(a) To have exactly one solution, the discriminant of the quadratic equation must be equal to zero.b² - 4ac = 1 - 4(1)(_) = 0
⇒ 1 - 4_ = 0
⇒ _ = 1/4
Substituting the value of _ in the original equation, we get:
x² + x + 1/4 = (x + 1/2)² = 0
⇒ x = -1/2 (as square of a number is always non-negative)
(b) Following the same approach as in part (a), we get:
(-_)² - 4(1)(1) = _² - 4 = 0
⇒ _ = ± 2
Substituting the values of _ in the original equation, we get:
For _ = 2: x² + 2x + 1 = (x + 1)² = 0
⇒ x = -1
For _ = -2: x² - 2x + 1 = (x - 1)² = 0
⇒ x = 1
(c) Following the same approach as in part (a), we get:
1 - 4(_) = 0
⇒ _ = 1/4
Substituting the value of _ in the original equation, we get:
x² + x + 1/4 = (x + 1/2)² = 0
⇒ x = -1/2
(d) Following the same approach as in part (a), we get:
(-_)² - 4(1)(4_) = _² - 16_ - 4 = 0
⇒ _ = 2 ± √5
Substituting the values of _ in the original equation, we get:
For _ = 2 + √5: x² + (2 + √5)x + 5 + 2√5 = (x + (1 + √5))² = 0
⇒ x = -1 - √5
For _ = 2 - √5: x² + (2 - √5)x + 5 - 2√5 = (x + (1 - √5))² = 0
⇒ x = -1 + √5
Hence, we have found the values of the constant _ for each of the given quadratic equations to have exactly one solution and determined the solution for each value.
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The product of complex numbers (4,3) and(5,-6) is?
Answer:
The answer of this is (38,9)
Step-by-step explanation:
Answer:
38,9
Step-by-step explanation:
6. x2= 1
—
100
Thank you (:
Answer:
Its asking what x 2=1 it would be
Step-by-step explanation: 0.5 or 1/2
How can you tell if three positive numbers form a
Pythagorean triple?
Answer:
Since a Pythagorean triple is three positive integers a, b, and c such that (a^2)+(b^2)=(c^2), where a and b are the two legs, and c is the hypotenuse, first take the sum of the squares of the two legs and make an estimate. For example, 3, 4, and 5 is a Pythagorean triple since 9+16=25.
1) Where is the midpoint of , when A (6, 7) and B (-9, -5)?
Answer:
(−1.5,1)
Step-by-step explanation:
Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (6,7) and p2 (-9,-5)
The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (-9-6)2+(-5-7)2
d = √ ((-15)2+(-12)2)
d = √ (225+144)
d = √ 369
The distance between the points is 19.2093727122985
The midpoint of two points is given by the formula
Midpoint= ((X1+X2)/2,(Y1+Y2)/2)
Find the x value of the midpoint
Xm=(X1+X2)/2
Xm=(6+-9)/2=-1.5
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(7+-5)/2=1
The midpoint is: (-1.5,1)
Answer:
(-1.5,1)
Step-by-step explanation:
the midpoint between 6 and -9 is -1.5
the midpoint between 7 and -5 is 1
(-1.5,1)
Can someone please help me with this? ^^"
Answer:
Not issue discussed plz full page
the statue of liberty in new york city is approximately 305 ft tall. how many u.s. half dollars would be in a stack of the same height? each half dollar is 2.15 mm thick.
There would be approximately 43,149 U.S. half dollars in a stack that is the same height as the Statue of Liberty.
To determine the number of U.S. half dollars that would be in a stack the same height as the Statue of Liberty, we need to convert the height of the statue from feet to millimeters and then divide it by the thickness of a single half dollar.
First, let's convert the height of the Statue of Liberty from feet to millimeters. We know that 1 foot is equal to 304.8 millimeters (rounded to the nearest tenth). Therefore, the height of the Statue of Liberty in millimeters is:
305 ft * 304.8 mm/ft = 92918 mm (rounded to the nearest whole number)
Next, we need to determine the thickness of a U.S. half dollar. Given that each half dollar is 2.15 mm thick, we can now calculate the number of half dollars in a stack that is the same height as the Statue of Liberty:
Number of half dollars = Height of stack / Thickness of a half dollar
Number of half dollars = 92918 mm / 2.15 mm
Number of half dollars ≈ 43149 (rounded to the nearest whole number)
Therefore, there would be approximately 43,149 U.S. half dollars in a stack that is the same height as the Statue of Liberty.
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Solve 2y = 3y - 20
A.20
B.-20
C.-4
D.4
Answer:
D. 4
Step-by-step explanation:
How many cholates can you buy with 10,80€ and the cholates are 0,90€
Answer:
12
Step-by-step explanation:
because if you do 10.80 divided by 0.90 you get 12
a balloon at standard pressure is placed in a cool oven at 20 degrees celsius. the balloon is removed from the oven when the internal temperature rises to 30 degrees celcius. if the volume of the balloon when It is removed from the oven is 3.75 L what is the initial volume of the balloon?
j4jrjrjttjtjtj
Step-by-step explanation:
jeejejehnnrnrnffjfjfc
Can anyone help me with this equation?
Answer:
false
Step-by-step explanation:
5+2=15÷(3+2)
5+2=15÷5
7=15÷5
7=3
false because they are different
Answer :
FALSEExplanation :
[tex] \frac{15}{3} + 2 = 15 \div (3 + 2) \\ 5 + 2 = 15 \div 5 \\ 7 = 3[/tex]
65% of 186
Please show work! (my teacher needs me to show work)
What is the right answer
The correct option is the first one, the leading coefficients are opposites.
What can we say about the leading coefficients?A general quadratic function is written as:
y = ax² + bx + c
The leading coefficient is a.
Here we have two quadratics, these are:
f(x) = ax² + bx + c
g(x) = kx² + jx + n
Notice that in the graph of (f + g)(x), we have a line instead of a quadratic, so the quadratic term is zero, this means that:
a + k = 0
a = -k
Then the leading coefficients are opposites, the correct option is the first one.
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-2(x+2)<14. i need the answer
Answer:
x > -9
Step-by-step explanation:
-2(x+2)<14
Divide by -2, remembering to flip the inequality
-2(x+2)/-2>14/-2
x+2 > -7
Subtract 2 from each side
x+2-2 > -7-2
x > -9
Evaluate
18/29
×
4/3
Give your answer as a fraction in its simplest form.
Answer:
The answer is 24/ 29
Consider the sequence 18, 15, 12, 9, 6, 3, . . . . What is f(5)?
Answer:
It is 6 because
Step-by-step explanation:
When you see 18 to go 15 its going 3 times down and when you count to 6 its the 5th number so I think it is 6.
F(5)=6
Janey is using a recipe that calls for two Tablespoons of oil for every every 4 tablespoons create a ratio table to determine how tsp of oil she would need if she used 10 water 
Planes X and Y and points J, K, L, M, and N are shown. Vertical plane X intersects horizontal plane Y. Point L is on the left half of plane Y. Point N is on the bottom half of plane X. Point M is on the right half of plane Y. Point K is on the top half of plane X. Point J is above and to the left of the planes. Exactly how many planes contain points J, K, and N?
Answer:
Plane X
Step-by-step explanation:
kindly find attached a rough sketch of the problem, that contains the drawing of the plane.
From the drawing we can see that the plane x contains points K and N.
It can be seen that point J is not located on any plane.
So the answer is only one plane which is plane x contain the point K and N.
A plumber has a 10' piece of PVC pipe how many 9/5 foot pieces can be cut from the 10' piece
Answer:
5.55555556
Step-by-step explanation:
Hope this helps!
in the diagram of movie theater seats, the incline of the floor, f, is parallel to the seats, s.
if m<1= 60, what is c?
if m<1= 68, what is y?
HELPPP PLEASEEE
Answer:
16. x = 40
17. y = 15
Step-by-step explanation:
16. Given that f is parallel to s, therefore by the corresponding theorem and linear pair theorem, <1 + 3x = 180°
60° + 3x = 180° (substitution)
3x = 180° - 60° (Subtraction property of equality)
3x = 120°
x = 120/3 (division property of equality)
x = 40
17. Since f and s are parallel, therefore,
m<1 = (5y - 7)° (alternate interior angles are congruent)
68° = 5y - 7 (substitution)
68 + 7 = 5y (addition property of equality)
75 = 5y
75/5 = y (division property of equality)
15 = y
help plz hurry Which sentence from "Object Lesson, Part 2" most likely causes the reader to feel nervous??
He even emptied Louise's three pots of geraniums and sifted the earth.
The 41 boys and girls were buzzing and giggling now.
Feverishly he went through the remaining dollar-sized strips of comic paper.
This strip had been cut from the top of the comic sheet.
C. Feverishly he went through the remaining strips of paper
Answer:
C
Step-by-step explanation:
The key word "Feverishly", helps me determine the answer. (Also, I just took the test)
Find the first 4 terms, a10, Jamini an n≥3 n-2' and a₁5 of the sequence with the following nth term.
The sequence with the given nth term is n-2. The first four terms of the sequence are a₁ = -1, a₂ = 0, a₃ = 1, and a₄ = 2. The term a₁₀ is equal to 8, a₉ is equal to 7, and a₁₅ is equal to 13.
The given nth term of the sequence is n-2, which means that each term is obtained by subtracting 2 from the corresponding value of n.
To find the first four terms of the sequence, we substitute the values of n from 1 to 4 into the nth term expression. Thus, we have a₁ = 1-2 = -1, a₂ = 2-2 = 0, a₃ = 3-2 = 1, and a₄ = 4-2 = 2.
To find a specific term, we substitute the corresponding value of n into the nth term expression. For example, a₁₀ = 10-2 = 8, a₉ = 9-2 = 7, and a₁₅ = 15-2 = 13.
In summary, the first four terms of the sequence are a₁ = -1, a₂ = 0, a₃ = 1, and a₄ = 2. The term a₁₀ is equal to 8, a₉ is equal to 7, and a₁₅ is equal to 13.
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Brenda went to the store with her dad to buy snacks. They bought a box of 16 snack-size bags of chips for $7.84 and a box of 24 snack-size bags of pretzels for $12.48. How much more do pretzels cost per bag than chips?
Answer:
subtracting 7.84 from 12.48 will give 15.44 this is equal to 12 packets if you dived 12 by the price of 15.44 you will get your answer you may need to round
$0.03 pretzels cost more than cost of bag of chips.
What is Unitary Method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
price of 16 snack- size bags of chips = 7.84
Cost of 1 bag of chip = 7.84 /16
= $0.49
and, price of 24 snack-size bags of pretzels = 12.48
Cost of 1 snack-size bags of pretzels = 12.48 / 24
= 0.52
Hence, by $0.03 pretzels cost more than cost of bag of chips.
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find the coordinates of point P along the directed line segment ST so that SP to PT is the given ratio. 1. S(6,4), T(-4, -8); 1 to 3 2. S(-6, 7), 7(9,25); 2 to 3
First, we find the length of ST and multiply it by the given ratio to get the length of SP. Then, we use the midpoint formula to find the coordinates of point P.1. S(6,4), T(-4, -8); 1 to 3
Let P be the point on the directed line segment ST such that SP : PT = 1 : 3. We need to find the coordinates of P.Step 1: Find the length of ST.
Let S(x1, y1) and T(x2, y2) be the coordinates of S and T respectively. Then we can use the distance formula to find the length of ST.
d(ST) = √[(x2 - x1)² + (y2 - y1)²]
d(ST) = √[(-4 - 6)² + (-8 - 4)²]
d(ST) = √(100 + 144)
d(ST) = √244d(ST) = 2√61
Find the length of SP.We know that
SP : PT = 1 : 3. Therefore,
SP = (1/4)ST.SP = (1/4)(2√61)SP = (1/2)√61
Use the midpoint formula to find the coordinates of P.Let (x, y) be the coordinates of P. Then we can use the midpoint formula to find
(x, y).x = (1/4)(2x2 + 2x1) = (1/4)(2(-4) + 2(6)) = 1y = (1/4)(2y2 + 2y1) = (1/4)(2(-8) + 2(4)) = -1
The coordinates of P are (1, -1).
Once we have the length of SP, we can use the midpoint formula to find the coordinates of P. In the first example, we found that the coordinates of P are (1, -1) if SP : PT = 1 : 3. In the second example, we will use the same method to find the coordinates of P when S(-6, 7) and T(9, 25) are the given points, and
SP : PT = 2 : 3.
We will also find the length of ST, the length of SP, and the coordinates of P.2. S(-6, 7), T(9, 25); 2 to 3Let P be the point on the directed line segment ST such that SP : PT = 2 : 3. We need to find the coordinates of P.Step 1: Find the length of ST.Let S(x1, y1) and T(x2, y2) be the coordinates of S and T respectively. Then we can use the distance formula to find the length of ST.
d(ST) = √[(x2 - x1)² + (y2 - y1)²]
d(ST) = √[(9 - (-6))² + (25 - 7)²]
d(ST) = √(225 + 324)
d(ST) = 3√61
We know that SP : PT = 2 : 3. Therefore,
SP = (2/5)ST.SP = (2/5)(3√61)SP = (6/5)√61
Use the midpoint formula to find the coordinates of P.Let (x, y) be the coordinates of P. Then we can use the midpoint formula to find (x, y).x = (2/5)(x2 + x1) = (2/5)(9 + (-6)) = -3/5 y = (2/5)(y2 + y1) = (2/5)(25 + 7) = 16
The coordinates of P are (-3/5, 16).
To find the coordinates of point P along the directed line segment ST so that SP to PT is the given ratio, we need to find the length of ST and multiply it by the given ratio to get the length of SP. Then, we use the midpoint formula to find the coordinates of point P.
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anybody help me? please
Answer:
0 because we can't have Repetitious x in function.
F(x)= -x^5 + 3x^3 - 3x
PLEASE HELP ME FAST IM CONFUSED!
Answer: (-2,1/2) (0,0) (2,1) (4,2)
Step-by-step explanation:
plug in the number in place of X
An education budget went from $ 800,000 to $ 900,000 . What is the approximate percent increase ?
Answer:
A i think
Step-by-step explanation:
The sum of one interior and one exterior angle of a triangle is degrees.
Answer:
the oppostite
Step-by-step explanation:
Anthony bought a rug for his office. He made a scale drawing of the office using a scale of 1 in = 4 ft.
What is the area of the office floor not covered by the rug?
What is the reason for each step in the solution of the equation?
-62 +72 +14=3
