solve the inequality

2r^2-13x+15<0​

Solution:

Distance between two points is given by:

[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]

We have to find the distance in the standard (x, y) coordinate  plane between the points (2,3) and (5,5)

From given,

[tex](x_1, y_1) = (2, 3)\\\\(x_2, y_2) = (5, 5)[/tex]

Substituting the values we get,

[tex]d = \sqrt{(5-2)^2 + (5-3)^2}\\\\Simplify\\\\d = \sqrt{3^2 + 2^2}\\\\d = \sqrt{9+4}\\\\d = \sqrt{13}\\\\In\ decimal\ form\\\\d = 3.605 \approx 3.6[/tex]

Thus distance between the points (2,3) and (5,5) is 3.6 units

The distance between the points (2,3) and (5,5) on the standard (x, y) coordinate plane is determined using the distance formula. After substituting the given coordinate points into the formula, we find that the distance is √13 units.

In Mathematics, the distance between two points in the (x, y) coordinate plane is given by the distance formula, which is √[(x₂-x₁)² + (y₂-y₁)²]. This formula is acquired from the Pythagorean theorem. Here, the points are (2,3) and (5,5). So, substituting these values in the distance formula, we get:

Distance = √[(5-2)² + (5-3)²] = √[3² + 2²] = √[9+4] = √13.

Therefore, the distance between the two points (2,3) and (5,5) on the standard (x, y) coordinate plane is √13 units.

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Answer:74

Step-by-step explanation:

Since RP is 72, you would divide 72 by 2. The quotient you would get is 36. So then Q=38, you would add 36+38 and get 74.

Answer:

116.9FT

Step-by-step explanation:

72 = l . w . h

72 = x . (x - 1) . (x + 9)

72 = (x² - x) . (x + 9)

72 = x³ + 9x² - x² - 9x

72 = x³ + 8x² - 9x

0 = x³ + 8x² - 9x - 72

0 = x² (x + 8) - 9 (x + 8)

0 = (x² - 9)(x + 8)

0 = (x - 3)(x + 3)(x + 8)

x = 3 or x = -3 or x = -8

so, x = 3

length = x = 3

width = x - 1 = 2

height = x + 9 = 12

Final answer:

To find the dimensions of the rectangular prism, set up an equation using the volume formula and solve for x. The dimensions of the box are 3 feet, 2 feet, and 12 feet.

Explanation:

To find the dimensions of the box, we need to set up an equation using the volume formula for a rectangular prism. The volume of a rectangular prism is given by V = length x width x height.

So, we have the equation x(x - 1)(x + 9) = 72.

Simplifying this equation, we get x³ + 8x² - 9x - 72 = 0.

Using factoring or synthetic division, we find that x = 3 is a solution to the equation. Therefore, the length of the box is 3 feet, the width is 2 feet, and the height is 12 feet.

Answer:

I think it is 8.5

Step-by-step explanation:

The height of the triangle is 8.5 feet

To find the height of a triangle when the area and the base are known, we use the formula Area = 1/2 x base x height, where A is the area, b is the base, and h is the height. Given that the area of the triangle is 93.5 square feet and the base measures 22 feet, we can rearrange the formula to solve for h: h = 2 × Area/Base

h = 2×93.5/22

h=187/22

h = 8.5 feet

Therefore, the height of the triangle is 8.5 feet.

Answer:

The answer is:

No, they are not independent because P(student)≈ 0.82 and P(student|pirate) ≈0.94

Step-by-step explanation:

so the answer is B

No, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94

The probability of being student P(student) = 0.82

The probability of perferring pirate P(pirate) = 0.94

These two events are not independent events.

Hence, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94

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Answer:

1 + 2i and 1 – 2i

Answer:

A) For line l = (2x + 8°) + (5x - 10°) = 180° ....... (i)

For line k = (3x + 42°) + (x + 34°) = 180° ....... (ii)

B) In line l, two angles are = 60° and 120°

In line k, two angles are =  120° and 60°

Step-by-step explanation:

Requirement A

To find the measure of each angle, we have to use equation.

According to the graph, line l and k are parallel, therefore, both are straight angle. We know that a straight angle is equal to 180°. Therefore, line l and k are 180°. As both the line are intersected by line j, the lines are separated by two angles. So, the equation for line l is -

(2x + 8°) + (5x - 10°) = 180° ....... (i)

the equation for line k is -

(3x + 42°) + (x + 34°) = 180° ....... (ii)

Requirement B

For line "l "

By solving the equations, we can measure the angles

(2x + 8°) + (5x - 10°) = 180°

or, 2x + 8° + 5x - 10° = 180°

or, 7x - 2° = 180°

or, 7x = 180° + 2°

or, 7x = 182°

or, x = 182° ÷ 7 [Dividing both the sides by 7]

or, x = 26°

Therefore, 2x + 8° = 2 × 26° + 8° = 52° + 8° = 60°

the other angle is = 5x - 10° = 5 × 26° - 10° = 130° - 10° = 120°

For line "k "

(3x + 42°) + (x + 34°) = 180°

or, 3x + 42° + x + 34° = 180°

or, 4x + 76° = 180°

or, 4x = 180° - 76° [Deducting 76° from the both the sides]

or, 4x = 104°

or, x = 104° ÷ 4

Hence, x = 26°

Therefore, 3x + 42° = 3 × 26° + 42° = 78° + 42° = 120°

The other angle is = x + 34° = 26° + 34° = 60°

Answer:

7/8

Step-by-step explanation:

Simplify the following:

(1 + 3/4)/2

Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:

(4/4 + 3/4)/2

4/4 + 3/4 = (4 + 3)/4:

((4 + 3)/4)/2

4 + 3 = 7:

(7/4)/2

7/4×1/2 = 7/(4×2):

7/(4×2)

4×2 = 8:

Answer:  7/8

yes is an equilateral triangle also a rhombus

Answer:

ues it is   a equilateral triangle

Step-by-step explanation:

from the meaning of equilateral, equilateral means all sides are equal in length.

a rrhombus has all its side equal.and therefore it s an  equilateral triangle

Answer:

0.00132450331

Step-by-step explanation:

just divide lol

To solve 8 divided by 6040, perform the division, resulting in approximately 0.0013245.

To solve the problem of 8 divided by 6040, follow these steps:

Answer:A. 36

Step-by-step explanation:2x+16=×+20 x=4

4+8=12. 4+20=24

12+24=36

Answer(s): 1/2, 1, 1/3, 1/4

Any of these could work. Any number beyond 1 could work. The fraction 1/12 is pretty small, and the bigger the number in fractions, the smaller they get.

Example: 1/24 is bigger than 1/64

Because 64 is a bigger number, you'd have to cut it up more and more, getting smaller pieces.

So,  any number smaller than 12 in a fraction could work- EXCEPT negatives. All whole numbers work as well.

Answer: Amount of change : $30

percent increase : 200%

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

To obtain the amount of change we have to subtract the wholesale price to the retail price:

Mathematically speaking:

45 -15 = $30

For the percent increase, the amount of change (30) is some percent of the original price (15). So:

30 / 15 =2 (decimal form)

If we multiply it by 100, the percentage is:

200%

Answer:

Step-by-step explanation:

[tex]15a\geq 75\\15(5)\geq75\\75\geq75\\True[/tex]

If we substituted 1 for a then:

[tex]15a\geq75\\15(1)\geq75\\15\geq75\\False[/tex]

Answer:

4/7

Step-by-step explanation:

you just flip the numbers across the division/fraction sign

Heya.

First, let us learn about reciprocals.

Basically, it's the fraction flipped. Easy as 1, 2, 3!

Let's do an example:

We have an equation that says Find the reciprocal of 5/2.

1. Flip the fraction.

2. We then have 2/5 as a final answer.

Now onto the question:

1. We need to flip the equation.

2. This results as 4/7.

Therefore, our answer is "4/7".

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Answer:

8:36

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/8

Answer:

C. $5.55

Step-by-step explanation:

Total cost of installing 60 square feet of flooring

= $253.00 + $80

= $333

Total number of square feet for flooring = 60

Now cost per square foot of the flooring

= total cost/total number of square feet

That’s

$333/60 = $5.55

Each square foot cost $5.55

The graph of g(x) = f(–2x) will be a horizontally stretched and reflected version of the graph of the parent function f(x) = x^3. The reflection occurs over the y-axis, and the stretch is by a factor of 1/2.

The student's question involves a transformation of a cubic parent function. The original function, f(x) = x3, represents a standard cubic graph, which is symmetric about the origin and increases from negative infinity to positive infinity as x does the same. The transformation g(x) = f(–2x) modifies the parent function in two notable ways. First, the multiplication by –2 reflects the graph over the y-axis (because of the negative sign) and also stretches it horizontally by a factor of 1/2 (because the absolute value of the number is greater than 1).

To visualize this, if we consider specific points on the graph of f(x) such as (1,1), (2,8), and (3,27), you would find their corresponding points on g(x) at (-0.5,1), (-1,8), and (-1.5,27), respectively. This indicates that every point on g(x) is twice as far from the y-axis as it is on f(x), and on the opposite side due to the reflection.

The effect of this transformation demonstrates the result of horizontal stretching and reflection when contrasts with the original function f(x), providing insight into how linear transformations affect the shape and position of graphs.

Answer:

Step-by-step explanation:

(4x^2-2x+8)+(x^2+3x-2)

Collect like terms

5x^2+x+6

5x^2+x+6 dont know if you need to siplify it any more

Answer: 1 1/40.

Step-by-step explanation:

Final answer:

To factor the quadratic expression 8x² – 18x – 5 completely, one finds factors of the coefficient product (–40) that sum to the x coefficient (–18). These factors are -20 and +2, which are used to rewrite and group the middle term, allowing us to factor by grouping into (4x + 1)(2x – 5).

Explanation:

To factor the quadratic expression 8x2 − 18x − 5 completely, we need to find two binomials that when multiplied together give us the original quadratic expression. This process generally involves finding two numbers that multiply to give us the product of the coefficient of x2 term (8) and the constant term (-5) and also add to give the coefficient of the x term (-18).

The product of the coefficient of x2 and the constant term is -40 (8 × -5). We need to find factors of -40 that will add up to -18. After testing several combinations of factors, we see that -20 and 2 work since -20 + 2 = -18. Now we rewrite the middle term using these two numbers:

8x² − 20x + 2x − 5

Next, we group the terms to facilitate factoring by grouping:

=(8x² − 20x) + (2x − 5)

Now we factor out the common factors from each group:

=4x(2x − 5) + 1(2x − 5)

At this point, we have a common binomial factor (2x − 5) that can be factored out:

=(4x + 1)(2x − 5)

This is the expression factored completely.

Answer:

f(200) =116

f(200) is the cost to rent the moving van and drive it 200 miles

Step-by-step explanation:

f(x) = 90 + 0.13x

Let x = 200

f(200) = 90+ .13(200)

          =90+26

          =116

f(200) is the cost to rent the moving van and drive it 200 miles

Answer:

1. 6100

2. 1150

3. 60

4. 50

Step-by-step explanation:

Answer:

2h+3 Because they bought 2 hot dogs and h represents the amount they cost. And the 3 represents the drink he purchased

Answer:

1

Step-by-step explanation:

Only 1 right angle can be in any triangle.

Answer:

151 trays, 1 left over

Step-by-step explanation:

907/6 = 151 remainder 1

The Bake Stars could sell 151 trays of caramel apples with 1 apple left over.

The Bake Stars picked 907 apples and sold them in trays of 6.

To determine how many trays they can sell, divide the total number of apples by the number of apples in each tray:

907 apples / 6 apples per tray = 151 trays with 1 apple remaining (since 907 = 151 * 6 + 1).

The resulting coordinate of X is (0, -2)

Given the coordinate point X (-3, -2). If the coordinate is translated using the rule (x, y) = (x+3, y + 4), the resulting coordinate will be (-3+3, -2+4) = (0, 2)

In conclusion, the resulting coordinate of X is (0, -2)

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After translation and reflection, the coordinate of X" is (0, -2).

To find the coordinate of X" after a translation and reflection, we need to first apply the translation rule to point X (-3, -2). Using the rule (x, y) = (x+3, y + 4), we add 3 to the x-coordinate and add 4 to the y-coordinate:

x' = -3 + 3 = 0

y' = -2 + 4 = 2

After the translation, the new coordinates are (0, 2). To reflect over the x-axis, we change the sign of the y-coordinate, giving us the final coordinate of X" as (0, -2).

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Answer:

The correct answer is 32.5

Answer:

17+3b+5c

Step-by-step explanation:

9-4b+(8+7b+5c)

9-4b+8+7b+5c

9+8-4b+7b+5c

17+3b+5c

Answer:

11+(2×4)

11+8

$19....

Answer:

Cost for 2 hours=19, Cost for 2 hours=11+4t