Algebra Word Problem, 9th Grade, Station 2, please help!

Answer:

fvbdsnbgb

Step-by-step explanation:

1. If the product of these integers is to be 1, then all of them must be either 1 or -1.

2. Since the product is positive (+1), it must be that there are an *even* number of negative ones (-1), if any.

3. If the sum were 0 it would mean that the number of +1's must equal the number of -1's. So that means there would have to be exactly 22/2=11 of each.

4. But if there were 11 of each, that means the number of -1's would be *odd* and there's no way the product could be +1 (as stated in 2 above).

Hence, the sum is never 0, if the product of 22 integers is equal +1.

Fun problem.

We have a positive product, so no zero factors.

We have a positive product, so an even number of negative factors.

We have a product of 1, so all the integers must be either +1 or -1.

If we have 2n factors of -1 we have 22-2n factors of 1 so a sum of

[tex]s = (-1)2n + (1)(22-2n) = 22-4n[/tex]

For that to be zero we need

[tex]0 = 22-4n[/tex]

[tex]n = 22/4 = 11/2[/tex]

That's not an integer; we've shown there's no even number of -1s that will make the sum zero, and since there must be an even number of -1s, the sum cannot equal zero.

15x = -75  Divide both sides by 15.

Final answer: -5

hope that helps

Solving the product of 15 and a number x is −75 equals to: -5.

To write the word sentence as an algebraic equation:

In this exercise, we are required to translate the word sentence into a mathematical (algebraic) expression and solve for the unknown variable (number):

The product of 15 and a number x:

[tex]15(x)[/tex]

Equating the above expression to -75, we have:

[tex]15x = -75[/tex]

Simplifying further, we have:

[tex]15x = -75\\\\x = \frac{-75}{15}[/tex]

x = -5

Therefore, the unknown number is -5.

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Hey there!!

Distance formula :

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

Coordinates given :

( 0,1 ) and ( 2,-3 )

( y2 = -3 ; y1 = 1 ) ( x2 = 2 ; x1 = 0 )

Plugging in the values :

... [tex]\sqrt{(-3-1)^{2}+(2-0)^{2} }[/tex]

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

... [tex]\sqrt{16+4}[/tex]

... [tex]\sqrt{20}[/tex]

... [tex]\sqrt{5}[/tex]×[tex]\sqrt{4}[/tex]

... 2[tex]\sqrt{5}[/tex] units is the distance.

Hope my answer helps!!

Answer:

Average decrease in car's value per year = 1800$

Explanation:

  The worth of car bought by Mr. Solan = 30000$

  Reduction of car's price = 5400$

  Number of years considered for measuring reduction of car's price = 3 years.

  Average of values = Total of the values/ Number of values.

  Average reduction per year = Total reduction/ Number of years.

                                                 = 5400/3 = 1800$

  So average decrease in car's value per year = 1800$

He weighs 5 times more

The equation which has no solution is:

                           Option: C

           c)     [tex]7y+9=7y-6[/tex]    

The equation is said to have a no solution if we get a false identity on solving the equation.

a)

[tex]5m-6=5m+7-m[/tex]

On combining the like terms in the right hand side of the equation we have:

[tex]5m-6=5m-m+7\\\\5m-6=4m+7\\\\5m-4m=7+6\\\\m=13[/tex]

Hence, we get a unique solution to the equation.

b)

[tex]3w+4-w=5w-2(2w-2)[/tex]

on using the distributive property in the right hand side of the equation we have:

[tex]3w+4-w=5w-2\times w-2\times (-2)\\\\3w-w+4=5w-2w+4\\\\2w+4=3w+4\\\\3w-2w=4-4\\\\w=0[/tex]

Again we get a unique solution to the equation.

c)

[tex]7y+9=7y-6[/tex]

on subtracting 7y from both the sides of the equation we have:

[tex]7y-7y-6=9\\\\-6=9[/tex]

which is a false identity.

Hence, the equation has no solution.

d)

[tex]4z+8=-4z-2\\\\i.e.\\\\4z+4z=-2-8\\\\8z=-10\\\\z=\dfrac{-10}{8}\\\\z=\dfrac{-5}{4}[/tex]

This equation has a unique solution.

x equals 12 because

3x-3= 2x+9

x=12

3(x-1) = 2x+9                  Remove the Brackets on the left

3x - 3 = 2x + 9               Add 3 to both sides

3x = 2x + 9 + 3              Collect like terms

3x = 2x + 12                   Subtract 2x from both sides.

3x - 2x = 2x-2x + 12

x = 12

you are multiplying 3 algebraic fractions together

[tex]\frac{1}{x-4}[/tex] × [tex]\frac{1}{x-4}[/tex] x [tex]\frac{1}{x-4}[/tex]

multiply the numerators together, that is 1 × 1 × 1 = 1

multiply the denominators together, that is

(x - 4 ) × (x - 4 ) × (x - 4 ) = (x - 4)³

thus the product of the multiplication is

[tex]\frac{1}{(x-4)^{3} }[/tex]

I’ve had this question back when i was in school.

You have to calculate at regular price.

4 x 9.75 = 39

Subtraction time. 10 people are renting, 4 are members  

10 - 4 = 6

6 that are nonmembers. 4 members  

6 x 3.95 = 23.70

4 x 2.95 = 11.80

Add all those up.

39 + 11.80 + 23.70 = 50.80 + 23.70 = 74.50

Answer: $74.50 :)

6 because -12/-2 would be positive 2

V=6

divide both sides by -2 to get variable v on one side

-12/-2=6

70 r − 21 < 19

70r<40

r=4/7

Answer:

r<  4/7

​

Step-by-step explanation:

take 5.99 divide by 13 and the unit rate is 0.46

The point (0,-5) is not located in Quadrant IV because it has a negative y-coordinate.

The point (0,-5) is not located in Quadrant IV because Quadrant IV is the bottom-right quadrant of the coordinate plane, where both the x-coordinate and the y-coordinate are positive. In Quadrant IV, the x-coordinate is positive and the y-coordinate is negative. A coordinate point with a negative y-coordinate would be located in Quadrants III or IV.

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Hello!

[tex]\frac{4}{9}-\frac{2}{9}[/tex]

First you had to used apply rule -(-b)=b

[tex]\frac{4}{9}+\frac{2}{9}[/tex]

Since the denominators are equal to it should be combine by the fractions.

[tex]\frac{4+2}{9}[/tex]

Then add 4+2=6

[tex]\frac{6}{9}[/tex]

[tex]\frac{4}{9}-\frac{-2}{9}[/tex]

Finally you had to cancel by the common factor of 3.

[tex]=Answer--->\frac{2}{3}[/tex]

Hope this helps! And thank you for posting at here on Brainly. And have a great day! -Charlie :)

7 x 4 = 28

The least common multiple of 7 and 4 = 28

The answer is 28. I have to type this because it wont let me simply answer your question.

Hi there,

58,000,000 in scientific notation is 5.8 x 10^7

this is because there are a least 7 zeros.

Hope this is correct :)

Have a great day

5.8 x [tex]10^{7}[/tex] is the answer.

The 2 points closest to the line is (4,12) and (20, 36)

The slope is the change in Y over the change in x:

Slope = (36-12) / (20-4)

Slope = 24 / 16

Slope = 1.5

So now you have y = 1.5x

To find the equation use the formula (y-y1) = m*(x-x1)

y-12 = 1.5(x-4)

Simplify the right side:

y-12 = 1.5x - 6

Add 12 to each side:

y = 1.5x +6

The answer is the 2nd one.

Hello!

You simply divide 78 by 171.

78÷171= 0.45614035

Rounded: 0.46

78 goes into 171 two times. This is because all you have to do is divide 171 and 78 and get 2.192307692. 78 goes into 171 two whole times. Hope this helps you.

Answer:

2.8 = 2y

1. y= 1.4

Answer:

-3 = x/5

x= -15

Explanation:

To find the variable use the opposite function so if its multiplication find x by dividing and vice versa for division

Final answer:

The x-intercept of the graph 2(y+0.5) = 3.5x + 2y is 2/7, and the y-intercept is 0.5.

Explanation:

To find the x and y intercepts of the graph of the equation 2(y+0.5) = 3.5x + 2y, we first simplify the equation. Start by distributing the 2 on the left side:
2y + 1 = 3.5x + 2y. Next, subtract 2y from both sides to get:
1 = 3.5x. Now, to find the x-intercept, set y to zero and solve for x:

x-intercept: y = 0
1 = 3.5x
x = 1 / 3.5
x = 2/7

To find the y-intercept, set x to zero and solve for y:

y-intercept: x = 0
1 = 2y
y = 1 / 2
y = 0.5

The x-intercept is 2/7, and the y-intercept is 0.5.

M has to pay at least $200 against his debt over the 8 months. If he is to pay every month the same amount, he must pay (at least) 200/8 = $25 per month to meet his goal

The answer is 5.84

   2.65

   3.19

 +------

5.84

Step by Step:

2.65 + 3.19 = Answer

Anwer:

A = 5.84 Miles

Comments:

N/A

Omar runs about 0.12 miles per minute.

To find this answer, you simply divide both 104 and 12, by 104. In doing so, you'll get 0.115... miles per 1 minute. Rounding up, you'll get 0.12 miles per minute.

I hope this helps!

The given quadratic equation y=x^2+4x+5 has no real solutions because the discriminant is negative. Therefore, there are no zeros for this equation, making option A (There are no zeros) the correct choice.

The question asks to identify any zeros of the quadratic equation [tex]y=x^2+4x+5.[/tex]To find the zeros, we need to set the equation equal to zero and solve for x. This is typically done using the quadratic formula, which is √x=(-b±√(b^2-4ac))/(2a), where a=1, b=4, and c=5 in our equation.

Substituting these values into the quadratic formula gives: x=(-4±√((4)^2-4*1*5))/(2*1) = (-4±√(16-20))/2 = (-4±√(-4))/2. Since the value under the square root sign (the discriminant) is negative, this equation has no real solutions. Thus, there are no zeros for the given quadratic equation, making option A the correct choice.

The car goes 23.2 miles every gallon, so with 15 gallons (15 * 23.2 = 348) it can go 348 miles. With the extra .25 that the car has, it can go 0.25 * 23.2 = 5.8 miles. 348 miles plus the 5.8 miles gets you 353.8 miles on 15.25 gallons.

A car that averages 23.2 miles per gallon can travel approximately 353.8 miles using 15.25 gallons of gasoline.

If a car averages 23.2 miles per gallon of gasoline, we can calculate the distance it can travel on 15.25 gallons by multiplying the car's fuel efficiency by the amount of gasoline.

To find the distance:

Multiply the car's average miles per gallon (MPG) by the number of gallons of gasoline.

Distance = 23.2 MPG * 15.25 gallons

Distance = 353.8 miles

Therefore car that averages 23.2 miles per gallon can go approximately 353.8 miles on 15.25 gallons of gasoline.

5 • 7^0 = 35^0

You would ignore the 0. And Just multiply the 7 and 5 to get 35.

If the power of any number is zero then the a⁰ is equal to 1. Then the expression 5 × 7⁰ is equivalent to 5.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

→ 5 × 7⁰

We know that if the power of any number is zero then the a⁰ is equal to 1.

⇒ 5 × 7⁰

⇒ 5 × 1

⇒ 5

More about the equivalent expression link is given below.

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To evaluate a function at a specific x value simply means to substitute that particular value in place of every occurrence of the variable x.

So, starting from [tex] f(x) = 6x+7 [/tex], we have

[tex] f(-3) = 6\cdot(-3)+7 = -18+7 = -11 [/tex]