in the equation c²-4=0 c is equal to

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range.

By factoring the numerator and denominator and setting them both to zero, the domain of a fraction function can be determined. The domain's values are the roots of the ensuing equation. Using the algebraic method of factoring is another method for determining the domain of a fraction function.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

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Answer:

A the answer is a

Step-by-step explanation:

it's corn a beautiful thing for me it has the juice

Given the Quadratic Polynomial:

You need to factor it using the Grouping Method.

You can identify that it has this form:

Notice that, in this case:

In order to rewrite it in a form that then you can apply the Grouping Method, you need to find two numbers whose product is the value of "c" and whose sum is the value of "b".

Notice that:

Therefore, you can set up that:

Hence, the answer is: Second option.

We have

Answer: A.

we have the following:

therefore:

therefore, the answer is 5/6

Answer:  (10,5) or (14,3) are two possible answers.

Infinitely many answers are possible. Pick one to write as the final answer to your teacher.

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

Explanation:

Focus on the points B(1,4) and C(5,2)

More specifically, focus on the x coordinates 1 and 5. To go from B to C, we move to the right 4 units since 1+4 = 5

We also move down 2 units since we go from y = 4 to y = 2

In short, the translation motion is "right 4, down 2". We can further abbreviate this into the vector notation <4, -2>. This translation vector only applies going from B to C.

The vector notation <4,-2> is the same as writing [tex](x,y) \to (x+4,y-2)[/tex] but the first method is much faster to write out since it avoids needing to write x or y.

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

Now if we want to construct a similar triangle A'B'C', we will use that vector to scale it up or down. Let's scale it up and double each coordinate.

<4, -2> doubles to <8,-4>

So instead of "right 4, down 2" we now follow the path "right 8, down 4". Take notice how both motions involve the same slope.

Start at B'(2,9) and move right 8 and down 4 to arrive at C'(10,5)

See figure 1 below.

This is one possible answer out of infinitely many. This is because we can change the scale factor to any nonnegative real number we want.

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

Another example:

Instead of doubling the coordinates of the translation vector, let's triple them.

<4,-2> triples to <12,-6>

Then start at B'(2,9) and move right 12 and down 6 to arrive at C'(14,3) which is another possible answer out of infinitely many.

See figure 2 below.

Pick whichever of (10,5) or (14,3) is your favorite to get the final answer, assuming your teacher wants you to write one (x,y) location only. Or pick some other scale factor (other than 2 or 3) and follow the same idea to get some other possible location of point C'.

Answer:

C' = (10, 5)

Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.

Step-by-step explanation:

If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.

Therefore, to maintain similarity (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.

Given vertices of triangle ABC:

Given vertex of triangle A'B'C':

If ΔABC is dilated by a scale factor of 2, with the origin as the center of dilation, B' = (2, 8).  If the triangle is then translated 1 unit up, B' = (2, 9), which matches the given coordinate of point B'.

Therefore, the series of transformations is:

Mapping Rule:  (x, y) → (2x, 2y + 1)

Therefore, the coordinates of point C' are:

⇒ C' = (2(5), 2(2) + 1) = (10, 5)

The student's survey of nine student with regards to the number of first cousins they have gives the standard deviation of the data as the option;

The standard deviation gives a measure of the variability or dispersion of a set of data.

The survey is with regards to a data obtained from a sample of the population (the first nine response),

The standard deviation of a sample is given by the formula;

[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } }} [/tex]

Where;

n = The data count = 9

[tex] \displaystyle{ \bar x = \frac{6+2+7+8+8+8+5+10+10}{9 } = \frac{64}{9} }[/tex]

Which gives;

[tex]\displaystyle{ \sum (x_{i} - \bar x)} [/tex]

(6-64/9)+(2-64/9)+(7-64/9)+(8-64/9)+(8-64/9)+(8-64/9)+(5-64/9)+(10-64/9)+(10-64/9) = 50.888889

Therefore;

[tex] \displaystyle{ s_x = \sqrt{\frac{ \sum (x_{i} - \bar x)}{ n - 1 } } = \sqrt{\frac{50.888889}{8}} \approx 2.52 } [/tex]

The standard deviation of the data is therefore;

2.52 first cousins

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x√3x is value of x in surds.

What is surds in maths?

= 4x√3x-x√√3x-2x√√3x

= √3x ( 4x - x - 2x )

= √3x ( 4x - 3x )

= √3x ( x)

= x√3x

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From the question,

We are given the equation

First, we will expand the RHS of the equation

This will give

By simplifying the RHS we will get

From the equation above, the terms on the LHS equal to the terms on the RHS

This implies that the equation has infinite number of solutions

That is, if we insert any value the equation will always be true

Solution

Step-by-step explanation:

we have:

Part 1) Find the x-intercepts of the parabola and write them as ordered pairs

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

For x=4 and x=-2 the equation is equal to zero

therefore

The x-intercepts are the points (-2,0) and (4,0)

Part 2) Write the equation y=(x-4)(x+2) in standard form

The quadratic equation in standard form is equal to

applying distributive property

where a = 1, b = -2, c = -8

Part 3) With the standard form of the equation from part ll, use the quadratic formula to identify the x-value of the vertex

we know that

the x-value of the vertex is -b/2a

we have

where a = 1, b = -2, c = -8

substitute

x = -b/2a = -2/2(1) = 1

therefore

The x-coordinate of the vertex is 1

Part 4) Substitute the x-value of the vertex from part lll into the original equation to find the y-value of the vertex.

we have

For x=1

substitute and solve for y

therefore

The y-coordinate of the vertex is -9

The coordinate of the vertex is the point (1,-9)

Answer:mark has 1 liter, lisa has an impossible -1 liter

Step-by-step explanation:

lets take m as slope

x1=4 y1=13 x2=5 y2=16

so we get the slope as 3.

so the answer is 3.

The function notation f(-5) has a value of -6

Functions are graphs, ordered pairs, relations, tables and equations that are used to relate independent and dependent variables

The function notation is given as

f(-5)

Also, we have the graphs to be f(x) and g(x)

This is represented by

So, we use the blue curve i.e. f(x)

On the blue curve, we have

f(-5) = -6

Hence, the value of the function is -6

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The savings plan balance (future value), after 4 years with an APR of 4% and monthly payments of ​$100, is $5,213.28.

The future value is the compounded amount of monthly payments after four years of monthly savings.

The future value can be computed using an online finance calculator.

N (# of periods) = 48 months (4 x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

PMT (Periodic Payment) = $100

Results:

Future Value (FV) = $5,213.28

Sum of all periodic payments = $4,800 ($100 x 48)

Total Interest = $413.28

Thus, in 4 years, the savings plan will have a future value of $5,213.28.

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Answer:

Step-by-step explanation: free throws are worth 1 point?

We have to find how many field goals he made.

We know that the number of free throws (FT) and the number of two-point field goals (FG) are two consecutive odd numbers. As they are consecutive odd numbers, they differ by two, so we can write:

There are no three-point field goals and the total number of points was 19, so this score has to be the sum of the points from free throws and the points from two-point field goals.

Answer:

He made 7 two-point field goals and 5 free throws.

He made 2 more field goals than free throws.

Answer: We have to find how many field goals he made.We know that the number of free throws (FT) and the number of two-point field goals (FG) are two consecutive odd numbers. As they are consecutive odd numbers, they differ by two, so we can write:There are no three-point field goals and the total number of points was 19, so this score has to be the sum of the points from free throws and the points from two-point field goals.Answer:He made 7 two-point field goals and 5 free throws.He made 2 more field goals than free throws.

Step-by-step explanation: hope this helps0^0

When c=0 It's 75 when x= 0 It's 75 when x= 100 It's 100 when x= 200 its 125 when x= 300 its 150

Step-by-step explanation:

For A, The printer would be 75 dollars and each newspaper printed is .25 cents

Answer:

c

Step-by-step explanation:

3/5 of the students are girls-

1-3/5 = 2/5

2/5 of the students are boys

1/3 of the girls have blonde hair.

So, multiply, the number of girls that have blonde hair (1/3) by the number of girls (3/5)

1/3 * 3/5 = 3 /15 = 1/5

of all students, 1/5 are girls with blonde hair.

For the boys;

1/2 of the boys have brown hair. of all students 2/5 are boys

2/5 * 1/2 = 2/10 = 1/5

Of all students 1/5 are boys with brown hair

as this is a vertical line, the slope is undefined

A store Mark's down toys by 15% in january. how much does each toy cost during january? use p for price in December

__________________________

P

Answer:

With what?

Step-by-step explanation:

ANSWER

EXPLANATION

Step 1: Given that:

Step 2: Expand the limit

Hence,

Given the equation:

The slope-intercept form will be as follows:

3a. What error did Han make?

He didn't divide 10 by 4

3b. What are the x- and y-intercepts of the line?

First, we will find the y-intercept

so, put x = 0

y = 5 - 0 = 5

So, the point of y-intercept is (0, 5)

Second, we will find the x-intercept

So, put y = 0

So,

So, the point of the x-intercept is (2, 0)

Answer:

m∠FGE=52.5 degrees

Explanation:

Angle FGE is formed by the intersection of two secants (BG and GD).

The intercepted arcs are BD and FE.

Therefore:

Substitute the given values:

Explanation

We have

Because upon solving we have

Therefore, it has no root

The answer is none

Op

The measure of angle c is 72.15.

What is angle sum property for a triangle?

Angle sum property of triangle states that The measure of all interior angles of a triangle is [tex]180^{o}[/tex] that is sum of all 3 interior angle is 180

We are given a Δ[tex]ABC[/tex]

Measure of interior angles of ABC is 180.

Hence the equation can be given as,

∠A+∠B+∠C=180

48.36+59.49+∠C=180

107.85+∠C=180

∠C=72.15

Hence the measure of ∠C is 72.15

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Answer:72.15

Step-by-step explanation:

We want to do the following operation:

To add fractions, we need to put both denominators in the same value. We need to find the LCM between 27 and 15. Factorizing those numbers in prime numbers, we have:

The LCM is the result of multiplying all those prime factors the most times they occur. Since 3 appears on both factorizations, we'll use only the most occuring 3(in this case, 3 times).

Now, we need to rewrite those fractions with the new denominator. To do that we just need to multiply both the numerator and the denominator by the same factor. To find those factors we just need to find the ratio between the denominator and 135.

Now, converting those fractions to this denominator:

Now, to finally do the addition, we just add the numerators.

Since 68 and 135 don't share any divisors, this is the simplest form of this fraction. The result is 68/135.

The general equation of line with passing points (a, b) and slope m is :

y = m(x - a) + b

In the given question :

A line goes through the point (2,1)

Passing point (a, b) = (2, 1)

a slope of 2

Slope : m = 2

Substitute these value in the general equation of line :

y = m( x - a ) + b

y = 2 ( x - 2) + 1

y = 2x - 4 + 1

y = 2x - 3

y = 2x - 3

A)

To plot on the graph :

We have one coordinate ( 2, 1)

Find one more coordinate

Substitute x = 1 in the equation os line :

y = 2x - 3

y = 2(1) - 3

y = ( - 1 )

So, (x, y) = ( 1, -1)

Plot the coordinates ( 2, 1) & ( 1, - 1)

y- intercept is the point on the line where x = o

Substitute x = 0 in the given equation of line :

y = 2x - 3

y = 2( 0 ) - 3

y = ( -3 )

Y -intercept : y = ( -3) , (x, y) = ( 0, -3)

In the graph y -intercept is :

The purple point in the graph represent the y -intercept.

B)

The general form of the equation of line in the form of slope intercept form :

y = mx + b

The equation of line y = 2x - 3

On compare with the general equation of slope intercept form we have : m - 2, b = (-3)

So, equation of line in the slope intercept form is : y = 2x - 3

y = 2x - 3

Answer : A) ( x, y) = (0, -3)

B) y = 2x - 3

The value of b is 18.

Here, we are given a triangle as shown in the figure above.

RS = RU

ST = b + 72

and TU = 5b

In triangle TRU, by Pythagoras theorem, we get-

(TU)² = (TR)² + (RU)²

⇒ (5b)² = (TR)² + (RU)²

(TR)² = (5b)² - (RU)²

Similarly, in triangle STR, we will get-

(TR)² = (b + 72)² - (SR)²

Equating the two equations, we get-

(5b)² - (RU)² = (b + 72)² - (SR)²

Since RS = RU,

(5b)² - (RS)² = (b + 72)² - (SR)²

25b² = b² + 72² + 2(72)b

24b² = 5,184 + 144b

b² = 216 + 6b

b² - 6b -216 = 0

Solving this quadratic equation will give us 2 values for b

b = 18 or b = -12

Since length of the side cannot be negative, the value of b will be 18.

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We have

we can reduce the expression

the solution is