Find the product. (7 q - 5)(7 q + 5)
49q^2 - 10q - 25
49q^2 + 10q - 25
49q^2 - 25

To compare the amount of paint Enya would use to paint all but the bottom surface of the storage cupboard to the amount she would use to paint the entire prism, calculate the surface area of the prism and the surface area of all but the bottom surface of the prism. Then, divide the surface area of all but the bottom surface by the surface area of the entire prism and multiply by 100. Round the final answer to the nearest tenth.

To compare the amount of paint Enya would use to paint all but the bottom surface of the storage cupboard to the amount she would use to paint the entire prism, we need to calculate the surface area of the prism and the surface area of all but the bottom surface of the prism.

Step 1: Calculate the surface area of the prism by adding the areas of all its faces. The prism has two rectangular faces with dimensions 2.3 ft by 3.6 ft, two rectangular faces with dimensions 2.3 ft by 2.3 ft, and one rectangular face with dimensions 3.6 ft by 2.3 ft.

Step 2: Calculate the surface area of all but the bottom surface of the prism by subtracting the area of the bottom surface from the total surface area of the prism. The bottom surface has dimensions 2.3 ft by 2.3 ft.

Step 3: Calculate the percentage by dividing the surface area of all but the bottom surface of the prism by the surface area of the entire prism and multiplying by 100. Round the final answer to the nearest tenth.

Answer: Yes it is possible for triangle JKL to be similar to triangle XYZ.

Step-by-step explanation:

Given: In ΔJKL

m∠J=71° ,  m∠K=52°

In ΔXYZ

m∠X=71° ,  m∠Z=57°

Using Angle sum property of triangle in ΔJKL, we have

m∠J+m∠K+m∠L=180°

⇒71°+52°+m∠L=180°

⇒m∠L=180°-123°

⇒m∠L=57 °

Now in ΔJKL and ΔXYZ , we have

m∠J=m∠X=71°

and m∠L= m∠Z=57°

Therefore , By AA-similarity criteria , we have

ΔJKL≈ΔXYZ

Hence, Yes it is possible for triangle JKL to be similar to triangle XYZ.

Answer: D

Step-by-step explanation:

The ordered pair of the system of equations is (8, 2).

Option D is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x  + 4 = 9 is an equation.

We have,

x + 2y = 12 _____(1)

x = 12 - 2y _____(2)

-x = -y - 6 _______(3)

Putting (2) in (3) we get,

-(12 - 2y) = -y - 6

-12 + 2y = -y - 6

-12 + 6 = -y - 2y

-6 = -3y

y = 2

Now,

y = 2 in (2)

x = 12 - 2 x 2

x = 12 - 4

x = 8

Thus,

The ordered pair is (8, 2).

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Phil's net winnings from the poker tournament are represented by the expression 'x - 100', where x is the prize amount he won. To calculate his actual profit, we subtract the cost of entry (100 dollars) from his prize money.

The student has asked what Phil's net winnings are from a poker tournament after he received a prize of x dollars and the entry to the tournament cost him 100 dollars. To answer this, we will create an expression to represent Phil's net winnings.

Net winnings are calculated by subtracting the cost of entering the tournament from the prize amount. Since Phil won x dollars and spent 100 dollars to enter, we subtract 100 from x.

Phil's net winnings = Prize amount - Entry cost

Phil's net winnings = x - 100 dollars

This expression shows the actual profit Phil made from participating in the tournament, after the cost of entry has been accounted for.

Final answer:

Phil's net winnings from the poker tournament can be expressed as x - 100, where x represents the prize money.

Explanation:

To find Phil's net winnings from the poker tournament, we need to calculate the difference between the prize money and the entry fee. Given that Phil received a prize of x dollars and the tournament cost him 100 dollars to enter, his net winnings can be expressed as:

x - 100

For example, if Phil won $500, his net winnings would be $500 - $100 = $400.

Answer:

(0.9)(0.77)  

Step-by-step explanation:

(0.9)(0.77)  

Since the two events are independent you can use the multiplication rule

Answer:

[tex]\frac{3\±\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Whe have the function [tex]3x^2-6x+2=0[/tex]

To solve this equation we must factor.

To factor, we need to find the points where the function is equal to zero. So we use the quadratic formula

[tex]\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

Where:

a = 3

b = -6

c = 2

Then

[tex]\frac{-(-6) + \sqrt{(-6)^2-4(3)(2)}}{2(3)} = \frac{3+\sqrt{3}}{3}\\\\and\\\\\frac{-(-6) - \sqrt{(-6)^2-4(3)(2)}}{2(3)}= \frac{3-\sqrt{3}}{3}[/tex]

finally the correct answer is  [tex]\frac{3\±\sqrt{3}}{3}[/tex]

Final answer:

To solve the quadratic equation 3x² - 6x + 2 = 0, apply the quadratic formula with a=3, b=-6, and c=2, ultimately finding the solutions x = 1 + √(3) / 3 and x = 1 - √(3) / 3.

Explanation:

To solve the quadratic equation 3x² - 6x + 2 = 0, we can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a) where a, b, and c are coefficients from the equation ax² + bx + c = 0. In this equation, it is given a = 3, b = -6, and c = 2. Substituting these values into the formula gives us:

x = (6 ± √((-6)² - 4 · 3 · 2)) / (2 · 3)

x = (6 ± √(36 - 24)) / 6

x = (6 ± √(12)) / 6

x = (6 ± 2 √(3)) / 6

x = 1 ± √(3) / 3

The two possible solutions for x are then x = 1 + √(3) / 3 and x = 1 - √(3) / 3.

The Galileo walk 480.97 or 481 meters up the inclined plane if the Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have:

Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters.

The plane with an inclined an 12°

Let's suppose the Galileo walk x meters up the inclined plane.

As per right angle triangle,  The ratio of Sin

[tex]\rm Sin12\° = \frac{100}{x}[/tex]

[tex]\rm x = \frac{100}{Sin12\°}[/tex]

Sin12° = 0.20791

x = 100/0.20791

x = 480.97 meters  or

x = 481 meters

Thus, the Galileo walk 480.97 or 481 meters up the inclined plane if the Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.

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we are given

[tex]f(x)=3-4x+6x^2-5x^3[/tex]

we can see that this is polynomial

so, firstly we will find degree and leading coefficients

Degree:

It is the highest exponent of the polynomial

highest exponent is 3

so, degree=3

which is odd

Leading coefficient:

It is the constant term multiplied to highest exponent term

we can see that

constant term is -5

so, leading coefficient is -5

which is negative

End behavior:

degree is odd and leading coefficient is negative

so, it rises to left and falls to right

or we can also write as

[tex]x-->-\infty, y-->\infty[/tex]

[tex]x-->\infty, y-->-\infty[/tex]

Answer:

Ends up in Quadrants II and IV

Step-by-step explanation:

Since the leading coefficient is −5 and the degree is 3, the function has the behavior described.

Answer:

1).90

2).-10

Step-by-step explanation:

1).

(3(1)^2)+(3(2)^2)+(3(3)^2)+(3(4)^2)

  3      +     12    +    27    +    48

=90

2). (-5(3)+20)+(-5(4)+20)+(-5(5)+20)+(-5(6)+20)

     (-15+20)  +  (-20+20)  + (-25+20)  +  (-30+20)

           5       +       0         +       -5       +      -10

=-10

Answer:

Distributive Property

Step-by-step explanation:

Use the distributive property to multiply each term in each parenthesis.

Example:

To simplify the expression (x-3)(x^2-4x-7), apply the distributive property. The distributive property states to multiply each term in each parenthesis.

x*x^2=x^3

x*-4x=-4x^2

x*-7=-7x

-3*x^2=-3x^2

-3*-4x=12x

-3*-7=21

This gives the expression x^3-4x^2-7x-3x^2+12x+21. Combine like terms and get x^3-7x^2+5x+21.

The second one, as shown in the attached picture.

- - - - - - - - - -

Notes

It is 54 because that is the ansewr to this question bra

Final answer:

The gym teacher's belief is justified by using the empirical rule, which describes the distribution of data in a normal distribution. Since 68% of the girls fall within 1 standard deviation of the mean, it's likely that 95% fall within 2 standard deviations, supporting her height range belief.

Explanation:

The gym teacher's belief can be justified by understanding the properties of the normal distribution and the empirical rule. The empirical rule states that for a normal distribution:

Approximately 68% of the data will fall within 1 standard deviation (±1σ) of the mean.

Approximately 95% of the data will fall within 2 standard deviations (±2σ) of the mean.

Approximately 99.7% of the data will fall within 3 standard deviations (±3σ) of the mean.

In the teacher's class, 68% of the girls are between 5'2” and 5'6”, which is within 1 standard deviation of the mean height of 5'4”. Therefore, it's likely that 95% of the girls would fall within 2 standard deviations, which explains her belief that 95% of the girls would be between 5’0” to 5’8”.