For this case we have a quadratic equation given by:
[tex]4x ^ 2 + 2x-1 = 0[/tex]
The roots are found by means of the quadratic formula below:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 4\\b = 2\\c = -1[/tex]
So, we have:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]
Or in an equivalent way we have:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2 + 4 (4) (1)}} {2 (4)}[/tex]
Answer:
The correct option will be:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]
Answer:
a = 4, b = 2 and c= -1
Step-by-step explanation:
Quadratic formula: x =√[-b ± v(b² - 4ac)]/2a
Here quadratic equation is 4x2 + 2x – 1
a = 4, b = 2 and c= -1
x =[-b ± √(b² - 4ac)]/2a
= [-2 ± √(2² - 4*4*-1)]/2*4
= [-2 ± √(4 + 16)]/8
= [-2 ± √20)]/8
= [-2 ± 2√5)]/8
= [-1 ± √5)]/4
x = [-1 ± √5)]/4
On a test, mean score was 70 and the standard deviation of the scores was 15.
What is the probability that a randomly selected test taker scored below 50?
Answer:
[tex]P(x\:<\:50)=0.0918[/tex]
Step-by-step explanation:
To find the probability that a randomly selected test taker scored below 50, we need to first of all determine the z-score of 50.
The z-score for a normal distribution is given by:
[tex]z=\frac{x-\bar x}{\sigma}[/tex].
From the question, the mean score is [tex]\bar x=70[/tex], the standard deviation is, [tex]\sigma=15[/tex], and the test score is [tex]x=50[/tex].
We substitute these values into the formula to get:
[tex]z=\frac{50-70}{15}[/tex].
[tex]z=\frac{-20}{15}=-1.33[/tex].
We now read the area that corresponds to a z-score of -1.33 from the standard normal distribution table.
From the table, a z-score of -1.33 corresponds to and area of 0.09176.
Therefore the probability that a randomly selected test taker scored below 50 is [tex]P(x\:<\:50)=0.0918[/tex]
Which shows the expressions rewritten with a common denominator?
x-5/x+3 and 4/x-3
The expressions (x-5)/(x+3) and 4/(x-3) can be rewritten with a common denominator of (x+3)(x-3) to become ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).
Explanation:The expressions stated are: (x-5)/(x+3) and 4/(x-3). In order to rewrite these expressions with a common denominator, you need to multiply the denominators together to create a common denominator. Therefore, the common denominator would be (x+3)(x-3).
Next, each expression must be rewritten so that they have this common denominator. For the first expression, we multiply the numerator and denominator by (x-3) so we get: ((x-5)(x-3))/((x+3)(x-3)).
For the second expression, we multiply the numerator and denominator by (x+3) so we get: 4(x+3)/((x+3)(x-3)). So, the expressions rewritten with a common denominator are ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).
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To find a common denominator for the given expressions, multiply the denominators together. The expressions, rewritten with the common denominator, are [tex](x-3)*(x-5)/(x+3)(x-3)[/tex] and [tex]4*(x+3)/(x+3)(x-3).[/tex]
Explanation:The goal here is to find a common denominator for the expressions x-5/x+3 and 4/x-3. A common denominator can be found by multiplying the denominators of both expressions together. So for these expressions, the common denominator would be [tex](x+3)*(x-3).[/tex]
Then you multiply the top and bottom of each fraction by the missing factor from the other denominator. The expressions rewritten with a common denominator would then be:
For the first expression, multiply (x-5) by (x-3), which gives (x-3)*(x-5).For the second expression, multiply 4 by (x+3), which gives 4*(x+3).So the expressions with a common denominator are: [tex](x-3)*(x-5)/(x+3)*(x-3)[/tex]and [tex]4*(x+3)/(x+3)*(x-3).[/tex]
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(x2 + 4)(x2 - 4) please help
([tex]x^{2}[/tex] + 4)([tex]x^{2}[/tex] - 4)
To solve this question you must FOIL (First, Outside, Inside, Last) like so
First:
(x^2 + 4)(x^2 - 4)
x^2 * x^2
x^4
Outside:
(x^2 + 4)(x^2 - 4)
x^2 * -4
-4x^2
Inside:
(x^2 + 4)(x^2 - 4)
4 * x^2
4x^2
Last:
(x^2 + 4)(x^2 - 4)
4 * -4
-16
Now combine all the products of the FOIL together like so...
x^4 - 4x^2 +4x^2 - 16
Combine like terms:
x^4 - 4x^2 +4x^2 - 16
- 4x^2 +4x^2 = 0
x^4 - 16 <<<This is your answer
Hope this helped!
~Just a girl in love with Shawn Mendes
PLEEEASEEEEEEEEE HELPPPPPP!
The coordinates of the point A before dilation is (-12,-12)
40 points with explanation please
Answer:
a = 80°
Step-by-step explanation:
Since PS and QR are parallel lines, then
a = 80° ( alternate angles )
Answer:
a = 80°
Step-by-step explanation:
Since PS and QR are parallel lines, then
a = 80° ( alternate angles )
What is the angle of depression from B to C?
Answer:
That is < 3.
Step-by-step explanation:
It is the angle between the (dotted) horizontal from B and the line going B and C.
identify one charcteristic of exponential growth
Answer:
Exponential growth is called growth because its curve increases really fast, so that's the main characteristic of exponential growth. I'm attaching an example of a function with exponential growth, which is the change of population size over time.
Determine the next step for solving the quadratic equation by completing the square.
0 = –2x2 + 2x + 3
–3 = –2x2 + 2x
–3 = –2(x2 – x)
–3 + = –2(x2 – x + )
= –2(x – )2
= (x – )2
The two solutions are .
The next step is to add (b/2a)^2 to both sides to complete the square, then balance the equation by adding the inverse of that value outside the parentheses.
Explanation:The student has asked for the next step in solving the quadratic equation 0 = −2x2 + 2x + 3 by completing the square.
After rewriting the equation and factoring out the coefficient of the x2 term, the next step is to add a specific value to both sides to form a perfect square trinomial.
This value is found by taking (b/2a)2, where a is the coefficient of x2 and b is the coefficient of x. For this equation, we therefore add −(2/2*(-2))2 = 1 to both sides inside the parentheses.
The completed equation becomes −3 + 1 = −2*(x2 − x + 1/4). Finally, we must balance the equation by adding the inverse of −<strong>2*1/4</strong> outside the parentheses.
Then, we can continue solving for x.
if X²+ X + 1 =0 then the value of x ^3n is
Recall that
[tex]1-x^n=(1-x)(1+x+x^2+\cdots+x^{n-1})[/tex]
So we have
[tex]x^2+x+1=0\implies\dfrac{1-x^3}{1-x}=0\implies x^3=1[/tex]
Then for any [tex]n[/tex], we have
[tex]x^{3n}=(x^3)^n=1^n=1[/tex]
where was George Washington born
Answer:
Westmoreland County, VA
Cook-n-Serve carries oven mitts that have a selling price of $13.80 a pair. Cook-n-Serve buys the mitts from a wholesaler and receives a 40% trade discount. What is the markup rate on cost and the markup rate on selling price?
Answer:
The oven mitts cost
$13.80
But, Cook-n-Serve buys from a wholesaler, so they receive a discount of 40%
This means that they pay
(1-0.4)*($13.80) = 0.6*($13.80) = $8.28 for each pair
The markup rate on cost is 60%
And they sell for
$13.80/$8.28 = 1.67 times the price
1.67*100% = 167%
The markup rate on selling price is 167%
The answer is need is for number 8
Answer: I make 15 dollars every week at my job
Step-by-step explanation: your x is likely representing a time like weeks and your y is most likely going to be the amount of something like money. so if x increases by one every time and y increases by 15 every time your scenario could be i make 15 dollars every week at my job.
Find the slope of the line.
Slope = m=
Answer: y=-8-4/1
Step-by-step explanation:
Answer:
The slope is m= 4.
Step-by-step explanation:
Do Rise over run method. Then divide the two numbers.
4(a + 2) = 14 – 2(3 – 2a)
–2
–1
no solution
all real numbers
All real numbers.
[tex]\boxed{TRUE}[/tex]
Step-by-step explanation:
Distributive property: a(b+c)=ab+ac
Expand: 4(a+2)=4a+8
Expand again: 14-2(3-2a)=4a+8
4a+8=4a+8
You subtract by 8 from both sides of an equation.
4a+8-8=4a+8-8
Simplify.
4a=4a
Then, subtract by 4a from both sides of an equation.
4a-4a=4a-4a
Finally, simplify.
4a-4a=0
0=0
True
All real numbers is the final answer.
Hope this helps you!
Have a nice day! :)
So Reflections
If P= (3,4), Find: Ry=5 (P)
Answer:
The reflected point is (3,6)
Step-by-step explanation:
we know that
The reflection Ry = 5, means a reflection is across the line y= 5
we have
the point P(3,4)
Since the point P has y-coordinate 4, its distance to the line y= 5 is equal to 1 units (P is located 1 units down the line y=5).
therefore
The reflection of the y-coordinate will be 1 units above the line y=5, which is equal to
5+1=6
Hence
the y-coordinate of the image is 6.
The reflected point is (3,6)
To reflect a point about the y-axis, negate the x-coordinate while keeping the y-coordinate the same.
Explanation:In this question, you are given the point P(3,4) and asked to find Ry=5(P). The notation Ry=5(P) represents the reflection of point P about the y-axis. To reflect a point about the y-axis, you need to replace the x-coordinate with its opposite (negate it) while keeping the y-coordinate the same.
So, P(3,4) reflected about the y-axis becomes (-3,4). The x-coordinate changes from 3 to -3, but the y-coordinate remains the same at 4.
Therefore, Ry=5(P) is (-3,4).
Which equation has the steepest graph?anyone need some help
Answer:
Yhe equation that jas the steepest gradient is D
Step-by-step explanation:
look at the numbers infront of the 'x' without looking at the negative sign. The
larger the number the steeper the gradient. Negative gradient only means that it is a downward slope
Answer:
Step-by-step explanation:
D
Find the measure of angleC in the following triangle
Answer:
C = 58.88 degrees
Step-by-step explanation:
We can use the law of cosines to find the missing angle measurement
c^2 = a^2 +b^2 -2ab cosC
Rearranging and solving for cos C
2ab Cos C = a^2 +b^2 - c^2
Divide by 2ab
cos(C) = a^2 + b^2 − c^2
------------------------
2ab
Substituting what we know a = 31 b = 21 c = 27
31^2 + 21^2 - 27^2
cos C = -----------------------------
2(31)(21)
cos C = .516897081
Take the inverse cos on each side
cos^-1 cos C = cos ^-1 (.516897081)
C = 58.88 degrees
what is the value of x?
Answer:
x = 3
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠QRT is an exterior angle of the triangle
∠RTS and ∠RST are the 2 opposite interior angles, thus
45x = 25x + 57 + x
45x = 26x + 57 ( subtract 26x from both sides )
19x = 57 ( divide both sides by 19 )
x = 3
The temperature in degrees Fahrenheit can be expressed by the function F(c)= 9/5 c + 32 where is C is the temperature in degrees Celsius find the temperature in degrees Fahrenheit to the nearest degree if it is 23°C outside.
Answer:
73
Step-by-step explanation:
F(c)= 9/5 c + 32
Let C = 23
F(23) = 9/5 (23) +32
= 41.4 +32
=73.4
To the nearest degree
73
Which of the following is the equation of a line in a slope intercept form for a line without 1/4 and y intercept at (0,-1)
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x-1}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{We have the slope}\ m=\dfrac{1}{4}\ \text{and the y-intercept}\ (0,\ -1)\to b=-1.\\\\\text{Substitute:}\\\\y=\dfrac{1}{4}x-1[/tex]
The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains point (3, −2). (4 points) y = 2x + 4 y = negative 1 over 2 x − 1 over 2 y = − 1 over 2 x − 7 over 2 y = 2x − 8
ANSWER
[tex]y = 2x - 8[/tex]
EXPLANATION
To find the equation of a straight line, we need the slope and a point on that line.
We were given the equation of another line that will help us determine the slope . The given line has equation:
[tex]y = 2x + 4[/tex]
This equation is of the form
[tex]y = mx + b[/tex]
where
[tex]m = 2 \: \: is \: the \: \: slope.[/tex]
Since our line of interest is parallel to this line, their slopes are the same.
The line also contains the point (3,-2).
So we substitute the slope and point into the slope-intercept formula:
[tex] - 2= 2(3)+ b[/tex]
[tex] - 2 =6 + b[/tex]
[tex] \implies \: b = - 2 - 6 = - 8[/tex]
The required equation is
[tex]y = 2x - 8[/tex]
Final answer:
The equation of a line parallel to y = 2x + 4 and passing through the point (3, −2) is y = 2x − 8.
Explanation:
To find the equation of a line parallel to line AB with the equation y = 2x + 4 that passes through the point (3, −2), we need to use the fact that parallel lines have the same slope. Line AB has a slope of 2, so our new line will also have a slope of 2. Now, we use the point-slope form of a line: y − y1 = m(x − x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting our point and slope in, we get y − (−2) = 2(x − 3). Simplifying, we get y + 2 = 2x − 6, and after moving the 2 to the other side, the final equation in slope-intercept form is y = 2x − 8.
classify the following triangles check all that apply
Answer:
A. Scalene since all sides have different lengths
E. Right since it has a right angle
a wall is 8 feet tall and 36 feet wide. tom wants to cover it with white paint that costs 2 dollars per ounce. if each ounce of paint can cover approximately 72 square inches of area, how much would it cost to buy enough paint to cover the entire wall
Answer:
1152
Step-by-step explanation:
First we need to find the area of the wall in square inches
8 ft = 8*12 = 96 inch tall
36 ft = 36 * 12 = 432 inches wide
The area = 96 * 432 =41472 in^2
Each ounce of paint cover 72 in^2 so divide by 72
41472/72 =576
We need 576 ounces to cover the wall
At 2 dollars per ounces
576*2 =1152 dollars to paint the wall
what is 1/2 × 4 plzzzzzzzzzzzzzzzzzzxzzzzzzzz helllllllllllllllllpppppppppppp
Answer:
2
Step-by-step explanation:
1/2 is the same as saying 0.5
0.5 x 4 is the same as saying 0.5 + 0.5 + 0.5 + 0.5
0.5 + 0.5 + 0.5 + 0.5 = 2
Please help me!!! 6 points! Find the vertical shift
Answer:
0.009 units in the positive y direction.
Step-by-step explanation:
Vertical shift is simply the value of the constant.
In this case, if you expand the formula by multiplying 0.9 into the parentheses,
y = 0.9 sin [(π/3) - x] + (0.9)(0.01)
y = 0.9 sin [(π/3) - x] + 0.009
Here the value of the constant is 0.009 and it is positive, hence the vertical shift is 0.009 units in the positive y direction.
•What is the domain for the graph below?
Answer:
D. All real numbers except 0.
Step-by-step explanation:
The figure show a particular case of a hyperbola, which is continuous for all values of x, except the value of x where discontinuity exists. Hence, the domain of the function is all real numbers except 0.
Which expression is equivalent to
Answer:
[tex]\frac{\sqrt[4]{3x^2} }{2y}[/tex]
Step-by-step explanation:
We can simplify the expression under the root first.
Remember to use [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
Thus, we have:
[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}} \\=\sqrt[4]{\frac{3x^{2}}{16y^{4}}}[/tex]
We know 4th root can be written as "to the power 1/4th". Then we can use the property [tex](ab)^{x}=a^x b^x[/tex]
So we have:
[tex]\sqrt[4]{\frac{3x^{2}}{16y^{4}}} \\=(\frac{3x^{2}}{16y^{4}})^{\frac{1}{4}}\\=\frac{3^{\frac{1}{4}}x^{\frac{1}{2}}}{2y}\\=\frac{\sqrt[4]{3x^2} }{2y}[/tex]
Option D is right.
what is the midpoint of a line segment joining the points (5,-4)(-13,12)
To find the midpoint, add the 2 x values together and divide by 2, then add the 2 Y values together and divide by 2.
(5-13)/2, (-4+12)/2
-8/2 , 8/2
-4,4
The answer is (-4,4)
The expression below is the factorization of what trinomial?
-1(x+ 7)(x-4)
A. -x^2 + 3x+ 28
B. -x^2 + 3x-28
C. -x^2 - 3х - 28
D. -x^2 - 3x+ 28
Answer:
D
Step-by-step explanation:
Given
- 1(x + 7)(x - 4)
each term in the second factor is multiplied by each term in the first factor, that is
leaving the multiplier of - 1 for the time being
x(x- 4) + 7(x - 4) ← distribute both parenthesis
= x² - 4x + 7x - 28 ← collect like terms
= x² + 3x - 28
Hence
- 1(x² + 3x - 28) = - x² - 3x + 28 → D
Answer:
D
Step-by-step explanation:
The expression below is the factorization of what trinomial?
-1(x+ 7)(x-4)
A. -x^2 + 3x+ 28
B. -x^2 + 3x-28
C. -x^2 - 3х - 28
D. -x^2 - 3x+ 28
Pls I need help ASAP!!
Answer:
Brown's experimental probability is closest to it's theoretical probability.
Step-by-step explanation:
Theoretical:
There are 5 colors so the probability of getting orange is 1/5
The probability of getting purple is 1/5
and so on... each color has the probability of 1/5 of being used
We just need to see what experimental probability is closest to .2
Experimental probability:
So Orange 118/625=.1888
Purple 137/625=.2192
Brown 122/625=.1952
Yellow 106/625=.1696
Green 142/625=.2272
So the closest from below .2 is .1952 (which is brown)
The closest from above .2 is .2192 (which is purple.
If you aren't sure which one is closer.. you can see which difference is closer to 0.
.2-.1952=.0048
.2192-.2=.0192
.1952 is the winner since .0048 is closer to 0 than .0192 is
So Brown !