use the quadratic formula to solve -5x^2-12x+8=0

Answers

Answer 1

[tex]\text{The quadratic formula:}\\\\ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\--------------------------------\\\text{We have}\ -5x^2-12x+8=0\\\\a=-5,\ b=-12,\ c=8\\\\\text{Substitute:}\\\\b^2-4ac=(-12)^2-4(-5)(8)=144+160=304\\\\\sqrt{b^2-4ac}=\sqrt{304}=\sqrt{16\cdot9}=\sqrt{16}\cdot\sqrt{19}=4\sqrt{19}\\\\x_1=\dfrac{-(-12)-4\sqrt{19}}{2(-5)}=\dfrac{12-4\sqrt{19}}{-10}=\boxed{-\dfrac{6-2\sqrt{19}}{5}}\\\\x_2=\dfrac{-(-12)+4\sqrt{19}}{2(-5)}=\dfrac{12+4\sqrt{19}}{-10}=\boxed{-\dfrac{6+2\sqrt{19}}{5}}[/tex]


Related Questions

which graph represents the function f(x)=0.25x+5

Answers

Answer:

Option D.

Step-by-step explanation:

Consider the given function

[tex]f(x)=0.25^x+5[/tex]

We need to find the graph of given function.

Substitute x=0 in the given function to find the y-intercept of the function.

[tex]f(0)=0.25^(0)+5[/tex]

[tex]f(0)=1+5[/tex]

[tex]f(0)=6[/tex]

So, y-intercept of the function is 6.

[tex](0.25)^x\rightarrow \infty[/tex] as [tex]x\rightarrow -\infty[/tex]

[tex](0.25)^x\rightarrow 0[/tex] as [tex]x\rightarrow \infty[/tex]

We can concluded that

[tex]f(x)\rightarrow \infty[/tex] as [tex]x\rightarrow -\infty[/tex]

[tex]f(x)\rightarrow 5[/tex] as [tex]x\rightarrow \infty[/tex]

Therefore, the correct option is D.

Answer:

D

Step-by-step explanation:

Solve for a in the equation a-17=42

Answers

Answer:

a = 59

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable (a). Add 17 to both sides

a - 17 = 42

a - 17 (+17) = 42 (+17)

a = 42 + 17

Simplify. Combine like terms

a = 42 + 17

a = 59

59 is your answer

~

Solve for a (this means they want you to get "a" by itself in the equation)

So:

a - 17 = 42     Add 17 on both sides to get "a" by itself

a - 17 + 17 = 42 + 17

a = 59

Someone help me on my question.

Answers

Answer:

C < A < B

Step-by-step explanation:


Answer:


Step-by-step explanation:The answer is C<A<B and the reason is is because angle A and C are the same and angle B is the largest.


Two parallel lines are crossed by a transversal . What is the value of k?

Answers

Answer:

k = 60

Step-by-step explanation:

2k + 11 is a same side corresponding angle, hence

2k + 11 = 131 ( vertically opposite angles )

subtract 11 from both sides

2k = 120 ( divide both sides by 2 )

k = 60


Answer:

Option C. k = 60

Step-by-step explanation:

There are two lines Z and Y and crossed by a transverse x.

We have to find the value of k.

Since opposite angle of ( 2k + 11 ) is corresponding angle of 131°

so opposite angle of ( 2k + 11 ) will be = (2k + 11)

and corresponding angles are equal in measure.

So 2k + 11 = 131

    2k = 131 - 11

   2k = 120

    k = 60

Option C k = 60 is the answer.

Tom knows that his school 10 out of every 85 students are left-handed. There are 391 students in Tom's school.

How many students in toms school are left-handed?
please show work if you help and i will mark as most BRAINLY THANK YOU GUYS!! ;)

Answers

I first divided 391 by 85 and got 4.6
then I multiplied 4.6 by 10 and got 46

so your and is 46

How do I factor quadratics?

Answers

Ok so factoring quadratics is fairly easy once you get the hang of it

So we have a quadratic [tex]x^2+x-2[/tex]

My first question would be what 2 numbers multiply to -2 and add to +1

the answer is 2 and -1

Second question what 2 values multiply to get [tex]x^2[/tex]

the answer x and x

your factored form would be [tex](x-1)(x+2)[/tex]

This is as far as i can explain there is a whole lot about quadratics to be learned. You have to ask your teacher on more information


If the sum of two numbers is 19 and their difference is 3. What are the two numbers?

Answers

Answer:

11 & 8

Step-by-step explanation:

11+8=19

11-8=3

Answer:

The answer is 8 and 11

Step-by-step explanation:

8 + 11 = 19

11 - 8 = 3

Bhavik bought 33 liters of milk and 55 loaves of bread for a total of \$11$11. A month later, he bought 44 liters of milk and 44 loaves of bread at the same prices, for a total of \$10$10. How much does a liter of milk cost, and how much does a loaf of bread cost?

Answers

Answer: The cost of 1 liter milk is $ 0.75  and the cost of a loaf of bread is $1.75

Step-by-step explanation:

Let the cost of one liter of milk  is m dollar and the cost of one loaf of bread is b dollar.

Since, the total cost of the 3 liter milk and 5 loaf of bread = $ 11

That is, 3 m + 5 b = 11   ----------(1)

And, the cost of the 4 liter of milk and 4 loaf of bread = $ 10

That is, 4 m + 4 b = 10 -----------(2)

4 × Equation (1),

12 m + 20 b = 44 -----------(3)

3 × Equation (2),

12 m + 12 b = 30 --------------(4)

Equation (3) - Equation (4),

We get, 8 b = 14

⇒ b = 14/8 = 1.75

 By putting the value of b in equation (1)

We get,

3 m = 11 - 1.75×5 ⇒ m = 2.25/3 = 0.75

Thus, the price of one liter of milk = $ 0.75

And, the price of one loaf = $ 1.75

Answer:

The cost of 1 liter milk is $ 0.75  and the cost of a loaf of bread is $1.75

Step-by-step explanation:

graph the solution set. please help

Answers

Answer:

In the attachment.

Step-by-step explanation:

Rewrite [tex]x\geq-3y-6[/tex] as a [tex]y\geq -\frac{1}{3}x-2[/tex]. Then mark each set with different color and take the intersection of these.

Jeramy took 6 hours to read 222 pages of his book. What is Jeramy’s reading speed

Answers

Answer:

37 pages/hour

Step-by-step explanation:

This is a unit rate problem.

You are trying to find the number of pages per hour.

Divide the number of pages by  the number of hours.

222 pages in 6 hours

(222 pages) / (6 hours) = 37 pages/hour

Answer:

37 pages/hour

Step-by-step explanation:

To find the reading speed, we take the pages read and divide by the time it took.

222 pages/ 6 hours

37 pages/hour

Salar's Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $3.50 each and he has $15.25 to spend, how many tickets can he buy?

Answers

Answer: 4 tickets


Step-by-step explanation: If $15.25 is Salar’s total and each ticket costs $3.50, we need to use division to figure out how many tickets Salar can purchase. When we divide 15.25/3.50, we get 4.35 (approximately). Salar can’t have .35 of a ticket, so we round down to 4 whole tickets.


To find out how many tickets Salar can buy, we would need to divide the money he has, for spending, by the cost of each ticket-first. This would look like:
[tex]15.25 \div 3.5[/tex]
Or
[tex]152.5 \div 35[/tex]
When simplified, the quotient (answer for a division problem) would be 4.357143.

4.357143 is not a whole number. Let's round it to nearest whole number: 4. After all, Salar can't exactly buy 4.357143 tickets. He would have to tear a ticket.

So, with $15.25, Salar can buy 4 tickets for the play.


You are working as an office apprentice for the bksb Newcastle Arena.




The arena is attempting to cut down on some of its running costs. Look at the table below that lists the costs for the previous five years.





Year Costs (£)
Year One 1.4 million
Year Two 1.6 million
Year Three 1.8 million
Year Four 2.5 million
Year Five 1.7 million





What is the mean amount of costs?

Answers

Answer:

Mean = £1.8 million


Step-by-step explanation:

The MEAN is the sum of all the numbers divided by the number of numbers.

There are 5 numbers in totalThe sum is [tex]1.4+1.6+1.8+2.5+1.7=9[/tex] million

Hence the mean is [tex]\frac{9}{5}=1.8[/tex] million

In a supermarket bin the number of packages of red to peppers to the number of packages of green peppers is in the ratio of 8 is to 13.The peppers are sold in 2 pound packages.What is the least possible weight of red peppers in the bin?

Answers

Answer:

16 pounds

Step-by-step explanation:

The ratio of no. of packages of red pepper to no. of packages of green pepper is given 8 is to 13.

So, atleast 8 packages of red pepper are sold

Therefore, least possible weight of red peppers in the bin = 2×8 = 16 pounds.


The least possible weight of red peppers in a supermarket bin with a ratio of 8 to 13 of red to green peppers, where each package weighs 2 pounds, is 16 pounds.

To find the least possible weight, we assume the smallest number of packages that maintain the ratio. Multiplying both numbers of the ratio by 2 pounds gives us the weight of the red and green peppers, but since we want the least possible weight of red peppers, we'll only calculate for red.

Therefore, if we have 8 packages of red peppers, each weighing 2 pounds, the calculation would be:

8 packages × 2 pounds/package = 16 pounds of red peppers

What is sin 60 degree

Answers

Answer: if talking square root, it is sqrt3/2. if talking decimals, it is about 0.87.


Answer:

Sine 60°= √3/2

=1.732/2

0.8660

Step-by-step explanation:

In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse).

From the triangle shown in the attachment

The sine of an angle =

Opposite/hypotenuse

Sine 60°= √3/2

=1.732/2

0.8660

Please help with this last question

Answers

The answer is the last one
2nd last choice is the ans
remember whenever the line is darkened its either greater than or equal to OR Less than and equal to

HELP I NEED THESE QUESTIONS ANSWERED BEFORE THERE DUE PLZ HELP!!!!!!!

Answers

Answer:

Please, see the answers in the attached files.

Step-by-step explanation:

Please, see the attached files.

Thanks.

which linear function represents a slope of 1/4

Answers

Answer: The second option represents a slope of 1/4

Step-by-step explanation:

To find slope, select two points along the line and plug them into this equation: (y2-y1)/(x2-x1)

We'll take the two points in the second graph and plug them into the equation above: (4-3)/(4-0)= 1/4

Therefore, the second option represents a slope of 1/4. Hope this helps:)

Answer:

(B) would be the best answer choice

Step-by-step explanation:

HURRY 30 POINTS! The diameter of mercury is approximately 4.9x10^3 kilometers. The diameter of Saturn is 1.2x10^5 kilometers. About how many times greater is the diameter of Saturn than the diameter of Mercury?

2.4
24
240
2400

Answers

Answer:

The answer is 2.4

Step-by-step explanation:

Divide 1.2x10^5 by 4.9x10^3 and you should get the answer of 2.44.

Hope this helps


Which of these sets of numbers contain all rational numbers?

A. π, 1/2, -13
B. -3.0541...,√99, 0.14363
C. -6, -√225, 4 7/8
D. √21, 0.75, 0

Answers

The answer is C, -6, -√225, 4 7/8.


Rational means that the number can be expressed as a fraction and integer numerators and denominators. -6 and 4 7/8 can clearly be expressed as a fraction. -6 can be expressed as -6/1 and 4 7/8 can be expressed as 39/8.

-√225 is equivalent to -15, which is rational.


A is wrong because the number includes Pi.

B is wrong because -3.0541 never ends and √99 is irrational.

D is wrong because √21 is also irrational.

Final answer:

The Set C.  -6, -√225, 4 7/8 is the only set that contains all rational numbers.

Explanation:

The set of rational numbers consists of numbers that can be expressed as a fraction of two integers. To determine which set of numbers contains all rational numbers, we need to check if all the numbers in each set can be expressed as a fraction.

In set A, only 1/2 is a rational number.

In set B, -3.0541... and 0.14363 can be expressed as fractions, but √99 cannot.

In set C, -6, -√225, and 4 7/8 can all be expressed as fractions.

In set D, √21 is not a rational number, while 0 and 0.75 are rational numbers.

Therefore, set C is the only set that contains all rational numbers.

Learn more about Rational numbers here:

https://brainly.com/question/24398433

#SPJ2

Mario made 6 batches of cookies. His friends asked him to make an extra batch. He used 15 3/4 cups of sugar and needs another 5/8 cup for the extra Batch. How many cups of sugar will Mario use altogether? Show work.

Answers

Answer:

57

Step-by-step explanation:

6x?=5/8x15 3/4

If p(x) is a cubic polynomial with zeros at -3,-1, and 2, and p(0)=6, find p(x).

Answers

Answer:

[tex]p(x)=-x^3-2x^2+5x+6.[/tex]

Step-by-step explanation:

If a cubic polynomial has zeros [tex]x_1,\ x_2,\ x_3,[/tex] then it has a form

[tex]p(x)=a(x-x_1)(x-x_2)(x-x_3).[/tex]

In your case, zeros are -3, -1 and  2, then the polynomial is

[tex]p(x)=a(x-(-3))(x-(-1))(x-2),\\ \\p(x)=a(x+3)(x+1)(x-2).[/tex]

If [tex]p(0)=6,[/tex] then

[tex]p(0)=a(0+3)(0+1)(0-2)=6,\\ \\-6a=6,\\ \\a=-1[/tex]

and

[tex]p(x)=-(x+3)(x+1)(x-2)=-x^3-2x^2+5x+6.[/tex]

PLZ HURRY
Which graph represents the function f(x) = 2|x|?

Answers

Answer:c

Step-by-step explanation:

Answer: Hey he got it right it's C

Step-by-step explanation:

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now.

Given that my age is an integer number of years, what is the smallest my age could be?

Answers

Answer: His smallest age could be 16 years.

Step-by-step explanation:

Since we have given that

Four-fifths of his current age is greater than three-quarters of his age one year from now.

Let his present age be x

So, According to question,

[tex]\frac{4}{5}x>\frac{3}{4}(x+1)[/tex]

Take the equality,

[tex]\frac{4}{5}x=\frac{3}{4}(x+1)\\\\\frac{4}{5}x=\frac{3}{4}x+\frac{3}{4}\\\\\frac{4}{5}x-\frac{3}{4}x=\frac{3}{4}\\\\\frac{16x-15x}{20}=\frac{3}{4}\\\\\frac{x}{20}=\frac{3}{4}\\\\x=\frac{3\times 20}{4}\\\\x=15[/tex]

So, [tex]x>15[/tex]

Hence, Nearest and smallest integer greater than 15 is 16 .

Therefore, His smallest age could be 16 years.

Answer:

Answer: His smallest age could be 16 years.

Step-by-step explanation:

Since we have given that

Four-fifths of his current age is greater than three-quarters of his age one year from now.

Let his present age be x

So, According to question,

Take the equality,

So,

Hence, Nearest and smallest integer greater than 15 is 16 .

Therefore, His smallest age could be 16 years.

Use slope formula to find the missing coordinate.

(r, 1) and (5, -7) Slope = 8/3

Answers

Answer:

r=8

Step-by-step explanation:

The formula for slope is

m = (y2-y1)/ (x2-x1)

Substitute in what we know.

8/3 = (-7-1)/(5-r)

Simplify

8/3 = -8/(5-r)

We can use cross products to help us solve.

8 * (5-r) = 3 * (-8)

divide each side by 8

8/8 * (5-r) = 3 * (-8)/8

5-r = -3

Subtract 5 from each side

5-r-5 = -3-5

-r = -8

Multiply by -1

r = 8

Am I right?
I want to know if I am right

Answers

Answer:

B $13

Step-by-step explanation:

Julie has 16.73  That is approximately 17 dollars

She buys a purse that is 4.12.   That is approximately 4 dollars

17 -4 = 13

She will have approximately 13 dollars left

No the answer to your question is B $13

Help!!!! (Must be done in 30 mins)

Answers

Answer:

w=-4

Step-by-step explanation:

w-20=6w

-20=5w

-4=w

I need help with this question quickly please! Show steps!

Answers

Answer:

A y = -x+2

Step-by-step explanation:

To find the slope of the line m we use the formula

slope = (y2-y1)/(x2-x1)

         = (-9--7)/(4-2)

         = (-9+7)/(4-2)

        = -2/2

        = -1

When lines are parallel, the slopes are the same.  We need to find a line with slope of -1

y = -1x+2 is written in the form y =mx+b where m is the slope

m=-1  so the slope is -1

This line has the same slope so it is parallel to the line above.


Answer:

would be A

Step-by-step explanation:

SLOPE HAS TO BE -1

if x - 4 , x + 2 and 3x + 6 form a geometric sequence, find x.

Answers

Answer:

x =7

Step-by-step explanation:

Remark

A geometric sequence always has terms that are separated by a common ratio. For example 3 9 27 81 243 .... Each term is multiplied by a common number and the term before it. In this case the common term is 3. To get the next term after 9, you multiply 9 by 3.To get the common ratio divide the second term by the first and then the third term by the second

Equation

(x + 2)/(x - 4) = (3x + 6)/ (x + 2)

Solution

I would begin this problem by taking out the common factor on the top right term. You'll see why in a second.

(x + 2)/(x - 4) = 3(x + 2)/ (x + 2)   Notice the two binomials on the right cancel.

(x + 2)/(x - 4) = 3/1                       Cross multiply(x + 2)*1 = 3*(x - 4)                       Remove the brackets on the right.x + 2 = 3x - 12                             Add 12 on both sides.x + 2 + 12 = 3x - 12 + 12              Simplifyx + 14 = 3x                                  Subtract x from both sides14 = 3x - x2x = 14                                        Divide by 2x = 14/2x = 7

Which system of inequalities is shown? A.y2 B.yx y<2 D.y>x y>2

Answers

Answer: y > x, y > 2

The horizontal line goes through 2 on the y axis. This boundary line is represented by the equation y = 2, since every point on this line has a y coord of 2. The shading above it means that the inequality is y > 2. Every point in the shaded region of y > 2 has a y coord that is larger than 2.

The other inequality is y > x because we shade above the dashed boundary line y = x, which is that slanted dashed line.

Combining the two regions of y > 2 and y > x leads to what is shown.

Final answer:

The question regarding systems of inequalities is incomplete, but linear inequalities like y < x or y > 2 can be graphically represented. The same is true for linear equations, with options A, B, and C all depicting linear forms.

Explanation:

The question which system of inequalities is shown seems to be missing some context or parts, but in general, inequalities can be represented on a graph and used to describe the relationship between variables. When dealing with linear inequalities, such as y < x or y > 2, these can be shown graphically with a line dividing the plane into two regions: one where the inequality is true and the other where it is false. For instance, y < x would be represented by a line that slopes upward to the right, and the region below this line (where y is less than x) is shaded. Similarly, for y > 2, a horizontal line is drawn at y=2, and the area above this line is shaded, indicating where y is greater than 2.

When looking at linear equations, all the options A. y = -3x, B. y = 0.2 + 0.74x, and C. y = -9.4 - 2x are indeed linear, as they can all be written in the form y = mx + b, where m and b are real numbers and represent the slope and y-intercept of the line, respectively.

What does this symbol “ mean in math

Answers

I think, it's the symbol of the inches.

3" = 3 inches

or it's the second derivative of the function

[tex]\dfrac{d^2y}{dx^2}=f''(x)[/tex]

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