What is the solution of the following system?
-2x - y = 1
-4x - 2y = -1
A. infinitely many solutions
B. no solutions
C. (3, 8)
D. (–3, –8)

Answer: Slope for both is 2/3

Step-by-step explanation:

The slope for blue is 4/6, or 2/3 simplified

The slope for yellow is 2/3

Therefore, the slope is the same for both. EA and AC have the same slope.

Answer:

it is the last one

Step-by-step explanation:

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Answer:

Step-by-step explanation:

I find it useful to graph the function using a graphing calculator. That answers most of the questions.

This function is written in standard form (terms have decreasing powers of x). It is a 2nd degree function, because the highest power of x is 2. A second-degree function is also called a quadratic. The leading coefficient is the coefficient of the term with the highest power of x. Here the leading coefficient is 4. The sign of it is positive, which tells you which way the graph opens (when the degree is even).

Opening

When the leading coefficient is positive, the function's graph opens upward. (If it were negative, the graph would open downward.)

Vertex

The vertex is the extreme point on the graph. If you want to find it algebraically, its coordinates are ...

  (-b/(2a), c -b^2/(4a))

where 'a', 'b', and 'c' are the coefficients of ax² +bx +c. In this function, a=4, b=-2, c=-3, so the vertex is ...

  (-(-2)/(2(4)), -3 -(-2)^2/(4(4)))  = (1/4, -3 1/4)

Axis of Symmetry

The axis of symmetry is the vertical line through the vertex. It will have the equation x=constant. Of course, the constant must be the x-value of the vertex (which is why we found the vertex first).

  x = 1/4

x-intercepts

The x-intercepts are where the graph crosses the x-axis. The attached graph shows an approximation of them, rounded to thousandths. You can compute the x-intercepts algebraically from the vertex and the leading coefficient.

  x-intercepts = (vertex x-value) ± √(-(vertex y-value)/(leading coefficient))

  x-intercepts = 1/4 ± √((3 1/4)/(4)) = 0.25 ±√0.8125 ≈ {-0.651388, 1.151388}

y-intercept

The y-intercept is the value of f(0), the point where the graph crosses the y-axis. It is always the constant in the polynomial, named 'c' above. The y-intercept is ...

  y-intercept = -3

_____

Additional comment

Sometimes you want the x- and y-intercepts written as coordinates. Of course the y-coordinate of the x-intercepts is 0. Similarly, the x-coordinate of the y-intercept is 0. The coordinate ordered pairs are shown on the graph.

These are fairly standard questions that are asked about quadratic functions. It can be worthwhile to get familiar with the way they are answered. (The computation of the x-intercepts shown here is perhaps a bit unusual, but is very effective once you have the function vertex. The values it gives are correct even when the "x-intercepts" are complex numbers.)

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Answer:

  (16, -23)

Step-by-step explanation:

We assume your notation means the figure is dilated by a factor of 3 with the origin as the center of dilation, then it is translated 2 units left and 4 units up.

These transformations can be written as ...

  (x, y) ⇒ (3x, 3y) . . . . . . . dilation by a factor of 3 about the origin

  (x, y) ⇒ (x -2, y +4) . . . . translation by (-2, 4)

These two transformations together give you ...

  (x, y) ⇒ (3x -2, 3y +4)

  (6, -9) ⇒ (3·6 -2, 3(-9) +4) = (18 -2, -27 +4) = (16, -23)

The point is transformed to (16, -23).

Answer:

0.75%

Step-by-step explanation:

First, do 3 divided by 4 which is 0.0075. But this is in decimal form, so we have to multiply this by 100. 0.0075 x 100 is 0.75, so therefore the fraction, 3/400 as an percentage is 0.75%. I hope this makes sense!

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Answer:

  10%

Step-by-step explanation:

We assume the "sum" being referred to in both cases is the principal amount invested. The simple interest formula tells you ...

  I = Prt . . . . . . interest on P invested at annual rate r for t years

We have ...

Filling in these values, we get ...

  0.3P = Pr(3)

  0.1 = r . . . . . . . . divide by 3P

The interest rate is 0.1×100% = 10% per year.

Answer:

a. 640 times 0.15 plus 8$ for monthly is 104dollars

b. kilowatts/hour, rise over run

c. 53-8 divided by 0.15 is 300 kilowatts

Answer:

B

Step-by-step explanation:

[tex]0.(81) = \frac{81}{99} = \frac{9}{11}[/tex]

Answer:

Step-by-step explanation:

Pick two points and calculate the slope (Rise/Run).

I picked (-2,0) and (2,-2)

Rise = (-2 - 0) = -2

Run = (2-(-2)) = 4

Slope (Rise/Run) = -2/4 or -1/2

The line has an intercept of -1  (the "b" in y=mx + b)

So the equation is y = -(1/2)x -1

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Answer:

  x = ab/c

Step-by-step explanation:

The applicable theorem tells you the product of chord lengths is the same for the two crossing chords:

  ab = cx

  x = ab/c . . . . . divide by the coefficient of x

36.25 miles

Answer:

answer is b

Step-by-step explanation:

The answer is B the second option.

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Answer:

  4%

Step-by-step explanation:

The multiplier for computing simple interest over a 3-year period is ...

  I = Prt . . . . . interest on principal P at rate r for t years

  I/P = rt = 3r

The multiplier for computing compound interest over a 3-year period is ...

  A = P(1 +r)^t . . . . amount with interest

  A/P -1 = (1 +r)^3 -1 . . . . multiplier for computing interest only

Then the multiplier for the difference in amounts of interest is ...

  ((1 +r)^3 -1) -3r = (1 +3r +3r^2 +r^3) -1 -3r = r^2(3 +r)

This means we need to solve the cubic ...

  r^2(3 +r) = 2.432/500

__

This can be solved a variety of ways. Perhaps my favorite is a graphical solution.  For that, we would rewrite the equation to the form ...

  f(x) = x^2(3 +x) -0.004864

so the solution is found where f(x) = 0. The graph shows the solution to be ...

  x = 0.04

The rate of interest is 0.04 = 4%.

_____

Additional comment

Using the above f(x) to develop a Newton's Method iterator, we find it to be ...

  x' = (x²(2x +3) +0.004864)/(3x(x +2))

This needs a starting value, so we need an initial clue as to the approximate interest rate.

That can be offered by rearranging the cubic we first developed:

  r = √(0.004864/(r +3))

Starting with r=0, this gives r ≈ 0.0402. At this point, we can either use this equation as an iterator, or use the Newton's method iterator above. Both will give an interest rate accurate to 4 or 5 decimal places in one iteration.

__

You may be aware from the development above that the polynomial that must be solved will have a degree equal to the number of years over which interest is computed. That is, solving the same question for a 10-year period would involve finding the root of a 10th-degree polynomial.

Answer:

12 divide mo 5 and result is 1 x 5

Answer: (4,-9)

hope i helped

Answer:75/100 or 75%

We can see that our fraction is 75/100, which means that 15/20 as a percentage is 75%.

Since 20 x 5=100 so 75/100

15 x 5=75

Hope this helped!

Have a great day!

Answer:

25thousand six hundred

Answer:

We need to know how many miles it takes to get to school

Edit:

100 miles

Explanation:

5 x 20 = 100  

Answer:

100mile

Step-by-step explanation:

5miles a day multiplied by 20 school days

Answer:  $5.50

Step-by-step explanation: because adding all the shampoo together

The cost of one bottle of shampoo is $ 7.8

The cost is $ 7.8

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of one bottle of shampoo be = x

Let the cost of one bottle of body wash be = y

Now ,

The total cost of a bottle of shampoo and a bottle of body wash = $ 14.50

Substituting the values in the equation , we get

x + y = 14.50   be equation (1)

And ,

The cost of 3 bottles of shampoo and 5 bottles of body wash = $ 56.90

Substituting the values in the equation , we get

3x + 5y = 56.90   be equation (2)

On simplifying equation (1) and equation (2) , we get

Multiply equation (1) with 5 , we get

5x + 5y = 72.5   be equation (3)

Subtract equation (2) from equation (3) , we get

2x = 15.6

Divide by 2 on both sides of the equation , we get

x = $ 7.8

Therefore , the value of x is $ 7.8

Hence , The cost of one bottle of shampoo is $ 7.8

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Answer:

there are 56 white frisbees

Answer:

92

Step-by-step explanation:

they must sell at least 92 because 92 times 5 equals 460 and so 460 is more than 455 so they made a profit

Answer:

W < 7

Step-by-step explanation:

1.

Step 1: Subtract 5 from both sides.

2. Check out the image below to see the graphed solution.

Two numbers that equal 130 when rounded by the nearest tenth are 129 and 131

Answer:

[tex] \frac{162.5}{325} = \frac{156}{x} \\ x = (325 \times 156) \div 162.5 = 312[/tex]

Answer:

This can solve by using corresponding triangles.

(TS/RT) = (VU/RV)

[tex](156 \div 162.5) \times 325 = vu[/tex]

VU = 309.12

= 309 m

Answer:

45 degrees, 135 degrees, 225 degrees, 315 degrees

Step-by-step explanation:

x = 45 degrees + k * 90 degrees

t^3-4t^2-.5t+2=0

t = 4

t = 2^.5/2

cosx=2^.5/2

The answer is the last one, [tex]2\frac{11}{12}[/tex]

Answer:

[tex] \longmapsto \: f(x) = {x}^{2} - 5x - 36 \\ \longmapsto \: g(x) = x + 4 \\ \longmapsto(f + g)(x) \\ = f(x) + g(x) \\ = ( {x}^{2} - 5x - 36) + (x + 4) \\ = {x}^{2} - 5x - 36 + x + 4 \\ = \boxed{ {x}^{2} - 4x - 32}[/tex]

Answer:

1/2

Step-by-step explanation:

1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 (common denominator: 6)

Answer:

[tex] \frac{1}{2} [/tex]

Step-by-step explanation:

[tex] \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2} [/tex]

──────────── ೄྀ࿐ ˊˎ-

PRELIMINARY

Fractions are part of a whole. For example, if an object is divided into two equal parts, the value of each part is half or one-half of the total number of objects. Fractions can be expressed in the form:

[tex] \frac{a}{b} [/tex]

DISCUSSION

Fractions also have fractions in different forms but have the same value which are called equivalent fractions. Fractions can also be simplified. To find a fraction equal to a fraction, we can multiply (×) or divide (÷) the numerator and denominator of the fraction by the same number. And to simplify fractions, we can divide (÷) the numerator and denominator of the fraction with the same number.

**

There are various forms of fractions, including:

**

Now from the discussion above, it turns out that ordinary fractions still have two more types, namely =

➳ A pure fraction is a fraction whose numerator is smaller than the denominator.

➳ An impure fraction is a fraction whose numerator is greater than its denominator.

**

The arithmetic operations also apply to fractions, including:

Subject: Mathematics

Grade: 5

Question Code: 2

Material : Chapter 5 - Fractions

Categorization Code : 5.2.5

Keywords: Definition of Fractions, Types of Fractions

Answer:

54 hours

Step-by-step explanation:

9 hours everyday, so you just mulitply the amount of the hours to the amount of days. equation: 9x6

The hours is the store open each week would be 54 hours

Suppose a, b and c are three numbers. Then we have:

a(b + c) = a x b + a x c

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space). This property is known by distributive law and applies to subtraction also.

Given that store is open 9 hours each day. It is open for 6 days each week.

Using Distributive property with multiplication and subtraction;

we just need to multiply the number of hours by the number of days. equation:

9 hour every day

9  x 6 = 54 hours

Hence, 54 hours every day the store is open each week.

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Answer:

I think its the lifo method im not sure but i had a question like this in class

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Answer:

  7(x +27) = 150

Step-by-step explanation:

Let x represent the number.

  "a number increased by 27" . . . . x +27

  "the sum multiplied by 7" . . . . . 7(x +27)

  "the result is 150" . . . . . . 7(x +27) = 150