Four less than the quotient of a number and 3 is - 10

To find the width of a rectangular garden with a total perimeter of 120 feet and a known length of 40 feet, use the perimeter formula. Solving the equation, the width is determined to be 20 feet.

To find the width of a rectangular garden when you know the total fencing needed and the length of the garden, you can use the perimeter formula for a rectangle. The formula for the perimeter P of a rectangle is P = 2l + 2w, where l is the length and w is the width. In your case, the total perimeter is 120 feet and the length l is 40 feet. Setting up the equation using the given perimeter:

120 = 2(40) + 2w

Solving for w, the width:

120 = 80 + 2w

120 - 80 = 2w

40 = 2w

w = 20 feet

So, the width of the garden is 20 feet.

The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Answer:

Step-by-step explanation:

It is 2x by the third power because i dont know lol

Final answer:

The probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real is approximately 0.6786. Then we calculate the length of the range [-3, 16] divided by the length of the entire interval [-12, 16].

Explanation:

To find the probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real, we need to determine the range of values for A that will result in real roots. For real roots, the discriminant (b^2-4ac) must be greater than or equal to 0. In this case, the equation can be rewritten as [tex]x^2+(1+A)x+(A+3)=0[/tex], so a = 1, b = (1+A), and c = (A+3). The discriminant is (1+A)^2 - 4(A+3), which must be greater than or equal to 0.

Expanding and simplifying, we get (A^2 + 2A + 1) - 4A - 12 ≥ 0. Combining like terms, we have [tex]A^2 - 2A - 11 > 0[/tex].

To solve the inequality, we can find the values of A that make the equation equal to 0. Factoring, we get (A - 4)(A + 3) ≥ 0. The solutions are A ≤ -3 or A ≥ 4.

Therefore, the probability that the roots of the equation are both real is the probability of A taking values in the interval [-12, -3] or [4, 16]. To find this probability, we divide the length of the interval [-3, 16] by the length of the entire interval [-12, 16].

P(A is in [-3, 16]) = (16 - (-3)) / (16 - (-12)) = 19 / 28 ≈ 0.6786.

Answer: 120

Step-by-step explanation:

The number of ways to arrange n things of which 'a' things are identical , 'b' things are identical and so on...... :-

[tex]\dfrac{n!}{a!\ b!......}[/tex]

Given Word : DEGREE

Total letters = 6

Here letter E is repeated 3 times.

Then, the number of unique ways to arrange the letters in the word "DEGREE " will be :-

[tex]\dfrac{6!}{3!}=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]

Hence, the number of distinct arrangements for the letters in the word "DEGREE "=120

4.953 is larger than 4.951 because when comparing the digits from left to right, the thousandths place is different, where 3 is greater than 1.

To determine which number is larger, we compare them digit by digit starting from the left:

Both numbers have the same digit in the units place: 4.

Both numbers have the same digit in the tenths place: 9.

Both numbers have the same digit in the hundredths place: 5.

In the thousandths place, 4.953 has a 3, and 4.951 has a 1.

Since 3 is greater than 1, 4.953 is larger than 4.951.

Answer:  1000 ft³.

Step-by-step explanation:

Since, The volume of a cube = ( side )³

⇒ 1000 = (side)³ ⇒ side = 10

Hence, the side of the given cube = 10 feet

Since, the base of a cube = square having side 10 feet.

When we tilted the cube by 2 units,

Then, the base of the new solid = Rhombus having height 10 meters and base 10 feet,

Since, the square and rhombus are lying in the same base ( Shown in diagram)

Area of rhombus (Base of new solid) = Area of square having side 10 feet = 100 ft²

Since, the height of new solid is also 10 feet. the volume of new solid = Area of its base × height

=  10 × 100

= 1000 ft

To find a line parallel to y = -3/2x+3 through the point (-2,4), we use the point-slope form of a line using the given slope and coordinates.

To find a line parallel to a given line, we need to note that parallel lines have the same slope. The given equation is in the form y = mx + b, where m is the slope. In this case, the slope of the given line is -3/2. So, our parallel line will also have a slope of -3/2. Using the point-slope form of a line, we can substitute the slope and the coordinates of the given point (-2,4) to find the equation of the parallel line: y - y1 = m(x - x1). This gives us: y - 4 = -3/2(x - (-2)), which simplifies to y - 4 = -3/2(x + 2).

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Answer: The correct option is f(x) has three real roots and two imaginary roots.

Explanation:

It is given that the roots of fifth degree polynomial function are -2, 2 and 4+i.

Since he degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.

According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).

Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).

From the the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.

Therefore, the correct option is f(x) has three real roots and two imaginary roots.

Answer:

True

Step-by-step explanation:

[tex]x = - 30 + 16 \\ \\ or \: \: x = - 14[/tex]

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-\pi}{4} \sin \bigg( \frac{\pi t}{4} \bigg)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \cos \bigg( \frac{\pi t}{4} \bigg)[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Your answer for this question is 0

To add the fractions 3/4 and 7/10, you need to find a common denominator, which in this case is 20. Both fractions are then converted to have this common denominator and added together to get the result 29/20.

The subject of your question is fraction addition. To add 3/4 and 7/10, first we need to find a common denominator. In this case, the common denominator is 20. Change 3/4 into a fraction with 20 as a denominator, you get 15/20. Change 7/10 to a fraction with denominator 20, you get 14/20. Add these two fractions together, we get (15+14)/20, which simplifies to 29/20.

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