What is vertex form of a quadratic equation?.

The number of real solutions to a quadratic equation depends on the coefficients of the quadratic equation.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are real numbers. This equation can have either 0, 1, or 2 real solutions. If a is equal to 0, then the equation is not a quadratic equation and can have any number of real solutions.

If the coefficient a is not equal to 0, then the number of real solutions depends on the value of the discriminant, b2 - 4ac. If the discriminant is positive, then there are two real solutions to the equation. If the discriminant is zero, then there is one real solution. If the discriminant is negative, then there are no real solutions.

In summary, a quadratic equation can have 0, 1, or 2 real solutions depending on the value of the discriminant.

Learn more about quadratic equation:

https://brainly.com/question/28038123

#SPJ4

The y intercept of the line A is 6 and the y intercept of the line B is -2 and the equation of line B is y = x - 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -3x + 6   be equation (1)

Now , the equation of line is is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the y intercept of the line A is b = 6

For the equation of line B , we get

Let the first point be P ( -1 , -3 )

Let the second point be Q ( 0 , -2 )

And , the slope of the line is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -2 - ( -3 ) ) / 0 - ( -1 )

On simplifying the equation , we get

Slope m = 1/1 = 1

And , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -3 ) = 1 ( x - ( -1 ) )

On simplifying the equation , we get

y + 3 = x + 1

Subtracting 3 on both sides of the equation , we get

y = x - 2

Hence , the equation of line B is y = x - 2 and the y intercept is -2

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ1

The area of the parallelogram is 78ft².

The area of a parallelogram can be calculated with the following formula:

A= b*h

Where "b" is the length of any base of the parallelogram and "h" is the height.

In this case, you can identify the values of b and h from the question given, which:

b = 6ft

h= 13ft

Then, knowing those values, you can substitute them into the formula shown above, as below:

A= b*h= 6*13

Finally, you must evaluate in order to find the area of the given parallelogram.

A= 78ft²

Thus, the area of the parallelogram is 78ft².

To know more about parallelograms visit: brainly.com/question/29147156

#SPJ4

Answer:

x = 34 degrees

Step-by-step explanation:

angles TWU and PSR are vertical and equal

if TSU = 4x and QSR = x then PSQ = 3x

triangle PSQ has 180 degrees

we know the three interior angles of the triangle are:

x, x, 112

we found the 112 by subtracting 68 from 180 since PQR is a straight line which has 180 degrees

to find 'x' we do the following:

x + x + 112 = 180

2x + 112 = 180

2x = 68

x = 34

Answer:

57.4

Step-by-step explanation:

Go to point A and draw a line straight down, perpendicular to HT.  Let's label the point where your drawn line hits AT as B.  Now you have the line segments HB, BT.  

HB + BT = 100

Solve for the height of the triangle, BA.

BA = sin35(80) = 45.9

HB = cos35(80) = 65.5

BT = 100 - 65.5 = 34.5

Now you can solve for AT, which is the hypotenuse of ΔBAT:

(AT)² = 45.9² + 34.5² = 3295

AT = √3295 = 57.4

Answer:

  yes, for positive numbers

Step-by-step explanation:

You want to know if the number of arrays that represent a number is equal to the number of factor pairs of that number.

We assume that we're only concerned with Natural numbers (positive integers).

We assume that the factor pair 2×3 is indistinguishable from the factor pair 3×2, and that an array of 2 rows and 3 columns is indistinguishable from an array of 3 rows and 2 columns.

Each array corresponds to a factor pair. One factor of the pair specifies the number of rows; the other factor specifies the number of columns. The product of those factors is the number of interest.

Example

  12 = 1·12 = 2·6 = 3·4 . . . . . factor pairs listed with smallest factor first

The attachment shows arrays associated with these factor pairs.

If the number is a square number, then there will be an odd number of divisors. One of the divisors is repeated to make the factor pair. This results in a square array as one of the arrays that represent the square number. The second attachment shows arrays for the square number 9.

There will be as many arrays as there are factor pairs.

The difference between tan and inverse tan functions is that, tan function has input as an angle whereas inverse tan function takes input as numbers.

In mathematics, the trigonometric functions sine, cosine and tangent are often represented by the symbols sin, cos and tan respectively.

The inverse of these functions, known as inverse trigonometric functions, are represented by the symbols sin^-1, cos^-1 and tan^-1.

These inverse functions are used to find the angle of a right triangle given the ratio of its sides.

In other words, if you know the values of the sides of a right triangle, you can use the inverse trigonometric functions to find the angles.

The inverse tangent function, also known as arctan, is particularly useful in finding the angle of a right triangle when the opposite and adjacent sides are known.

Read more about Trigonometric Functions:

https://brainly.com/question/29090818

#SPJ4

The value of x = -1 and y = 3.

To solve the system of equations using substitution, we can start by isolating one of the variables in one of the equations. For example, in the first equation, 7x - y = -10, you can add y to both sides to get y = 7x + 10.

Then we can substitute this expression for y into the second equation, 3y - x = 10, to get:

3(7x + 10) - x = 10

This simplifies to:

21x + 30 - x = 10

20x = -20

x = -1

Now we know that x = -1, we can substitute that back into the first equation or the expression we found for y to find the value of y

y = 7x + 10

y = 7(-1) + 10

y = -7 + 10

y = 3

So the solution of the system is x = -1 and y = 3

To understand substitution better, visit:

https://brainly.com/question/22340165

The full question is:

Solve the given equations by substitution and find the value of x and y. Equationns: 7x-y=-10 and 3y-x=10

Answer:

Read the entire problem several times.

Look for keywords like more, less, is, etc.

Replace the keywords with their mathematical operations and shorten the words to variables. Solve the resulting equation. Answer the problem clearly in a complete sentence.

Step-by-step explanation:

hope this helps

The nth term of the sequence 100 is 592

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

[tex]a, ar, ar^2, ar^3, \cdots[/tex]

 (till the terms to which it is defined)

Thus, the nth term of such sequence would be  [tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).

Given;

Sequence=-2,4...

D=4-(-2)

=6

Now, we have to find 100th term

So, n=100

an = a + (n – 1)d

=-2+(100-1)6

=-2+99x6

=592

Therefore, the answer of given sequence will be 592

Learn more about geometric sequence here:

https://brainly.com/question/2735005

#SPJ1

Answer:

24

Step-by-step explanation:

you multiply 5 by 3 to get 15 so you multiply 8 by 3 also

Answer: 240cm^3

Step-by-step explanation:

To find the answer to this question, you use the solution that is given; height x length x width. If you put in the numbers you have into that solution, you will get an answer of 240. I really hope this helps- because I'm not that good at explanation! :)

For values of k between 9 and 9, the quadratic equation's roots are real and equal.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

In other words, if a times the square of the expression that comes after b plus b times the same expression that wasn't squared plus c equals 0, you get an equation that has the form of a quadratic.

The supplied formula is 3x 2 + 2kx + 27=0.

Here a=3, b=2k, and c=27.

Roots being real and equal is a given.

∴ b \s2 \s −4ac=0

⇒ (2k) \s2 \s −4(3)(27)=0

⇒ 4k \s2 \s −324=0

⇒ 4k \s2 \s =324

⇒ k \s2 \s =81

∴ k=±9

To learn more about quadratic equation's here:

https://brainly.com/question/1863222

#SPJ4

Full Question = For what value of k are the roots of the quadratic equation 3x2 +2kx+27=0 real and equal?

Step-by-step explanation:

By Arithmetic Progression,

The first term a1=70.1

Common difference, d= 72.2-70.1=74.3-72.2= 2.1

Nth term, T_n=a1+(n-1)d where n=time taken in minutes

T_n=70.1+[2.1*(n-1)]

(b) n=12

T=93.2°F

Negative numbers don't actually have square roots because a square can only be either positive or zero. No, we cannot find the square root of the negative value.

When two numbers of the same sign are added, the result is always positive.

Theorem: Negative Numbers' Square Roots Using the number as if it were a positive integer and adding an I in front of it as a coefficient is one way to simplify an expression that involves the square root of a negative number. Or, to put it another way, for any x, where x is a positive integer or if x is a negative number, x=ix x = I x.

The worth of root 4 is equivalent to precisely 2. In any case, the roots could be positive or negative or we can say there are dependably two roots for some random number. Subsequently, root 4 is equivalent to ±2 or +2 and - 2 (positive 2 and negative 2).

To learn more about square roots here:

https://brainly.com/question/12434939

#SPJ4

Jamie multiplied 3x and 7 by -5 to eliminate the parentheses.

This procedure is justified by the distributive property.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

When we need to multiply a number by the sum of two numbers, the distributive property of multiplication over addition comes into play. Let's multiply 7 by the sum of 20 plus 3 as an illustration. This can be expressed mathematically as 7(20 + 3).

The distributive rule of multiplication over addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed. Both addition and subtraction are under the scope of the distributive law.

Jamie multiplied 3x and 7 by -5 to eliminate the parentheses.

This procedure is justified by the distributive property.

To learn more about Distributive Property refer to :

https://brainly.com/question/5637942

#SPJ1

Answer:

36 lbs

Step-by-step explanation:

44lbs -> $550

X -> $450

Cross-multiplication:

X × 550 = 44 × 450

X = (44×450)/550

X =36 lbs

So the answer is 36 lbs of apples

Another way to solve it :

550/44 = 12.5 which means $12.5 for every 1lbs of apples

Now if we have $450

Divide it by 12.5

450/12.5 = 36 lbs

The y=5x-10 function is nonlinear.

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.  Although the linear functions are also represented in terms of calculus as well as linear algebra. The only difference is the function notation. Knowing an ordered pair written in function notation is necessary too. f(a) is called a function, where a is an independent variable in which the function is dependent. Linear Function Graph has a straight line whose expression or formula is given by; y = f(x) = px + q
Since you are using y, instead of f(x), I think it's more appropriate to call it a relationship. The equation y=5x-10 describes a set of points that fall on a line, but for it to be a linear function, it should be denoted as f(x)=5x-10.

The distinction isn't so interesting in this case, but how about the case x = y^2? This is a totally valid relationship, but it cannot be a function of x, since a function requires just one output for a given input.

No. If it was a linear function we should have y(λx)=λy(x), ∀x. But that's not what happens. Actually, this function is called an affine function. So, we can see that affine functions are obtained from the linear functions simply by performing a rigid movement.

The linear functions are those that have the form: y=ax.

Therefore, The y=5x-10 function is nonlinear.

To learn more about functions visit:brainly.com/question/12431044

#SPJ4

The formula for the area of a triangle is A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle. To solve for h, rearrange the formula to 2*A/bh = 2*28/10h = 5.6 yards.

Height is a measure of vertical distance, often measured from the ground up. Its most typical application is to express the size of a person, object, or other item. Height is often measured in inches, feet, and millimetres. It is also used to determine the elevation of a piece of land or a building.

To calculate the height of a triangle, use the area of a triangle formula, A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle. Because we know the triangle's area is 28 square yards and its base length is 10 yards, we can rearrange the formula to find h:

h = 2*A/b

h = 2*28/10

h = 5.6 yards

As a result, the triangle's height is 5.6 yards.

To know more about height, visit

brainly.com/question/20669844

#SPJ1

Since the function y = 80 + 2x represents his grade, y, after x weeks, the meaning of the slope of the line is: D. He increases his grade by 2 points each week.

In Mathematics, a slope is sometimes referred to as rate of change or gradient and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Based on the information provided, we have the following function which represents Joseph's grade after a certain number of weeks;

y = 80 + 2x

where:

In this context, we can reasonably infer and logically deduce that Joseph's grade increases by 2 points each week.

Read more on slope here: brainly.com/question/23086745

#SPJ1

The measurement of angles C and F are 63°  and 59° respectively

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

In the given image, you notice that angles A, B and C form a right-angled triangle. So the measurement of angle C is 90°. Also, the sum of angles in a triangle is 180°. Thus:

A + B + C = 180°

27° + 90° + C = 180°

117° + C = 180°

C =  180° - 117°

C = 63°

Likewise, angles D, E and F form a right-angled triangle. So the measurement of angle E is 90°. Also, the sum of angles in a triangle is 180°. Thus:

D + E + F = 180°

31° + 90° + F = 180°

121° + F = 180°

F =  180° - 121°

F = 59°

Learn more about trigonometry on:

brainly.com/question/29354606

#SPJ1

Answer:

0  is both a number and a numerical digit used to represent that number in numerals.

Step-by-step explanation:

For example positive and negative

The equation of line is y= 1/4x -1

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Step1:

Given:

slope = 1/4 and y intercept = -1

Using slope- intercept form

Step2:

y= mx + b

y= 1/4x + (-1)

y= 1/4x -1

Learn more about slope refers to;

https://brainly.com/question/19000990

#SPJ1

$a^4 - 3a^2 + 9$ can be factorised as $(a^2 - 3)(a^2 + 3)$

To factor $a^4 - 3a^2 + 9$ as a product of two monic quadratics with integer coefficients, we can use the difference of squares factorization.

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b).

$a^4 - 3a^2 + 9$ can be factored as $(a^2 - 3)(a^2 + 3)$

Notice that both factors are monic quadratics with integer coefficients.

So, $a^4 - 3a^2 + 9$ = $(a^2 - 3)(a^2 + 3)$

To learn more about quadratic equations visit: brainly.com/question/22364785

#SPJ4

The number of integral solutions of the given equation x₁ + x₂ + x₃ = 0 with [tex]x_{i}[/tex] ≥ (-5) is 136.

Suppose we wish to determine the number of integer -tuples (₁,…,[tex]x_{k}[/tex])

such that

₁ +⋯+ [tex]x_{k}[/tex] = , [tex]x_{i}[/tex] ≥ [tex]c_{i}[/tex] …(1)

The transformation [tex]y_{i}[/tex] = [tex]x_{i}[/tex] − [tex]c_{i}[/tex], 1 ≤ ≤ reduces (1) to

₁ +⋯+ [tex]y_{k}[/tex] = − (₁ +⋯+ [tex]c_{k}[/tex]), [tex]y_{i}[/tex] ≥ 0…(2)

The number of solutions to (2)

is given by the binomial coefficient [tex]\binom {(n-c_{1}- ... -c_{k})+k-1 }{k-1}[/tex].

For the given problem, = 3, = 0, and each [tex]c_{i}[/tex] = −5. Therefore, the number of solutions is

[tex]\binom {17}{2}=^{17}C_2=\frac{17!}{2!(17-2)!}[/tex]

= 136.

Thus, 136 integral solutions are there to x₁ + x₂ + x₃ = 0 with [tex]x_{i}[/tex] ≥ (-5).

--The given question is incorrect; the correct question is

"How many integral solutions does x₁ + x₂ + x₃ = 0 have if  [tex]x_{i}[/tex] ≥ (-5)?"--

To know more about binomial coefficient, here

https://brainly.com/question/14216809

#SPJ4

Answer:

14 batches of cookie

Step-by-step explanation:

Cora has 7/2 cup of flour

3/4 of flour= 1 batch of cookie

7/2= ?

7/2×1×4/3=14/3

14 batches

The probability that both of Eduardo’s partners for the group project will be girls is   24/65

To learn more about probability refers to:

brainly.com/question/2517253

#SPJ1

The height of the cone is sin 210° × 12 cm = 10.39 cm.

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. It is typically measured in either centimeters or feet and inches, and is most commonly used to describe the stature of a person. Height is an important physical characteristic, as it affects a person's overall body proportions and can influence their physical appearance.

The curved surface area of the cone can be calculated using the formula: 2πrh. Where π is the constant pi, r is the radius of the circle, and h is the height of the cone. The height of the cone can be determined by using the trigonometric function sine, where 210° is one of the angles of the triangle. Therefore, the height of the cone is sin 210° × 12 cm = 10.39 cm.

Using the formula 2πrh, the curved surface area of the cone is 2 × π × 12 cm × 10.39 cm = 75.52 cm². As the volume of a cone is one-third the product of its curved surface area and its height, the volume of the cone is 25.17 cm³ (rounded to three significant figures).

To know more about height click-
https://brainly.com/question/28122539
#SPJ1

If 1500 g can be divided evenly into batches of bread that are 70 g each, then the baker should choose the 1500 g package.

To check this, we can divide 1500 g by 70 g to see how many batches of bread can be made:

1500 g / 70 g = 21.428571428571427

Since this is a non-whole number, it means that some of the dough would be wasted if the baker chooses a package of 1500 g. The baker should choose the 1500 g package, as it can be divided evenly into batches of bread that are 70 g each.

You can learn more about division at

https://brainly.com/question/941863

#SPJ4

No, You would need 68.4 liters of gasoline to fill the tank, which is equivalent to 17.8 gallons. With 19.7 miles/gallon, you would only be able to drive a maximum of 350.7 miles before running out of gas.

The Gallon Conversion Theory is a mathematical formula that can be used to convert between different units of liquid measure.

The formula is based on the fact that each gallon of liquid measure is equal to four quarts, eight pints, sixteen cups, or 32 gills. It is useful for converting between different units of liquid measure when measuring large volumes.

The theory used in this question is the conversion of liters to gallons. By converting from liters to gallons, we were able to determine how far the truck could drive before running out of gas.

To do this, we first determined that the fuel tank holds 68.4 liters of gasoline.

We then converted liters to gallons by multiplying the number of liters by 0.26. This gave us 17.8 gallons. We then multiplied 17.8 gallons by 19.7 miles/gallon to get the maximum distance that could be driven before running out of gas, which was 350.7 miles.

Since the distance from Yuma to Las Vegas is 322 miles, this means that the truck would run out of gas before reaching its destination.

To learn more about Gallon Conversion Theory, visit

brainly.com/question/28486130

#SPJ1