How many solutions does the system of equations have?
y=-2x+3
y = x² - 6x +3

Answer:

a=-3

Step-by-step explanation:

5a+a=-10-8

6a=-18

a=-18/6

a=-3

Answer:

  a = -3

Step-by-step explanation:

This is a linear equation in one variable that has a constant term and a variable term on each side of the equal sign. It can be solved in 3 steps, so can be called a "3-step equation."

The three steps involve separating the variable and constant terms, then dividing by the variable's coefficient.

__

  -a -10 = 5a +8 . . . . . . given

To separate the variable and constant terms, we eliminate one of the variable terms by adding its opposite to both sides of the equation. It is generally convenient to choose the variable term with the lowest coefficient value. When we add the opposite of that to both sides of the equation, the resulting variable term will have a positive coefficient. (Dealing with positive numbers generally reduces errors.)

Here the two variable terms are -a and 5a. The coefficient -1 is less than the coefficient 5, so we choose to add the opposite of -a to both sides.

  -a +a -10 = 5a +a +8 . . . . . add a to both sides

  -10 = 6a +8 . . . . . . . . . . . simplify

Now there is only one variable term, but it has a constant added to it. We can eliminate that constant by adding its opposite.

  -10 -8 = 6a +8 -8 . . . . . add -8 to both sides

  -18 = 6a . . . . . . . . . . . simplify

This equation gives us the value of a multiple of the variable (6a). To get the variable by itself, we multiply by the reciprocal of the variable's coefficient. The product of the coefficient and its reciprocal is 1, so we will have the variable alone.

Multiplying by 1/6 is the same as dividing by 6. Often, it is easier to think in terms of division. However, when the coefficient is a fraction, it can be useful to think in terms of multiplying by the reciprocal of that fraction.

  (1/6)(-18) = (1/6)(6a) . . . . . . multiply by 1/6

  -3 = a . . . . . . . . . . . . . . . simplify

The solution to the equation is a = -3.

_____

Additional comment

When we say "add" or "multiply" the equation by some number, we mean that operation to be performed on both sides of the equation. The properties of equality say we can do whatever we like to an equation, as long as we do the same thing to both sides of the equation.

Answer + Step-by-step explanation:

GRASS method is an acronym for Given, Required, Analysis, Solution, and Statement.

Given:

Required:

Analysis:

50 (total) = x + 1/4 + 5/8 than solve for x

how much money leftover (x)

= total - spent on gif card - spent on new wallet

x = 50 - 1 / 4 - 5 / 8

Solution:

x = 50 - 1/4 - 5/8

x = 50 - 12.5 - 5/8

x = 50 - 12.5 - 31.25

x = 6.25

Statement:

We found that the leftover amount is $6.25.

Therefore, the leftover amount of money with a starting amount of $50.00 and purchasing a gift card and new wallet is in fact $6.25.

Answer:

I'd rather ask G.oogle

Step-by-step explanation:

btw brainliest me

The value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We know that:

P + Q are complementary, which means that

P+Q = 90°

Then R is a right angle, i.e. it measures 90°.

sin(90-x) = cos (x)

cos(90-x) = sin (x)

Then sinQ = 4/5  

cos(90-Q) = cosP = 4/5

Now sin²(P) + cos²(P) = 1

sin²(P) = 1 - cos²(P)

sin²(P) = 1 -[4/5]² =9/25

sin(P) = 3/5

cos(Q) = sin(P) = 3/5

cos(P) + cos(Q) = 4/5 + 3/5 = 7/5

Thus, the value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

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Answer:

To graph [tex]y=ax^2[/tex], you stretch or compress the graph of [tex]y=x^2[/tex] vertically by a factor of a.  If [tex]a < 0[/tex], the parabola is also reflected in the x-axis.

To graph [tex]y=ax^2[/tex], you stretch or compress the graph of [tex]y=x^2[/tex] vertically by a factor of a.  If [tex]a > 1[/tex] or [tex]a < -1[/tex], the graph is stretched vertically by a factor of a.

To graph [tex]y=(x-h)^2[/tex], you translate the graph of [tex]y=x^2[/tex] horizontally h units.  If [tex]h < 0[/tex], the graph is translated h units to the left.

#39

Then

The parabola is reflected about x axis

#40

a>1 or a<-1

Theis should be vertically streched by factor a

*41

horizontal translation=hunits

So the graph is shifted h units left

5x² + 3x + 6 is the only trinomial from the given expressions

An expression is combination of variables, numbers and operators.

A trinomial is a polynomial with three terms. In the given options, we need to identify the expression that has exactly three terms.

√11x - 7, has two terms: √11x and -7.

It is not a trinomial because it doesn't have three terms.

x - 1, has two terms: x and -1.

It is not a trinomial for the same reason as option OA.

2x + 4, has two terms: 2x and 4.

It is not a trinomial because it doesn't have three terms.

5x² + 3x + 6, has three terms: 5x², 3x, and 6.

It fits the definition of a trinomial because it has three terms.

Therefore, 5x² + 3x + 6, as it is the only expression among the options that is a trinomial.

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Answer:

[tex]16x^{5} + 16x^{4}[/tex]

As the sample size increases, the margin of error decreases.

A margin of error is known to be a statistical measurement that states the difference between apparent and projected results in a random sample survey.

From the formula:

MOE = z × √σ²/n

Where

σ = standard deviation

z = quantile

n = sample size

MOE = margin of error

From the formula, sample size is inversely proportional to the margin of error.

Hence, as the sample size increases, the margin of error decreases.

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Answer:

17/10 or 1 7/10

Step-by-step explanation:

Step 1: Write down the number as a fraction of one:

1.7 = 1.7/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 1 numbers after the decimal point, we multiply both numerator and denominator by 10. So,

1.7/1

= (1.7 × 10)/ (1 × 10)

= 17/10

(This fraction is alread reduced, We can't reduce it any further).

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 17/

10 is also equal to 1 7/10 when expressed as a mixed number.

The data display that  is best for Anne's purpose is: D. a histogram, because the bars show the frequency of data points within different ranges.

Histogram is a graph that help to  the following into different rages

Based on the data given Anne should make us of histogram based on the fact that the graph shows the frequency of the data points that are within different ranges.

 Therefore the correct option is D.

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The probability of spinning a green, spinning a purple, and then flipping a coin that lands on tails will be 0.02

From the information given, the probability of spinning a green, spinning a purple, and then flipping a coin that lands on tails will be calculated thus:

= 1/5 × 1/5 × 1/2

= 0.2 × 0.2 × 0.5

= 0.02.

Therefore, the probability is 0.02.

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The values of n that either player has a winning strategy is when the number of points are odd such as 3:-

The game is begun by A and then its chance of B to play the game alternatively, then all the possible moves are 1,2; 2,3; 1,3 in which all possible pairs are selected.

If the game end on an even number of moves then the game is won by A. For B to win, these points should be connected at the very end of the game.

Similarly, for even number of moves B wins the game when number of points is odd.

If the number of points is even the opposite of this happens that is, for even moves B wins and for odd number of moves A wins.

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The exact value of the y in the similar right triangle is 2.2360679775 units

The triangles are similar.

Similar triangles have corresponding sides of equal ratio.

The corresponding angles of similar triangle are equal.

Therefore, using similar ratio,

y / 5 = 1 / y

cross multiply

y × y = 5 × 1

y² = 5

square root both sides

y = √5

Therefore,

y = 2.2360679775 units

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Answer:

Step-by-step explanation:

Givens

Observe the small triangle at the right. The smallest side is one.

The hypotenuse is y

In the largest tringle, the hypotenuse is 5

The smallest side is y

You can set up a ratio for this situation

Equation

smallest side -  smallest triangle       Largrest triangel -- largest side

============================         =========================

hypotenuse - smallest triangle            hypotenuse -- largest triangle

1/y = y / 5                   Cross Multiply

Solution

y^2 = 1*5                    Take the square root of both sides.

√y^2 = √5

y = √5

or

y =

Answer: the answer is C

Step-by-step explanation:

Hi student, let me help you out! :)

. . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to describe the graph shown in the attached picture.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Please see below! ^^

[tex]\boxed{\mathrm{Yes}}[/tex] ⇒ It passes the Vertical Line Test (Draw a vertical line through the graph; if the line touches the graph once (only once), then the graph is a function.

[tex]\boxed{\mathrm{No}}[/tex] ⇒ It doesn't pass the Vertical line test. The line touches the graph more than once.

[tex]\underline{\rule{50}{1}}[/tex]

Since the line touches the graph only once, this graph is a function, and Option A. is not right; we can cross it out.

One down, three to go! ^^

[tex]\boxed{\mathrm{Yes}}[/tex] ⇒ It passes the horizontal line test; it touches the graph only once.

[tex]\boxed{\mathrm{No}}[/tex] ⇒ It doesn't pass the test; the line touches the graph

[tex]\underline{\rule{50}{1}}[/tex]

Since a horizontal line touches the graph more than once, this function is not one-to-one.

Option B. isn't right either.

Two down, two to go! ^^

However, look what Option C. is. The graph we're given is indeed a function, and it's not one-to-one.

So I choose Option C.

Let's ensure our answer is correct by checking the last option:

[tex]\boxed{\mathrm{Yes}}[/tex] ⇒ Its graph is a straight line.

[tex]\boxed{\mathrm{No}}[/tex] ⇒ Its graph isn't a straight line.

[tex]\underline{\rule{50}{1}}[/tex]

As we can see, the given graph is not a staight line; thus, Option D. is also wrong.

Thus, Option C. is the correct answer.

Hope it helps you out! :)

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

16/25 or 0.64

Step-by-step explanation:

First we separate the 5 from 5√x :

4 = 5×√x

Now we divide both sides by 5 :

4/5 = √x

Now we square both sides :

(4/5)² = x

Simplify :

16/25 = x

0.64 = x

Hope this helped and brainliest please

Answer:

I assume ur asking for x and y

Step-by-step explanation:

[tex]3x + 2y = 39 \: \: \: \: \: 1 \ \\ \ 5x - y = 13 \: \: \: \: \: \: \: \: 2 \\ y = 5x - 13 \: \: \: \: \: \: \: \: 3 \\ 3 > 1 \\ 3x+ 2(5x - 13) = 39 \\ 3x + 10x - 26 = 39 \\ 13x = 39 + 26 \: \: \: \: \: \: ( \div 13) \\ x = 5 \\ x = 5 > 3 \\ y = 5(5) - 13 \\ y = 12[/tex]

Answer:

(5, 12 )

Step-by-step explanation:

3x + 2y = 39 → (1)

5x - y = 13 → (2)

multiplying (2) by 2 and adding to (1) will eliminate y

10x - 2y = 26 → (3)

add (1) and (3) term by term to eliminate y

13x + 0 = 65

13x = 65 ( divide both sides by 13 )

x = 5

substitute x = 5 into either of the 2 equations and solve for y

substituting into (1)

3(5) + 2y = 39

15 + 2y = 39 ( subtract 15 from both sides )

2y = 24 ( divide both sides by 2 )

y = 12

solution is (5, 12 )

Answer:

m = 10

Step-by-step explanation:

Find 'n' first..... then pythag theorem for 'm'....

n is to 5    as  15 is to n

n/5   = 15/n

n^2 = 75     n = sqrt (75)

Then   m^2 =  n^2 + 5^2

            m^2 = 75  +  25       s-o-o-o-o:     m = 10

Answer:

the value of x is 12 and the measure of angle MNQ is 23

Answer: [tex](\frac{\sqrt{3} }{2} ,-\frac{1}{2} )[/tex]

Step-by-step explanation:

this forms a 30 degree reference angle

and this is in the 4th quadrant

When the angle is 30 degrees, the coordinates are:

[tex](\frac{\sqrt{3} }{2} ,-\frac{1}{2} )[/tex]

The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).

The polar coordinate system in geometry is a two-dimensional latitude and longitude that uses the distance from a reference point and the angle from an optical axis are used to identify each point's location on a plane. This polar axis is the ray emanating from the pole in the direction of the point of comparison, which is referred to as the pole.

The cartesian coordinate is (x, y) and polar coordinate is (r, θ). Then the relation is given as,

x = r cos θ

y = r sin θ

The angle is 330° and the radius is one. Then we have

x = 1 x cos 330°

x = (√3) / 2

y = 1 x sin 330°

y = - 1/2

The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).

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Answer:

13.5

Step-by-step explanation:

speed  = distance/time

let the time be x

40 = 9/x

so, x = 9/40

to convert it  into minutes,

(9/40)*60 = x

(9*60)/40 = x

540/40 =x

54/4 = x

27/2  = x

13.5 = x

hope this helps :)

Answer:

27/2 is the answer

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x

≥

9

Interval Notation:

[

9

,

∞

)

Step-by-step explanation:

Answer:

The first option

Step-by-step explanation:

the sign only flips when there is a negative number.

i hope this is correct

Answer:

7/10

Step-by-step explanation:

An equation is formed of two equal expressions. The equation of the perpendicular bisector is y=(1/3)x.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation of the line that passes through  (2, 4), (3, 1), and (4,-2), are,

m = (4-1)/(2-3) = 3/-1 = -3

Since the product of the slope of two perpendicular lines is -1. The slope of the perpendicular line is,

m₁m₂ = -1

(-3) m₂ = -1

m₂ = 1/3

Since the line is the perpendicular bisector it will pass through midpoint,

1 = (1/3)(3) + C

1 = 1 + C

C = 0

Hence, the equation of the perpendicular bisector is y=(1/3)x.

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Step-by-step explanation:

it is very simple :

the midpoint coordinates are created as the midpoint of the x coordinates, and the midpoint of the y coordinates.

the x coordinate of the midpoint is

(0 + 10)/2 = 10/2 = 5

the y coordinate of the midpoint is

(-2 + -6)/2 = -8/2 = -4

Answer:

“two negatives = positive” rule works for multiplication and division.

Step-by-step explanation:

-5 + (-3) example

imagine a number line with 0 in the center. From (0) You move left 5 places to (-5) on the number line. Now you move another 3 more to the left (-3) and land on (-8).

You are combining the negatives. I hope this helps.