Factor the expression. 4x(x^2 − 7) + 3(x^2 − 7)

The side length of the smallest square plate required to fit a 40-cm chopstick along its diagonal without any overhang is approximately 28.284 cm.

To find the side length of the smallest square plate in which a 40-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem. The diagonal of a square is the hypotenuse of a right-angled triangle formed by two sides of the square. Since the sides of the square are equal, if one side is s, then the diagonal d can be calculated using the equation d = s√2, where √2 is the square root of 2 (approximately 1.4142).

Therefore, to fit a 40-cm chopstick along the diagonal:

Let d = 40 cm.

Use the equation s√2 = 40 cm to find s, the side of the square.

s = 40 cm / √2.

s ≈ 28.284 cm when rounded to three decimal places.

So, the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang is approximately 28.284 cm.

The balance after 2 years when the interest is compounded daily is

$1,725.39.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Given:

P= $1500

R= 7%

T = 2 years

Now, using

A = P[tex](1 + r/n)^{nt[/tex]

A = 1,500.00[tex](1 + 0.07/365)^{(365)(2)[/tex]

A = 1,500.00[tex](1 + 0.00019178082191781)^{(730)[/tex]

A = $1,725.39

Hence, the balance is $1,725.39.

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Answer:

make the other brainliest but its false

Step-by-step explanation:

The  Price for Desk after tax is $265.614.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Ben bought a desk for $249.99.

Tax rate = 6.25%

So, the price for desk after tax

= 249.99 + 249.99 x 6.25%

= 249.99 + 249.99 x 0.0625

= 249.99 +15.62

= $265.614

Hence, the Price for Desk after tax is $265.614.

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Answer:

11.1 cm, 4.9 cm

Let's solve this step by step.
a. We begin by establishing the relationship between the width (w) and the length (l) using the total amount of fencing available (500 feet). Since one side of the pen is against the barn, we only need to fence the other three sides. Thus, the total amount of fencing used will be for two widths and one length, or \(2w + l\).
Setting up the equation for total fencing, we get:
\[2w + l = 500\]
Now, to express \(l\) in terms of \(w\), we solve for \(l\):
\[l = 500 - 2w\]
Next, we can write the function for the area \(A\) of the enclosure in terms of \(w\). Since area is \(width \times length\), we substitute our expression for \(l\):
\[A(w) = w \cdot l\]
\[A(w) = w \cdot (500 - 2w)\]
\[A(w) = 500w - 2w^2\]
This is the function that expresses \(A\) in terms of \(w\).
b. To find the width \(w\) that maximizes the area, we take the derivative of \(A(w)\) with respect to \(w\) and set it equal to zero to find the critical points.
\[A'(w) = \frac{d}{dw}(500w - 2w^2)\]
\[A'(w) = 500 - 4w\]
Setting \(A'(w)\) equal to zero and solving for \(w\):
\[500 - 4w = 0\]
\[-4w = -500\]
\[w = \frac{500}{4}\]
\[w = 125\]
The width that maximizes the area of the enclosure is 125 feet.
c. Now let’s find the maximum area by substituting \(w = 125\) back into the area function \(A(w)\):
\[A(125) = 500 \cdot 125 - 2 \cdot 125^2\]
\[A(125) = 62500 - 2 \cdot 15625\]
\[A(125) = 62500 - 31250\]
\[A(125) = 31250\]
The maximum area that Warren can enclose is 31,250 square feet.

The simplified expressions are:

12x + 3 − 4x + 7 = 8x + 10

8 − 7x − 13 + 2x = −5x − 5

−3x − 18 + 5x − 2 = 2x − 20

A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.

To simplify each expression, we combine like terms:

Expression 1:

12x + 3 − 4x + 7 = (12x − 4x) + (3 + 7)

12x + 3 − 4x + 7 = 8x + 10

Expression 2:

8 − 7x − 13 + 2x = (−7x + 2x) + (8 − 13) = −5x − 5

Expression 3:

−3x − 18 + 5x − 2 = (−3x + 5x) + (−18 − 2) = 2x − 20.

Therefore, the simplified expressions are:

12x + 3 − 4x + 7 = 8x + 10

8 − 7x − 13 + 2x = −5x − 5

−3x − 18 + 5x − 2 = 2x − 20

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Answer:

Option 4th is correct.

[tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]

Step-by-step explanation

The explicit sequence of the geometric sequence is given by:

[tex]a_n = a_1r^{n-1}[/tex]              ....[1]

where,

r is the common ratio

n is the number of terms

[tex]a_1[/tex] is the first term

As per the statement:

The explicit rule for a sequence is:

[tex]a_n=9(-5)^{n-1}[/tex]

On comparing [1] we have;

[tex]a_1 = 9[/tex] and r=  -5

Recursive formula for the geometric sequence is given by:

[tex]a_n = r \cdot a_{n-1}[/tex]  for [tex]n\geq 2[/tex]

Substitute the given values we have;

[tex]a_n = -5 \cdot a_{n-1}[/tex]

Therefore, the recursive rule for the sequence is, [tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]

Answer:

Step-by-step explanation:

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

⇒ -3,  

⇒ 0.59,  

⇒ 3.41