Simplifying algebraic expressions

The discriminant of the quadratic equation 2x + 5x² = 1 is 24.

The discriminant of a quadratic equation is the value calculated from the coefficients of the quadratic equation and it gives information about the nature of the roots of the equation. The discriminant can be used to determine the number and type of solutions/roots of the equation.

-If the discriminant is greater than zero, the equation has two distinct, real solutions (or roots).

-If the discriminant is equal to zero, the equation has one real solution (or root).

-If the discriminant is less than zero, the equation has no real solutions (or roots), only complex solutions.

The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.

Plug in the values and solve for the discriminant of the quadratic equation 2x + 5x² = 1.

b² - 4ac = (2)² - 4(5)(-1) = 24

Hence, the discriminant is 24.

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The value of q in the given equation x²- 5x + q = 0 will be 4.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

given an equation x²- 5x + q = 0 and the question states that it has a root that is equal to 2

Since 2 is the root of this quadratic equation it will satisfy the equation

Substituting the values in the equation

4 - 5*2 + q = 0

q = 6

Equation will be

x²- 5x + 6 = 0

The root of the given equation using the fraction method

x²- 3x - 2x + 6= 0

(x -2)(x - 3) = 0

The root of the given equation are 2 and 3

Therefore, In the given equation x²- 5x + q = 0 the value of q will be 4.

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Answer:

a)=57

b)=26

C)= 35

Step-by-step explanation:

there is 100 people recorded when they only wanted 65 so the 35 extra answers are not recorded.

Answer:

c) 4750

Step-by-step explanation:

Take a calculator and divide it or long division. You get 950.

Answer:

c) 4750

Step-by-step explanation:

c) 4750 is the answer of your question .

hope it is helpful to you

During the winter, the grill was marked at $85. In June, the price was changed to $110. 50. So, 23.08% is the change in percentage.

When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Comparing two amounts while re basing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.

Given that,

the grill was marked at $85

the price was changed to $110. 50.

Now, percentage change:

= [{(110. 50 - 85)/110.50} × 100]

= (0.2308 × 100)

= 23.08%

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Answer: Any of the following angles are not congruent to angle 5.

The only exception being that if angle 5 is 90 degrees, then so are the remaining four angles shown above (in fact, all 8 angles are right angles).

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

Explanation:

Angles 2 and 5 are supplementary since line p is parallel to line r. This means angle 2 and angle 5 add to 180 degrees. The two angles are only congruent if both are right angles (aka 90 degree angles); otherwise, they are not congruent angles.

Angle 2 = angle 4 because they are vertical angles. So because these two angles are congruent, and angle 2 does not have the same measure as angle 5, this consequently leads to angle 4 also not being the same measure as angle 5 (unless both are right angles).

Angle 2 = angle 8 because they are alternate interior angles. Following the same logic path as the last paragraph, we see that angles 8 and angle 5 aren't the same measure. Or we could note that angle 5 and angle 8 form a straight angle, so they must add to 180 degrees. The two angles are only congruent if they were 90 degrees each, or otherwise not congruent at all.

Similar logic can also show that angle 6 is not congruent to angle 5.

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

An alternative path is to find all the angles that are always congruent to angle 5 and they are...

And everything else is not congruent to angle 5.

Using the concept of fraction, the percentage edited on the video is 62.5 percent.

What is Percentage

Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.

In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;

percentage edited = (2.5 / 4) × 100

Percentage = 0.625 × 100

Percentage = 62.5 %

From the above, Thorton has edited 62,5 percent of the video for his school project.

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

to get the equation of any straight line, we simply need two points off of it, let's use (-6,10), (-4,18)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{8}{-4 +6} \implies \cfrac{ 8 }{ 2 } \implies 4[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y -10 = 4 ( x +6) \end{array}} \\\\\\ y-10=4x+24\implies -4x+y=34\implies \stackrel{standard~form}{{\Large \begin{array}{llll} 4x-y=-34 \end{array}}}[/tex]

Approximately [tex]130.1[/tex] cm more centimeters of wood will need to complete the support.

Right triangle is a triangle in which one angle is of [tex]90^0[/tex] .

We have,

Hypotenuse [tex]=92[/tex] cm

Let,

Perpendicular [tex]= x[/tex] cm

Base [tex]=x[/tex] cm

So,

Using the Pythagoras theorem,

[tex]H^2=P^2+B^2[/tex]

So,

[tex]92^2=x^2+x^2[/tex]

[tex]92^2=2x^2[/tex]

⇒

[tex]2x^2 = 8464[/tex]

[tex]x^2 = 4232[/tex]

⇒[tex]x=65.05[/tex]

So,

Perpendicular [tex]= 65.05[/tex] cm

Base [tex]=65.05[/tex] cm

So,

The required wood to complete support [tex]=65.05+65.05=130.1[/tex] cm

Hence, we can say that approximately [tex]130.1[/tex] cm more centimeters of wood will need to complete the support.

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Answer:

6n-5

Step-by-step explanation:

let 'n' equal 'a number'

the equation above means you are multiplying 6 and that number, then reducing it by 5

1.14 is the answer just do 19%=1.14

Answer:

t = 5, 6

Step-by-step explanation:

Given the equation:

[tex]\displaystyle{11t-t^2=30}[/tex]

First, arrange the expression in the standard quadratic form ax² + bx + c = 0

[tex]\displaystyle{t^2-11t+30=0}[/tex]

Then factor the expression, find two numbers that add up which result in -11  and multiply which result in 30 - that two numbers are -6 and -5

[tex]\displaystyle{(t-6)(t-5)=0}[/tex]

Solve like a linear equation

[tex]\displaystyle{t=5,6}[/tex]

Therefore, the solutions to the equation are t = 5, 6

Answer:

The solution set is {5, 6}.

Step-by-step explanation:

11t-t^2=30

t^2 - 11t + 30 = 0

(t - 5)(t - 6) = 0

t = 5, 6.

Answer:

when the ratio of the first measurment is already there, get the pot, put it in place and chec the correct ratio, the slope should help the gaurdian. so in that case, the answer is 75inch

Answer:

V = 200 π

Step-by-step explanation:

x = 5√y ,   x = 0 ,   y = 4

Determine the volume of the solid V

when x = 0  y = 0

we can calculate the volume of the solid by applying the washer method

V = π ₀⁴∫ [ 0 + ( 5√y )^2 ]  dy

   = π ₀⁴∫ [ 0 + ( 25(y) ) ]  dy

V  = π [ 0 + 25/2 ( y^2 ) ] ⁴₀

V = π [ 25/2 ( 16 ) ]

  = 200 π

Answer:

get a job....

Answer:

El vendedor ambulante debe vender 80 camisetas para obtener una ganancia de 400 €.

Step-by-step explanation:

La ganancia que obtiene el vendedor es el resultado de restar el costo total menos las ventas totales. El costo total es igual al costo por camiseta por el número de camisetas y las ventas totales son iguales al precio de venta por el número de camisetas vendidas, lo que se puede expresar de la siguiente forma:

x=11y-6y

x=5y, donde:

x es la ganancia

y es el número de camisetas

Dado que se quiere obtener una ganancia de 400, este valor sería x, y debes despejar y:

400=5y

y=400/5

y=80

De acuerdo a esto, la respuesta es que el vendedor ambulante debe vender 80 camisetas para obtener una ganancia de 400 €.

Answer: (x−7)2+y2=100. Explanation: the standard form of the equation of a circle is.

Step-by-step explanation:

Step-by-step explanation:

=(1+ sin^2 A/cos^2 A).cos^2 A

=[(cos^2 a+sin^2 a)/cos^2 a].cos^2 A

=[1/cos^2 a] . cos^2 a

=1

Answer:

it is actually -5 because -1.5/0.3=-5

Step-by-step explanation:

Answer:

5 hours

Step-by-step explanation:

Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.

So she needs to work for 685 / 137 = <<685/137=5>>5 hours

Answer:

The slope is 7!

Step-by-step explanation:

Answer:

The slope is 7

Step-by-step explanation:

Use the distributive property to distribute 7 to x and -7. 7(x-7) is the same as 7(x)+7(-7) which is 7x-49. Therefore, the equation will be y+4=7x-49. We want to isolate y so we have to subtract 4 from both sides. y=7x-53. The number with the x is the slope. Therefore, the slope is 7.

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Answer:

Equation 1: 6 + (-10) = -4

Step-by-step explanation:

1st segment starts at 0 and goes 6 units right so: +6

Second segment starts at 6 and goes 10 units left, so: -10

Finally the second segment lands on -4, so all together:

+6 + (-10) = -4 or 6 + (-10) = -4

Hope this helps!

Correct options are: A. Zeros: -2 and 1

E. x-Intercepts: (-2, 0) and (1, 0)

What are zeros & x-intercepts of quadratic function?

The zero of the function is where the y-value is zero.

The x-intercept is where the graph crosses the x-axis.

The zeros of a quadratic function are the values of x for which the function equals zero. In other words, they are the solutions to the equation f(x) = 0. For the given quadratic function, the zeros

are -2 and 1.

The x-intercepts of a function are the points at which the function crosses the x-axis. In other words, they are the solutions to the equation f(x) = 0 when y = 0. For the given function, the x-intercepts are (-2, 0) and (1, 0) which are the points on the x-axis where the function crosses it.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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Answer:

Below

Step-by-step explanation:

Error :    (8.25 - 7.5)

% error :    ( 8.25-7.5) / 8.25    * 100%  = 9.1 %

Jim's percent error is 9.09%.

What is the percentage error?

The percentage error is given as the difference between the actual value and the estimated value divided by the actual value, multiplied by 100%.

The percentage error is a relative value that compares the actual value and the estimated value to explain any deviations.

Estimated width of wall = 7.5 feet

The actual width of the wall = 8.25 feet

The difference in estimate = (8.25 - 7.5) = 0.75 feet

Percentage Error = (0.75/8.25 x 100) = 9.09%

Thus, we can conclude that Jim made a percentage error of 9.09%  in his estimate of the width of the wall.

Answer:interquartile range IQR

Step-by-step explanation:ApE x

Answer:

ANSWER IS IQR

Step-by-step explanation:

DID THE TEST

The numbers of milligrams of the vitamin that are in a drink is 60 milligrams.

The recommended daily allowance (RDA) for the vitamin is 40 mg. A new health drink has 150% of the RDA.

To find out how many milligrams of the vitamin are in a drink, you can use the following formula:

(RDA) x (percentage/100) = milligrams in a drink

So,

(40mg) x (150/100)

= 60mg

Therefore, there are 60 milligrams of the vitamin in a drink.

Note that the RDA of vitamins can vary depending on age, gender, and other factors, so always consult a doctor or nutritionist before starting to consume any new supplement.

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