Solve the quadratic equation -x^2=4

Answer: A. 6

A. 4.3%

Step-by-step explanation:

The total number of singers = 4

To choose singers = 2

The number of ways to choose 2 singers from 4= [tex]^4C_2=\frac{4!}{2!(4-2)!}=3\times2=6[/tex]

Hence, A is the right option.

The total number of water purifiers  T= 280

The number of defective purifiers D= 12

The probability that a water purifier chosen at random will be defective (in percent)=[tex]\frac{\text{T}}{\text{D}}\times100[/tex]

[tex]=\frac{12}{280}\times100\\=0.042857\times100\\=4.2857\%\approx4.3\%[/tex]

Hence, A is the right option.

Algebra tiles are used to factorize a polynomial. The factorization of the given trinomial will be very difficult to perform using the algebra tiles due to the large number of tiles used.

The given quadratic polynomial or trinomial is [tex]x^2 + 18x + 80[/tex].

The algebra tiles required to solve the given trinomial are,

So, the total number of times required will be 1+18+80 or 99 tiles.

Now, it will be very difficult to drag or arrange so many tiles on the board. Also, the space could be a problem in this case.

Therefore, the factorization of the given trinomial will be very difficult to perform using the algebra tiles due to a large number of tiles used.

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5v+7(2.85)=28.70

5v+19.95 = 28.70

5v = 8.75

v = 1.75

Answer:

defiantly a false!!

Step-by-step explanation:

Answer: The correct answer is [tex]f(x)=x^2+2x-5[/tex]

Step-by-step explanation:

A Quadratic equation is defined as the equation in which the highest power of the variable is 2. The general form of this equation represents:

[tex]ax^2+bx+c=0[/tex]

where, [tex]a\neq 0[/tex]

From the given options:

1. [tex]f(x)=-8x^3-16x^2-4x[/tex]: Here, the highest power of the variable is 3. Therefore, it is not a quadratic equation.

2. [tex]f(x)=x^2+2x-5[/tex]: Here, the highest power of the variable is 2. Therefore, it is a quadratic equation.

3. [tex]f(x)=+1[/tex]: Here, the highest power of the variable is 0. Therefore, it is not a quadratic equation.

4. [tex]f(x)=0x^2-9x+7[/tex]: Here, the highest power of the variable is 1. Therefore, it is not a quadratic equation.

Hence, the correct answer is [tex]f(x)=x^2+2x-5[/tex]

Answer:

D

Step-by-step explanation:

Given the following data  

x  1   2  3  4  5  

f(x)  243  81  27  9  3

The rate of change between the second and the first points is computed as  

(f(x2) - f(x1))/(x2 -x1) =  (81 - 243)/(2-1) = -162

Analogously, between 3rd and 2nd points and between  4th and 3rd points:

27 - 81 = -54

9 - 27 = -18

Therefore, the average rate of change is (-162 -54 -18)/3 = -78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round .

Answer: False

Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event.

A. True

B. False

Final answer:

The vertex of the profit function f(x) = -x^2 + 16x - 60 is (8, 4), meaning the maximum profit is $4 when 8 candles are sold. The x-intercepts are (6,0) and (10,0), indicating zero profit when either 6 or 10 candles are sold.

Explanation:

The function given is a quadratic equation of the form f(x) = ax2 + bx + c, where the constants are a = -1, b = 16, and c = -60. To find the vertex of the parabola, we can use the formula -b/(2a) for the x-coordinate of the vertex.

Calculate the x-coordinate of the vertex: x = -b/(2a) = -16/(2 * -1) = 8.

Substitute x = 8 into the original function to find the y-coordinate: f(8) = -(8)2 + 16(8) - 60 = -64 + 128 - 60 = 4.

The vertex is at the point (8, 4). In the context of the problem, this point represents the maximum daily profit of $4, which occurs when 8 candles are sold.

To determine the x-intercepts, we set f(x) to zero and solve for x, which represents the number of candles sold when the profit is zero.

Set the function equal to zero and solve for x: 0 = -x2 + 16x - 60.

Apply the quadratic formula x = [-b ± sqrt(b2 - 4ac)]/(2a) to find the x-intercepts. In this case, a = -1, b = 16, and c = -60.

Calculate the discriminant, sqrt(162 - 4(-1)(-60)) = sqrt(256 - 240) = sqrt(16) = 4.

Find the two x-intercepts: x = [16 ± 4]/(2 * -1) which yields x = 6 and x = 10.

The x-intercepts (6,0) and (10,0) indicate the number of candles sold at which the profit would be zero, specifically at 6 and at 10 candles sold.

Step-by-step explanation:

To find out what 16% of 17 is, we create a cross multiply equation

16/100=17/x

Cross multiply

(16 * x  = 16x)

(100 * 17 = 1700)

16x = 1700

1700/16 = 106.25

surface area = 4*pi*r^2

using 3.14 for pi

452.39 = 4*3.14*r^2=

452.39=12.56* r^2

r^2 = 452.39/12.56 = 36.0

sqrt(36) = 6= r

diameter = 2r = 6*2= 12

 diameter = 12 feet

24^2 = 18 * (18 +y)

576 = 324+18y

252 =18y

y = 252/18 =14

 y = 14

The value of y is 14.

'A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant'

According to the given problem,

We know,

⇒ 18 ( 18 + y ) = 24²

⇒ 324 + 18y = 576

⇒ 18y = 576 - 324

⇒ 18y = 252

⇒ y = 252/18

⇒ y = 14

Hence, we can conclude, the value of y is 14.

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The correct option is (3).

An acute angle is defined as an angle that measures less than 90 degrees that is measure between 0° to 90°.

Given that if two angles are acute, their sum is never a straight line.

The hypothesis of this would be the one which would satisfy the opposite of the given statement

1)  their sum is never a straight line which is Incorrect.

2) two angles are acute which is incorrect because this is given.

3) If  two angles are acute they are straight lines which is right.

Hence, the correct option is (3).

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The equation of the parabola with a vertex at (-2, -20) and a y-intercept at (0, -12) is y = 2x^2 + 8x - 12.

To find the equation of the parabola, we can use the vertex form of a parabola's equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola, and 'a' is a coefficient that determines the parabola's width and direction. Since we have the vertex (-2, -20) and the y-intercept (0, -12), we can plug in these values to solve for 'a':

y = a(x - (-2))^2 - 20

Using the y-intercept:

-12 = a(0 - (-2))^2 - 20

-12 = 4a - 20

8 = 4a

a = 2

The equation of the parabola is therefore:

y = 2(x + 2)^2 - 20

Expanding the equation:

y = 2(x^2 + 4x + 4) - 20

y = 2x^2 + 8x + 8 - 20

y = 2x^2 + 8x - 12

The final quadratic equation of the parabola is:

y = 2x^2 + 8x - 12

In this exercise we have to apply the Pythagorean theorem to know that it is possible to form a certain triangle, so we have:

A) No
B) Yes
C) Yes
D) Yes

Knowing that the Pythagorean theorem is given by:

[tex]a^2 = b^2 +c^2[/tex]

They are putting the values ​​informed we have:

A) [tex]6^2 = 4^2 + 5^2[/tex]

B) [tex]10^2 = 6^2 + 8^2[/tex]

C) [tex]17^2=15^2+8^2[/tex]

D) [tex]13^2 = 12^2 + 5^2[/tex]

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Answer:

[tex]y^3 - 8y^2 + 8y+5)[/tex]

Step-by-step explanation:

Take [tex]2y^2 - 3y - 5[/tex] from [tex]y^3 - 6y^2 + 5y[/tex]

Subtract [tex]2y^2 - 3y - 5[/tex] from [tex]y^3 - 6y^2 + 5y[/tex]

[tex]y^3 - 6y^2 + 5y-(2y^2 - 3y - 5)[/tex]

Multiply negative sign inside the parenthesis

[tex]y^3 - 6y^2 + 5y- 2y^2 + 3y +5[/tex]

Combine like terms

[tex]y^3 - 8y^2 + 8y+5[/tex]

Answer:

Step-by-step explanation: y3 - 8y2 + 8y + 5 (Take 2y 2 - 3y - 5 from y 3 - 6y 2 + 5y. Select the correct answer.)

The equation that can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex]

The area of the right triangle shown is 24 square feet.

We have to determine

Which equations can be used to find the lengths of the legs of the triangle?

According to the question

From the given figure the base of the triangle is x.

And the height of the triangle is (x+2).

The area of the triangle is given by half the product of the height and base.

[tex]\rm Area = \dfrac{1}{2} \times base \times height\\ [/tex]

Substitute all the values in the formula;

[tex]\rm Area \ of \ right \ triangle= \dfrac{1}{2} \times base \times height\\ \\ \rm 24= \dfrac{1}{2} \times x \times (x+2)\\\\ \rm 0.5(x)(x + 2) = 24[/tex]

The equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].

Hence, the equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].

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Since the new machine is three times faster, it takes (12 hours) / 3 = 4 hours for the new machine to make 10,000 cans alone.

Let's denote the time it takes the older machine to make 10,000 cans as "t" hours.

The new machine can make 10,000 cans three times faster than the older machine, which means it takes "t/3" hours for the new machine to make 10,000 cans.

When both machines are working together, they can make 10,000 cans in 9 hours.

Now, we can set up an equation based on the work rates of the two machines:

Work rate of the older machine + Work rate of the new machine = Combined work rate

The work rate is the amount of work (number of cans made) per unit of time (hours).

For the older machine:

Work rate of the older machine = 10,000 cans / t hours

For the new machine:

Work rate of the new machine = 10,000 cans / (t/3) hours

Combined work rate when both machines work together:

Combined work rate = 10,000 cans / 9 hours

Now, the equation becomes:

10,000 cans / t hours + 10,000 cans / (t/3) hours = 10,000 cans / 9 hours

To solve for "t," we can start by finding a common denominator for the fractions on the left side of the equation:

t/3 is the same as (1/3)t. So the equation becomes:

10,000 cans / t hours + 10,000 cans / (1/3)t hours = 10,000 cans / 9 hours

Now, to combine the fractions, we find the common denominator, which is 3t:

(3t * 10,000 cans) / (3t * t hours) + (t * 10,000 cans) / (3t * t hours) = 10,000 cans / 9 hours

(30,000t + 10,000t) / (3t^2 hours) = 10,000 cans / 9 hours

Combine the terms on the left side of the equation:

40,000t / (3t^2 hours) = 10,000 cans / 9 hours

Now, cross-multiply to solve for "t":

40,000t * 9 hours = 10,000 cans * 3t^2 hours

360,000t hours = 30,000t^2 hours

Now, rearrange the equation:

30,000t^2 - 360,000t hours = 0

Divide by 30,000t to simplify the equation:

t - 12 = 0

Now, solve for "t":

t = 12 hours

Therefore, it takes the older machine 12 hours to make 10,000 cans.

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