A bus travelled for 3 3⁄4 hours at an average speed of 48 km per hour. What is the total distance
covered by the bus?

Using quadratic equations, we can find the zeros of the equation are -4 and 12.

Quadratic equations are second-degree algebraic expressions because they have the form ax² + bx + c = 0. The word "quadratic" is derived from the Latin word "quadratus," which meaning "square," and alludes to the fact that the equation's variable x is squared. To put it another way, a "equation of degree 2" is a quadratic equation.

Given equation:

2x²-16x-96=0

Factor out of the terms on the left side:

2 × x² - 2 × 8x - 2 × 48 = 0

⇒ 2 (x² - 8x - 48) = 0

⇒ x² - 8x - 48 = 0

⇒ x² + 4x - 12x - 48 = 0

⇒ x (x+4) -12(x+4) = 0

⇒ (x+4) (x-12) = 0

⇒ x = -4 or x = 12.

Therefore, zeros of the equation are -4 and 12.

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Answer:

integers 3 and 18

Step-by-step explanation:

The distance between the points (-3.5, 0), and (1.5, 0), shown on the coordinate plane, obtained using the distance formula; is 5 units

The correct option is; 5 units

The distance formula is a formula that can be used to calculate the distance between the points (x₁, y₁), and (x₂, y₂) on the coordinate plane using the following equation;

d = √((x₂ - x₁)² + (y₂ - y₁)²).

The distance between the points (-3.5, 0), and (1.5, 0), on the graph can be obtained using the distance formula which is; d = √((x₂ - x₁)² + (y₂ - y₁)²

Where;

(x₁, y₁) = (-3.5, 0)

(x₂, y₂) = (1.5, 0), we get;

d = √((1.5 – (-3.5))² – (0 – 0)²) = 5

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So, the quotient is. [tex]Q(x) = x^3 - x^2 - x + 1/(x - 2)[/tex], and the remainder is. [tex]R(x) = 1.[/tex]Therefore, we can write:

[tex]f(x) / d(x) = Q(x) + R(x) / d(x)\\f(x) / d(x) = x^3 - x^2 - x + 1/(x - 2) + 1/(x - 2)[/tex].

Algebraic division is the process of dividing one algebraic expression by another. It involves applying the same rules of arithmetic division but with algebraic terms instead of numbers.

In algebraic division, the dividend, which is the expression being divided, is written on the top, while the divisor, which is the expression doing the dividing, is written below it. The division process involves finding how many times the divisor can fit into the dividend, and then subtracting that amount from the dividend. This process is repeated until there is no remainder left.

To divide [tex]f(x) = x^4 - 2x^3 + x^2 - 2x + 1[/tex] by[tex]d(x) = x - 2,[/tex] we can use long division as follows:

[tex]x^3 - x^2 - x + 1/ (x - 2)[/tex]

[tex]x - 2 | x^4 - 2x^3 + x^2 - 2x + 1[/tex]

     [tex]-x^4 + 2x^3[/tex]

      -----------

      [tex]0 - x^2[/tex]

      [tex]0 + x^2[/tex]

          ----------

                [tex]- 2x[/tex]

               [tex]+ 2x[/tex]

                  -----

                      1

                      1

                      -

                      0

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Answer:

6

Step-by-Step Explanation:

if you were to move the bottom triangle to the top, it would make the parallelogram a perfect rectangle.

the area is 60 units^2.

area=length*width

and the one side is 10. 60/10 =6 so 6 units is the answer

The approximate perimeter of the entire shape is 77.69 inches.

The perimeter of a figure is the sum of the whole sides of the figure.

Therefore, the perimeter of the entire shape can be calculated as follows:

The shape is made of three sides of a square and half a circle.

Therefore,

circumference of the semi circle [tex]= \pi r[/tex]

[tex]r = 17 \div 2 = 8.5 \ \text{inches}[/tex]

circumference of the semi circle [tex]= 8.5\pi[/tex]

Hence,

perimeter of the shape [tex]= 17+17+17+ 8.5\pi[/tex]

perimeter of the shape [tex]= 51 + 8.5(3.14)[/tex]

perimeter of the shape [tex]= 51 + 26.69[/tex]

Therefore,

perimeter of the shape = 77.69 inches

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The area of the triangle is 4.64 square meters and that of the trapezoid is 61.6 square inches.

A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides.

A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.

The formula for the area of a triangle is:

A = (1/2) * b * h

where b is the base of the triangle and h is the height of the triangle.

Substituting the given values, we get:

A = (1/2) * 2.9 m * 3.2 m

A = 4.64 square meters

Therefore, the area of the triangle is 4.64 square meters.

The formula for the area of a trapezoid is:

A = (a + b) * h / 2

where a and b are the lengths of the parallel bases, and h is the height of the trapezoid.

Substituting the given values, we get:

A = (10 + 12) * 5.6 / 2

A = 22 * 2.8

A = 61.6 square inches

Therefore, the area of the trapezoid is 61.6 square inches.

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Answer: The Missouri Compromise of 1820 was a landmark agreement in American history that temporarily resolved the issue of slavery in the western territories. The compromise was driven by a sense of nationalism among Americans in the early 1800s, who were concerned about preserving the unity of the country and avoiding the outbreak of civil war.

The Missouri Compromise reflected this sense of nationalism by seeking to maintain a balance of power between the slave states and the free states. The compromise allowed Missouri to enter the Union as a slave state, but it also admitted Maine as a free state, and prohibited slavery in any new states formed north of the 36°30′ parallel. By preserving this balance of power, the Missouri Compromise helped to ease tensions between the North and the South, and prevent the outbreak of civil war for several decades.

John Quincy Adams's diary entry provides some insights into the political climate of the time, and the debates surrounding the Missouri Compromise. In his diary entry of February 24, 1820, Adams writes:

"The Missouri question still hangs over us like a black cloud. The ground of the controversy is evidently an apprehension of the preponderance of power in the Union, which by some is feared to be passing from the South to the North."

This quote suggests that there was a growing concern among some Southerners about the balance of power in the Union, and that this concern was driving the debates over the Missouri Compromise. Adams goes on to describe the debates in Congress, noting that "the debates upon the Missouri question are exceedingly able, ingenious, and eloquent." He also provides some insights into the strategies being used by different sides of the debate, noting that "the argument for restriction upon Missouri, is that it will preserve the balance of power in the Union; that the balance of power is a fundamental principle of the Constitution; and that this principle is essential to the preservation of the Union."

These quotes suggest that the Missouri Compromise was a highly contentious issue, and that the debates surrounding it were marked by a strong sense of nationalism among both supporters and opponents of the compromise. The compromise ultimately reflected a desire among Americans to maintain the unity and stability of the country, even as it grappled with the divisive issue of slavery.

Step-by-step explanation:

As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .

A point together in two-dimensional plane can be found using coordinates, which are pairs of numbers. Each point is represented by an ordered pair of absolute values (x,y), where x represents the horizontal coordinate and y represents the vertical coordinate, in the Cartesian geometry. The x-axis is the horizontal axis, while the y-axis is the vertical axis. The origin is the intersection of the two axes and bears the following coordinates: (0,0). A point's coordinates might be plus, negative, or zero depending on where it is in relation to the axes and the origin.

given

We may use the section formula to determine the coordinates of point C, which divides line segment AB in a ratio of 1:3.

Let point C's coordinates be (x, y). Next, we have

x = [(3/4) * (-2)] + [(1/4) * 6] = -3/2

y = [(3/4) * (-5)] + [(1/4) * 3] = -21/4

As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .

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According to trigonometry, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.

What is trigonometry?

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations.

The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations.

There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc).

The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

To draw a diagram of the situation:

[tex]tan(28°) = opposite / adjacent\\tan(28^{0}) = 250 / x\\x = 250 / tan(28^{0})\\ x= 478.7 ft[/tex]

Therefore, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.

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Answer:

a = 2

Step-by-step explanation:

Geometric series:

          r = 3

          n = 6

         [tex]S_n=728[/tex]

      [tex]\boxed{\bf S_n = \dfrac{a(r^n - 1)}{r- 1}}[/tex]

           [tex]\dfrac{a*(3^6 - 1)}{3-1}=728\\\\ \dfrac{a * (729 -1)}{2}= 728\\\\ \dfrac{a * 728}{2} = 728[/tex]

                   [tex]a = 728 * \dfrac{2}{728}\\\\a = 2[/tex]

To calculate the interest that Margo will pay, we first need to determine how much interest she will accrue over the 17-month period.

We can use the formula:

Interest = Principal x Rate x Time

Where:

Principal is the amount borrowed, which is $700 in this case.

Rate is the annual interest rate, which is 3% or 0.03 as a decimal.

Time is the time period expressed in years, which is 17/12 or 1.4167 years in this case (since there are 12 months in a year).

Therefore, the interest that Margo will pay can be calculated as:

Interest = $700 x 0.03 x 1.4167

Interest = $29.75

So Margo will pay $29.75 in interest. Rounded to the nearest cent, the answer is $29.8.

Answer:

oc

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

We can write the following equation to find the value of x based on above mentioned information:

10x - 20 = 7x + 4

10x - 7x = 20 + 4

3x = 24

x = 8

To find each angle measure, replace x with 8:

10x - 20 would be 10 × 8 - 20 = 60

Since angles are congruent the other one also would be 60°.

Answer:

60

Step-by-step explanation:

Since this is a right triangle, the longest side can be solved using the Pythagorean Theorem

x^2 + y^2 = z^2

So

15^2 + 20^2 = 225 + 400 = 625 = 25^2.

So 25 is hypotenuse.

Add them all together : 25+15+20 = 60.

So your answer is 60.

Answer:

60

Step-by-step explanation:

A squared + B squared = C squared

15 squared + 20 squared = C squared

225 + 400 = C squared

625  = C squared

Use radicals to find the square root of 625

Which is 25

C = 25

25 + 15 + 20 =

60

Answer: To make "w" the subject of the formula "P+aw=b", we need to isolate "w" on one side of the equation.

First, we can subtract "P" from both sides of the equation to get:

aw = b - P

Next, we can divide both sides of the equation by "a" to get:

w = (b - P) / a

Therefore, the solution is:

w = (b - P) / a

Step-by-step explanation:

Answer:

22 * 100

Step-by-step explanation:

It would defintely be 22 * 100 because the other ones may be troubling to do mentally, especially 88 * 25. But with 22 * 100, you can easily get an answer of 2200.

Answer:

To solve 34x23 ≡ r (mod 13), we can first calculate the product 34x23 = 782. Next, we need to find the remainder when 782 is divided by 13. To do this, we can divide 782 by 13 and find the remainder: 782 ÷ 13 = 60 remainder 2 Therefore, 782 is equivalent to 2 (mod 13). So, the solution to the original equation is r ≡ 2 (mod 13).

Answer:

The slope of the curve ƒ(x) = x^2 + 2 at x = 3 can be found by taking the derivative of the function with respect to x and evaluating it at x = 3.

ƒ(x) = x^2 + 2

Taking the derivative:

ƒ'(x) = 2x

Substituting x = 3:

ƒ'(3) = 2(3) = 6

Therefore, the slope of the curve ƒ(x) = x^2 + 2 at x = 3 is 6.

Answer:

54

Step-by-step explanation:

16/4 + 56 - (3 + 4 - 1)

= 16/4 + 56 - (6)

= 4 + 56 - (6)

= 4 + 56 - 6

= 60 - 6

= 54

So, the answer is 54 !

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[tex] \sf \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \cancel \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 4 + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - (3 + 3)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - 6[/tex]

[tex] \: [/tex]

[tex] \sf \fbox{ \: \sf \blue{ 54 }\: \: }[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps!:)

Using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

The right rectangular prism has four rectangle-shaped side faces and two parallel end faces that are perpendicular to each of the bases.

Parallelograms make up the sides of an oblique prism, a non-right rectangular prism.

A cuboid is yet another name for a right rectangle prism.

So, the volume of the right rectangular prism:

V = wlh

Insert values:

V = wlh

V = 6*8*4.5

V = 216cm³

Now, the volume of the cube:

V = a³

V = 2³

V = 8cm³

Then, the number of cubes that can be fitted in the right rectangular prism:

216/8 = 27

Therefore, using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

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Correct question:

How many cubes, with side measures of 2 cm, will fit inside a right rectangular prism with dimensions of 6 cm by 8 cm by 4 1/2 cm?

Group of answer choices

a. 24

b. 27

c. 108

d. 54

Original Equation:

2x + 5y = 0

Explanation:

The slope intercept form is y = mx + b, so first we have to get x onto the other side, to do that, we subtract 2x from both sides and end up getting:

5y =  - 2x

Now we divide both sides by 5 to isolate y

[tex]y = -\frac{2}{5} x[/tex]

That's our equation!

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Without further context about the triangle and the lengths of its sides, it is not possible to solve for sin(B) using just the given information about cos(A).

Answer:

then she will have 139.67 left

Answer:

there is no image so i cannot solve your question.

Step-by-step explanation:

Answer: [tex]-3\sqrt{3}[/tex]

This the expression [tex]-3\times\sqrt{3}[/tex] or "-3 times the square root of 3"

[tex]\rule{300}{1.5}[/tex]

Work Shown:

Factor each term inside the square root so that a perfect square is one of the pieces. Then break up the roots and simplify as shown below.

[tex]-4\sqrt{12}+\sqrt{75}[/tex]

[tex]-4\sqrt{4\times3} +\sqrt{25\times3}[/tex]

[tex]-4\sqrt{4} \times\sqrt{3} +\sqrt{25} \times\sqrt{3}[/tex]

[tex]-4\times2\times\sqrt{3} +5\times\sqrt{3}[/tex]

[tex]-8\sqrt{3}+5\sqrt{3}[/tex]

[tex](-8+5)\sqrt{3}[/tex]

[tex]\bold{-3\sqrt{3}}[/tex]

To solve this problem, we can use the trigonometric functions sine, cosine, and tangent.

First, let's draw a diagram:

             A (top of the mountain)

            /|

           / |

         /    |  h (height of mountain)

       /      |

     / θ     |

B /_____|

   d (distance from base)

We are given that the distance from the base of the mountain to point B is 1/2 mile, or 2640 feet (since there are 5280 feet in a mile). We are also given that the angle of elevation from point B to point A is 65 degrees, and that the angle between the ski lift and the ground is 15 degrees.

Let's start by finding the height of the mountain h. We can use the tangent function, since we know the opposite (h) and the adjacent (d) sides of the right triangle formed by points A, B, and the foot of the mountain (call it point C):

tan(65) = h / d

h = d * tan(65)

Plugging in the values, we get:

h = 2640 * tan(65)

h ≈ 7855 feet

Next, let's find the length of the ski lift. We can use the cosine function, since we know the adjacent (d) and hypotenuse (L) sides of the right triangle formed by points B, the foot of the mountain, and the base of the ski lift (call it point D):

cos(15) = d / L

L = d / cos(15)

Plugging in the values, we get:

L = 2640 / cos(15)

L ≈ 2736 feet

Therefore, the length of the ski lift from the beginning to the end is approximately 2736 feet.

The team that has the largest overall size hat for their players is the Seahawks; they have a larger mean value of about 23 inches. The correct option is b.

The two most frequently used measures of center are mean and median. When we compare the mean numbers for the Pelicans and Seahawks, we can see that the Pelicans have a mean of roughly 22 inches and the Seahawks have a mean of roughly 23 inches.

Nevertheless, when the data is skewed or contains outliers, the mean may not be the best approximation of the center because the mean can be altered by extreme values or outliers. Thus, we also need to compare the median values. The median is the midway value in the ordered set of data.

Thus, the correct option is b, Seahawks; they have a larger mean value of about 23 inches.

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Answer:

Step-by-step explanation:

the right answer is b 23 inches seahawkS BRAINLIST and verified answer wanted