Allison is saving money to buy a video game system. in the first week her savings were $8 less than 2/5 the price of the system. in the second week, she saved 50 cents more than 1/2 the price of the system. she was still $37 short. find the price of the system.

The solution set of the equation 3X=-6/1-X for x # 1 is {-2,1)

3x = -6/(1-x)

3x(1-x) = -6

3x – 3x2 = -6

Taking 3 as common from both sides

x –x2 = -2

x2 – x +2 =0

Using factorisation method we will get two factors

Factoring quadratics is a method of expressing the quadratic equation ax2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax2 + bx + c = 0. This method is also is called the method of factorization of quadratic equations. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.

( x – 2)(x+1)=0

So, x = 2 , -1

Now, when x ≠ 1

The solution of the equation will vary from {-2,1) .

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Answer: D = -6

Step-by-step explanation:

[tex]\frac{D-8}{-2} =12[/tex]  

1) Divide both sides by -2

[tex]D - 8=-6[/tex]

2) Add 8 to both sides

[tex]D=-6[/tex]

Answer: 5y + x + 12

Step-by-step explanation:

9y + 3 - 4y + x + 9

Group together 9y and -4y

5y + 3 + x +9

Group together 3 + 9

5y + 12 + x

Reorder the expression.

5y + x + 12

Answer:

Since we need to Round the Nearest Tenths, First we need to find what is the thenths.

So the order of numbers are

Hundreds - Tens - Ones - . - Tenths - hundreths

So tenths is the digit after the decimal Dot

When we convert .964 to the nearest tens

since there is .064, the number will be greater than .964

so the rounded number will be 1.000

we did this with only .964m but when we add 28.964 then the answer will be

28.000 = 1.000 - 29.000

Hope U will be clear

Answer:

28

Step-by-step explanation:

5(6) + (-2) = 30 + (-2) = 30-2 = 28

Answer:

28

Step-by-step explanation:

x=5  y=2

5x + y

5(6) + (-2)

30 + (-2)

30 - 2

28

Answer:

-98

Step-by-step explanation:

-412 + 314 = 314 -412

= -98

Tip:

Write the opposite symbol in the equation, then in the answer, write the opposite symbol

Just do 412 - 314

which is 98

opposite of 98 is -98

Answer is -98

Answer:

Step-by-step explanation: lengthxwidth

Answer:

5 acute

6 acute

3 obtuse

4 obtuse

Step-by-step explanation:

Hope this helps

Answer:

[tex]-\sqrt{2}[/tex]

Step-by-step explanation:

Note that:

[tex]a^2-2ab+b^2=(a-b)^2 = 4ab \\ \\ a^2 + 2ab+b^2 = (a+b)^2 = 8ab \\ \\ \implies \frac{a+b}{a-b}=\frac{\sqrt{8ab}}{-\sqrt{4ab}}=-\sqrt{2}[/tex]

Answer:

[tex]\sf \dfrac{a+b}{a-b}= -\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sf a^2 + b^2 = 6ab \qquad where\:\:0 < a < b[/tex]

Basic formula:

[tex]\sf (a + b)^2 = a^2 +b^2 +2ab[/tex]

[tex]\sf (a - b)^2 = a^2 + b^2 -2ab[/tex]

solve for a + b

[tex]\sf \rightarrow a^2 + b^2 = 6ab[/tex]

[tex]\sf \rightarrow (a+b)^2-2ab = 6ab[/tex]

[tex]\sf \rightarrow (a+b)^2 = 6ab+2ab[/tex]

[tex]\sf \rightarrow (a+b)^2 = 8ab[/tex]

[tex]\sf \rightarrow a+b = \pm \sqrt{8ab}[/tex]

solve for a - b

[tex]\sf \rightarrow a^2 + b^2 = 6ab[/tex]

[tex]\sf \rightarrow (a-b)^2 + 2ab = 6ab[/tex]

[tex]\sf \rightarrow (a-b)^2 = 6ab-2ab[/tex]

[tex]\sf \rightarrow (a-b)^2 = 4ab[/tex]

[tex]\sf \rightarrow a-b = \pm \sqrt{4ab}[/tex]

Now solve for (a + b)/(a - b)

[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \dfrac{\pm\sqrt{8ab} }{\pm\sqrt{4ab} }[/tex]

[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt\dfrac{8ab }{4ab}[/tex]

[tex]\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt{2}[/tex]

As, the value of b is greater than the value of a and both the values a  and b are greater than 0. It turns the value of expression negative as the denominator will be always evaluated to negative integer and the numerator value always > 0. So, the answer will be negative, -√2.

[tex]\sf \rightarrow \dfrac{a+b}{a-b}= - \sqrt{2}[/tex]

There is space to identify the important talents, abilities, and competencies a person will need because every company aims to attain financial stability by streamlining its operations using resources.

Every firm strives to achieve financial stability by streamlining its operations with resources, thus there is room available to identify the critical talents, abilities, and competencies a person will require.

Due to the advancement of financial deregulation, many nations around the world have experienced the benefits of rapid financial industry growth since the 1980s.

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The values of a=60, b=750, c=3, a+b+c= 813 as determined by Pythagorean Theorem..

What is Pythagorean Theorem?

A geometric theorem states that the square of a right triangle's hypotenuse equals the sum of the squares of its other two sides.

Call the circle's center O, the unicorn's tether point A, and the final spot where the rope reaches tower B. Triangle OAB is a right triangle since BA is a tangent line at point B and OB is a radius. We determine the horizontal component of AB has length [tex]4\sqrt{5}[/tex] using the Pythagorean Theorem.

The cylinder is "unrolled" to become a flat surface. Let C be the rope's bottom tether, D the point below A on the ground, and E the point directly beneath B. Triangles CDA and CEB share characteristics of right triangles. The Pythagorean Theorem states that CD=8cdotsqrt6.

Let x represent the size of CB.[tex]CD=8\cdot\sqrt{6}[/tex]

[tex]\[\frac{CA}{CD}=\frac{CB}{CE}\implies \frac{20}{8\sqrt{6}}=\frac{x}{8\sqrt{6}-4\sqrt{5}}\implies x=\frac{60-\sqrt{750}}{3}\][/tex]

Therefore,

a=60, b=750, c=3,a+b+c= 813 as determined by Pythagorean Theorem.

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The population of the dark city in 2015 will be 449,245.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The dark city had a population of 350,000 in 1990 and has increased exponentially since then, to 475,000 in 2008. Then the equation will be

350,000 = a(b)      ...1

475,000 = a(b)¹⁸      ...2

From equations 1 and 2, then we have

475,000 / 350,000 = b¹⁷

b = 1.018

Then the value of the variable a will be

350,000 = 1.018a

a = 343768.87

Then the equation will be

y = 343,768.87 (1.018)ˣ

The population in 2015 will be

y = 343,768.87 (1.018)¹⁵

y = 343,768.87 x 1.3068

y = 449,245

The population of the dark city in 2015 will be 449,245.

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15/20 gramos equivalen a 0 . 75 en forma decimal. Si se supone que las cantidades decimales deben sumarse, entonces 1 . 5

-------------------------------

Espero que esto te ayude.

Que tengas un buen día y que Dios te bendiga. :)

The statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A

From the information given, we have that;

The linear equation is ;

-2x + 3 = 6

Let's solve for x

First, collect like terms

-2x = 6 - 3

-2x = 3

Divide both sides by - 2

x = 3/ -2

The linear inequality is;

-2x + 3 < 6

collect like terms

-2x < 6 - 3

Make 'x' the subject by dividing both sides by -2

-2x/ -2 = 3/ -2

x = 3/ -2

We can see that the linear equation and the linear inequality have the same solution and steps.

Thus, the statement that is true is completing the solution for the equation is the same as completing the solution for the inequality. The student would divide both sides by -2 in either case. Option A

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Answer:

Im sleepy. How are you?

Answer:

oh thx im good how are you

Step-by-step explanation:

Answer:

y=-1/3x+1

Step-by-step explanation:

Slope-Intercept Form: y=mx+b

m is the slope

b is the y-intercept

In the given statement it tells us the point is (-3,1).

-3 is the x-intercept while 1 is the y-intercept

In the given statement it tells us the slope is -1/3

Plug in the m for -1/3 and the b for 1

y=-1/3x+1

Hope this helps.

Answer:

10

Step-by-step explanation:

Distance formula:

d = √(x₂-x₁)²+(y₂-y₁)²

A (1,2) D (4,3)

d = √(4-1)²+(3-2)² = 3.16227766

All 4 sides of a square are equal lengths.

The equation for the area of a square:

A = a²

A = (3.16227766)² = 10

Answer:

188.57 in

Step-by-step explanation:

Circumference = 2πr = 2πd/2 = πd

[tex] = \frac{22}{7} \times 60 \: in[/tex]

= 188.57 in ( approx.)

Answer:

The answer should be 10.5 from what i have seen in the past

Step-by-step explanation:

Greetings from Brasil...

The small green lines on the line segments indicate that TR = RA, as well as the small red lines indicate that MR = RH, then

TR = RA

3X + 5 = X + 17

X = 6

Answer: -6/7

Step-by-step explanation: combine like terms.

Same signs; add, different signs; subtract.

Answer: this may not be correct but I think that the answer is 6.8 being greater than 6.6 since it is more closer to 7.0.

Step-by-step explanation:

Answer:

The first, third, and fourth.

Step-by-step explanation:

Those answers involve scaling the measurement up, which requires a positive power of 10. For scaling down, you'll need a negative power of 10, e.g., 2x10^-2=0.02.

The slope intercept of the line is y = -1/3x -11

Slope-intercept is one of the special forms of line equation

The slope intercept of a line can be found by solving the slope-intercept equation of a line which is parallel to that line.

Slope-intercept equation is

y = mx + b

where m is the slope and b is the intercept.

The slope-intercept equation of the parallel line is

y = -1/3x + 4

The slope will be the same for both lines as they were parallel to each other.

Thus m = -1/3

The point in which the line passes is given as (-6,-9)

So with these data, We can find the intercept of the line

y = mx + b

where m = -1/3 and (x,y) is (-6,-9),Thus

-9 = -1/3(-6) +b

-9 = 6/3 +b

-9 = 2 + b

b = -9-2

b = -11

Thus the intercept of the line passing through the point (-6,-9) is -11

Thus, the slope-intercept equation of the line we need to find is

y = -1/3x -11

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Answer:

x = 16

Step-by-step explanation:

Answer:

a power function is a function with a single term that is the prudoct of a real number

Answer:

I will be your human calculator! top to bottom!

1. (+1)     5. (+28)  9. (+8)

2. (+4)    6. (+3)   10. (-5)

3. (+14)   7. (+24) 11. (+6)

4. (-3)      8. (-3)     12. (+1)!    Good Luck!

If [tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex]  then the value of h(3) = -13/8  , h(4) = -59/24 ,  h(-1/2) = 31/24 .

In the question , the equation is given as

[tex]h(x)=\frac{-5}{6} x+\frac{7}{8}[/tex]      ....(i)

Part(a)

To find the value of h(3)

we substitute the value of x=3 .

On substituting the value of x=3 in equation (i),

we get ,

h(3) = (-5/6)3+7/8

= -15/6+7/8

taking LCM of 6 and 8 as 24, we get

= -60/24 + 21/24

= (-60+21)/24

= -39/24

Writing in the simplest form we get

= -13/8

so, the value of h(3)= -13/8 .

Part(b)

for h(4) ,we substitute the value of x=4 .

On substituting the value of x=4 in equation (i) ,

we get ,

h(4) = (-5/6)4+7/8

= -20/6+7/8

taking LCM of 6 and 8 as 24, we get

= -80/24 + 21/24

= (-80+21)/24

= -59/24

so , the value of h(4)= -59/24 .

Part(c)

for h(-1/2) ,we substitute the value of x as -1/2 .

On substituting the value of x = -1/2 in equation (i) ,

we get ,

[tex]h(\frac{-1}{2} )=\frac{-5}{6} *\frac{-1}{2} +\frac{7}{8}[/tex]

= 5/12 +7/8

taking LCM of 12 and 8 as 24, we get

= 10/24 + 21/24

= (10+21)/24

= 31/24

so , the value of h(-1/2)= 31/24 .

Therefore , if h(x) = (-5/6)x+7/8 the the value of h(3)= -13/8  , h(4)= -59/24 and h(-1/2)= 31/24 .

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Answer:

204 ÷ 34 = 6

Step-by-step explanation:

204 ÷ 34 = 6

Check:

34

x 6

------

204

hope this helps :)

Answer : 6

Explanation :

34 + 34
68
68 + 34
102
102 + 34
136
136 + 34
170
170 + 34
204

OR just simply use Multiplication
34 x 6