Find the value of the discriminant. Then describe the number and type of roots for the equation -3x2-18x+5=0

Answer:

420 miles

Step-by-step explanation:

Distance = rate × time

Let's say that the distance is D and that John's speed is S.  We know that:

D = S × 6

When Elliot drives at speed S+14:

D = (S+14) × 5

Setting D = D:

S × 6 = (S+14) × 5

6S = 5S + 70

S = 70

Therefore, the distance D is:

D = 70 × 6

D = 420

The distance from John's house to Miami is 420 miles.

The distance from John's house to Miami, Florida is 420 miles, calculated by first determining John's speed using the given information and then applying the formula distance = speed times time.

To calculate the distance from John's house to Miami, Florida, we need to use the formula distance = speed times time. John's travel time is 6 hours. We are not directly given John's speed; instead, we know that Elliot drives 14 mph faster than John and it takes him 5 hours to cover the same distance. Let's denote John's speed as 's'. Therefore, Elliot's speed is 's + 14 mph'. Setting up an equation based on Elliot's travel information, we have distance = (s + 14 mph) times 5 hours.

Since they both travel the same distance, we can also write John's travel information as distance = s times 6 hours. Equating both expressions for distance, we get: s times 6 = (s + 14) times 5. Simplifying, we have 6s = 5s + 70, which leads to s = 70 mph. This means John's speed is 70 mph.

To find the distance to Miami, we return to the distance formula and substitute John's speed: distance = 70 mph times 6 hours = 420 miles. Hence, the distance from John's house to Miami, Florida is 420 miles.

Answer:

second choice

third choice

Step-by-step explanation:

righty whighty edg 2020

From the given diagram of triangle DEF:

Triangle DEF is shown in the image attached below/.

Triangle DEF has the following sides:

The triangle also shows that:

Also,

In summary, from the given diagram of triangle DEF:

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Answer:

Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.

119g + 100t + 6p = 6592

t = 3/4g

p = 2g

119g + 100(3/4)g + 6(2g) = 6592

g = 32

t = 3/4(32) = 24

p = 32(2) = 64

A golden ticket costs $32. A regular ticket costs $24. A platinum ticket costs $64. Hope this helps!

Answer:

Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.

119g + 100t + 6p = 6592

t = 3/4g

p = 2g

119g + 100(3/4)g + 6(2g) = 6592

g = 32

t = 3/4(32) = 24

p = 32(2) = 64

Step-by-step explanation:

Answer:

Step-by-step explanation:

maybe 2 by 4 and 7 by 4 then add sorry if i'm wrong

Perimeter of a square = side*side

4*4=16cm^2

The perimeter of a square piece of plastic with each side measuring 4 centimeters is 16 centimeters.

The question is asking for the perimeter of a square piece of plastic with sides that are 4 centimeters long. To calculate the perimeter of a square, you multiply the length of one side by four. Since a square has four equal sides, the calculation in this case would be 4 cm (side length) times 4 (number of sides), which equals 16 cm. So, the perimeter of the square piece of plastic is 16 centimeters.

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Answer:

Josh's salary is 20% less than Jeff's.

Step-by-step explanation:

Let

x----> Jeff's salary

y----> Josh's salary

we know that

x=1.25y

Solve for y

y=(1/1.25)x

y=0.8x

therefore

Josh's salary is 80% of Jeff's salary

or

Josh's salary is 20% less than Jeff's.

Answer: 15

Step-by-step explanation: because there are 6 sides. 1/6*90=15

Hoped this helped!

When rolling a fair six-sided die 90 times, the expected number of times you would roll a 5 is about 15, calculated by multiplying the probability of rolling a 5 (1/6) by the number of rolls (90).

If you roll a fair six-sided die 90 times, you would expect each number to appear with equal probability because the die is fair. For each individual roll, the probability of getting a 5 is 1 in 6, as there are six possible outcomes. To find the expected number of times you would get a 5 in 90 rolls, you simply multiply the probability of rolling a 5 by the total number of rolls.

Expected number of fives = Probability of rolling a 5 × Total number of rolls
= (1/6) × 90

= 15

Therefore, you would expect to roll a 5 approximately 15 times out of 90 rolls.

Answer: 10.5 gallons

Step-by-step explanation:

One imperial gallon is approximately 1.2 US gallons. The US gallon is used in the United States and is equal to exactly 231 cubic inches or 3.785411784 liters. The Imperial gallon or UK gallon is used in the United Kingdom and is equal to approximately 277.42 cubic inches. Its exact value is defined as 4.54609 liters.

Final answer:

To find the value of f(x) when x=2 for the function f(x) = 42x - 100, substitute 2 for x, giving f(2) = 84 - 100, which simplifies to f(2) = -16.

Explanation:

The student is asking to evaluate the function f(x) = 42x - 100 when x = 2. To do this, we simply substitute 2 for x in the equation, which gives us f(2) = 42(2) - 100. Performing the multiplication first, we get 84 - 100. Thus, f(2) equals -16.

The subject is mathematics, specifically related to the evaluation of functions, which is a topic typically covered in high school algebra courses. This is a straightforward example of how to evaluate a function at a given point.

x in (-oo:+oo)

2/7 = x/14 // - x/14

2/7-(x/14) = 0

2/7-1/14*x = 0 // - 2/7

-1/14*x = -2/7 // : -1/14

x = -2/7/(-1/14)

x = 4

x = 4

i hope this helps

Answer:

x*14 = 7*4

Step-by-step explanation:

The probability of drawing 3 oranges from a basket of 6 oranges and 4 tangerines is 1/6 or approximately 0.167.

This problem is a probability question in the field of mathematics. It is asking us to find the probability that all three fruits drawn from the basket are oranges. This can be solved using the concept of combinations from probability theory.

The total number of fruits in the basket is 10 (6 oranges and 4 tangerines). We want to draw a sample of 3 fruits. The number of ways to draw 3 fruits from a total of 10 (regardless of type) is given by the combination formula C(n, r), where n is the total number of items and r is the number of items to choose. So we have C(10, 3) = 120 possible ways.

Next, consider the scenario we're interested in--drawing 3 oranges. The total number of ways to draw 3 oranges from a total of 6 oranges is C(6, 3) = 20 possible ways.

So, the probability of drawing 3 oranges is the number of ways to draw 3 oranges divided by the total number of ways to draw 3 fruits. So, the probability is 20/120 = 1/6 or approximately 0.167.

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Final answer:

The probability of drawing 3 oranges from a basket containing 6 oranges and 4 tangerines is found using combinations. The calculation shows that the probability of selecting all oranges in a draw of 3 fruits is 1/6.

Explanation:

The question asks to find the probability that when three fruits are drawn from a basket containing 6 oranges and 4 tangerines, all three are oranges. This is a problem of probability without replacement, which can be solved using combinations.

To find the probability of drawing 3 oranges out of 3 fruits, we calculate the combinations of choosing 3 oranges from 6 and then divide it by the combinations of choosing 3 fruits from the total 10 fruits in the basket.

The number of ways to select 3 oranges out of 6 is given by the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items, and k is the number of items to choose. So, we have:

Ways to pick 3 oranges: C(6, 3)

Total ways to pick 3 fruits: C(10, 3)

Then the probability is calculated by:

P(all oranges) = C(6, 3) / C(10, 3)

Calculating the combinations, we have:

Thus, the probability that all three fruits are oranges is 1/6.

ANSWER

The slope is 4

EXPLANATION

We want to find the slope of the line goin through (3,9) and (1,1)

We use the slope formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

We substitute the points into the slope formula to get;

[tex]m = \frac{1 - 9}{1 - 3} [/tex]

This simplifies to:

[tex]m = \frac{ - 8}{ - 2} [/tex]

[tex]m = 4[/tex]

Hence the slope of the line is 4.

Answer:

You could divide $12 with either method

If you divided 12 by 1/4 you would get $48.

Divided by 1/3, $36.

Answer:

The equation is:

[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]

[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]

The sum is:

[tex]S=\frac{211}{243}[/tex]

--------------------------------------------------------------------

If the sequence is infinite, the formula is:

[tex]S = \frac{a_1}{1-r}[/tex]

-------------------------------------------------------------------

Step-by-step explanation:

We must calculate the radius of the geometric series

[tex]r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}[/tex]

The first term of the series is: [tex]a_1=\frac{1}{3}[/tex]

The last term of the series is: [tex]a_n=\frac{16}{243}[/tex]

If the sequence is finite then the formula is:

[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]

[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]

[tex]S=\frac{211}{243}[/tex]

If the sequence is infinite then by definition as the radius  are [tex]0 <| r | <1[/tex] then the formula for the sum of the geometric sequence is:

[tex]S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1[/tex]

Answer:

A

Step-by-step explanation:

got it right on edge

Answer:

4

Step-by-step explanation:

Final answer:

The expression equivalent to (X^3)^4 is X^12. You calculate this by multiplying the exponents, resulting in X raised to the power of 3 times 4, which equals 12.

Explanation:

The expression (X^3)^4 is equivalent to X^(3*4), which is X^12. This follows the rule that when you raise a power to a power, you multiply the exponents. A number raised to the fourth power, like in this case, means that number is multiplied by itself four times. Generalizing this, for any base 'n' and exponents 'a' and 'b', the expression (n^a)^b is equal to n^(a*b).

For example, similar to (5^3)^4 being 5^(3*4) or 5^12, which is twelve fives multiplied together. Therefore, our given expression simplifies to X multiplied by itself a total of twelve times.

Hello There!

To find a cylinder, we use the formula Pi*radius “squared” *height

First, let’s put in our values. Our radius is 5 but in our formula, we have to square 5 so we get a product of 25.

Then we multiply 25 by 9 because you will see in our formula we have to multiply by the height. 25*9 equals 225

Now, we are putting our value in terms of pi so our answer would be 225

Answer “C”

Answer:

175

Step-by-step explanation:

APEXX!!!!

Answer:

abc is the one that must be a simicircle

Answer:

A. ABC.

Step-by-step explanation:

We have been given an image of a circle. We are asked to choose the arc, which must be a semicircle of our given circle.

Upon looking at our given diagram, we can see that AC divides our given circle into two semicircles ABC and ATC.

From our given choices, we can see that option A is the correct choice.

Answer: 3 yd

Step-by-step explanation: The radius is 3 yards because the diameter is 6 and the radius is d/2. 6/2 is equal to 3.

Hope this helps!

ANSWER

An ordered pair that is the solution to the system of equations lies on the y-axis.

The y-coordinate of a solution to the system of equations is 4.

EXPLANATION

The given system has equations:

[tex]y = {x}^{2} + 2x + 4[/tex]

[tex]y = - x + 4[/tex]

We equate both equations to get:

[tex] {x}^{2} + 2x + 4 = - x + 4[/tex]

This implies that,

[tex] {x}^{2} + 2x + x + 4 - 4 = 0[/tex]

[tex] {x}^{2} + 3x = 0[/tex]

[tex]x(x + 3) = 0[/tex]

[tex]x = 0 \: or \: x = - 3[/tex]

When x=0, y=-(0)+4=4

When x=-3, y=-(-3)+4=7

The solutions are: (0,4) and (-3,7)

The true statements about the system of equations are:

The system of equations is given as:

f(x)=−x^2+2x+4

g(x)=−x+4

From the graph of the system of equations (see attachment), we have the following point of intersections

(x,y) = (0,4) and (3,1)

So, the true statements about the system of equations are:

(a), (c), (d) and (e)

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Answer:

Blank 1 ⇒ supplementary

Blank 2 ⇒ complementary

Step-by-step explanation:

* Lets revise some facts to solve the problem

- The tangent to a circle is a line touch the circle at one point

- The tangent and the radius of a circle are perpendicular to each

 other at the point of contact

- If the two angles are supplementary, then the sum of their measure

 is 180°

- If the two angles are complementary, then the sum of their measure

 is 90°

* Now lets solve the question

∵ CB and CA are two tangents to the circle O at B and A

∵ OB and OA are radii

∴ OB ⊥ BC at point B and OA ⊥ AC at point A

∴ m∠OBC = 90° and m∠OAC = 90°

- In figure CBOA is a quadrilateral

∴ The sum of the measures of its interior angles is 360°

∵ m∠CBO + m∠BOA + m∠OAC + m∠BCA = 360°

∵ m∠CBO = 90° , m∠OAC = 90°

∴ 90° + m∠BOA + 90° + m∠BCA = 360°

∴ 180° + m∠BOA + m∠BCA = 360° ⇒ subtract 180 from both sides

∴ m∠BOA + m∠BCA = 180°

∴ ∠BOA and ∠BCA are supplementary

- In Δ CBO

∵ The sum of the measures of the interior angles of any triangle is 180°

∴ m∠BOC + m∠BCO + m∠CBO = 180°

∵ m∠CBO = 90°

∴ m∠BOC + m∠BCO + 90° = 180° ⇒ subtract 90° from both sides

∴ m∠BOC + m∠BCO = 90°

∴ ∠BOC and ∠BCO are complementary

Answer:

Blank 1: Supplementary

Blank 2:Complementary

Step-by-step explanation: I picked these and got it right

Answer:

Step-by-step explanation:

Use the given information to determine what the angles can be.

  g = 2x -90 . . . . given

  g > 0 . . . . . . . . . given

  2x -90 > 0

  2x > 90 . . . . . add 90

  x > 45 . . . . . . divide by 2

__

  h = 180 -2x

  h > 0

  180 -2x > 0

  180 > 2x

  90 > x

__

The requirement that both angles be greater than zero puts limits on x:

  45 < x < 90

We can put this back into the given relations for g and h:

  g = 2x -90

  x = (g +90)/2

  45 < (g +90)/2 < 90 . . . . substitute for x

  0 < g/2 < 45 . . . . . . . . . . subtract 45

  0 < g < 90 . . . . . . . . . . . . g is an acute angle

Similarly, ...

  h = 180 -2x

  x = (180 -h)/2 = 90 -h/2

  45 < (90 -h/2) < 90 . . . . substitute for x

  -45 < -h/2 < 0 . . . . . . . . . subtract 90

  90 > h > 0 . . . . . . . . . . . multiply by -2; h is an acute angle

__

We can add the angle measures to see if they are supplementary or complementary:

  g + h = (2x -90) +(180 -2x)

  g + h = 90 . . . . . simplify; the angles are complementary

__

The relevant observations are ...

The area is 64. Area, as you probably know, is the length times the width of the figure. The length from A to C is approximately radical 128, and the length from C to D is approximately radical 32 (btw, the radical is the check mark with line that goes above and next to the radicand (the number on the inside of the radical)). Multiply these two to get the area, and you should end up with 64.

If the quadrilateral has vertices at (-8, 0), (-4,-4), (0,8), and (4,4). Then the area of the quadrilateral will be 64 square units.

It is a polygon with four sides. The total interior angle is 360 degrees.

The quadrilateral shown below has vertices at (-8, 0), (-4,-4), (0,8), and (4,4).

Then the area of the quadrilateral will be

Assume the points

(x₁, y₁) = (-8, 0)

(x₂, y₂) = (-4, -4)

(x₃, y₃) = (4, 4)

(x₄, y₄) = (0, 8)

Then the area of the quadrilateral is given as

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)]|

Area = 1/2|[(-8 × -4 + -4×4 + 4×8 + 0×0) - (0 × -4 + -4 × 4 + 4 × 0 + 8 × -8)]|

Area = 1/2|[(32 - 16 + 32) - ( -16 - 64)]|

Area = 1/2|[48 + 80]|

Area = 1/2|128|

Area = 64

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Answer:

120 square units

Step-by-step explanation:

In triangle PSQ, PS=SQ. Let PS=SQ=x units.

Since SQ-PQ=1, PQ=SQ-1=x-1 units.

The perimeter of the triangle PSQ is 50 units, so

PS+SQ+PQ=50 units.

Substitute PS=SQ=x un. and PQ=x-1 un.

x+x+x-1=50

3x=51

x=17

Hence

PS=SQ=17 units,

PQ=16 units.

Use Heron's formula to find the area:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where p is semi-perimeter and a,b,c are lengths of sides.

[tex]p=\dfrac{17+17+16}{2}=25,\\ \\\\A=\sqrt{25(25-17)(25-17)(25-16)}=\sqrt{25\cdot 8\cdot 8\cdot 9}=5\cdot 8\cdot 3=120\ un^2.[/tex]

Answer:

Step-by-step explanation:

 11,566,740

+6,978,730

--------------------

  18545470

Not much explaining, just add. A calculator can be used.

The combined population of the city will be 18,545,470.

Addition is the mathematical operation of adding two numbers to get total.

We have,

Population of One city = 11,566,740

And,

Population of another city = 6,978,730

Now,

To get combined population,

Add population of both city,

i.e.

Combined population = Population of One city

+ Population of another city

                                     = 11,566,740 + 6,978,730

i.e.

Combined population = 18,545,470

Hence, we can say that the combined population of the city will be 18,545,470.

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Answer:

9.

The probabilities are the same

10.

1/3

Step-by-step explanation:

9.

Assuming the coin is fair;

The probability of getting heads in a single toss is, P(H) = 1/2

The probability of getting tails in a single toss is, P(T) = 1/2

Now, P(H,H,H) is the probability of obtaining 3 heads in the e tosses. Since each toss is independent of the others,;

P(H,H,H) = P(H)*P(H)*P(H)

              = 1/2 * 1/2 * 1/2 = 1/8

On the other hand, P(H,T,H) is the probability of obtaining a head followed by a tail followed by a final head. Using the independence property;

P(H,T,H) = P(H)*P(T)*P(H)

              = 1/2 * 1/2 * 1/2 = 1/8

Therefore, P(H,H,H) = P(H,T,H)

10.

We are informed that a coin is tossed and a number cube is rolled. We are to determine the following probability;

P(heads, a number less than 5)

Assuming the coin is fair;

The probability of getting heads in a single toss is, P(H) = 1/2

Assuming the number cube is fair as well, the probability of rolling a number less than 5 is;

4/6 = 2/3

This is because there are 4 numbers less than 5, (1, 2, 3, 4) while the cube has 6 sides.

P(heads, a number less than 5), the events presented here are independent since the outcome from tossing the coin does not in any way determine the outcome from rolling the number cube. Therefore,;

P(heads, a number less than 5) = P(heads)*P(a number less than 5)

                                                    = 1/2 * 2/3 = 1/3

Answer:

16

Step-by-step explanation:

Exterior angle theorem - the sum of two interior angles (which in this case would be angle R and N) is equal to the measure of the exterior angle.

Answer:

C.

Step-by-step explanation:

Answer:

The correct answer is C.

Step-by-step explanation:

We have given some pattern in the series.

We need to find the next step which follows and continue the series.

We know that, we have three given patterns in the question. In the first we have given a pattern which is made by the joining of three dots, and in the second pattern made by the joining of five dots and in the third pattern made by the joining of the five dots.

In the following way, we can say that the next step in the series and fourth pattern follows same pattern as given in the above. That's why next pattern made by the joining of seven dots, but in the following given options next to next pattern is given which is joining by nine dots, therefore we choose option which is the next step in the series.

I think the answer is 32,2000cm^3

Answer: C

Step-by-step explanation: i got 100% on test

Answer:

The answer is the second option

Minimum = 203, Q1 =217, median = 230, Q3 = 245, maximum = 290

Step-by-step explanation:

First order the data from lowest to highest

203, 216, 217, 224, 224, 236, 245, 245 ,262 ,290

Minimun = 203

Maximum =290

Now divide the data in half

203, 216, 217, 224, 224,            236, 245, 245 ,262 ,290

Divide half of the first half of the data. The data of the medium is the first quartile

1) 203, 216, [217], 224, 224

                      Q1

Divide half of the second half of the data. The data of the medium is the third quartile

2)  236, 245, [245] ,262 ,290

                         Q3

The average between the two values that are in the center of the 10 ordered data is the median

203, 216, 217, 224,  [224, 236], 245, 245 ,262 ,290

[tex]Median =\frac{224+236}{2}=230[/tex]

Median=230

The answer is the second option

Minimum = 203, Q1 =217, median = 230, Q3 = 245, maximum = 290

Answer:

the answer is B :D

Step-by-step explanation: