A system of linear equations contains two equations with negative reciprocal slopes. How many solutions will it have?

Answer:

x = -80

Explanation

-40 divided by 1/2 is -80

Answer:

x = 6 ± 3√10

Step-by-step explanation:

Since this is an unfactorable expression, apply the Quadratic Formula, -b ± √b² - 4ac\2a, according to the Quadratic Equation, y = Ax² + Bx + C. Applying the Quadratic Formula will give you the above answer.

NOTE: -b = OPPOSITE of b

I am joyous to assist you anytime.

Final answer:

To solve x² - 12x + 36 = 90 for x, we simplify the equation to x² - 12x - 54 = 0 and use the quadratic formula to find x = 6 + 3√10 and x = 6 - 3√10.

Explanation:

To solve the equation x² - 12x + 36 = 90, we can first simplify it by subtracting 90 from both sides to set it equal to zero:

Now we use the quadratic formula, which states that for any quadratic equation of the form ax² + bx + c = 0, the solutions for x can be found using:

Applying this to our equation with a = 1, b = -12, and c = -54, we get:

Thus, the solutions are x = 6 + 3√10 and x = 6 - 3√10.

Answer:

Part a)  In order to solve the equation, we will simplify both of them.  Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.

Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.

Part c)  As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.

Step-by-step explanation:

You can simplify the explanation, also if you play ROBLOX, follow me at my username: BAMUNJI, or 24KBlingYT

By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.

Part (a)  We shall simplify both of them in order to find the solution to the equation.

Part (b)  When x=-1/2, the answers to the second expression, 2x2, change to -1, and we eventually arrive in 1.

Part (c)  As we can see, the expressions are identical, thus we can demonstrate that they are equal if x is any number other than -1/2.

Learn more about expressions here:

https://brainly.com/question/723406

#SPJ2

Answer:

C

Step-by-step explanation:

Givens

Original cost = 29 dollars.

Discount = 40% on the second shirt.

Formula

cost after discount = (2 × list price) – (list price × discount percentage)

Solution

Cost after discount = 2 * 29 - 29*40/100

Cost after discount = 58 - 11.60

Cost after discount = 46.40

Answer:

Slope= 7/5

Step-by-step explanation:

The slope of a line is determined as a ratio of the change in y to the change in x.

Slope=Δy/Δx

Δy=y₂-y₁

Δx=x₂-x₁

Therefore we can use the the x and y coordinates from the points given, (-3,0) and (2,7) to calculate the slope.

m= (7-0)/(2-⁻3)

Slope= 7/5

When a negative number is subtracted from a number it the operation sign changes to addition.

Answer: Last option

[tex]slope=\frac{7}{5}[/tex]

Step-by-step explanation:

The equation to find the slope m of a line is:

[tex]m=\frac{y_2-y_2}{x_2-x_1}[/tex]

Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points through which the line passes

In this case the points are: (-3, 0) and (2, 7)

Therefore the slope is:

[tex]m=\frac{7-0}{2-(-3)}[/tex]

[tex]m=\frac{7}{2+3}[/tex]

[tex]m=\frac{7}{5}[/tex]

The answer is the last option

Answer:

The value of f(-4) = -80

Step-by-step explanation:

It is given that,  f(x) = -5x²

To find the value f(-4)

Let  f(x) = -5x²

To find the value of f(-4), substitute -4 instead of x

f(-4) =  -5 * (-4)²

 = -5 * 16      [ since (-4)² = -4 * -4 = 16 ]

 = -80

Therefore the value of f(-4) = -80

Answer:

4 x  [tex]10^{12}[/tex])

Step-by-step explanation:

(6 x [tex]10^{8}[/tex]) / (1.5 x [tex]10^{-4}[/tex])

=  ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) / ([tex]10^{-4}[/tex])

=  ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) x ([tex]10^{4}[/tex])

=  [tex]\frac{6}{1.5}[/tex] x [tex]10^{12}[/tex]

=  4 x  [tex]10^{12}[/tex]

Step-by-step explanation:

6*10^8 /1.5*10^-4

6/1.5 * 10^8/10^-4

4 * 10^8-(-4)

4*10^8+4

4*10^12

Answer:

cam bought 12 books 7 at $0.35 and 5 at $0.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}2x-3y=-9\\-x+3y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad x=-3\\\\\text{put the value of x to the second equation:}\\\\-(-3)+3y=6\\3+3y=6\qquad\text{subtract 3 from both sides}\\3y=3\qquad\text{divide both sides by 3}\\y=1[/tex]

Answer:  $24

Step-by-step explanation:

Let x represent the amount of Carrie's allowance.

[tex]\dfrac{1}{4}x+\dfrac{1}{3}x+8=22\\\\\\\dfrac{1}{4}x+\dfrac{1}{3}x=14\\\\\\(12)\dfrac{1}{4}x+(12)\dfrac{1}{3}x=(12)14\\\\\\3x + 4x = (12)14\\\\\\7x=(12)14\\\\\\x=(12)2\\\\\\x=24[/tex]

Answer:

-x(x^2 +3x +4)

Step-by-step explanation:

-x^3-3x^2-4x

Factor out a -x

-x(x^2 +3x +4)

We cannot factor inside the parentheses, so this is complete

Answer:

[tex]( {a}^{2} - b)(5 {a}^{2} + 6b) \\ 5 {a}^{4} + 6 {a}^{2} b - 5 {a}^{2} b - 6 {b}^{2} \\ = 5 {a}^{4} + {a}^{2} b - 6 {b}^{2} [/tex]

Answer:

The best cluster would be Philadelphia which percentage of 27% is nearly close to 28% of the whole united states population percentage.

Step-by-step explanation:

The correct option for the city which would be considered as the best cluster is B. Miami,  16% of the population are MyBook users.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

Now given that,

Amount of population that are MyBook users = 28%

Thus,

Amount of population that do not uses MyBook = 100% - 28% = 72%

Thus, Philaldephia and Denver cannot be percentage of the population who are MyBook users.

Thus, the correct option for the city which would be considered as the best cluster is B. Miami, 16% of the population are MyBook users.

To learn more about survey :

brainly.com/question/17373064

#SPJ2

Answer:

a=1

Step-by-step explanation:

2a + 3(a + 1) = 8

Distribute

2a +3a +3 = 8

Combine like terms

5a +3 =8

Subtract 3 from each side

5a+3-3=8-3

5a = 5

Divide by 5

5a/5 = 5/5

a=1

Question 1:

For this case we have that by definition, the volume of a prism is given by:

[tex]V = a * b * c[/tex]

Where:

a: It is the long

b: It is the width

c: It is the height

According to the data we have:

[tex]a = 18m\\b = 9m\\c = 6m[/tex]

Substituting:

[tex]V = 18 * 9 * 6\\V = 972[/tex]

Thus, the volume of the building is[tex]972 \m ^ 3[/tex]

Answer:

Option B

Question 2:

For this case we have that by definition, the volume of a prism is given by:

[tex]V = a * b * c[/tex]

Where:

a: It's the long

b: It is the width

c: It is the height

According to the data we have:

[tex]a = 26in\\b = 14in\\c = 18in[/tex]

Substituting:

[tex]V = 26 * 14 * 18\\V = 6552[/tex]

Thus, the volume of the tank is [tex]6552 \in ^ 3[/tex]

Answer:

Option A

Question 3:

For this case we have that by definition, the volume of a cube is given by:

[tex]V = l ^ 3[/tex]

Where:

l: It's the side of the cube

According to the data we have that the cube side is 7.2ft.

Substituting we have:

[tex]V = (7.2) ^ 3\\V = 373.25[/tex]

Rounding off we have that the volume of the cube is [tex]373.25 \ ft ^ 3[/tex]

Answer:

Option B

Question 4:

For this case we have that by definition, the volume of a cube is given by the following formula:

[tex]V = l ^ 3[/tex]

Where:

l: It's the side of the cube

According to the data we have that the cube side is 4.5 yards.

Substituting we have:

[tex]V = (4.5) ^ 3\\V = 91.125[/tex]

Rounding off we have the cube volume is[tex]91.13 \ yd ^ 3[/tex]

Answer:

Option C

Answer:

Possible values of x are   50 < x < 110.

Step-by-step explanation:

Consider the perimeter of the field:

2x + 2(x + 30) < 500

2x + 2x + 60 < 500

4x < 440

x < 110.

Consider the area of the field:

x(x + 30 ) > 4000

x^2 + 30x - 4000 > 0

(x - 50)(x + 80) > 0

The critical values are x = -80 and 50.

As x is a width it must be positive so x > 50.

Answer:

(x-10)(x-2)

Formula:

a^{2} - b^{2} = (a-b)(a+b)  

Explanation:  

(x-6)^2-4^2

Then we can simplify to, (x-6-4)(x-6+4)

Which comes to your answer,  (x-10)(x-2)

Answer:

Step-by-step explanation:

x² − 12x − 20 = 0

a = 1;  b = (-12);  c = (-20)

b²-4ac = (-12)² - 4 * 1 * (-20) = 144 + 80 = 224

√b²-4ac = √ 224 = √ 2*2*2*2*2*7 = 2*2*√(2*7) = 4√14

delta = -b ± √b²-4ac / 2a

         = -(-12) ± 4√14

                    2 * 1

          = (12 ± 4√14)/2

           = 2 ( 6 ± 2√14) / 2

           =  6 ± 2√14

x =   6 + 2√14;  x =  6 - 2√14

Answer:

240

Step-by-step explanation:

200 divided by 100, to get the amount per percent, then multiply it by 120, to get 240.

Answer:

Step-by-step explanation:200 multipled by 120%

200 • 120/100

Reduce the numbers with the greatest common divisor 100

2 • 100

2 •120

Multiply the numbers

THE ANSWER IS 240

Answer:(4,0) and (-9,0)

Step-by-step explanation:

a sequence is a function whose domain is the set of natural numbers.

natural numbers are all the negative and positive integers

A sequence exists as a function whose domain is the set of natural numbers.

A sequence exists as a function whose domain is the set of natural numbers or a subset of the natural numbers. Usually use the symbol a to describe a sequence, where n is a natural number and a stands for the value of the function on n. Intuitively, a sequence exists just as an ordered list of (possibly infinitely many) numbers.

To learn more about Sequence refer to:

https://brainly.com/question/5873081

#SPJ2

Step-by-step explanation:

There can be two situations

1. When maggie is older

The equation becomes x = y + 3

It can also be expressed as y = x - 3

2. When maggie is younger

The equation becomes y = x + 3

Table of possible values

1. x    y          2. x    y

  5   2              2   5

  6   3              3   6

Answer:

The required equation is [tex]|y-x|=3[/tex]. If maggies is elder, then [tex]y_1=x-3[/tex] and if maggies is younger, then [tex]y_2=x+3[/tex].

Step-by-step explanation:

Let the x represents maggies age and y represents terrance age, make a table of possible values for x and y.

It is given that the difference between maggies age and terrance age is 3.

It means

[tex]|y-x|=3[/tex]

On simplification, we get

[tex]y-x=\pm 3[/tex]

[tex]y=x\pm 3[/tex]

Case 1: If maggies is elder.

[tex]y_1=x-3[/tex]

Case 2: If maggies is younger.

[tex]y_2=x+3[/tex]

The table of values is

x      y₁      y₂

-3    -6      0

0    -3      3

3     0      6

The graph of both functions are shown below.

Answer:

(2, 9)

Step-by-step explanation:

We've been given the exponential function;

f(x) = 25(3/5)^x

We need to determine the value of f(x) when x = 2, that is;

f(2) = 25(3/5)^2

Using a calculator we obtain

f(2) = 9

Thus the next point she plots on the graph will be (2, 9)

Answer:

C

Step-by-step explanation:

4y-2y=10

y=5

Answer:

-1 1/3

Step-by-step explanation:

To change and improper fraction (larger number in the numerator than the denominator) to a mixed number

divide the numerator by the denominator

4/3 =1  with 1 left over

Take the leftovers and put it over the denominator

1/3

The mixed number is 1 1/3

Since the number was negative, we put the negative out front

-1 1/3

Answer:

Step-by-step explanation:

Look at the picture.

The range: -6 ≤ y ≤ 9

The domain: x ≤ 0

[tex]\text{Hey there!}[/tex]

[tex]\text7x}^2\text{- 32x - 60}[/tex]

[tex]\text{The answer is: (7x + 10)(x - 6)}[/tex]

[tex]\text{Because if you follow the step to the answer (first you have to distribute}[/tex] [tex]\text{then combine the like terms after distributing) after all of that you SHOULD}[/tex] [tex]\text{get the equation back!}[/tex]

[tex]\text{Distribute}\downarrow\\\\\text{7x(x)=7x}^2\\ \text{7(-6x)= -42}\\\text{10(x)= 10x}\\\text{10(-6)= -60}[/tex]

[tex]\text{Combine your like terms (terms that has the almost the same thing)}\downarrow[/tex]

[tex]\text{-42x + 10x = -32x}[/tex]

[tex]\text{The other terms stays the same because they DON'T have like terms}[/tex]

[tex]\text{Original problem: 7x}^2\text{- 32x -60}[/tex]

[tex]\boxed{\boxed{\bf{Answer: (7x+10(x -6))}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

9

Step-by-step explanation:

12 - 3 = 9

Hello :D

Answer:

[tex]\boxed{9}\checkmark[/tex]

The answer has a positive sign.

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponents

Multiply

Divide

Add

Subtract

Left to right

[tex]|-12|-|3|[/tex]

[tex]12-3=9[/tex]

[tex]\boxed{9}[/tex], which is our answer.

Hope this helps! :D

Time= distance/speed (T = d/s)

Rate or speed are similar since they both represent some distance per unit time such miles per hour and kilometers per hour. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

distance = rate x time To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.

This is because, speed of the object refers distance travelled divided by time or it expressed as, Furthermore, 1 could also explain the relationship of the time with other two variables using this formula. Speed could be of 2 types, relative or average.

from the formula,

Distance = time * speed

Speed = distance/time

Time= distance/speed (T = d/s)

So basically distance divided both of them when it find speed distance divide time when fine time distance divide speed.

Learn more about Distance, time and speed here https://brainly.com/question/9834403

#SPJ2

Answer:

x=42

Step-by-step explanation:

2x42

Answer:

42

Step-by-step explanation:

tell me if i am wrong by reporting

Answer:

2n² = 12 + n

2n² - n - 12 = 0

[tex]n = \frac{1 ± \sqrt{ {( - 1)}^{2} - 4(2)( - 12)} }{2(2)} [/tex]

[tex]n = \frac{1 ± \sqrt{97} }{4} [/tex]