: The line LMU is basically 180, so what you'll do is 90 degree KLM plus 50 degree LMK which will give you 140 degree. A whole triangle is a supplementary angle so it's 180 degree. To find KMU, you do (180 - 140) - (180 - 40) = 140. So the answer for angle KMU is 140.

Answer:

8

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

if x/6=3, the you can use the mulitplication property of equations to solve. so multiply each side by 6. it will eliminate the fraction on the left side of the equal side, leaving you with x and then 6x3=18, therefore

x=18

Answer:

x = 18

Step-by-step explanation:

Multiply 6 on both sides.

x = 18

Answer:

Step-by-step explanation:

I wonder if it wants 3.80 per gallon?

Perhaps the imperial value which would have been 4.50 per gallon which is an imperial gallon (used in Canada). It's hard to tell. I would have thought 3.78 should be more than close enough.

Answer:

$3.79/$4.55

Step-by-step explanation:

1. How many liters in a gallon: 3.79 l (US), 4.55 l (Imp)

2. Cost of gas/gallon: 3.79 liter * $1/liter = $3.79 (US), $4.55 (Imp)

From what you say, using the US gallon, since both answers round to the same number (since there is no currency below the cent), it wouldn't matter too much. Also, unit conversions should not lead to different answers.

Answer:

x = 0.417 or x = -0.917

Step-by-step explanation:

We are given the following expression and we are to solve it for the variable x:

[tex] x ^2 + \frac { 1 } { 2 } x + \frac { 1 } { 1 6 } = \frac { 4 } { 9 } [/tex]

We will find the least common multiple of 2. 6 and 9:

[tex]x^2 \times 144 +\frac{1}{2}x \times 144 +\frac{1}{16} \times 144 = \frac{4}{9} \times 144[/tex]

Simplifying it to get:

[tex]144x^2+72x+9=64[/tex]

[tex]144x^2+72x+9-64=0[/tex]

[tex]144x^2+72x-55=0[/tex]

Using the quadratic formula to solve for x:

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

[tex]x=\frac{-72 \pm\sqrt{72^2-4(144)(-55)} }{2a}[/tex]

[tex]x=\frac{5}{12}[/tex] or [tex]0.417[/tex]

[tex]x=-\frac{11}{12}[/tex] or [tex]-0.917[/tex]

Answer:    B

Step-by-step explanation:

Answer a is incorrect because only the seniors were questioned and answer c is incorrect because nothing was mentioned in the question about only testing males.

Your answer is B

Answer:

b

Step-by-step explanation:

was on khan academy <3

Answer:

140

Step-by-step explanation:

this is because of alternate suplementry lines

Answer:

The sample space is SG,GG,SS,GS. I know this because the sample space is the set of all possible outcomes of an experiment.

Hope this helped!

The sample space when the spinner that's divided into two sections is spun twice is; {SG, GG, SS, GS}

We are given that the sections are labeled STOP and GO.

Now the spinner is divided into two equally sized sections as S and G.

Now, if the spinner is spun twice, we could get the following results;

SG, SS, GS, GG.

Thus, the sample space is given by the total possible outcome of the spin which is;

{SG, SS, GS, GG}

Read more at; https://brainly.com/question/3560578

Answer:

D

Step-by-step explanation:

g(x) = √(x - 2) - 3

The range is all the possible values of g(x).  Since we can't take the square root of a negative number, the lowest that g(x) can be is:

g(x) = √0 - 3

g(x) = -3

The highest that g(x) can be is:

g(x) = √∞ - 3

g(x) = ∞

So the range is:

[-3, ∞)

Answer:

[tex]\large\boxed{\bold{NO\ REAL\ SOLUTIONS}}\\\boxed{x=4-2i,\ x=4+2i}[/tex]

Step-by-step explanation:

[tex]Domain:\\c-4\neq0\ \wedge\ c-5\neq0\Rightarrow c\neq4\ \wedge\ c\neq5\\\\\dfrac{c}{c-5}=\dfrac{4}{c-4}\qquad\text{cross multiply}\\\\c(c-4)=4(c-5)\qquad\text{use the distributive property}\\\\c^2-4c=4c-20\qquad\text{subtract}\ 4c\ \text{from both sides}\\\\c^2-8c=-20\qquad\text{add 20 to both sides}\\\\c^2-8c+20=0\qquad\text{use the quadratic formula}[/tex]

[tex]\text{for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac<0,\ \text{then the equation has no solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x^2-8x+20=0\\\\a=1,\ b=-8,\ c=20\\\\b^2-4ac=(-8)^2-4(1)(20)=64-80=-16<0\\\\\bold{NO\ REAL\ SOLUTIONS}[/tex]

[tex]\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\\text{therefore}\ \sqrt{b^2-4ac}=\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\\x=\dfrac{-(-8)\pm4i}{2(1)}=\dfrac{8\pm4i}{2}=\dfrac{8}{2}\pm\dfrac{4i}{2}=4\pm2i[/tex]

[tex] \frac{c}{c - 5} = \frac{4}{c - 4} [/tex]

[tex](c - 5)(c - 4) \times \frac{c}{c - 5} = \frac{4}{c - 4} \times (c - 5)(c - 4)[/tex]

[tex](c - 4) \times c = 4(c - 5)[/tex]

With c≠4, 5

[tex] {c}^{2} - 4c = 4c - 20[/tex]

[tex] {c}^{2} - 8c + 20 = 0[/tex]

[tex]c = \frac{2 - + \sqrt{2 - 20} }{2} [/tex]

But 2-20 is negative, therefore there isn't any real solution to this equation.

Answer:

5x^2 - 13x + 6

Step-by-step explanation:

(8x^2 - 6x + 2) - (3x^2 + 7x - 4) =

First, drop the first set of parentheses because they are unnecessary.

= 8x^2 - 6x + 2 - (3x^2 + 7x - 4)

Now, distribute the minus sign to the left of the set of parentheses. Think of that negative sign as -1 multiplied by the parentheses. You change every sign inside the parentheses.

= 8x^2 - 6x + 2 - 3x^2 - 7x + 4

Next, group like terms together.

= 8x^2 - 3x^2 - 6x - 7x + 2 + 4

Finally, combine like terms.

= 5x^2 - 13x + 6

Answer:

Step-by-step explanation:

X = number of Yan's marbles.  x-3 = number of Geraldo's marbles

annswer: x + (x - 3) = 21

hopes this helps :)

Answer:

Yan has 12 marbles and Geraldo has 9

Step-by-step explanation:

Because 12 + 9 =21 and 9 is 3 less than 12.

Answer:

a) exactly one triangle

Step-by-step explanation:

two sides and a non included angle is given

The key to solve this problem is using ratios and proportions.

Ratio is the relationship between two numbers, defined as the quotient of one number for the other. So:  The ratio between two numbers a and b is the fraction a/b and it is read a to b. This reason can also be written a : b.

Given two reasons a/b and c/d we say that they are in proportion if a/b = c/d. The terms a and d are called extremes while b and c are the means.  In every proportion the product of the extremes is equal to the product of the means: a.d = b.c

A student uses the ratio of 4 oranges to 6 fluid ounces of juice to find the numbers of oranges needed to make 24 fluid ounces of juice.

The ratio of 4 oranges to 6 fluid ounces of juice is 4/6.

The ratio of x oranges to 24 fluid ounces of juice is x/24

Writing the proportion

4/6 = x/24

Clear x to obtain the oranges needed

x = (4)(24)/6 = 96/6 = 16

Then, the proportion is:

[tex]\frac{4}{6} = \frac{16}{24}[/tex]

The error in the student's work was that they reversed the reason, 24/16 instead of 16/24.

The student's error is in setting up the proportion and not cross multiplying correctly. The correct proportion is 4/6 = x/24. By cross multiplying and solving for x, we find that 16 oranges are needed to make 24 fluid ounces of juice.

The error in the student's work is in setting up the proportion. The correct proportion should be:

4/6 = x/24

To find the number of oranges needed to make 24 fluid ounces of juice, we can cross multiply and solve for x.

Cross Multiplying: 4 * 24 = 6 * x

Simplifying the equation: 96 = 6x

Dividing both sides by 6, we find x = 16.

Therefore, the correct answer is that 16 oranges are needed to make 24 fluid ounces of juice.

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Answer:

The desired equation is y = x + 8.

Step-by-step explanation:

As we move right from (-2,6) to (4,12), x increases by 6 and y also increases by 6.  Thus, the slope, m, m = rise / run, is m = 6/6, or just m = 1.

Start with the slope intercept form y = mx + b.  Since m = 1, we now have y = x + b.  Subbing 4 for x, 12 for y, we can find b:  12 = 4 + b.  Thus, b = 8.

The desired equation is y = x + 8.

Answer:

The answer to your question is y=1x+8

Step-by-step explanation: We already know that the slope formula is:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substitute the values to find the slope

m= 12-6/4-(-2)

m= 6/4+2

m= 6/6

m=1, so, therefore, the slope is 1

And the y-intercept would be 8

Hope this helps and Please mark my answer as the brainliest

Answer: A, B & D

I hope this helps answer helps you out! :3