Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number
solutions does the equation have?
Discriminant = b2-4ac
0
1
2
o 12
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Answers
Step-by-step explanation:
work is shown and pictured
The discriminant of quadratic equation is,
⇒ D = 0
What is Quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form: ax² + bx + c = 0
We have to given that;
Quadratic equation is,
⇒ - 3 = x² + 4x + 1
Now, We can write as;
⇒ x² + 4x + 1 + 3 = 0
⇒ x² + 4x + 4 = 0
Hence, Discriminant of quadratic equation is,
⇒ D = b² - 4ac
⇒ D = (4)² - 4×1×4
⇒ D = 16 - 16
⇒ D = 0
Thus, The discriminant of quadratic equation is,
⇒ D = 0
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Related Questions
A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank.
Required:
a. Write a formula that expresses v in terms of t.
b. As t increases from 3 to 6, v varies from _________ to _________
Answers
Answer:
a) [tex]V(t) = 24 - 2t[/tex]
b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Step-by-step explanation:
The volume of the tank in terms of the time can be described by the following equation:
[tex]V(t) = V(0) - at[/tex]
In which V(0) is the initial volume and a is the hourly decrease rate.
a. Write a formula that expresses v in terms of t.
The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]
Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]
Then
[tex]V(t) = V(0) - at[/tex]
[tex]V(t) = 24 - 2t[/tex]
b. As t increases from 3 to 6, v varies from _________ to _________
[tex]V(t) = 24 - 2t[/tex]
[tex]V(3) = 24 - 2*3 = 18[/tex]
[tex]V(6) = 24 - 2*6 = 12[/tex]
So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Solve for m:
-3(1 – 5m) = — 38 + 8m
Answers
Answer:
m = - 5
Step-by-step Explanation:
[tex]-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}[/tex]
Answer:
-5
Step-by-step explanation:
can someone please help me it’s urgent!!!!!
Answers
Answer:
6/4
Explanation:
If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.
Hope this helps!
What’s the correct answer for this?
Answers
Answer:
C
Step-by-step explanation:
Measure of Arc FED = 51+79
= 130°
Since the measures of arcs and angles are the same
Hence
<FED = 130°
An amount was invested at % r per quarter. What value of rwill ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answers
Answer:
42.67%
Step-by-step explanation:
The annual growth factor for interest at annual rate r compounded quarterly is ...
(1 +r/4)^4
You want that value to be 1.5:
1.5 = (1 +r/4)^4
1.5^(1/4) = 1 +r/4
(1.5^(1/4) -1) = r/4
4(1.5^(1/4) -1) = r ≈ 0.426728
The rate r must be about 42.67%.
_____
Comment on the wording
We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."
The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."
Which is the graph of f(x) = 2(3)^x?
Answers
Answer: The graph is:
If f(x)=x³-2x², which expression equivalent to f(i)?
Answers
Answer:
f(x) = x³ - 2x²
=>
f(i) = i³- 2i²
Hope this helps!
:)
Leroy is 22 years old. His car averages 31 miles
per gallon. His car payments are $165.32 per
month, and he has 36 more payments to
make. How old will he be when he pays off his
car?
Answers
Answer:
he will be 25
Step-by-step explanation:
36 monthly payments left/12 payments a year = 3 years. 22 + 3 = 25
Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standard deviation of 80. Parul Monga is trying desperately to get into this program. What is the minimum score that she must earn to get admitted?
Answers
Answer:
The minimum score that she must earn to get admitted is 523.
Step-by-step explanation:
As the scores are normally distributed, we can calculate the probability using the z-score.
The distribution has a mean of 420 and a standard deviation of 80.
We have to calculate the z-score z* that satisfies:
[tex]P(z>z^*)=0.1[/tex]
This happens for z*=1.28155.
Then, we can calculate the score as:
[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]
Please answer this correctly
Answers
Answer: 363 cm squared
Step-by-step explanation:
So we can split the shape into 1 triangle and 3 rectangles.
We can start with the top right rectangle which is a 4 by 5.
4*5 = 20 cm squared
We can now do the horizontal rectangle. We need to find the dimensions firs by subtracting 4 from 31 to find the length and add 4 and 5 to find the height.
This means the dimensions are 27 by 9.
27 * 9 = 243 cm squared
Now the final square toward the bottom left will be a 10 by 7.
10 * 7 = 70 cm squared.
Now for the final piece is the triangle in the bottom left. We need to first find the height which we can determine by taking the the right hand side values of 10 , 4 and 5 and adding those together then subtracting that number by 13 to get the missing length that will add to 6 to find the height.
10 + 4 + 5 = 19
19 - 13 = 6
6 + 6 = 12
Now that we have the height and base of the triangle we solve for the area.
0.5 * 5 * 12 = 30 cm squared
Now we add all the areas together to find the total area.
20 + 243 + 70 + 30 = 363 cm squared
Dustin is buying carpet for the living room. How many square feet of carpet will he need to buy?
Answers
Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
from a deck of 52 cards, what is the probability of getting a four or diamond.
Answers
Answer:
4/13
Step-by-step explanation:
There are 13 diamonds in a deck and 3 fours that aren't diamond
13+3=16
16/52 = 4/13
Show that an implicit solution of 2x sin2(y) dx − (x2 + 10) cos(y) dy = 0 is given by ln(x2 + 10) + csc(y) = C. Differentiating ln(x2 + 10) + csc(y) = C we get 2x x2 + 10 + dy dx = 0 or 2x sin2(y) dx + dy = 0. Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
Answers
Answer:
Step-by-step explanation:
[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]
Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.
Problem solved
someone pls pls pls help me
Answers
Answer:
A, C, D, E
Step-by-step explanation:
According to the rational root theorem, any rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
The constant is 8, and its divisors are 1, 2, 4, 8.
The leading coefficient is 6, and its divisors are 1, 2, 3, 6.
So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:
A, 2/3C, -8D, 4E, -1/6NEED HELP ASAP
Solve the equation or inequality for the unknown number. Show your work.
Answers
Answer:
5
Step-by-step explanation:
3(14+x) = 57
42 +3x = 57
3x = 15
x = 5
Ania kupiła w księgarni dwie książki i zapłaciła 37,20, a jurek za swoje zapłacił trzy razy więcej. Ile zapłacił jurek
Answers
Answer:
111.60
Question:
Ania bought two books in a bookstore and paid 37.20, and Jurek paid three times more for his. How much did Jurek pay?
Step-by-step explanation:
This is a question on multiplying decimals by natural numbers.
Number if books bought by Ania = 2
Cost for the two books = 37.20
Jurek paid = 3 times the amount Ania paid
Amount Jurek paid = 3×37.20
To multiply decimals with whole numbers, first multiply without the decimals
3×3720 = 11160
3 has no decimal place
37.20 has 2 decimal place
Therefore the answer would be in two decimal place = 111.60
So 3× 37.2= 111.60
~I will mark as BRANLIEST and give you 55 points if you answer correctly.
Answers
Answer:
The lines would intersect at: (6, -4)
Step-by-step explanation:
I graphed both lines.
Answer:
(4,-2)
Step-by-step explanation:
The equation for the graphed line is [tex]y=\frac{1}{2} x-4[/tex] as it has a slope of [tex]\frac{1}{2}[/tex] and a y-intercept of -4.
Now that we have the two equations, we can set them equal to each other to find the x-value at which they intersect
[tex]\frac{1}{2} x-4=-x+2[/tex]
First, we can add 4 to each side
[tex]\frac{1}{2} x=-x+6[/tex]
Then we can add x to each side
[tex]\frac{3}{2} x=6[/tex]
Now we need to divide both side by [tex]\frac{3}{2}[/tex], which is the same thing as multiplying by [tex]\frac{2}{3}[/tex]
[tex]x=6*\frac{2}{3} \\\\x=\frac{12}{3} \\\\x=4[/tex]
Now that we have the x-value, we can plug it into one of the equations to see the y-value for where they intersect.
[tex]y=-x+2\\\\y=-(4)+2\\\\y=-2[/tex]
This means that the coordinates for the intersection of these two lines would be [tex](4,-2)[/tex]
Arlinda says there is a linear relationship between the price (p) of 500ml soft drink and the number sold (x). The formula is x = ap + b where a and b are constants. At N$20 she sells 1500 of the 500ml soft drinks but the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. At what price will 600 of the 500ml energy drinks be sold?
Answers
Answer: 600 of the 500ml energy drinks be sold be sold at $45
Step-by-step explanation:
The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as
x = ap + b
At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be
1500 = 20a + b - - - - - - - - -1
the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300
The price at which they were sold is
20 + (50/100 × 20) = $30
The second equation would be
1300 = 30a + b - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
200 = - 10a
a = 200/- 10 = - 20
Substituting a = - 20 into equation 2, it becomes
1300 = 10 × - 20 + b
1300 = - 200 + b
b = 1300 + 200 = 1500
The linear relationship becomes
x = - 20p + 1500
If x = 600, then
600 = - 20p + 1500
- 20p = 600 - 1500 = - 900
p = - 900/ - 20
p = $45
The freezer contains vanilla and chocolate ice cream. Chocolate ice cream contains 12 servings less than vanilla. How many servings of vanilla ice cream are in the freezer if there are a total of 40 servings of ice cream? (Solve by building an equation)
Answers
Answer:
26 servings
Step-by-step explanation:
Let the number of servings of vanilla ice cream be x.
Number of servings of chocolate ice cream
= x -12
(since it has 12 servings less than vanilla)
Total servings= servings of chocolate+ vanilla
x + x-12= 40
2x -12 =40 (simplify)
2x= 40 +12 (+12 on both sides)
2x= 52 (simplify)
x= 52 ÷2
x= 26
Therefore, there are 26 servings of vanilla ice cream in the freezer.
Please help. I’ll mark you as brainliest if correct!
Answers
Answer:
a= -3/8
b= 1/8
Step-by-step explanation:
To remove i from the denominator, we need to multiply the numerator and denominator by -i
[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]
This simplifies to
[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]
This further simplifies to
[tex]\frac{i-3}{8}[/tex]
This can be rewritten as
[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]
a= -3/8
b= 1/8
Answer:
[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]
Step-by-step explanation:
[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]
hord
12 cm
5 cm
Resu
5 cm
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the
height of the prism is placed inside the prism, as shown in the figure.
SUME
The volume of the space outside the pyramid but inside the prism is
cubic centimeters,
Answers
Answer:
The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.
Step-by-step explanation:
To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.
The prism and pyramid's bases is 25 cm²
The pyramid's height is 12÷2 or 6 cm
The volume formula for a prism is l×w×h
The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h
The area of the prism is 5×5×12 or 300 cm³
The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³
300 cm³-75 cm³=225 cm³
The volume outside the pyramid but inside the prism is 225 cm³.
Twice the difference of a number and 4 is equal to three times the sum of the number and 6. Find the number.
The number is
Answers
Answer:
-26
Step-by-step explanation:
2(x-4)=3(x+6)
2x-8=3x+18
2x-2x -8 = 3x-2x +18
-8 =X+18
-8-18=x+18-18
-26 = x
The value of the unknown number is -26.
Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number x.
Twice the difference of a number and 4 = 2(x-4)
Three times the sum of the number and 6 = 3(x+6)
So, equation is 2(x-4)=3(x+6)
⇒ 2x-8=3x+18
⇒ 3x-2x=-8-18
⇒ x=-26
Therefore, the value of the unknown number is -26.
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Sick computers: Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose
P(V) = 0.47, P(W) = 0.37, P(Vand W) = 0.01
(a) Find the probability that the computer contains either a virus or a worm or both.
(b) Find the probability that the computer does not contain a worm
Part 1 of 2
(a) Find the probability that the computer contains either a virus or a worm or both.
The probability that the computer contains either a virus or a worm or both is
Х
5
Part 2 of 2
(b) Find the probability that the computer does not contain a worm
The probability that the computer does not contain a worm is
Х
Answers
Answer:
0.83
0.63
Step-by-step explanation:
P(V or W) = P(V) + P(W) − P(V and W)
P(V or W) = 0.47 + 0.37 − 0.01
P(V or W) = 0.83
P(not W) = 1 − P(W)
P(not W) = 1 − 0.37
P(not W) = 0.63
a. the probability that the computer contains either a virus or a worm or both is 0.83
b. The probability that the computer does not contain a worm is 0.63.
Calculation:(a)
The probability is
P(V or W) = P(V) + P(W) − P(V and W)
P(V or W) = 0.47 + 0.37 − 0.01
P(V or W) = 0.83
(b) The probability is
P(not W) = 1 − P(W)
P(not W) = 1 − 0.37
P(not W) = 0.63
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Classify the following triangle. Check all that apply.
35°
10.1
7
102"
6
O A. Isosceles
O B. Equilateral
O c. Obtuse
O D. Right
O E. Scalene
F. Acute
Answers
Answer: obtuse and scalene
Step-by-step explanation:
Answer:
Obtuse And Scalene
Step-by-step explanation:
trust me!
Omar has three t shirts: one red, one green and one yellow. He has two pairs of shorts one black and red.
-How many different outfits can Omar put together?
-What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Answers
Answer:
Omar can put together 6 outfits.
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
-How many different outfits can Omar put together?
For each t-shirt, that are two options of shorts.
There are 3 t-shirts.
3*2 = 6
Omar can put together 6 outfits.
What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Red t-shirt and red shorts
Red t-shirt and black shorts
Green shirt and red shorts
Yellow shirt and red shorts
4 desired outcomes.
4/6 = 0.6667
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
Select all fractions that are equal to 3/4
Answers
3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..
I hope this is what you are looking for :)
The equation 4x-45=y is used to find your profit y in dollars from buying $45 of supplies and washing cars for $4 what does the x stand for
Answers
what is the midpoint of the segment shown below?
(1, 2) (1,-5)
A. (1, -3/2)
B. (2, -3/2)
C. (2, -3)
D. (1, -3)
Answers
Answer:
The answer is A (1,-3/2)
Step-by-step explanation:
Add both x coordinates, divide by 2
Add both y coordinates, divide by 2
Find the volume of the cone.
Please help
Answers
Answer:1232m^3
Step-by-step explanation:
1/3 *22/7*7^2*24
1232m^3
Please help. I’ll mark you as brainliest if correct!!!!
Answers
Answer:
a= 2/5
b= -3/5
Step-by-step explanation:
We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator
[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]
This simplifies to:
[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]
This further simplifies to:
[tex]\frac{-3i +2}{5}[/tex]
Can be rewritten as:
[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]
a = 2/5
b = -3/5
