Graph the equation y=-x^2-12x-35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex
Answers
Please check the image attached aside with the graph of the quadratic equation.
How to graph a quadratic equation by matching three pointsIn this problem we have a quadratic equation, of which we should plot the graph by matching five points. We can make use of its vertex, two roots, y-intercept and other point. First, determine the vertex of the quadratic function:
- x² - 12 · x - (35 + y) = 0
x² + 12 · x + (35 + y) = 0
12² - 4 · 1 · (35 + y) = 0
144 - 4 · (35 + y) = 0
144 - 140 - 4 · y = 0
4 · y = 4
y = 1
- x² - 12 · x = 36
x² + 12 · x + 36 = 0
(x + 6)² = 0
x = - 6
The vertex of the quadratic equation is (x, y) = (- 6, 1).
Second, calculate the roots of the quadratic equation:
- x² - 12 · x - 35 = 0
x² + 12 · x + 35 = 0
(x + 5) · (x + 7) = 0
The roots of the quadratic equation are (x, y) = (- 5, 0) and (x, y) = (- 7, 0).
Third, determine the y-intercept of the quadratic equation:
y = - 0² - 12 · 0 - 35
y = - 35
The y-intercept of the quadratic equation is (x, y) = (0, - 35).
And fourth, find another point by evaluating the quadratic equation:
y = - 1² - 12 · 1 - 35
y = - 48
The remaining point is (x, y) = (1, - 48).
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Related Questions
h (x) = -2x-4, find h (2)
This my last one
Answers
Answer: -8
Step-by-step explanation:
-2(2)-4 -> -4-4 = -8
Quadrilateral B is a scaled copy of quadrilateral A.
Its shortest side is 5 units long.
What is the scale factor from A to B?
Answers
By using the concept of dilation, we find that scale factor from A to B is equal to l' / 5, where l' is the length of the shortest side of the quadrilateral B.
What is the scale factor between two quadrilaterals?
Scale factor is a key variable used to dilate lengths and distances by rigid transformations. Then, the length of the shortest side of the quadrilateral B is equal to the product of the scale factor and the length of the shortest side of the quadrilateral A. Mathematically speaking, this kind of rigid transformation is represented by the following formula:
r = l' / l
Where:
r - Scale factorl - Length of the shortest side of the quadrilateral A.l' - Length of the shortest side of the quadrilateral B.If we know that l = 5, then the length of the shortest side of the quadrilateral B is equal to the following linear equation:
l' = 5 · r
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The formula for potential energy is p=mgh, where p is potential energy, m is mass , g is gravity and h is height . Which expression can be used to represent g
Answers
Answer:
The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters.
Step-by-step explanation:
Left-handedness is ________ common than usual among mathematicians and ________ common than usual among artist
Answers
Left-handedness is _more_______ common than usual among mathematicians and ___more_____ common than usual among artist
The relationship between handedness and mathematical ability is still highly controversial.
While some researchers have claimed that left-handers are gifted in mathematics and strong right-handers perform the worst in mathematical tasks, others have more recently proposed that mixed-handers are the most disadvantaged group.
However, the studies in the field differ with regard to the ages and the gender of the participants, and the type of mathematical ability assessed.
To disentangle these discrepancies, we conducted five studies in several Italian schools (total participants: N = 2,314), involving students of different ages (six to seventeen) and a range of mathematical tasks.
The results show that (a) linear and quadratic functions are insufficient for capturing the link between handedness and mathematical ability; (b) the percentage of variance in mathematics scores explained by handedness was larger than in previous studies.
The last theory drawing a causal link from handedness to mathematical ability through cognition is the hemispheric indecision hypothesis.
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Evaluate the expression 3^5 five is small and on top
Answers
Answer:
243
Step-by-step explanation:
3 to the power of 5
3 x 3 x 3 x 3 x 3
3 x 3 = 9 x 3 = 27 x 3 = 81 x 3 = 243
What is Ah Fo's reply to the magician giving him the three brass pennies?
A. Ah Fo asks for a day to think about the decision.
B. Ah Fo immediately tells the magician what he wants.
C. Ah Fo asks the magician for suggestions.
D. Ah Fo tells the magician that he doesn't want a reward for his help.
Answers
The inference is that Ah Fo's reply to the magician giving him the three brass pennies is D.
Ah Fo tells the magician that he doesn't want a reward for his help.
How to illustrate the information?It should be noted that the information is about how the character helped the magician. Despite the help, he didn't request for anything in return.
Therefore, the inference is that Ah Fo's reply to the magician giving him the three brass pennies is that Ah Fo tells the magician that he doesn't want a reward for his help.
In conclusion, the correct option is D.
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Read the excerpt from "The Three Brass Pennies."
“And what might your decision be?” asked the magician, as he spread out the three brass pennies before him.
“I would ask first,” went on Ah Fo, “for the power to read accurately the thoughts of others; secondly, for the power to foretell my own future at least a month in advance of any given moment; third, for the power to acquire all learning without any effort!”
When he had finished, the magician sat back with a gasp, took off his spectacles and wiped them, put them on once more, and stared at Ah Fo in astonishment and not a little dismay. “This is most unusual,” he stammered, “not to say somewhat dangerous! Have you duly considered, my son, the extent of all you ask?”
What does the pair of equations y = 1, z = 7 represent? in other words, describe the set of points (x, y, z) such that y = 1 and z = 7.
Answers
The intersection of two plans is represented by the pair of equations y = 1, z = 7. The set of points is (0,1,7) and the line is parallel to the x axis.
What is intersection of planes?In geometry, a plane is a flat plate which extends in all directions to infinity.
Intersecting planes are non-parallel planes that always intersect in a straight line.The two planes cannot cross more than one line.A good illustration of intersecting planes is the two connecting borders, the binding side of a book, where all of the papers (planes) meet.Now, as per the question;
Consider the following equation.
y = 1 denotes a vertical plane in the xy plane.
Z = 7 denotes a horizontal plane parallel to the xy plane.
Both planes intersect and are perpendicular to each other.
y = 1 and z=7 is the intersection of two plans where x is zero and y = 1 and z = 7.
Therefore, the points are (0,1,7), and also the line is parallel to the x axis.
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y=ax^2+b please solve this
Answers
Evaluate the expression 4 with small 4 on top
Answers
Answer:
256
Step-by-step explanation:
That just means to multiply the number by itself 4 times.
4 x 4 = 16 x 4 = 64 x 4 = 256
7-7+5x-5x+2+2x^2+2x
Combine like terms
Answers
Answer:
2x^2+2x+2
Step-by-step explanation:
7-7+5x-5x+2+2x^2+2x
ok first off i see 7-7, which is zero so we can leave that out
i also see 5x-5x which is also zero
now we have 2+2x^2+2x left, and to order it properly we put the number with the exponent and variable first, then the number with the variable, and then the number
so your final answer would be
2x^2+2x+2
i hope that helps! if you have any questions just ask!
Type either> or < in the blank.
X
95⁰
y
Answers
Answer:
<
Step-by-step explanation:
Since the angle is greater than 95, y must be greater than x
Find the GCF 1.16,60 2.52,84 3.32,89,144 4.48,96,108 5.144,176,1
Answers
Answer:
The GCF is 1.
Step-by-step explanation:
The factors of 1 are: 1
The factors of 1 are: 1
The factors of 2 are: 1, 2
The factors of 3 are: 1, 3
The factors of 4 are: 1, 2, 4
The factors of 5 are: 1, 5
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 89 are: 1, 89
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The factors of 176 are: 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
Then the greatest common factor is 1.
using ratios.
1. The ratio of male employees to
female employees is 1:3. If
there are 144 female
employees in total, how many
males are there?
Answers
Answer:
48
Step-by-step explanation:
set up a proportion of 1/3 and x/144 and then divide 144 by 3 which is 48
[tex]\stackrel{\textit{ratio of 1~:~3}}{\cfrac{males}{females}~~ = ~~\cfrac{1}{3}}\implies \cfrac{males}{144}~~ = ~~\cfrac{1}{3}\implies 3males=144 \\\\\\ males=\cfrac{144}{3}\implies males=48[/tex]
1. One-half of a number y is more than 22.
Answers
Answer:
1/2 y > 22
Solved: y > 44
Step-by-step explanation:
We are trying to write an inequality
One-half of a number y
1/2 y
is more than
>
22
1/2 y > 22
Solving the inequality
Multiply each side by 2
1/2y * 2 > 22*2
y > 44
<6 and <7 form a linear pair. Twice the measurement of <6 is twelve more than four times the measurement of <7. Find the measurement of each angle.
Answers
A linear pair , m∠7 = 58°, m∠6 = 122° are the measurement of each angle.
What is Linear Pair?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Linear Pairs add up to equal 180°.
Step 1: Define
m∠6 + m∠7 = 180°
2m∠6 = 4m∠7 + 12
Step 2: Rewrite systems of equations
I will set m∠6 = x and m∠7 to y
x + y = 180°
2x = 4y + 12
Step 3: Rewrite 2nd equation
2x = 2(2y + 6)
x = 2y + 6
Step 4: Use Substitution
2y + 6 + y = 180
3y + 6 = 180
3y = 174
y = 58°
Step 5: Find x by plugging y back into an original equation
x + 58 = 180
x = 122°
Step 6: Rewrite
x = m∠6
y = m∠7
m∠6 = 122°
m∠7 = 58°
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Two shops rent kayaks for a rental fee plus a fee per hour. How many hours must a kayak be rented for the total costs to be the same? Shop A Rental fee: $8 Hourly fee: $3 Shop B Rental fee: $3 Hourly fee: $4 The total costs are the same when a kayak is rented for hours.
Answers
The total costs are the same when a kayak is rented for 5 hours
How do we determine the hours that both have the same costs?
The hours that both shops have the same cost is determined by equating the total cost in shop A to the total cost in shop B, in short, we need to first of all , model the total cost in each shop based on the straight-line equation formula shown below since the total cost is made of fixed charge and variable charge
y=a+bx
y=total cost
a=fixed charge for each shop
b=hourly fee
x=number of hours
Shop A:
total cost=8+3x
Shop B:
total cost=3+4x
8+3x=3+4x
8-3=4x-3x
5=x
At 5 hours both Shops A and B would have the same cost
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The hours when the cost of renting the kayaks would be the same is 5 hours.
The total cost of renting a kayak is $23.
When would the total cost be equal?The equation that can be used to represent the total cost of renting a kayak is a linear function. A linear equation is an equation whose graph is a straight line. A linear equation increases by a predetermined constant. An example of a linear equation is x + 2.
The form that the equation would be is:
Total cost = rental fee + (hourly fee x number of hours)
Total cost at Shop A = $8 + $3h
Total cost Shop B = $3 + $4h
Where h is the number of hours the kayak was rented.
When the total costs are equal, the two above equations would be equal.
$3 + $4h = $8 + $3h
Combine similar terms: $4h - $3h= $8 - $3
Add similar terms together: h = 5 hours
Total cost = $3 + $4(5)
$3 + $20 = $23
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LESSON 2: STAYING SHARP
PRACTICING SKILLS & CONCEPTS
1. Write the numbers of dots in the next three steps of
this pattern:
1
6
10
15
2. W
Ar
Ev
Answers
Answer:
Step-by-step explanation:
1
6
10
15
id
id
Help please!! I need it quick
Answers
Applying the triangle proportionality theorem, the length of line EC is: 7.2 units.
How to Apply the Triangle Proportionality Theorem?Since lines AC and DE are parallel to each other in the triangle, and DE intersects sides AB and AC, then we would have the following proportion based on the triangle proportionality theorem:
BD/DA = CE/EA
BD = 18 units
DA = 15 units
CE = ?
EA = 6 units
Plug in the values
18/15 = CE/6
(18)(6) = (CE)(15)
108 = CE(15)
Divide both sides by 15
108/15 = CE(15)/15
7.2 = CE
EC = 7.2 units
Therefore, applying the triangle proportionality theorem, the length of line EC is: 7.2 units.
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expression for "the quotient of 6 and y."
Answers
Answer:
Step-by-step explanation:
That expression can be written as:
Hope it helped,
Complete the equation, and tell which property you used.
0 + _________ =47
Answers
Answer:
0 + 47 = 47
Step-by-step explanation:
➟ 0 + __ = 47
Let's Change __ to x
➟ 0 + x = 47
Calculate 0 + x = x
➟ x = 47
∴ 0 + 47 = 47
Property used is Identity property of addition
marine biologist captured and tagged 12 seals near Avila Beach. Recapture results found that 27% of the seals were tagged. Approximately how many seals are near Avila Beach
Answers
Based on the number of seals that were tagged near Avila Beach, the approximate number of seals near Avila Beach is 44 seals
How many seals are there?The number of seals near Avila beach can be said to be x. If it is x, then the formula is:
12 = 27% x ×
27%x = 12
0.27x = 12
Solving for x then gives:
x = 12 / 0.27
x = 44.44
= 44 seals
In conclusion, there are approximately 44 seals near Avila beach.
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Can an inverse and
contrapositive both have false truth values?
Answers
Answer:
thyjdbbdhehwjwnwjehe
J + 6 4/7 = 12 1/21
What is j
Answers
Three answers all equivalent:
5.476190...
115/21
5 10/21
pick whichever is applicable, they are all the same
Answer:
68 tadkfidekmfmvovovffrffffgHihi! make sure you double-check before submitting and answer, and also provide a reasonable explanation. It has happened on one too many instances where people got an answer wrong, and "just didn't check", and I had to suffer because they simply went to fast
So please just make sure you are correct or I won't give 5 stars, thanks, and might be reported. that's all!
Answers
Answer:
0.6
Step-by-step explanation:
Divide 2 by 3 to convert 2/3 in its decimal form.
The quotient obtained on dividing 2 by 3 will be 0.6
So, the decimal form of 2/3 is a non-terminating and recurring decimal number 0.6
An algorithm that uses a constant number k of integer variables to find a number list's minimum value has space complexity s(n) = _____ and auxiliary space complexity s(n) = _____.
Answers
According to the given statement:
Minimum value has space complexity S(N) = N
Auxiliary space complexity S(N) = k.
The correct option is D.
Briefing:The given algorithm returns the minimum value from the a list of N items using k constant integer variables, so its space complexity S(N) is N or O(N), since the list needs N total bytes to store N items.When storing the constant number k of arithmetic operations to find the minimum value from a list of N items, the auxiliary space complexity S(N) will be equal to k. The auxiliary space complexity required by the algorithm is k.The right answer is therefore option N,k.To know more about complexity visit:
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I understand that the question you are looking for is:
An algorithm that uses a constant number k of integer variables to find a number list's minimum value has space complexity S(N) = _____ and auxiliary space complexity S(N) = _____.
Group of answer choices:
A. k, N
B. N, N
C. k, k
D. N, k
MAPS Leila is walking from the park at point P to a restaurant at point R. She wants to stop for a break when the distance she has traveled and the distance she has left to travel has a ratio of 3:5. At which point should Leila stop for her break?
Answers
The point at which Leila should stop to take break is (6.25 , 3.75)
Given P(10 , 3) and R (0 , 4)
The ratio is 3:5
Let the break point be point B.
The formula is : (n(x₁) ₊ m(x₂)/ m₊n , n(y₁) ₊ m(y₂)/ m₊n)
P(10,3) = (x₁ , y₁)
R(0,4) = (x₂ , y₂)
m:n = 3:5
B = (5(10) ₊ 3(0)/3₊5 , 5(3) ₊ 3(4)/3₊5)
B = (50₊0/8 , 15₊12/8)
B = (50/8 , 27/8)
B = (6.25 , 3.75)
Hence Leila should stop at point (6.25 , 3.75) for her break.
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What is the solution set of this compound inequality? 1 ≤ |x + 3| ≤ 4
Answers
The solution is:
[tex]-7\leq x\leq -4[/tex] or [tex]-2\leq x\leq 1[/tex]
вычислите: 164,358-104,55
Answers
What is the place value of the 2 in 150.1235?
Hundredths
Tenths
Tens
Thousandths
Answers
Answer:
The 2 is placed in the Hundredths place
Step-by-step explanation:
Hope it helps! =D
Triangle ABC was transformed to be triangle DEF using
one transformation.
What transformation was performed?
translation
rotation
dilation
reflection
Answers
Answer:
reflection
Step-by-step explanation:
triangle ABC reflected to become triangle DEF
