What are the zeros of the quadratic function f(x)=6x^2+12x-7?


(Please pick from one of the options in the photo)

The solution of the given quadratic equation is x=-2 or x=-3.

The given quadratic equation is x²+5x+6=0.

The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.

By using the splitting middle term method we can solve x²+5x+6=0.

That is, x²+2x+3x+6=0

⇒x(x+2)+3(x+2)=0

⇒(x+2)(x+3)=0

⇒(x+2)=0, (x+3)=0

⇒x=-2 or x=-3.

Therefore, the solution of the given quadratic equation is x=-2 or x=-3.

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Answer:

Step-by-step explanation:

Comment

I'm going to assume that this is not a closed figure. The top is open like a water trough for horses.

There are 2 semicircular ends which add up to 1 whole circle.

There is 1 base area. The base area has a width of one of the semicircles. It has a length of 15 cm.

Solution

2 semi circles

r = d / 2

r = 20/2

r = 10

Area = pi r^2    This area is for 2 semicircles which = 1 circle.

Area = 3.14 * 10^2

Area = 3.14 * 100

Area =                                                  314

Trough

r = d / 2  

d= 20

r = 20/2

r= 10

w = 2*pi*r / 2

w = 2*3.14 *10/2

w = 31.4 cm

L = 15 cm

Area = 15 * 31.4

Area =                                                   471

Total Area =                                         785                              

Using translation concepts, the correct statement is given by:

If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:

x    1  2  3   4    5

f(x) 9 15 33 87 249

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Answer:

The CORRECT answer is:

1. f(x)

2. decreased by 4

3. (4, 87)

Step-by-step explanation:

Took the test

The length of the kite string is 50 ft

The string and the kite form a right triangle.

So, the length can be calculated using Pythagoras theorem as follows:

c^2 = 30^2 + 40^2

This gives

c^2 = 2500

Take the square roots

c = 50

Hence, the length of the kite string is 50 ft

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The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the distance from the man side of the house to the gutter is 15 m, since the drainpipe comes in lengths of 2.5 m, hence:

Number of drainpipe needed = 15 m / 2.5 m = 6

The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

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The required quantity of drainpipe is mathematically given as six.

L=6

Generally, Let's say the distance from the male side of the house to the gutter is 15 meters. Since the length of the drainpipe typically comes in increments of 2.5 meters, we may reason as follows:

In conclusion, The required quantity of drainpipe is equal to 15 meters divided by 2.5 meters, which is equal to six.

L=15/2.5

L=6

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Answer:

25/36

Step-by-step explanation:

put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's

The point which lies on the graph of the given function is; Choice D; (0, 2).

The point which lies on the graph of the given function; y = 2*3^x is it's y-intercept. The y-intercept which corresponds to the value of y when variable X is set to zero.

Hence, y = 2*3^0;

y = 2 ×1 = 2.

Hence, the point is; (0,2).

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Answer:

7

Step-by-step explanation:

The length of AB is the distance between A and B which is B-A -> 13-6= 7

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

we find the volume as if it were a parallelepiped and we remove the volume of the missing part.

8 * 6 * 10 = 480 cm³

480 - 2 * 3 * 10 = 420cm³

Answer:

[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]

Step-by-step explanation:

Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Quadratic equation: ax² + bx + c = 0, where a ≠ 0

Given: 3x² + 9x - 2 = 0

⇒ a = 3, b = 9, c = -2

Substitute the given values into the formula and simplify:

[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]

Therefore, the correct answer is A.

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Option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.

The measurements of the sides and angles of two or more geometrical figures determine their congruence. For example triangle's size is determined by its three sides, and its shape is determined by its three angles.

We have:

The diagram represents an unfolded paper kabuto, a samurai warrior's helmet.

Unfolded paper can be seen in the provided figure. The sheet is square.

The diagonals, in this case, are FN and AK, and the midline is CM and OI. At point R, all of these lines converge.

FR ≅ NR

AO ≅ ON

RC ≅ RO

NO ≅ NM

DV ≅ HV

Thus, option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.

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Answer:

6n+1

Step-by-step explanation:

Eliminate the parenthesis by changing the symbol of each term inside

3+[5n-2+n]

Eliminate the bracket and group similar terms

5n+n+3-2

Simplify terms

6n+1

Answer:

operant conditioning and schedules of reinforcement

The length of the box made by Mr. Baker is 10-inch

Mr. Baker has strip of 48- inch long  oak, by this strip he is making the rectangle box of width 14-inch.

The rectangle is 4 sided geometric shapes whose opposites are equal in lengths and all angles are about 90°.

As Mr. Baker has a strip that is 48-inch long and he made a rectangle box with it.

The width of the  box = 14 inches
now the length of the box = (total length of the strip - 2* width of the box)/2
⇒ length of the box = (48 - 2*14)/2
⇒ length of the box = 10 inches

Thus the Mr. Baker made the box which is 10 inches long.

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Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9 ( divide through by 9 )

x + y = 1 ( subtract x from both sides )

y = 1 - x

Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9

First, take 9x to the right side.

9y = 9 - 9x

9y = 9 ( 1 - x )

Divide both sides by 9.

y = 1 - x

The probabilities are:

a) P = 0.024

b) P = 0.5

a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.

There are 5 colas, and 16 drinks in total, so the probability is:

P = 5/16

The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:

Q = 4/15

Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:

Z = 4/14

The joint probability is:

prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024

b) If the two first persons grabed colas, then in the cooler we have:

3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.

Then the probability of grabbing a root beer is:

p = 7/14 = 1/2 = 0.5

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Answer:

(4, -3)

Step-by-step explanation:

A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)

Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:

[tex]6\sigma = 800 - 200[/tex]

[tex]\sigma = 100[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

To ensure a margin of error of 20, we solve for n when M = 20, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]20 = 1.96\frac{100}{\sqrt{n}}[/tex]

[tex]20\sqrt{n} = 1.96 \times 100[/tex]

[tex]\sqrt{n} = 1.96 \times 5[/tex]

[tex](\sqrt{n})^2 = (1.96 \times 5)^2[/tex]

n = 96.04.

Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.

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The area of wafer required to make the ice cream cone 68.75 cm²

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

Given:

r= 2cm, l=9 cm

Surface area,

=πr(l +r)

=3.14*2(9 + 2)

= 6.25*11

=68.75 cm²

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Answer:

[tex]2a^{4} + 5a^{3} - 13a^{2} + 19a - 28[/tex]

Step-by-step explanation:

Answer:

A.4

Step-by-step explanation:

Using the sine rule

sin(α)/A equals sin(β)/B

From the question & inserting values,

sin(90°)/8 equals sin(30°)/x

∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8

∴x equals 4

You can learn more on the sine rule in case you get confused.

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 8 ( divide both sides by 2 )

x = 4

We know immediately that the line must pass through (-4, 3).

The time taken for Terick to run one complete mile is determined as 12 minutes

The speed of chad is calculated as follows;

s = distance/time

s = (3.25 miles)/(40)

s = 0.08125 miles/min

2/3 of a mile = 8 mins

1/3 of a mile = ?

1/3 of a mile  =  4mins

1 mile = 8 mins + 4 mins = 12 mins

Thus, the time taken for Terick to run one complete mile is determined as 12 minutes.

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Answer:

you can buy 98 beds and buy dresses by rest of the money

Answer:

95%

Step-by-step explanation:

5 player won, meaning 95 player didn't.

This means that 95% of the players didn't win.

[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]

Answer: correct radical forms are:

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

Step-by-step explanation:

Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.

therefore,  

radical form of given values are :

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

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Answer:

30%

Step-by-step explanation:

First we find out the difference between them:

$654,030 - $457,821 = $196,209

Then we compare it with the original price:

196,209/654,030 = 0.3

Since 0.3 is 30%, that is 30% decrease in value.