Answers
Answer:
We have 2 rational solutions
0 irrational solutions
0 complex solutions
Step-by-step explanation:
a^2 + 8a + 12 = 0
Using the discriminant
b^2 -4ac where ax^2 + bx+ c
so a =1 b = 8 and c = 12
8^2 -4(1)*12
64 - 48
16
Since the discriminant is greater than 0, we have 2 real solutions
since we can take the square root of 16, we have rational solutions
We have 2 rational solutions
Since this is a quadratic equations, there are only 2 solutions so there are
0 irrational solutions
0 complex solutions
Answer:
2 Rational Solutions
0 Irrational Solutions
0 Complex Solutions
Step-by-step explanation:
The discriminant of the quadratic formula is the name given to the portion underneath the radical (or the square root)"
\(x = \frac{1}{2} (-b\frac{ + }{ - } \sqrt{ {b}^{2} - 4ac })\)
Discriminant = D = b²-4ac
If D is less than 0 you have two complex solutions.
If D is equal to 0 you'll have one real solution.
If D is bigger than 0 you'll get two real solutions.
So here we have:
a=1
b=8
c=12
Which means D=64-4(1)(12)=64-48=16>0
D is bigger than 0, so you'll have two real solutions. And since 16 is a perfect square, they'll both be rational numbers.
Related Questions
6a. In King County the sales tax is 9.5%. What is the total tax collected (tax ONLY) on a purchase of $222.00?
6b. In Renton the sales tax is 9%. What is the total cost including tax on a $20 purchase?
Answers
Answer:
6a. The interest is: $21.09
6b. The total cost is: $21.80
which expression is equal to 4 to the power of 5 times 4 to the power of -7 divided by 4 to the power of -2
Answers
Andre cycled a distance 25km in 150 minutes. What was his average speed (km/h)?
Answers
Answer:
10 km/h
Step-by-step explanation:
First, convert 150 minutes to hours:
150/60
= 2.5 hours
Then, to find his speed, divide the km by the number of hours:
25/2.5
= 10 km/h
Answer:
10 km / hr
Step-by-step explanation:
We want to find the average speed in kilometers per hour.
We know that Andre cycled 25 kilometers in 150 minutes.
First, we have the convert 150 minutes to hours.
There are 60 minutes in 1 hour, so we can divide 150 by 60.
150/60= 2.5
Next, find the average speed in kilometers per hour.
Divide the kilometers traveled by the hours.
speed = kilometers / hours
Andre cycled 25 kilometers in 2.5 hours.
speed= 25 km /2.5 hrs
speed = 10 km/hr
Andre’s average speed was 10 kilometers per hour.
DUE IN A FEW MINS PLEEEASE HELP QUICKLY TY
A bank offers two different types of savings account which pay interest as shown below. Hannah wants to invest £3200 in one of these accounts for 13 years. a) Which account will pay Hannah more interest after 13 years? b) How much more interest will that account pay? Give your answer in pounds (£) to the nearest 1p. Account 1 Simple interest at a rate of 5% per year Account 2 Compound interest at a rate of 4% per year
Answers
Part A: account 2 gives the more interest when Compounding.
Part A: account 2 give more interest of amount £1170.
Explain about the Simple interest?Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).
Given data:
Account 1 - Simple interest at a rate of 5% per year.
Account 2 - Compound interest at a rate of 4% per year.
Principal P - £3200
Time t - 13 years.
Part A:
SI = PRT/100
SI = 3200*4*13 / 100
SI = £1664
CI = A - P
CI = P\((1 + r)^{t}\) - P
CI = 3200\((1 + 0.05)^{13}\) - 3200
CI = 6034 - 3200
CI = £2834
Thus, account 2 gives the more interest when Compounding.
Part B:
Difference = CI - SI
Difference = 2834 - 1664
Difference = 1170
Thus, account 2 give more interest of amount £1170.
Know more about the Simple interest
https://brainly.com/question/25793394
#SPJ1
Question 4 of 10
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
□A. √2:√2
B. 15
□ C. √√√√5
□ D. 12
DE √3:3
OF. √2:√5
←PREVIOUS
SUBMIT
Answers
The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).
In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.
A. √2:√2
The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.
B. 15
This is a specific value and not a ratio. Therefore, option B is not applicable.
C. √√√√5
The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.
D. 12√3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.
E. √3:3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.
F. √2:√5
This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.
For more such questions on lengths
https://brainly.com/question/28322552
#SPJ8
a. (5x -9) - (2x -7) b. (6x -10) -(2x-8)
Answers
Answer:
!!
Step-by-step explanation:
(5x-9)-(2x-7)
(5x-2x)-(9-7)
3x-2
2 / 3
x=2/3 or 0.6666666666666667
f the recommended adult dosage for a drug is d (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417d(a + 1). suppose the dosage for an adult is 100 mg. (a)
Answers
The slope of graph is 4.17 (a+1). It represents the annual rise in dose a.
Who are pharmacists ?Excellent understanding of medications, their mechanisms of action, side effects, interactions, mobility, and toxicity are prerequisites for practicing pharmacy. Thus, pharmacists are the key healthcare professionals who maximize the use of medicine for the benefit of patients. They are also the world's foremost authorities on drug therapy.
The pharmacist use equation C= 0.0417 d (a+1)
Applying in (mg)
So d = 100 mg
Therefore c = 0.0417×100 (a+1)
C= 4.17 (a+1)
4.17 (a+1) is the slope for the graph of c, which reflects the annual rise in dose a.
kid requires. Given that a newborn is age 0, the appropriate dosage is
c(0) = 4.17 (a+1)
Complete question is -If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417D(a + 1). Suppose the dosage for an adult is 200 mg.
(a) Find the slope of the graph of c. What does it represent?
To know more about about pharmacists from given link
https://brainly.com/question/17207269
#SPJ4
Then draw a position vs. time graph describing the motion. Have students help you complete the graph. Is the line straight? Is it curved?
Answers
Position vs. time graph is a graph that shows the position of an object over time. It can be a straight line or a curved line depending on the motion of the object.
What is graph ?
A graph is a mathematical structure used to represent relationships between objects. In a graph, objects are represented by vertices (or nodes) and relationships are represented by edges (or arcs). Graphs can be used to model a wide variety of real-world systems, including networks of roads, social networks, and the internet.
The position vs. time graph is a visual representation of an object's motion, where the position of the object is plotted on the y-axis and the time it took to reach that position is plotted on the x-axis. The graph helps to show the relationship between the position and time of an object in motion. The line on the graph can be either straight or curved, depending on the type of motion the object is undergoing. If the object is moving at a constant speed, the line will be straight. If the object is accelerating or decelerating, the line will be curved.
Position vs. time graph is a graph that shows the position of an object over time. It can be a straight line or a curved line depending on the motion of the object.
To learn more about graph visit : brainly.com/question/17267403
#SPJ4
Suppose the total benefit derived from a given decision, Q is B(Q)=40Q−2Q^2 , and the corresponding total cost is C(Q)=4+2Q^2. What level of Q will yield the maximum net benefits? How much is the maximum level of benefits? o 4,96 o 4. 92 o 5,92 o 5,96
Answers
The level of Q that will yield the maximum net benefits is 4.92, and the maximum level of benefits is 96.
To find the level of Q that maximizes net benefits, we need to calculate the difference between the total benefits (B(Q)) and the total costs (C(Q)). In this case, the net benefits (NB) can be represented as NB(Q) = B(Q) - C(Q).Given B(Q) = 40Q - 2\(Q^2\) and C(Q) = 4 + 2\(Q^2\), we can substitute these expressions into the net benefits equation:
NB(Q) = (40Q - 2\(Q^2\)) - (4 + 2\(Q^2\))
Simplifying, we get:
NB(Q) = 40Q - 2\(Q^2\) - 4 - 2\(Q^2\)
NB(Q) = -4\(Q^2\) + 40Q - 4
To find the level of Q that maximizes net benefits, we need to find the value of Q that maximizes NB(Q). This can be done by finding the maximum point of the quadratic function. In this case, the maximum point occurs at the vertex of the quadratic.
The formula for the x-coordinate of the vertex of a quadratic function of the form a\(x^2\) + bx + c is given by x = -b / (2a). In our case, a = -4 and b = 40.
Calculating the x-coordinate of the vertex:
Q = -40 / (2 * -4)
Q = 40 / 8
Q = 5
Therefore, the level of Q that yields the maximum net benefits is Q = 5. Plugging this value back into the net benefits equation, we can calculate the maximum level of benefits:
NB(5) = -4\((5)^2\) + 40(5) - 4
NB(5) = -4(25) + 200 - 4
NB(5) = -100 + 200 - 4
NB(5) = 96
Hence, the maximum level of benefits is 96.
Learn more about quadratic function here:
https://brainly.com/question/18958913
#SPJ11
Latoya earns 41 dollars per week working part-time at a book store. She makes one dollar more for each book that she sells. The amount, A (in dollars), that Latoya earns in a week if she sells b books is given by the following.
A=41+b
How much does Latoya earn in a week if she sells 16 books?
Answers
Answer:
57$
Step-by-step explanation:
The equation is A= 41 + b
A represents the entire amount she makes that week.
41 is the minimum she makes every week.
b represents any books she sells which earn an extra 1 dollar.
Plug in 16 books into the equation.
A= 41+ 16
A= 57
7. What is the slope of the line
Problem Set #4
2-y=8x ?
Answers
Answer:
To find the slope of the line, you can use the formula for slope: slope = (y2 - y1)/(x2 - x1). In this case, you can rewrite the equation 2-y = 8x as y = 2 - 8x. This is the standard form of a line: y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
Since the equation of the line is already in standard form, you can find the slope by looking at the coefficient of the x term. In this case, the coefficient of the x term is -8, so the slope of the line is -8.
Alternatively, you can plug in the coordinates of two points on the line into the formula for slope to find the slope. For example, if you know that the line passes through the points (1, -14) and (2, -10), you can use these points to find the slope:
slope = (y2 - y1)/(x2 - x1) = (-10 - (-14))/(2 - 1) = (-10 + 14)/1 = 4/1 = 4
This method gives the same result as using the standard form of the equation.
Step-by-step explanation:
answers surface area of the prism round to the nearest tenth choose the correct units
Answers
Here, we want to get the value for the surface area of the prism
Mathematically, this is the sum of the surface area of the base and that of the sides
Now, as we can see, we have two triangular bases (with the areas given)
What we need next is to get the area of the face, which is a rectangle of side measure 8.1 in by 12 in
The value here is the product of the dimensions
We have this as;
\(\text{Area}=\text{ 8.1 }\times\text{ 12 = 97.2 square inches}\)Finally, we know that the net of a triangular prism contains 3 rectangles and 2 triangles
Answer:
Trying to find the surface area of our rectangular prism.
Step-by-step explanation:
Which two expressions are equivalent?
a.) 2a and 9/3 (a)
b.) 5a and 3(2a)
c.) 4a - 2a and a+a
d.). 4a - a and 1+1+1+a
Answers
Answer:
C) 4a-2a=a+a
Step-by-step explanation:
4a-2a=2a
2a=a+a
2a=2a
answer:
option c is correct!
explanation:
hope this helped! <3 i answered your question & hope you have a great day! if you wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)
I need help!!!!!!!!!!!
Answers
Answer:
6.28 miles
Step-by-step explanation:
C=πd=π·2≈6.28319mi
i hoped this helps you <3
3.1x^3-2.4x² +6x – 3 = 4x² + 3x +2
solving problem
Answers
Answer:
The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;
x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i
Step-by-step explanation:
The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2
Which gives;
3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0
3.1·x³ - 6.4·x²+ 3·x - 5 = 0
Factorizing online, we get;
3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0
Therefore, the possible solutions are;
x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0
The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;
x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i
Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;
x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.
find a number if 0.7 of it is 3.43.
Answers
It shouldn’t be a trick question just fake 3.43 minus .7!
Blaine and Lindsay McDonald have total assets valued at $346,000 and total debt of $168,000. What is Blaine and Lindsay's asset-to-debt ratio? a-0.49 b. 0.51 c.2.06 d.1.00
Answers
The correct answer is option (c) 2.06. For every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets
The asset-to-debt ratio for Blaine and Lindsay McDonald can be calculated by dividing their total assets by their total debt. Using the given values, the calculation would be as follows:
Asset-to-debt ratio = Total assets / Total debt
= $346,000 / $168,000
The asset-to-debt ratio is a financial metric that provides insight into the financial health and leverage of an individual, company, or entity. It measures the proportion of assets to debt and is used to assess the ability to meet financial obligations and the level of risk associated with the amount of debt.
In this case, Blaine and Lindsay McDonald have total assets valued at $346,000 and total debt of $168,000. By dividing the total assets by the total debt, we obtain the asset-to-debt ratio of approximately 2.06. This means that for every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets. A higher asset-to-debt ratio generally indicates a stronger financial position and lower risk, as there are more assets available to cover the debt obligations.
Learn more about asset-to-debt ratio here:
https://brainly.com/question/30253017
#SPJ11
I need some help quick
Answers
Answer:
B. 110.... i think because the whole question is not showing
Step-by-step explanation:
if 8 is 70 and you want to know of 7 because 180 is a line then you do 180-70 and get 110
Answer:
D
Step-by-step explanation:
Corresponding means they are m∠=8
The temperature last evening was 15°Fahrenheit. It dropped 33° last night (-33). By noon today, it has warmed up only 5°. Add positive & negative numbers to tell what the temperature was at noon today?
Answers
Answer:
-13°
Step-by-step explanation:
Start at 15°
Subtract 33° -----> 15-33= -18°
It has warmed up by 5° (+5) -----> -18+5= -13°
Which expression can be used to determine the volume of water in a rain barrel after days if there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day?
Answers
The required expression is given by 179.2 - 10.6d.
There were 179.2 gallons of water in the barrel and 10.6 gallons are used each day
Volume, is defined as the ratio of the mass of object to its density.
the volume of water in a rain barrel after "d"days
When there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day.
since the amount of water is getting consumed day by day
therefore, the expression can be given as
= 179.2 - 10.6d
Thus, the required expression is 179.2 - 10.6d.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ1
Urgent please answer will award brainliest
Answers
(x - 5)(5x + 2) = 0 (please help)
Answers
Answer:
x=-5
Step-by-step explanation:
please tell me if im wrong lol
Answer:
\( (5 , - 0.4)\)
What is the opposite of negative seven?
Answers
Answer: 7 is the opposite of negative 7
Step-by-step explanation:
Hope this helps :)
Can someone help me solve for
Answers
Which equation represents a line that passes through 5 1 and has a slope of StartFraction one half EndFraction?.
Answers
The equation of line which passes through point (5,1) and having slope ½ is (y-1) = ½ (x-5).
What is the equation of a line?
The equation of a line is given as:
y = mx + c
The equation for the point on slope line is given as:
y - y1 = m ( x - x1 )
Substituting the above given values and the slope:
y - 1 = \(\frac{1}{2}\) ( x - 5)
Hence, the equation of line which passes through point (5,1) and slope ½ is (y-1) = ½ (x-5).
Learn more about line equation, here:
brainly.com/question/2564656
#SPJ4
Solve the question :
5x > - 12
Answers
Answer:
x> -12/5
Step-by-step explanation:
Divide both sides (5x and 12) and re write
5x ÷ 5 > -12 ÷ 5
Thus the solution given above
Answer : x> - 12
5
divide both side by 5
x + ( 12/5 ) > 0
The city of Houston received 8 more inches of rain than the town of Groesbeck. Which algebraic expression represents the amount of rain in Houston?
Answers
Answer:
8-i=g
Step-by-step explanation:
g= amount of rain Groesbeck gout
i = inches of rain
Answer:
saw this question on egde its b
A bowl contains 15 blackberries. There are 5
blackberries for every 3 raspberries. How mar
raspberries are in the bowl?
Answers
So there are 5 raspberries in the bowl.
Define Unitary Method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
Define ratio and proportion.Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.
We know that for every 3 raspberries, there are 5 blackberries.
We can set up an equation to represent this relationship:
5 blackberries = 3 raspberries
We also know that there are a total of 15 blackberries in the bowl.
We can use the equation to find the number of raspberries in the bowl:
15 blackberries = 3 raspberries
15 blackberries / 3 raspberries = 5 raspberries
So there are 5 raspberries in the bowl.
To learn more about unitary method visit:
brainly.com/question/28276953
#SPJ1
How many variables are in the equation? 7y + 2x + 8 = 29 *
Answers
Answer:
Y and X AKA 2
Step-by-step explanation:
write the sequence of natural numbers which leaves the remainder 3 on didvidng by 10
Answers
The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)