Write the standard form of the equation of the line that passes through the given points.
(5, 3) and (8, -2)

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

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.

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

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.

The measure of the side AB will be 45. The correct option is A.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Use the Pythagorean theorem to calculate the length of AB as below,

OB² = AB² + OA²

(BC + OC)² = AB² + OA²

(27 + 24)² =  AB² + 24²

AB² = 51² - 24²

AB = 45 units

Therefore, the correct option is A. The value of length AB is 45.

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Answer:

A. 0.4

Step-by-step explanation:

Final answer:

Jeremy needs to create an inequality to represent his new earning goal higher than $160 a week, leading to the inequality 8x + 10y > 160. This can be graphed by first converting to intercept form, plotting the intercept and slope, drawing a dashed boundary line, and shading the region above this line.

Explanation:

Jeremy is working two jobs to save for his college education and needs to create an inequality to represent the amount he needs to make each week, now more than $160. Let's denote the number of hours Jeremy works busing tables as x and the number of hours he spends tutoring as y. He makes $8 per hour busing tables and $10 per hour tutoring.

To express Jeremy's goal of making more than $160 a week, we can write the following inequality:

8x + 10y > 160

To graph this inequality:

First, rewrite the inequality as y > (-4/5)x + 16 to get the intercept form.

Plot the y-intercept at (0, 16) on the graph.

Use the slope of -4/5 to determine another point. From (0, 16), move 5 units to the right (positive x-direction) and 4 units down (negative y-direction), then plot this second point.

Draw a dashed line through the two points to represent the boundary of the inequality (dashed because the inequality is strict and does not include the line itself).

Shade above the line to indicate that all solutions to the inequality lie in this area, where Jeremy would be earning more than $160.

Your answer for this question is 0

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:

1.  13, 17                       Option D

2. -2                            Option B

3. 2                             Option C

4. F(n) = 3+4(n-1)        Option D

Step-by-step explanation:

1.  

Given sequence is:   1, 5, 9....

Common difference =  5-1 = 9-5 = 4

Next term is :

9+4 = 13

and

13+4= 17

So, next two terms are:  13 & 17.

2.

Given sequence is :

102, 100, 98, 96....

Common difference = 100 - 102 = 98 -100 = 96 - 98 = -2

3.

Given rule is :

Aₙ  = -14 + (n - 1)(2)

Find the 9th term

so, we put n = 9

A₉ = -14 + (9-1)*2

A₉ = -14 + 8*2 = -14 + 16

A₉ = 2

Ninth term is 2.

4.

Given sequence is:

3, 7, 11, 15.....

Write the nth term

Formula is :

F(n) = a₁ + (n-1)d

Where a₁ is first term

n is number of terms

d is common difference

a₁ = 3

d = 7-3 = 11-7 = 15 - 11 = 4

So nth term is :

F(n) = 3 + 4(n-1)

That's the final answer.

Answer:

1.  13, 17    Option D

2. -2      Option B

3. 2      Option C

4. F(n) = 3+4(n-1)     Option D

Step-by-step explanation:

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.

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

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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