Answers
The solutions to the given quadratic equation are as follows:
x = 1.10, x = 10.9.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation in item D is:
-x² + 12x - 12 = 0
x² - 12x + 12 = 0
Hence the coefficients are:
a = 1, b = -12, c = 12.
Then the solutions to the equation are found as follows:
Delta = (-12)² - 4 x 1 x 12 = 96x1 = 0.5(12 + sqrt(96)) = 10.9x2 = 0.5(12 - sqrt(96)) = 1.10The solutions are:
x = 1.10, x = 10.9.
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Related Questions
Determine the area between the curves by integrating over the x-axis or y-axis.
x=y^2
x=-|y|+12
Answers
When [tex]y\ge0[/tex] (above and on the [tex]x[/tex]-axis), we have [tex]|y|=y[/tex]. The parabola [tex]x=y^2[/tex] intersects with [tex]x=-|y|+12[/tex] in this region when
[tex]y^2 = -y + 12 \implies y^2 + y - 12 = (y-3)(y+4) = 0 \implies y=3[/tex]
On the other hand, when [tex]y<0[/tex] (below the [tex]x[/tex]-axis, we have [tex]|y|=-y[/tex], and so the curves intersect when
[tex]y^2 = -(-y) + 12 \implies y^2 - y - 12 = (y - 4)(y+3) = 0 \implies y=-3[/tex]
The area between the curves is then given by the definite integral,
[tex]\displaystyle \int_{-3}^3 (-|y| + 12) - y^2 \, dy[/tex]
The integrand is symmetric about the [tex]x[/tex]-axis, so the integral is equivalent to
[tex]\displaystyle 2\int_0^3 12 - y - y^2 \, dy = 2 \left(12y - \frac{y^2}2 - \frac{y^3}3\right)\bigg|_0^3 = \boxed{45}[/tex]
о
О A. y< x
у>4
О B. y< x
y<4
( C. y> x
у>4
о D. y> x
y<4
-5
5
5
Answers
Answer:
b
Step-by-step explanation:
B
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y,z)=x2 y2 z2; 3x 4y−3z=34
Answers
The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).
An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.
A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.
predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.
By lagranier multi plur
of = hog
(2x, is, 22>= 25-47
8x=42
10x + 2 = 42
2
28
2x=4, 4= 2
=2
722 (4)
(4.9,2) = (4.2-8)
(4,2-8)= 84
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SinA=√1-x÷√1+X
Find the value of cosA
Answers
The value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
Trigonometric ratios
It is important to note that
sin A = opposite/ hypotenuse
cos A = adjacent/ hypotenuse
Then,
opposite = [tex]\sqrt{1} - x[/tex]
Hypotenuse = [tex]\sqrt{1} + x[/tex]
Let's find the adjacent side using the Pythagorean theroem
[tex](\sqrt{1} + x)^2 = (\sqrt{1 -x } )^2 + x^2[/tex]
[tex]1 + x^2 = 1 - x^2 + x^2[/tex]
[tex]x = \sqrt{\frac{1 + x^2}{1 -x^2} }[/tex]
cos A = x/hypotenuse
[tex]cos A = \frac{\sqrt{\frac{1+x^2}{1 -x^2} } }{\sqrt{1} +x}[/tex]
cos A = √(1 + x²)/ (1 - x²) /√1 + x
Thus, the value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
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What is equivalent to x^3y^-7
Answers
Answer: [tex]\displaystyle\\\frac{x^3}{y^7}[/tex].
Step-by-step explanation:
[tex]\displaystyle\\x^3y^{-7}=\frac{x^3}{y^7} .[/tex]
What is the slope of the line that passes through the points (-5,7) and (-2,4)?
Answers
Answer:
m = -x
Step-by-step explanation:
Helppppppp show the steps to your answer
Answers
The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.
How to find the numeric value of an expression?The numeric value of an expression is found replacing each letter by it's attributed value.
In this problem, the expression is:
-a² - 2bc - |c|
The attributed values are:
a = -3, b = -5 and c = 2
Hence the numeric value will be given by:
-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.
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What is the volume of a square pyramid that is 8 feet tall with base edges of 3 feet?
8 ft
3 ft
3 ft
Answers
Explanation :
You can find the volume of a regular square pyramid using the formula volume = base area × height / 3. Hope it helps.
Ujarak has 100mL t of a strong toothpaste with a 1.1% concentration of sodium fluoride. They have a weaker toothpaste with a 0.3% concentration of sodium fluoride.
What volume, in milliliters, of the weaker toothpaste would Ujarak need to add to the strong toothpaste to create a blend with a 0.8% concentration of sodium fluoride?
Answers
The volume of the 0.3% concentration of sodium fluoride required to mix with 100mL of a strong toothpaste with a 1.1% concentration of sodium fluoride to create a blend with a 0.8% concentration of sodium fluoride is 60 mL.
What are mixtures?Mixtures refers to substances which are composed of two or more substances physically combined together.
The 1.1% concentration of sodium fluoride will form a mixture with the 0.3% concentration sodium fluoride.
Let the volume of the 0.3 % concentration toothpaste required be x.
Final volume of toothpaste = (100 + x) mL
Amount of mixture = 0.8 * (100 + x)
100 ml * 1.1 + x * 0.3 = 0.8 * (100 + x)
solving for x
110 + 0.3x = 80 + 0.8x
110 - 80 = 0.8x - 0.3x
30 = 0.5x
x = 60
Therefore, 60 mL of the 0.3% concentration of sodium fluoride is required.
In conclusion, the volume of the weaker solution of the sodium fluoride solution required is obtained from the method of mixtures.
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What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, increases in value. As x increases in value, decreases in value. B. As x decreases in value, increases in value. As x increases in value, increases in value. C. As x decreases in value, decreases in value. As x increases in value, increases in value. D. As x decreases in value, decreases in value. As x increases in value, decreases in value.
Answers
The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
Which method can be used to find the end behavior of the graph?The given coordinates on the graph are;
(-3, 0), (0, 3), (2, 4), and (5, 5)
The coordinates of the starting point of the graph = (-3, 0)
Shape of the graph = Extends from point (-3, 0), upwards and to the right
Therefore;
As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.
However, given that the graph is for a square root function, the correct option is option C;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
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help pls with math lotsss of points!!!
Answers
Answer:
5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2)
Step-by-step explanation:
In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:
x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)
x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)
Now that you have factored out the two quadratics, plug them into the equation.
5x - 3
(x+4)(x+2) (x+5)(x+2)
Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.
5x (x+5) - 3(x+4)
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:
5x^2+25x - (3x+12) = 5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
The circumference of the great circle of a hemisphere is 19π inches. Which statements about the hemisphere are true? Check all that apply. (Use 3.14 for π and round answers to the nearest tenth, if necessary. Recall that the formula for the surface area of a hemisphere is S = 3πr2 and the formula for the circumference of the great circle is C = πd.)
Answers
The radius of the hemisphere is 9.5 inches.
The diameter of the hemisphere is 19 inches.
The surface area of the hemisphere is 850.2 inches²
How to find the surface area of an hemisphere?circumference of a circle = 2πr
where
r = radiusTherefore,
19π = 2πr
2r = 19
r = 19 / 2
r = 9.5 inches
diameter = 9.5 × 2 = 19 inches
Therefore,
surface area of an hemisphere = 3πr²
surface area of an hemisphere = 3 × 3.14 × 9.5²
surface area of an hemisphere = 850.155 inches²
surface area of an hemisphere = 850.2 inches²
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Of all the numbers whose difference is 10, find the two that have the minimum product
Answers
Answer: -9
Step-by-step explanation: You might think that the smallest two numbers are 11 and 1 but there are negative numbers. 1 - (-9) is equal to 10. 1 x (-9) is -9.
GEOMETRY STUFF!! PLSS HELPP, NEED ANSWERS AND SOLUTIONS RN!!
Answers
Applying the angle bisector and triangle proportionality theorem, the solutions are:
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6.
What is the Angle Bisector Theorem?The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.
16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]
Cross multiply
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² - 3x² + 3x - 4 + 6x = 0
-2x² + 9x - 4 = 0
Factorize -2x² + 9x - 4
(−2x + 1)(x − 4)
-2x = -1
x = 1/2
or
x = 4
17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)
(2x + 2)(2x + 2) = (4x - 2)(x + 3)
4x² + 8x + 4 = 4x² + 10x - 6
Combine like terms
4x² - 4x² + 8x - 10x = -4 - 6
-2x = -10
x = -10/-2
x = 5
18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
Expand
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize x² - 5x - 6 = 0
(x+1)(x−6) = 0
x = −1 or x = 6
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A plane travels 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. when a tailwind is present, the plane’s speed increases by x kilometers per hour. the time it takes the plane to travel the same distance with the tailwind, t(x), is defined by the function . what is the meaning of the y-intercept for this function? the time it takes the plane to travel without the tailwind the speed of the plane when there is no tailwind present the minimum amount of time it takes the plane to travel 2,000 km the time it takes the plane to travel when the speed is decreased by 900 kph
Answers
The meaning of the y-intercept exists in the time required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. [tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
What is the meaning of the y-intercept for the function[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]?The time it takes the plane to travel 2,000 kilometers with the tailwind, t(x), exists determined by the function
[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]
where x exists the increase in speed when the plane travels with the wind (tailwind).
The y-intercept exists at x=0, then
[tex]$&t(0)=\frac{2,000}{900}+x \\[/tex]
[tex]$&t(0)=\frac{20}{9}=2 \frac{2}{9}[/tex] hours
[tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
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A train traveled 1/5 of the distance between two cities in ¾ hour. at this rate, how many hours will it take the train to travel the entire distance between these two cities?
Answers
Answer:
3 3/4 hour
Step-by-step explanation:
(3/4) ÷ (1/5) = (3*5) / (4*1)
= 15/4 hour
15/4 = 12/4 + 3/4 = 3 + 3/4 hour
= 3 3/4 hour
Find the largest 4-digit number which is a perfect square.
Answers
Answer:
To find the biggest 4-digit number which is a perfect square, we have to take the square of biggest 2-digit number. ∴ The biggest 4-digit number which is a perfect square = 9801.
Step-by-step explanation:
mark as brainlest answerAnswer:
9801
Step-by-step explanation:
well we know 100 squared is the first 5 digit square number so it must be 99 squared, which is 9801
Name the rule for this sequence.
27, 21, 15, 9, 3,...
A) divide the previous term by 0.06
B) divide the previous term by 0.6
C) add 6 from the previous term
D) subtract 6 from the previous term
Answers
Answer:
D) subtract 6 from the previous term
Step-by-step explanation:
27-6=21, 21-6=15, 15-6=9, and 9-6=3
Please answer quickly,thanks you shall be marked a branliest
Answers
Answer:
18.0 cm to 1 decimal point.
Step-by-step explanation:
First work out the unknown side (s) of the right triangle using the Pythagoras theorem:
s^2 = 13^2 - 5^2
= 169 - 25 = 144
s = sqrt 144 = 12 cm.
Now consider the other triangle:
s = 12
The missing angle = 180 - 65 - 40 = 75 degrees.
By the Sine Rule:
x / sin 75 = 12 / sin40
x = 12 sin 75 / sin 40
= 18.03
-
Lamar is taking a stunt man training course. he scored a 99 on his first test, but he only scored an 85 on his second test. what is the lowest score that lamar can make on his third and final test in order to have an overal average of 90?
Answers
Answer:
86.
Step-by-step explanation:
His total score is 99 + 85 + x where x is score on third test,
99 + 85 + x = 3 *90 (as his average must be 90, so:
184 + x = 270
x = 270 - 184
= 86.
Answer:
86
Step-by-step explanation:
Let x be the required score for Lamar's third test in order to get an average of 90 or higher.
Start with the initial equation:
[tex]\frac{99+85+x}{3}\geq 90[/tex]
Simplify the numerator in the fraction:
[tex]\frac{184+x}{3}\geq90[/tex]
Multiply both sides by 3 to cancel out division on left side of equation:
[tex]184+x\geq 270[/tex]
Subtract 184 from both sides to isolate the x variable:
[tex]x\geq86[/tex]
Leaving us with x must be greater than or equal to 86.
Find the sum of the convergent series. (round your answer to four decimal places. ) [infinity] (sin(9))n n = 1
Answers
The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
For given question,
We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]
We need to find the sum of given convergent series.
Given series is a geometric series with ratio r = sin(1)
The first term of the given geometric series is [tex]a_1=sin(1)[/tex]
So, the sum is,
= [tex]\frac{a_1}{1-r}[/tex]
= sin(1) / [1 - sin(1)]
This means, the series converges to sin(1) / [1 - sin(1)]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
= [tex]\frac{sin(1)}{1-sin(1)}[/tex]
= [tex]\frac{0.8415}{1-0.8415}[/tex]
= [tex]\frac{0.8415}{0.1585}[/tex]
= 5.31
Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
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4a. In a cookie mix, we find no-bake cookies, vanilla cookies, and cinnamon cookies in a ratio of 2 2 2 If a bag of the mix contains 40 no-bake cookies, how many vanilla cookies are there? please help
Answers
Answer:
40 vanilla cookies
Step-by-step explanation:
Lets say that
N = No-bake cookies
V = Vanilla cookies
C = Cinnamon cookies
If the ratio is 2 : 2 : 2
And there are 40 no-bake cookies
It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same
( N : V : C )
( 40 : 40 : 40 )
Hope this helps (๑ > ᴗ <)وxx
( I am so sorry if this is wrong!!)
PLS HELP!!!! Pointtssss!! The temperature during a very cold day is
recorded every 2 hours for 12 hours. The
data are given in the table below.
Answers
The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)
What kind of polynomial does fit best to a set of points?
In this question we must find a kind of polynomial whose form offers the best approximation to the point set, that is, the least polynomial whose mean square error is reasonable.
In a graphing tool we notice that the least polynomial must be a cubic polynomial, as there is no enough symmetry between (10, 9.37) and (14, 8.79), and the points (6, 3.88), (8, 6.48) and (10, 9.37) exhibits a pseudo-linear behavior.
The type of polynomial that would best model the data is a cubic polynomial. (Correct choice: D)
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Find the area in square units of ABC△ plotted below.
Answers
Answer:
71
Step-by-step explanation:
Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
-f(*) = (x + 2)(x - 6)
f(x) = (x - 4)(x + 3)
f(x) = (x - 12)(x 1)
f(x) = (x -3)(x + 4)
Answers
The standard form of the given quadratic equation in factored form is
(x+2) (x-6) = x²-4x-12
(x-4) (x+3) = x²-x-12
(x-12) (X+1) = x²-11x-12
(x-3) (x+4) = x²+x-12
what are quadratic equations?
A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero
To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.
f(x) = (x+2) (x-6)
x²+2x-6x-12
x²-4x-12
similarly, the standard form of equations 2,3 and 4 are :
(x²-x-12)
(x²-11x-12)
(x²+x-12)
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Answer:
B, D, A, C
Step-by-step explanation:
f(x) = (x + 2)(x – 6)
✔ B
f(x) = (x – 4)(x + 3)
✔ D
f(x) = (x – 12)(x + 1)
✔ A
f(x) = (x – 3)(x + 4)
✔ C
An athlete trains for 80 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 400min.
Answers
80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible. This can be obtained by converting the given statements into algebraic equation.
Find the required equation for the given question:Here in the question it is given that,
Athlete trains for 80 min each day,that is each day the athlete spends 80 min.
We have to assume the variable d the number of days the athlete spends training.Finally we have to find an equation that relates the number of days d that the athlete spends training when the athlete trains for 400 min.So we can write that,
400 min is the time spent by the athlete
400 min = number of days × time spent by the athlete in one day
400 min = d × 80
⇒ 80d = 400
Hence 80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible.
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Find the missing side lengths. Leave your answers as radicals in simplest form.
Answers
The missing side length of the right triangle are as follows;
v = 1 units
u = 2 units
How to find side of a right triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
Therefore,
tan 60 = opposite / adjacent
tan 60 = √3 / v
cross multiply
v = √3 / tan 6-
v = √3 / √3
v = 1
Hence,
sin 60 = opposite / hypotenuse
sin 60 = √3 / u
cross multiply
u = √3 / sin 60
u = √3 × 2 / √3
u = 2√3 / √3
u = 2
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PLS HELP. I tried and cant figure it out.
Answers
Answer:
I x² +12x I = -32
Step-by-step explanation:
Absolute value equation:
x = -4 ; x = -8
x + 4 = 0 and x + 8 = 0
(x +4)(x + 8) = 0
x*x + x*8 + 4*x + 4*8 = 0
x² + 4x + 8x + 32 = 0
x² + 12x + 32 = 0
Absolute value equation:
I x² + 12x I = -32
What is the value of x in the equation x-3y = 30, when y = 15?
1
04
8
80
200
Answers
Answer:
x = 75
Step-by-step explanation:
Given information from the question:
x - 3y = 30
y = 15
We can substitute y = 15 into the equation to find x.
x - 3(15) = 30
x - 45 = 30
x - 45 + 45 = 30 + 45
x = 75
Answer:
75
Step-by-step explanation:
x-3y=30
x-3×15=30
x-45=30
x=30+45
x=75
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
Answer:
[tex]-4\leq x[/tex] is what it looks like simplifed. In word form this means x is greater than all values equal to or greater than four. This means that the FOURTH graph is correct.
Step-by-step explanation:
[tex]13-2x\leq 37+4x = -24\leq 6x.[/tex]
Simplify this into [tex]-4\leq x[/tex] or [tex]x\geq -4[/tex]
This in words translates into x is greater than or equal to the value of four. Meaning all values larger than 4 and 4 are equal to x
Meaning the 4th graph is correct because it shows exactly what the word form says.
-------------------------
Have a great day,
Nish