Mathematics High School

What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth?

x ≈ −3.23 and x ≈ 0.23
x ≈ −2.72 and x ≈ −0.28
x ≈ 0.28 and x ≈ 2.72
x ≈ −0.23 and x ≈ 3.23

Answers

Answer 1
First 
[tex] 4x^{2} + 12x + 3 = 0 [/tex]
determine if this equation were factorable, it's not for this one
so I use quadratic formula, try to search the formula online

[tex]x1 = \frac{-12 + \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 + 4\sqrt{6} }{8} = \frac{4(-3 + \sqrt{6}) }{8} = \frac{-3 + \sqrt{6}}{2} = - 0.28[/tex]
[tex]x2 = \frac{-12 - \sqrt{(12)^{2} - 4*4*3} } {2*4} = \frac{-12 - 4\sqrt{6} }{8} = \frac{4(-3 - \sqrt{6}) }{8} = \frac{-3 - \sqrt{6}}{2} = - 2.72[/tex]

x ≈ −2.72 and x ≈ −0.28 is the solution

Related Questions

SOS!!
In your own words explain the difference between the following two expressions:
(-1)^2/4 and (-1)^1/2

Answers

The only difference between the two following expressions is their exponent though it’s equal. If you would analyze carefully, the two expressions are equal since 2/4 is just equal to ½. The two expressions are equal in value so the presentation of the exponent is their only difference.

since my uncles farmyard appears to be overrun with dogs and chickens. i asked him how many of each he had. he responded that his dogs and chickens had a total of 148 legs and 60 heads. how many dogs and chickens are there on my uncles farm?

Answers

Assuming that all the animals are dogs, the number of legs there are would be 240.
60*4=240 legs
240-148=92 legs
All the 92 legs belong to the chickens, so there are 46 chickens.
Since there are 46 chickens,
60-46=14 dogs
Final answer:

There are 14 dogs and 46 chickens on your uncle's farm.

Explanation:

To solve this problem, we can set up a system of equations. Let x be the number of dogs and y be the number of chickens on your uncle's farm.

The number of legs equation can be written as: 4x + 2y = 148 (since dogs have 4 legs and chickens have 2 legs).

The number of heads equation can be written as: x + y = 60 (since both dogs and chickens have 1 head).

We can solve this system of equations by substitution or elimination. Let's use elimination:

Multiplying the second equation by 2, we get 2x + 2y = 120.

Subtracting the new equation from the first equation, we can eliminate the 2y term: (4x + 2y) - (2x + 2y) = 148 - 120. Simplifying, we have 2x = 28.

Dividing both sides of the equation by 2, we find that x = 14. Substituting this value back into the second equation, we find that 14 + y = 60. Solving for y, we get y = 46.

Therefore, there are 14 dogs and 46 chickens on your uncle's farm.

write y=(-3/4)x+3 in standard form using integers.
Please help:D will fan and medal

Answers

To make all the values integers, that means we need to remove any fractions. The x variable is multiplied by "-3/4." To make it an integer, multiply both sides of the equation by 4. Therefore,  
4y = -3x + 12  
To check your work, you can divide both sides by 4 and see that -3x/4 = (-3/4)x and 12/4 = 3.

Write true or false. The figure has rotational symmetry

Answers

true although it looks irregular but if it is regular this statement is true

this problem is true

TRIANGLE GEOMETRY PLEASE HELP

Answers

The altitude is the mean proportional between the left and right parts of the hyptenuse

#13

12/z = z/3
z² = 36
z = 6

By the Pythagorean theorem:
x = √(12²+6²) = √(144+36) = √180 = 6√5
y = √(3²+6²) = √(9+36) = √45 = 3√5

The answers are x=6√5, y=3√5, z=6

#14

2/y = y/6
y² = 12
y = √12 = 2√3

By the Pythagorean theorem:
x = √((√12)²+6²) = √(12+36) = √48 = 4√3


The answers are x=4√3, y=2√3

Consider △DFE. What are the inputs or outputs of the following trigonometric ratios? Express the ratios in simplest terms.

sin(?) = 4/5
cos(F) = ?
tan(D) = ?

Answers

Answer:
sin F = 4/5
cos F = 3/5
tan D = 3/4

Explanation:
First, we have sin an angle = 4/5
In a right-angled triangle:
sin theta = opposite / hypotenuse
This means that in triangle DFE:
The hypotenuse = 5 units
one of the sides = 4 units
Use Pythagoren theorem to get the other side as follows:
hypotenuse^2 = side1^2 + side2^2
5^2 = 4^2 + side2^2
side2^2 = 9
The second side of the triangle = 3 units

The special trig functions are as follows:
sin theta = opposite / hypotenuse
cos theta = adjacent / hypotenuse
tan theta = opposite / adjacent

From the attached figure and based on the calculations above:
sin F = 4/5
cos F = 3/5
tan D = 3/4

Hope this helps :)

Answer:

Sin(F)=4/5

Cos(F)=3/5

Tan(D)=3/4

Step-by-step explanation:

A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.



What is the maximum area that can be enclosed by the fencing?

Enter your answer in the box.


ft²

























Answers

Let x represent the length of the side of the pen that is parallel to the barn. Then the area (y) will be
.. y = x(300 -x)/2
This describes a downward opening parabola with zeros at x=0 and x=300. The vertex (maximum) will be found at the value of x that is halfway between those, x = 150.

For that value of x, the pen area is
.. y = 150(300 -150)/2 = 150^2/2 = 11,250 . . . . . square feet.

Answer:

11250ft2

Step-by-step explanation:

i took the test to make sure the other guy was right

simpliy completely 4m^3/3m^2n * 9n^2/30m^2n^2
2n / 3 m

2 m / 5 n

2 / 3 m n

2 5 m n

Answers

Hey there!

(KEY POINT HERE) 

[tex]\searrow\searrow\searrow\searrow\searrow\searrow\searrow\searrow\searrow\searrow \ \swarrow\swarrow\swarrow\swarrow\swarrow\swarrow\swarrow\swarrow\swarrow \\ \\ \boxed{(((((4* \frac{(M^3)}{3} *(m^2))*n)*9)* \frac{n^2}{30} *m^2)*n^2}[/tex]

Now that we have considered that equation above, we would now understand what is clear to be your (correct answer).

Your correct answer to this question listed above would be (option B).

[tex]\boxed{\boxed{2 m / 5 n}}[/tex]

I hope this helps you!
the answer is 2/5mn

see attached picture for steps:

I need help with this question

Answers

Which one? Is it both or just one
#3

5/20 = 1/4

260 * 1/4 = 65

C. 65 is the correct answer.

#4

45% = 0.45

1,300 * 0.45 = 585

B. 585 is the correct answer.

write the number in scientific notation
0.0000024

please help

Answers

2.4 x [tex] 10^{-6} [/tex]
Hello there! I can help you! The number shows is 24 ten millionths. It is in decimal form, so the exponent for the power of 10 will definitely be negative. The first number has to be greater than or equal to 1, but less than 10. If we look at this number and you place the decimal between the 2 and the 4, we can use 2.4 as the front number, because it's greater than 1, but less than 10. Now, we can move that decimal to the left a certan number of times to get that number shown below. If you count from the decimal, you move to the left 6 times. That makes the power of ten 10^-6. And when you multiply 2.4 * 10^-6 (0.000001), you get 0.0000024. There. The number in scientific notation is 2.4 * 10^-6.

What are the roots of the polynomial equation? x^2−12x−64=0

Answers

Final answer:

The roots of the polynomial equation x²−12x−64=0 are 16 and -4. These roots are calculated using the quadratic formula and represent the points where the function intersects the x-axis. The importance of finding real roots in quadratic equations is significant in solving real-world problems.

Explanation:

Roots of Polynomial Equation

The roots or solutions of the polynomial equation x²−12x−64=0 can be calculated using quadratic formula. In general, the quadratic function is written as ax²+bx+c=0 and its roots are given by -b ± √(b² - 4ac) / 2a. In this case, a=1, b=-12 and c=-64.

Applying those values into the formula we get 12 ± √((-12)² - 4(1)(-64)) / 2(1) = 12 ± √(144 + 256) / 2 = 12 ± √400 / 2 = 12 ± 20 / 2. This gives us two possible roots: 16 and -4.

Graphically, these roots represent the x coordinates or points where the quadratic function intersects the x-axis on a two-dimensional graph. It is important to note that quadratic equations constructed on physical data always have real roots, which are important for solving real-world problems.

Learn more about Quadratic Equations here:

https://brainly.com/question/30098550

#SPJ12

The total​ cost, after using a 55cents​-off ​coupon, is ​$3.30. If c represents the cost of the fruit in dollars per​ pound, what equation could you use to find the value of​ c?

Answers

T= total cost= $3.30
c= cost of fruit per pound
x= # of pounds of fruit purchased

EQUATION
T= (c)(x) - $0.55 coupon

to find c, substitute $3.30 total for T
$3.30= cx - $0.55
add $0.55 to both sides
$3.85= cx
divide both sides by x
$3.85/x= c

Hope this helps! :)


If a cylinder has a surface area of 59 square inches and its radius
is 2.1 inches, how tall is the cylinder in inches?
Round to the nearest tenth.

Answers

123.9 inches i think
_______________________________________________________________

Answer:

5.8

Step-by-step explanation:

Bryan's puppy has been gaining weight for the last year. The graph shows data about the puppy's weight over time.

Answers

I would say 25 pounds because the graph displays a proportional relationship( a straight line) so the next point in the line would be 25 pounds.
I hope this helped! :-)

Answer:

Option 2. 25 pounds

Step-by-step explanation:

As per graph weight gain of Bryan's puppy is represented by a linear function which is a straight line.

Therefore equation of the line will be y = mx + c

to calculate the value of m we will take two points (endpoints) on the line (0, 0) and (50, 6)

So m = (50-0)/(6-0) = 50/6 = 8.33

since this passes through (0, 0) so c = 0

Equation will be y = 8.33x

Now we have to get the value of y (weigh of puppy) at x = 3.

y = 8.33×3 = 24.99 ≈ 25 lb.

Option 2 is the answer.

Factor by grouping 5x^2 -40x + 3x +24

Answers

add -40x and 3x to get -37x
5x² - 37x + 24 is your Answer

Fill in the table, then graph f(x)=-2x-4

Answers

The attached graph shows a table. If it doesn't have your values, it is because you didn't share them with us.

A tree has 53 leaves. During a storm, it loses 29 leaves. How many leaves does the tree have left?

29 leaves

24 leaves

82 leaves

42 leaves

Answers

the answer would be 24 because 53-29=24

helpppppppppppppppppppppppppppppppp

Answers

The equation is [tex]y=(x-7)^2+7[/tex].

We are looking for a function with a vertex above the x-axis and a function that opens upward (has coefficient a > 0).

The first function opens downward and intersects the x-axis. The second function has a vertex below the x-axis. The third function satisfies our requirements. The fourth function has a vertex on the x-axis.

We can solve this algebraically with the knowledge that the real solutions of a quadratic are its x-intercepts. If there are no x-intercepts (because it lies entirely above or below the x-axis), then there are no real solutions. This is true when the discriminant [tex]b^2-4ac \ \textless \ 0[/tex]. You can see that from the quadratic formula. This holds true for both answers A and C, so to find the correct one, we remember that when the coefficient a of the [tex]x^2[/tex] term is positive, the graph opens upwards, so we choose C.
Answer:
choice c is the correct one

Explanation:
The equation that lies completely above the x-axis should be the one having its y-values greater than zero.

squaring a number will certainly give a positive value.
looking at the choices:
choice a: might give a -ve value if the squaring gives a number greater than 7
choice b: might give a -ve value if the squaring gives a number less than 7
choice c: will always be positive
choice d: might give a zero at x=7

Explain how employee benefits affect total employment compensation

Answers

Final answer:

Employee benefits, such as health insurance and retirement plans, add value to the total compensation received by workers. They account for about one-quarter of average hourly compensation, contributing to the overall attractiveness of the compensation package and promoting employee well-being and job satisfaction.

Explanation:

Employee benefits affect total employment compensation by adding to the overall value of the compensation package. They provide additional forms of remuneration beyond wages and salaries, such as health insurance, retirement plans, employer payments to Social Security, unemployment and worker's compensation insurance, and other benefits like Medicare.

These benefits contribute to the total compensation received by workers, accounting for about one-quarter of the average hourly compensation. So, for example, if a worker's wages are $20 per hour, the total compensation per hour might be around $26 when considering the value of benefits.

By providing employee benefits, employers aim to attract and retain talented employees, promote employee well-being, and enhance job satisfaction and productivity. These benefits play a crucial role in improving the overall compensation package and incentivizing employees to stay with the company.

Final answer:

Employee benefits, such as health insurance and retirement plans, greatly impact total employment compensation. These benefits, in addition to wages and salaries, make up the overall compensation received by workers.

Explanation:

Employee benefits have a significant impact on total employment compensation. These benefits include things like health insurance, retirement plans, employer payments to Social Security, and unemployment and worker's compensation insurance. When these benefits are added to wages and salaries, they make up the total compensation received by workers.

For example, if a worker's hourly wage is $20 and they receive $5 per hour in benefits, their total compensation per hour is $25. This means that employee benefits increase the overall value of compensation that workers receive.

Employee benefits are important for attracting and retaining employees, as well as promoting employee well-being and job satisfaction. They can also have an impact on the cost of labor for employers, as they must budget for these benefits in addition to wages and salaries.

What is the quotient of 22,389 and 13?

Answers

1,722.23077. If I am correct, because 22,389 divided by 13 is 1,722.23077.

Answer:1,722 R3

Step-by-step explanation:

The sum of the deviations about the mean always equals _________.

Answers

it always equal 0 
hope this helps :)                                                            

Final answer:

The sum of the deviations about the mean always equals zero because positive and negative deviations cancel out. This concept is essential for calculating variance and standard deviation in statistics.

Explanation:

The sum of the deviations about the mean always equals zero. When analysing a set of data, each data value has a deviation from the mean, which is the difference between the value and the mean. These deviations illustrate the spread of the data around the mean. Positive deviations occur when a data value is greater than the mean, while negative deviations occur when a data value is less than the mean.

If we sum all the deviations, the positive and negative values will cancel each other out, resulting in a sum of zero. This happens because the mean is the point where the total amount above it is equal to the total amount below it. This concept is core to understanding the calculation of other statistics such as variance and standard deviation, which provide measures of data spread. Variance is the mean of the squared deviations from the mean, and the standard deviation is the square root of the variance.

The fact that the sum of deviations equals zero is important when working with the Central Limit Theorem, as it assures that the mean of sample means will equal the population mean, assuming the sample size is sufficiently large.

Minimun commun multiple of 1,2,3,8

Answers

1
2
3
2*4(from here we take only 4 because 2 is already there)

1*2*3*4=24
Minumum Common Multiple is also the Least Common Multiple
List out multiples

1.) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, etc
2.) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, etc
3.) 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. etc
8.) 16, 24, 32, etc

The LCM is 24
or
The Minimum Common Multiple is 24

Use the graphing calculator to locate the solutions of this system of equations: y = x2 + x – 2 y = –x + 1

Answers

Answer:

(–3, 4) and (1,0)

Step-by-step explanation:

Answer:

(-3,4) and (1,0)

Step-by-step explanation:

Sorbet is a frozen dessert that is often made from fruit. how many portions each weighing 1/10 of a kilogram can a french dessert chef create from 3 kilograms of sorbet

Answers

To know how many servings can be done what we should do in this case is to divide the total amount of kilograms of sorbet between the amount of each of the servings.
 We then have to do the division:
 N = (3) / (1/10)
 N = 30
 Answer: 
 a french dessert chef can create 30 portions each weighing 1/10 of a kilogram from 3 kilograms of sorbet

Final answer:

A French dessert chef can make 30 portions of sorbet from 3 kilograms, with each portion weighing 1/10 of a kilogram, by simply dividing the total weight by the weight of one portion.

Explanation:

The subject of this question is Mathematics, specifically related to division and units of measurement. To find out how many portions each weighing 1/10 of a kilogram can be made from 3 kilograms of sorbet, we divide the total amount of sorbet by the weight of one portion. Therefore, we perform the division:

Determine the weight of one portion: 1/10 kg.

Divide the total weight of sorbet by the weight of one portion: 3 kg ÷ (1/10 kg).

The division gives us the result of 30 portions because 3 ÷ (1/10) is equivalent to 3 × 10.

So, a French dessert chef can create 30 portions of sorbet, with each portion weighing 1/10 of a kilogram.

Please answer!!! 1st one to answer with work and accurate answers will be brainliest for 30 points!!!!!!!!!!!!

Answers

Find the decimal equivalent of 2 1/3
2 1/3 = 7/3 = 2.333333

(4x + 9)/ 2.333333 = 3x / 0.5 Now cross multiply
0.5 * (4x + 9) = 3x * 2.333333
2x + 4.5 = 7x Transfer 2x to the right side.
4.5 = 5x
x = 4.5/5
x = 0.9

We'd best check this one
Left hand side.
(4x + 9)/2.333333
(4*0.9 + 9)/2.333333
(3.6 + 9)/2.333333
12.6/2.333333
5.4

Right hand side
3x/0.5
= 3*0.9/0.5
= 2.7/0.5
= 5.4

And it checks.

helppppppppppppppppp

Answers

For this case, the first thing you should do is rewrite the function taking into account the properties of the logarithm.
 Then take out common factor of the terms that allow it.
 Finally you must clear the value of n to find the solution.
 Answer:
 n = 1
 See attached image.

Answer: I think its 5/9

Step-by-step explanation:

Amy notices that her credit card company has charged too high an interest rate for delayed payment this month. Which law protects her from this issue?
Fair Debt Collection Practices Act

Identity Theft and Assumption Deterrence Act

Magnuson-Moss Warranty Act

Fair Credit Reporting Act Credit Card

Accountability, Responsibility and Disclosure Act

Answers

The Law that protects Amy from this issue is the Fair Debt Collection Practices Act. This law was enforced by The Federal Trade Commission (FTC) in order to prohibit the debt collectors from collecting abusively and unfairly from the consumers and also prohibits the use of deceptive practices

E:Credit Card Accountability, Responsibility and Disclosure Act

Brianna bought an assortment of 16 apples. A medium-sized apple weighs around 5.2 ounces. Which response gives the best estimate for the cost of the apples?

Answers

16 apples• 5.2 ounces/1 apple•1 pound/16 ounces•$1.29/1pound =6.71=7.00

Answer:

$7.00

Step-by-step explanation:

16 apples ⋅ 5.2 ounces1 apple ⋅ 1 pound16 ounces ⋅ $1.291 pound ≈ $7.00

Russel throws a soda from the balcony of his house to his friend Jones in the pool. If the soda is released 20 feet from the ground, and is thrown with a downward velocity of 2 ft/s, how long till the soda hits the pool, ignoring air resitance? Use the formula , where h is the height of the soda in feet and t is the time in seconds since Russel threw it. Round your answer to the nearest tenth.

A. 0.5 seconds B. 0.8 seconds C. 1.1 second D. 1.6 seconds

Answers

Using the formula S = ut +1/2at²
S=h= 20ft, u = 2ft/s, and a = 10m/s²
Thus; 20 =2t + 20t²
Therefore; 20t²+2t-20=0
Solving the equation quadratically for the value of t,
we get; t = 1.057 or t=-1.182
But t can not be negative,
 Therefore, t= 1.1 seconds (to the nearest tenth)


Answer:

C. 1.1 seconds

Step-by-step explanation:

The formula to use is :

[tex]h=ut+\frac{1}{2}at^{2}[/tex]

Where: h is the height of 20 ft, u is the velocity of 2ft/s and a is the gravitational acceleration of 9.8m/s². The acceleration should be converted to ft/sec² to simplify calculations. The value is then 32.15ft/sec².

Substituting these values into the equation:

[tex]20=2t+0.5*32.15t^{2} \\20=2t+16.075t^{2} \\0=16.075t^{2}+2t-20[/tex]

Using the quadratic formula, t can be solved.

a = 16.075, b = 2, c = -20:

[tex]t=\frac{-b+-\sqrt{b^{2}-4ac} }{2a} \\t=\frac{-2+-\sqrt{2^{2}-4(16.075)(-20)} }{2(16.075)}\\t=\frac{-2+-35.92}{32.15}\\t=1.055 \\OR\\t=-1.179[/tex]

The answer cannot be negative, therefore the answer is t = 1.055 ≈ 1.1seconds

WILL GIVE A BRAINLEST

What is the value of [-1.1]
–2
–1
0
1

Answers

Final answer:

If the brackets in the expression “[-1.1]” are interpreted as the floor function, the value is “-2”, because the floor function always rounds a number down to the closest lesser whole number.

Explanation:

The question appears to be asking for the value of the mathematical expression “[-1.1]”. However, the notation is a bit unclear. If the brackets denote the floor function, which rounds a number down to the nearest whole number, then the value of “[-1.1]” is indeed “-2” because -1.1 is rounded down to -2.

The floor function basically chops off all decimal points and moves a number to the next lower integer if it's not already an integer. Hence, the correct answer based on the interpretation of the floor function is “-2”.

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