On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula to find the location of point R?

The x-coordinate of the vertex is 2 and the y-coordinate is -10. The discriminant is 144.

The quadratic function can be rearranged into the form ax² + bx + c = 0, where a = 2, b = -8, and c = -10. To find the x-coordinate of the vertex, we use the formula x = -b / (2a). Plugging in the values, we get x = -(-8) / (2*2) = 2. The y-coordinate of the vertex can be found by substituting the x-coordinate into the original function. Plugging in x = 2, we get f(2) = 2(2)² - 8(2) - 10 = -10.

The discriminant is calculated as b² - 4ac. Plugging in the values, we get (-8)² - 4(2)(-10) = 64 + 80 = 144.

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Answer: the answer will be 165.2

Step-by-step explanation:

To solve for the surface area of the pyramid, we make use of the formula:

A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))

where,

l and w are the base of the pyramid = 100 mm

h is the height of the pyramid = 75 mm

Substituting the given values into the equation:

A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))

A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)

A = 20,148.90 mm^2

Therefore the surface area of the pyramid is about 20,149 mm^2.

Answer:

It takes to the plane [tex]162.792[/tex] seconds to fly once around a circle whose radius is 2850 m at a speed of [tex](110)\frac{m}{s}[/tex]

Step-by-step explanation:

The first step in this exercise is to find the total distance that the plane will fly.

This distance is equal to the perimeter of a circle whose radius is 2850 m.

Given a circle of radius R, the perimeter ''P'' can be calculated as :

[tex]P=\pi .d=\pi  .2.R[/tex]

Where ''d'' is the diameter of the circle that is equal to 2.R

The distance that the plane will fly in the exercise is :

[tex]P=\pi .2.R=\pi .2.(2850m)=17907.078m[/tex]

Now, the speed is equal to distance divided by time.

[tex]speed=\frac{distance}{time}[/tex]

We have the speed of the plane and the distance (that is the perimeter ''P'' of the circle). We only need to replace this values in the equation and find the time variable.

[tex](110)\frac{m}{s}=\frac{(17907.078)m}{t}[/tex]

[tex]t=\frac{(17907.078)m}{(110)\frac{m}{s}}=(162.792)s[/tex]

[tex]t=(162.792)s[/tex]

We find that the time is [tex]162.792[/tex] seconds.

Answer:

The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.    

Step-by-step explanation:

Hope this helps any of you! :)

Answer:

Overweight low probability outcomes

UNderweight High probability outcomes.

Step-by-step explanation:

Amos Tversky and Daniel Kahneman proposed the prospect theory that aimed to explain and understand the behavior of individuals, giving them a sample of choices to take, when put in front to the different decisions that had to be made, people often valued chances that were 99% probable to happen with a 95 to 85% chance, meaning that the didn´t give enough credit to the number and probabilities, and when facing risks of 1% probability of happening, they outweigh them with a 5 to 15 %.

To make line segment AB parallel to line segment CD, we calculate the slope of CD and ensure AB has the same slope. The slope of CD is −1/4.5, and setting the slope of AB equal to this value leads to the conclusion that y = −2 for point A.

To determine the value of y such that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8), we need to ensure that the slope of line AB is equal to the slope of line CD. The slope m of a line passing through two points (x1, y1) and (x2, y2) is given by m = (y2 − y1) / (x2 − x1).

For line CD, the slope is (8 − 6) / (−2 − 7) = 2 / (−9) = −1/4.5. To find the value of y for point A so that line AB is parallel to CD, we need to set the slope of AB equal to −1/4.5:

(−4 − y) / (6 − (−3)) = −1/4.5
(−4 − y) / 9 = −1/4.5
−4 − y = −9 / 4.5
y = −4 + 2 = −2

Therefore, the correct value of y that makes line AB parallel to line CD is −2.

The triangle ABC is mapped to A'B'C' through a 180-degree rotation about the origin, as all the points' x and y coordinates have changed signs, consistent with this transformation.

To determine which transformations can map the original triangle ABC to the new triangle A'B'C', we must closely examine the coordinates given and analyze the possible transformations.

Looking at the coordinates:

A(2, 2) to A'(-2, -2) suggests a reflection over the origin, which can be considered as a 180-degree rotation around the origin.

B(4, 1) to B'(-1, -4) also suggests a similar transformation, as the x and y values are negated and swapped in position.

C(4, 5) to C'(-5, -4) follows the same pattern.

All these transformations indicate that the original triangle has been rotated 180 degrees about the origin. This can also be observed by noting that the x and y coordinates have simply changed their signs, an effect of 180-degree rotation about the origin. This satisfies the claim of the classical geometry theorem which states that such transformations can be expressed as either a translation or a rotation. In this case, it's purely a rotation as there's no translation component.

Answer:

The answer on Imagine Math is...

-The volume of the left-hand cylinder is less than the volume of the right-hand cylinder.

Step-by-step explanation:

I got the answer correct on Imagine Math. Hope my answer helps those who need it :)

God bless you all day every day!

The solution is, The ratio of the volumes is the cube of this: 27 : 1.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

The ratio of the lengths is 75 : 25 or 3 : 1

The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2

(In working out the area the radius is squared)

and, we have,

The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3

(In working out the volume the radius is cubed)

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Hence, the inequality that will represent the marks he needs  is:

4x+8y≥50

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points.

Lorenzo needs at least 50 points on the final to earn a "B" in the class.

Let x be the number of correct multiple-choice questions, and y, the number of correct word problems.

Hence, the inequality that will represent the marks he needs  is:

4x+8y≥50

Answer: The answer is (B) [tex]47\dfrac{7}{12}[/tex].

Step-by-step explanation:  We are given to find the difference between the following two numbers:

[tex]n_1=126\dfrac{1}{4},~~~n_2=78\dfrac{2}{3}.[/tex]

To find the difference, we need to subtract the smaller number from the larger one.

Since, [tex]n_1>n_2[/tex], so the difference is given by

[tex]d\\\\=n_1-n_2\\\\=126\dfrac{1}{4}-78\dfrac{2}{3}\\\\=\dfrac{505}{4}-\dfrac{236}{3}\\\\=\dfrac{505\times3-236\times4}{12}\\\\=\dfrac{1515-944}{12}\\\\=\dfrac{571}{12}\\\\=47\dfrac{7}{12}.[/tex]

Thus, (B) [tex]47\dfrac{7}{12}[/tex] is the correct option.

The expanded form of 310, 763, 136 is:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

310, 763, 136

This can be written in expanded form as,

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

Thus,

The expanded form is:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

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The least common multiple of 2/3 5/6 and 9/4 is 12.

A fraction represents a part of a number or any number of equal parts.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We are given that;

The numbers 2/3 5/6 and 9/4

Now,

To find the least common multiple of fractions, we need to find the least common multiple of their denominators and divide it by the greatest common factor of their numerators. The steps are:

Multiples of 3: 3, 6, 9, 12, 15, 18,

Multiples of 6: 6, 12, 18,

Multiples of 4: 4, 8, 12,

Find the greatest common factor of 2, 5 and 9. This is the largest number that can divide all three numbers without leaving a remainder. One way to do this is to list the factors of each number and find the largest one that they have in common. For example:

Factors of 2: 1 and 2

Factors of 5: 1 and 5

Factors of 9: 1,3 and9

The only common factor is 1, so this is the greatest common factor of the numerators.

Divide the least common multiple of the denominators by the greatest common factor of the numerators. This gives us:

12 /1 =12

Therefore, the LCM of given fraction will be 12.

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To find the angle formed by a diagonal of a rectangular box with its base, calculate the base diagonal using the Pythagorean Theorem and then use the inverse tangent function with the height and base diagonal as arguments.

The angle formed by a diagonal of the rectangular box with the base of the box can be found using the Pythagorean Theorem. In this case, the box has a length of 6, a width of 4, and a height of 5. The diagonal of the base can be calculated as the hypotenuse of a right triangle formed by the length and the width. According to the Pythagorean theorem, this diagonal (D) is √(6² + 4²) which is √(36 + 16) or √52. To find the angle between the box's base diagonal and the body diagonal (which includes the height), we need to use trigonometry, specifically the inverse tangent function (tan-1). So we have the length of the box's base diagonal (D) and the height (H), forming a right triangle with the body diagonal as the hypotenuse. The angle θ can be calculated using tan-1(H/D), where H is the height of the box and D is the length of the diagonal on the base. This equates to tan-1(5/√52). Evaluating this expression with a calculator gives us the angle θ formed by the body diagonal with the base of the box.

The graphs of y = |x| and y = |x| - 4 are similar in their overall V-shape and slope behavior, but differ in their vertical position due to the constant term difference in the equations. The second graph is essentially a downward translation of the first by 4 units.

Similarities:

Both represent absolute value functions.

Both graphs pass through the origin (0, 0)

Both graphs have a slope of 1 for positive values of x and a slope of -1 for negative values of x.

Differences:

The graph of y = |x| - 4 is shifted downwards by 4 units

The y-intercept is different for both graphs.

Answer:

The answer by Equinimity is incorrect. On my test, those weren't even options. The answer is:

C = 10n; A = 25n

(the symbol that looks like 'n' anyway)

1. It's what the answer is on pretty much every other version of this question on brainly.

2. I did the math.