Emilia has a pencil box that is 12 inches long, 5 inches wide, and 3 inches tall. Richard's pencil box is 8 inches long and 5 inches wide, but it is twice as tall as Emilia's pencil box. How many cubic inches larger is Richard's pencil box than Emilia's pencil box?​

Answer:

   41. (2) x² - 3x - 4 =0

Step-by-step explanation:

Question 41

Standard form of polynomial

Answer:

(2)  [tex]x^2-3x-4=0[/tex]

Step-by-step explanation:

Standard form of a quadratic equation:  [tex]ax^2+bx+c=0[/tex]

When factoring a quadratic (finding the roots) we find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers.

So if the roots sum to 3 and multiply to -4, then the two numbers would be 4 and -1.

[tex]\implies b=1+-4=-3[/tex]

[tex]\implies ac=1 \cdot -4[/tex]

As there the leading coefficient is 1, [tex]c=-4[/tex].  

Therefore, the equation would be:  [tex]x^2-3x-4=0[/tex]

Proof

Factor  [tex]x^2-3x-4=0[/tex]

Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

The two numbers that multiply to -4 and sum to -3 are:  -4 and 1.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies x^2-4x+x-4=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies x(x-4)+1(x-4)=0[/tex]

Factor out the common term  [tex](x-4)[/tex]:

[tex]\implies (x+1)(x-4)=0[/tex]

Therefore, the roots are:  

[tex](x+1)=0 \implies x=-1[/tex]

[tex](x-4)=0 \implies x=4[/tex]

So the sum of the roots is:  -1 + 4 = 3

And the product of the roots is:  -1 × 4 = -4

Thereby proving that  [tex]x^2-3x-4=0[/tex]  has roots whose sum is 3 and whose product is -4.

Answer:

A. 2(x+3)(x^2+1)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The given expression is

Taking out the common factor.

The complete factor form of given expression is . Therefore the correct option is A.

The number of unique triangle can be formed using the angles 30 degrees, 90 degrees and 100 degrees is 0.

According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.

The measure of angles are given as,

To create a triangle with these angles, the sum should be equal to 180 degree of three angles.

90+100+30 > 180

90+90+30 > 180

90+90+100 > 180

100+100+30 > 180

30+100+30 < 180

30+90+30 < 180

There is no combination of angles, which is equal to the 180 degree.

Hence, the number of unique triangle can be formed using the angles 30 degrees, 90 degrees and 100 degrees is 0.

Learn more about the triangle angle sum theorem here;

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Answer:

[tex]\sf \cos(G)=\dfrac{1}{2}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\implies \sf \cos(G)=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

c=2.2feet

The solution in the attached file

Answer:

The circumference of the circle is 25.12 meters

Step-by-step explanation:

By definition, the circumference of a circle is the perimeter or the length around the circle.

To find the circumference of a circle, all we need to do is multiply the radius by pi and 2. Giving us the equation :

C = 2 * pi * r

We are also given that the diameter of the circle is 8 meters. With this, we can cut it in half to get the radius. 8 / 2 = 4

Now, we plug in our values:

2 * 3.14 * 4

When we evaluate this, we get the answer to be : 25.12

The circumference of the circle is 25.12 meters

Extra references for the definitions of radius and circumference.

The radius is the length from the center of the circle, to the outside (perimeter aka circumference point) of it. The diameter is the length across one end of the circle, to the other end, crossing through the center point.

Answer:

[tex]x=\frac{\pi}{2}, x =\frac{3\pi}{2}[/tex]

Step-by-step explanation:

Tyler concludes that 5x² will always have a larger output for the same value of x.

Look at the graph below and the table given

Take a random value: x = 0

Here, 1 > 0, making 2^x > 5x²

Hence, 2^x is greater than 5x² at this point. making Tyler's point not applicable.

Disagree with Tyler's point.

No it won't be

Take x =9

But

Clearly 2^x surpasses 5x²

So Tyler is wrong

Answer:

[tex] \sqrt{29-12\sqrt{5} }[/tex]

[tex]\sqrt{9 - 12 \sqrt{5} + 4 \times 5}[/tex]

[tex]\sqrt{ {3}^{2} - 12 \sqrt{5} + {(2 \sqrt{5}) }^{2} }[/tex]

[tex]\sqrt{{(3 - 2 \sqrt{5} )}^{2}}[/tex]

[tex]{(3 - 2 \sqrt{5} )}[/tex]

Answer:

Answer:

Equation of the parabola:  or

Vertex form:

Intercept form:

Step-by-step explanation:

Answer:

[tex]\frac{93458}{19435}[/tex] ≈ 4.81

Step-by-step explanation:

[tex]\frac{93458}{19435}[/tex] can not be simplified

A percentage is a way to describe a part of a whole. The total tax of Tegan's earnings will be £8,520(£6,400+£1,200).

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Since there is no tax for the first £11,000, therefore, the earnings which will be taxed,

£48,300 - £11,000 = £37,300

The amount of tax for the income of £11,000 to £43,000, will be,

20% of (£11,000 to £43,000)

= 20% × (£43,000 - £11,000)

= £6,400

The amount of tax for the income of £11,000 to £150,000, will be,

40% of (£43,000 to £48,300)

= 40% × (£5,300)

= £2,120

Hence, the total tax of Tegan's earnings will be £8,520(£6,400+£1,200).

Learn more about Percentages:

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Answer:

a) 540° b) 108°

Step-by-step explanation:

Formula: (n-2)×180°

a) (5-2)×180°

3×180°=540°

b) 540°÷5=108°

n means nr of sides

Answer:

The answer to this question should be 28.3

Answer:

7 things an investor should consider when picking stocks:

Trends in earnings growth.

Company strength relative to its peers.

Debt-to-equity ratio in line with industry norms.

Price-earnings ratio as an indicator of valuation.

How the company treats dividends.Effectiveness of executive leadership.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Let the missing side be 'x'.

Using Pythagorean Theorem, we can find the missing side.

Answer: 56.7%

Step-by-step explanation:

1) First we need to find the number of girls out of the class of 30:

30-13 = 17 -> 17 girls in the class

2) Then we can set up a part-whole equation like this (I don't know if this is how you learned it, I recommend searching up "part whole percent" if you're confused):

[tex]\frac{17}{30} \frac{x}{100}[/tex]      it follows this template: [tex]\frac{part}{whole} \frac{percent}{100}[/tex]

Since we're trying to find the percent and the problem gives us the rest of the info (by the way, that 100 will always stay there, it will never change)

3) Then we cross multiply

17 x 100 = 1700

1700/30 = 56.6666666

4) And since the answer has to be in the 1 decimal place, it would be 56.7

So that means approximately 56.7% of the class are girls

Step-by-step explanation:

Line L passes through point (0,2) and (4,0)

If you want to find the gradient of Line L, you can use this formula :

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex]m = \frac{0 - 2}{4 - 0} [/tex]

[tex]m = \frac{ - 2}{4} [/tex]

[tex]m = - \frac{1}{2} [/tex]

Answer:

Step-by-step explanation:

Step-by-step explanation:

4(5x²) + 16 = 400

5x² + 4 = 100

5x² = 96

x² = 19.5

x = ±sqrt(19.5) = ±4.415880433...

Answer:

x+46

Step-by-step explanation:

x+46 because you do math and dont worry ive done this problem pls can you help me with my problem

What are polynomials?

Polynomials are mathematical expressions made up of many terms.

How to simplify a polynomial?

To simplify the maximum of a polynomial, you must group all like terms and rearrange them from highest to lowest power.

we solve ⇒ 4(-8x+5)-(-33x-26)

To distribute

add up the numbers

Combine like terms.

Multiply by 1.

Answer:

9876540

Step-by-step explanation:

it’s the biggest number because it has the numbers in order from least to greatest! Please tell me if you need help with another question similar to this I will help you.

Answer:

9876540

Step-by-step explanation:

saying the digit number you count the big number