PLEASE HELP!!! For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
y = -2x2 + 2x +2
You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P($5 then $10).
Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:
Part A: Passes through (−2, 1) and parallel to 4x − 3y − 7 = 0
Part B: Passes through (−2, 1) and perpendicular to 4x − 3y – 7 = 0
Final answer:
The equation of the line for Part A is y = (4/3)x + 11/3, since it is parallel to the given line with a slope of 4/3. The equation for the line in Part B is y = (-3/4)x - 1/2, as it is perpendicular to the given line and the slope is the negative reciprocal of 4/3.
Explanation:
Writing Equations of Lines
To find the equation of a line in the form y = mx + b, we first need to determine the slope (m) and the y-intercept (b). For Part A, since the line needs to be parallel to 4x - 3y - 7 = 0, the slope of our line must be the same as the slope of this given line. To find the slope of the given line, we can rewrite it in slope-intercept form:
4x - 3y = 7
-3y = -4x + 7
y = (4/3)x - 7/3
The slope is 4/3. Since parallel lines have the same slope, our line's slope is also 4/3. Using the point (-2, 1) it passes through, we can substitute into the equation y = mx + b to find b:
1 = (4/3)(-2) + b
1 = -8/3 + b
b = 1 + 8/3
b = 11/3
Thus, the equation of the line for Part A is y = (4/3)x + 11/3.
For Part B, to find a line perpendicular to the given line, we need the negative reciprocal of its slope. The negative reciprocal of 4/3 is -3/4. We then use the given point (-2, 1) to find the y-intercept:
1 = (-3/4)(-2) + b
1 = 3/2 + b
b = 1 - 3/2
b = -1/2
So, the equation for the line in Part B is y = (-3/4)x - 1/2.
4x=(cd)/(yz) solve for z
How do I solve this (step-by-step preferred) using common denominators?
Factor: 100x^2−121
x^2 is x to the second power
The product of twenty one negative integers is negative? True of false
Find the point P along the directed line segment from point A(-8,-3) to point B(6,12) that divides the segment in the ratio 1 to 7
I think that it is c - P[-3/4, - 1/8]
BMK
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 9?\
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
Answer:
The graph of y = f(x) will shift down 9 units.
Step-by-step explanation:
With the graph of y = f(x)-9 the graph of y=f(x) will shift down 9 units. For example:
if f(0) = 0, then y = f(0) -9 = -9.
if f(1) = 9, then y= f(1) - 9 = 9-9 = 0.
The same proccess with all x in the domain of f(x).
Name an angle adjacent to ∠DGE.
A. ∠FGI
B. ∠EGH
C. ∠HGJ
D. ∠JGI
A mathematics journal has accepted 14 articles for publication. However, due to budgetary restraints only 9 articles can be published this month. How many ways can the journal editor assemble 9 of the 14 articles for publication? A. 726,485,760 B. 14 C. 2,002 D. 126
Answer:
A. 726,485,760
Step-by-step explanation:
A mathematics journal has accepted 14 articles for publication.
However, due to budgetary restraints only 9 articles can be published this month.
As the journals are published one by one (arranged combination), so the order matters in this case.
So permutation should be used in this case, rather than combination.
Hence, the number of ways the journal editor can assemble 9 of the 14 articles for publication is,
[tex]=\ ^{14}\text{P}_9=\dfrac{14!}{(14-9)!}=\dfrac{14!}{6!}=726,485,760[/tex]
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
Find the area of each regular polygon. Round your answer to the nearest tenth. Show your work.
a. Octagon with side lengths 5in.
b. Hexagon with radius 5in
PLEASE HURRY!!! 30 POINTS
DIMENSIONAL ANALYSIS
A water cooler can hold 50 pt of water.
About how many liters of water can it hold?
1 L≈1.06 qt
23.6 L
26.5 L
94.3 L
106.0 L
The answer is 23.6 if I pretty sure
Jillian’s begins to solve a linear equation that results in a variable expression set equal to the same variable as expression. Which is the best interpretation of this solution
the equation has infinite solutions
Answer:
infinity solutions
Step-by-step explanation:
Find the area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06
The area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 is 0.9776.
Given that, z₁ = -2.8 and z₂ = 2.06.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 will be calculated as follows:
The standard normal table represents the area under the curve.
P(z<-2.8) ∩ P(z>2.06)=P(z<-2.8) + P(z>2.06)------(1)
According to the standard normal table, we have
z = -2.8 correspond to an area of = 0.0026
z = 2.06 correspond to an area of = 0.9750
Substitute these values in equation 1, we have
P(z<-2.8) + P(z>2.06) = 0.9750 + 0.0026 = 0.9776
Therefore, the area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 is 0.9776.
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HELP PLEASE !!! Find the measure of <2
Answer:
40
Step-by-step explanation:
An interior angle of a regular polygon has a measure of 108°. What type of polygon is it? The polygon is .
The polygon is a penthagon.
In a regular polygon with n sides, the sum of the interior angles is
[tex] 180(n-2) [/tex]
But we also know that each interior angle has a measure of 108, and of course there is a total of n angles. So, we also know that the sum of the interior angles is
[tex] 108n [/tex]
Since we have two expressions for the same quantity, these expressions must equal each other:
[tex] 180(n-2) = 108n [/tex]
To solve for n, let's start by expanding the left hand side:
[tex] 180n-360 = 108n [/tex]
Now move all terms involving n to the left hand side, and all constants to the right hand side:
[tex] 180n-108n = 360 [/tex]
Simplify the right hand side:
[tex] 72n = 360 [/tex]
And finally, divide both sides by 72:
[tex] n = \frac{360}{72} = 5 [/tex]
The correct polygon is, Pentagon
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
An interior angle of a regular polygon has a measure of 108°.
Since, We know that;
In a regular polygon with n sides, the sum of the interior angles is
⇒ 180 (n - 2)
Here, The sum of the interior angles is,
⇒ 108n
Hence, We can formulate;
⇒ 108n = 180 (n - 2)
⇒ 108n = 180n - 360
⇒ 360 = 180n - 108n
⇒ 72n = 360
⇒ n = 5
Thus, It shows the Pentagon.
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write an equation thats parellel to the given line & that passes through the given point y=5/2x-10;(6,-29)
A rectangular area is to be fenced in with 600 feet of chicken wire. find the maximum area that can be enclosed.
The maximum area that can be enclosed is 22500 feet²
A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other.
Let x represent the length and y represent the width. Hence:
perimeter = 2(length + width)
600 = 2(x + y)
300 = x + y
y = 300 - x
The area of a rectangle (A) = length * width
A = x * (300 - x)
A = 300x - x²
The maximum area is at dA/dx = 0, hence:
dA/dx = 300 - 2x
300 - 2x = 0
2x = 300
x = 150 feet
y = 300 - x = 300 - 150 = 150 feet
The maximum area = x * y = 150 * 150 = 22500 feet²
The maximum area that can be enclosed is 22500 feet²
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Help please on that one
the circle is divided into 8 sections
5 are shaded
so 5/8 are shaded
5 divided by 8 = 0.625
0.625 = 62.5%
Round to 63% if you need to.
The graph of f(x) = x3 − 7x − 6 is shown. Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6? x = −6 x = −2, −1 x = −2, −1, 3 x = −6, −2, −1, 3
Answer:
c
Step-by-step explanation:
e2020
Which function has the range (-infinity,0)u(2,infinity)?
A. y = sex x
B. y = cot (2x) - 1
C. y = cos (x+1)
D. y = csc(x) + 1
Answer:y=csc(x) -1
Step-by-step explanation:
The correct answer is option D. y = csc(x)+1
To determine which function has the range (-infinity, 0) U (2, infinity), we need to analyze each option:
A. y = sec(x): The range of sec(x) is [tex](-\infty,-1] \cup[1,\infty)[/tex], not matching our target range.B. y = cot(2x) - 1: The range of cot(x) is [tex](-\infty,\infty)[/tex], so cot(2x) also has a range of [tex](-\infty,\infty[/tex]). Shifting it down by 1 unit, the range becomes [tex](-\infty, \infty) - 1 = (-\infty, \infty)[/tex], also not matching.C. y = cos(x + 1): The range of cos(x) is [-1, 1], so cos(x + 1) still has a range of [-1, 1] after translating horizontally, which does not match.D. y = csc(x) + 1: The range of csc(x) is [tex](-\infty,-1]\cup[1,\infty)[/tex]. When we add 1 to it, we get [tex](-\infty,0]\cup[2,\infty)[/tex] - which simplifies to our target range of [tex](-\infty,0]\cup[2,\infty)[/tex].Therefore, the function is y = csc(x) + 1.
Orlando bought a new couch for $2,904, using the furniture store's finance plan. He will pay $121 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
Select one:
a. y=2,904+121x
b. y=2904−121x
c. y=121x−2,904
d. y=121x
If angle SUT is 39, what does that tell us about angle TUV? What arc measure describes arc VTS? How can we make any assertions about these angle and arc measures? b. Which line segments’ length can be calculated based on knowing the radius length? Explain. c. If angle MOP is 49, which other angle measures can we calculate? What arc measures can we calculate? Describe which lesson concepts allow us to make these calculations.
In a circle, corresponding arc measures are equal to the angle at the center, while any chord, secant, or tangent length can be determined with a known radius. Furthermore, other angles and arcs can be obtained via properties of circles such as vertical angles, linear pairs, or the properties of quadrilaterals inscribed in circles.
Explanation:You've asked about the properties of angles, lines, and arc measures within a circle. For the first part, if angle SUT is 39 degrees, then since angle TUV is a vertical angle to it, angle TUV is also 39 degrees because vertical angles are equal. For the arc measure of VTS, since we know the measure of angle SUT, arc VTS will be 2 times that, or 78 degrees, due to the concept of inscribed angles.
Next, the lengths of any chord, secant, or tangent line segments can be calculated knowing the radius length, as they all relate back to the radius in some way. This knowledge comes from our study of circles.
For the third part, if angle MOP is 49 degrees, we can find other angle and arc measures because of the properties of circles. Other angle measures can be found using concepts like vertical angles, linear pairs, or the properties of quadrilaterals inscribed in circles, while arc lengths can be determined by the concept of inscribed angles or central angles. Understanding these concepts allows us to make calculated assertions on angles and arcs within circles.
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what is the area of this rhombus?
The sides of a rhombus with angle of 60° are 6 inches. find the area of the rhombus. 9√3 in2 18√3 in2 36 in2
Drop a perpendicular from an obtuse vertex.
That makes a 30 - 60º right triangle, with
hypotenuse 6 and short leg 3. So the long leg,
which is the height of the rhombus, is 3√3 .
Since a rhombus is a parallelogram, its area
is base x height = 6 x 3√3 = 18√3 .
Drop a perpendicular from an obtuse vertex.
That makes a 30 - 60º right triangle, with hypotenuse 6 and short leg 3. So the long leg, which is the height of the rhombus, is 3√3 .
Since a rhombus is a parallelogram, its area is base x height = 6 x 3√3 = 18√3
What reduced fraction corresponds to 92%?
Write any algebraic expression with at least two operations and the word phrase it represents.
Store employees are handing out coupons. Every 10th customer gets a $1 coupon. Every 12th customer gets a $2 coupon.
Which customer is the first to receive both coupons?
correct answer 60th costumer