Answers
To determine equations with no real solutions, assess for a negative discriminant or no x-intercepts in quadratic equations. Steps include identifying unknowns, choosing appropriate equations, simplifying terms, and checking for reasonableness.
Explanation:To select each equation that has NO real solution, we must assess the equations provided, looking for specific characteristics that indicate the absence of real solutions. One of the hallmarks of such equations is when they represent a quadratic equation with no x-intercepts or the discriminant (b^2 - 4ac) in the quadratic formula is negative, which means the roots are complex numbers.
When working on problems like these, it's crucial to go through several steps: Identify the unknown, identify the knowns, choose an equation, eliminate terms to simplify the algebra, and then check the answer to see if it is reasonable.
Let's use an example equation: x^2 + 4 = 0. To determine if this has real solutions, we can identify the unknown (x), the knowns (coefficients of x), solve the equation or calculate the discriminant (4^2 - 4*1*-4 = 16 +16 = 32, which is positive), and confirm whether the solutions are real or not. In this case, because the discriminant is positive, this equation does have real solutions, and therefore would not be included in a list of equations with no real solutions.
The equations 2x² - 4x + 5 = -3, x² - 12x + 60 = 12, and x² + 3x + 6 = 0 have no real solutions, based on their negative discriminants.
We need to determine the discriminant (b² - 4ac) of each equation to check for real solutions. A negative discriminant indicates no real solutions.
Equations Analysis
2x² + 2x = 2: Rewrite as 2x² + 2x - 2 = 0. Here, a = 2, b = 2, c = -2. The discriminant is 2² - 4(2)(-2) = 4 + 16 = 20 (positive, so there are real solutions).2x² - 4x + 5 = -3: Rewrite as 2x² - 4x + 8 = 0. Here, a = 2, b = -4, c = 8. The discriminant is (-4)² - 4(2)(8) = 16 - 64 = -48 (negative, so there are no real solutions).x² - 12x + 60 = 12: Rewrite as x² - 12x + 48 = 0. Here, a = 1, b = -12, c = 48. The discriminant is (-12)² - 4(1)(48) = 144 - 192 = -48 (negative, so there are no real solutions).x² - 4 = 0: This is already in quadratic form with a = 1, b = 0, c = -4. The discriminant is 0² - 4(1)(-4) = 16 (positive, so there are real solutions).x² + 3x + 6 = 0: Here, a = 1, b = 3, c = 6. The discriminant is 3² - 4(1)(6) = 9 - 24 = -15 (negative, so there are no real solutions).Equations with No Real Solutions
2x² - 4x + 5 = -3x² - 12x + 60 = 12x² + 3x + 6 = 0Complete Question - Select each equation that has no real solution.
2x² + 2x = 22x² - 4x + 5 = -3 x² - 12x + 60 = 12 x² - 4 = 0 x² + 3x + 6 = 0Related Questions
Can you guys help me figure this out ?
Answers
1 the side opposite ∡L is NM-------------- > is true
2 the side opposite ∡N is ML-------------- > is true
3 the hypotenuse is NM------------> is false
because the hypotenuse is the side NL
4 the hypotenuse is the side NL---------- > is true
5 the side adjacent ∡L is NM-------------> is false
because the sides adjacent are ML and NL
6 the side adjacent ∡N is ML-------------> is false
because the sides adjacent are NM and NL
what is a solution to the equation 6t=114
Answers
The value of √222 is between which two integers?
a) between 13 and 14
b) between 14 and 15
c) between 15 and 16
d) between 12 and 13
Answers
15 = √225
√196 < √222 < √225
14 < √222 < 15
b) between 14 and 15
A certain car costs $11,595 before taxes are added. Taxes are $860 and license tags cost $95. What is the overall tax rate (to the nearest tenth)?
0.8%
7.4%
8.2%
12.1%
Answers
[tex]860 + 95 = 955 [/tex]
Then, we can make the following rule of three:
11595 ---------> 100%
955 ------------> x
From here, we clear the value of x.
We have then:
[tex]x = (955/11595) * (100) [/tex]
x = 8.2%
Answer:
The overall tax rate (to the nearest tenth) is:
8.2%
Answer:
8.2%
Step-by-step explanation:
o-ware
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why ΔLMN ≈ΔOPQ?
Check all that apply.
A. LL
B. LA
C. SAS
D. HL
E. ASA
F. AAS
Answers
HL congruence theorems or postulates used to prove ΔLMN ≈ΔOPQ.
What is Congruency?Congruent figures have sides that are the same length and angles that are the same measurement. In other words, congruent figures are those in which one figure superimposes another.
If two line segments have the same length, they are said to be congruent. If two angles have the same measure, they are said to be congruent. If the matching sides and angles of two triangles are equal, they are said to be congruent.
We have two Triangles as ΔLMN and ΔOPQ
As, per the figure both triangles are Right angles Triangle.
Also, LM = OP
MN = PQ
LN = OQ
and, the hypotenuse of both triangles also Equal.
Thus, both triangle are Congruent using HL theorem.
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The average age of instructors at a local college is 55, with a standard deviation of 6 years; the average salary is $37,000 with a standard deviation of $4100. which is more variable?
Answers
CV = (SD/X) x 100
Where: CV = Coefficient of Variance
X = Mean/average
SD = Standard Deviation
To determine which one is more variable, just get the coefficient of both and compare.
AGE SALARY
CV = (6/55) x 100 CV = (4,100/37,000) x 100
= 10.90 = 11.08
Based on the results, salary is more variable because 10.90<11.08.
Andrew is given a weekly allowance of $17.50 he uses $4.50 for lunch on Monday what amount at the most can he spend each day if he wants to spend the same amount each of the remaining 4 days write an inequality and solve
Answers
The inequality representing Andrew's spending limit is d <= $3.25, where d is the daily spending amount for the remainder of the week. Solving this, Andrew can spend at most $3.25 per day for the next 4 days.
Andrew received a weekly allowance of $17.50. He spent $4.50 on lunch on Monday. The question is how much at most can he spend each day for the remaining 4 days if he spends the same amount each day. To answer this, we subtract the amount spent on Monday from the total weekly allowance to find the remaining balance. Then, we divide this remaining balance by the number of days left in the week to find the daily spending limit:
Total allowance = $17.50
Spent on Monday = $4.50
Remaining balance = Total allowance - Spent on Monday
= $17.50 - $4.50
= $13.00
Days left in the week = 4
Daily spending limit = Remaining balance \/ Days left
= $13.00 / 4
= $3.25
On average how many words can 400 turtles type in 400 minutes?
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Using fermat's little theorem, find the least positive residue of $2^{1000000}$ modulo 17.
Answers
[tex]a^p[/tex]≡a mod p
If we divide both sides by a, then
[tex]a^{p-1}[/tex]≡1 mod p
=>
[tex]a^{17-1}[/tex]≡1 mod 17
[tex]a^{16}[/tex]≡1 mod 17
Rewrite
[tex]a^{1000000}[/tex] mod 17 as
[tex]=(a^{16})^{62500}[/tex] mod 17
and apply Fermat's little theorem
[tex]=(1)^{62500}[/tex] mod 17
=>
[tex]=(1)[/tex] mod 17
So we conclude that
[tex]a^{1000000}[/tex]≡1 mod 17
By applying Fermat's Little Theorem, we can find the least positive residue of [tex]2^{1000000[/tex] modulo 17. Using the repeated squaring method, we calculate that [tex]2^{16[/tex] is congruent to 1 modulo 17. Therefore, [tex]2^{1000000[/tex] is also congruent to 1 modulo 17.
Fermat's Little Theorem states that if p is a prime number and a is any positive integer that is not divisible by p, then a raised to the power of p-1 is congruent to 1 modulo p. In this case, we need to find the least positive residue of 2 raised to the power of 1000000 modulo 17.
First, we need to find the value of 2 raised to the power of 16 modulo 17, since 17 is a prime number. Using the repeated squaring method, we can calculate:
[tex]2^2[/tex] = 4 (mod 17)
[tex]2^4[/tex] = [tex](2^2)^2[/tex] = [tex]4^2[/tex] = 16 (mod 17)
[tex]2^8[/tex] = [tex](2^4)^2[/tex] = [tex]16^2[/tex] = 1 (mod 17)
[tex]2^{16[/tex] = [tex](2^8)^2[/tex] = [tex]1^2[/tex] = 1 (mod 17)
Now, we can find the value of [tex]2^{1000000[/tex] modulo 17 using the fact that [tex]2^{16[/tex] is congruent to 1 modulo 17:
[tex]2^{1000000[/tex] = [tex](2^{16})^{62500[/tex] x [tex]2^0[/tex] = [tex]1^{62500[/tex] x 1 = 1 (mod 17)
Therefore, the least positive residue of [tex]2^{1000000[/tex] modulo 17 is 1.
bonnie had 6 bags of 6 gel pens. she wanted to give the same number of gel pens to 9 friends. how many gel pens did each friend get?
Answers
Hope that helps!
If a ball is dropped near the surface of the earth, then the distance it falls is directly proportional to the square of the time it has fallen. A ball is dropped over the edge of a vertical cliff and falls 39.2 meters in two seconds. Determine the distance (in meters) the ball would have dropped in 3.5 seconds.
Answers
Explanation:
1) That the distance fallen is directly proportion of the square of the time, means:
distance = k * t^2 => k = distance / t^2
2) Use it for the two set of data given:
a) 39.2 m, 2 s => k = 39.2 m / (2 s)^2
b) x, 3.5 s => k = x / (3.5 s)^2
3) Equal the two expressions for k:
39.2 m / (2s)^2 = x / (3.5s)^2
=> x = 30.2 m * (3,5s)^2 / (2s)^2 = 39.2m * 12.25 / 4 = 120.05m = 120 m
I would like to sell 3 gallon cans of peaches. what would the diameter of the base of the can need to be for it to be 6 inches tall and able to hold 3 gallon(s) of liquid? (note: 1 gallon = 231 cubic inches)
Answers
.. V = π*(d/2)^2*h
.. 3*(231 in^3) = (π/4)*d^2*(6 in) . . . . fill in the give numbers
.. (3*231*4)/(6π) in^2 = d^2 . . . . . . . . divide by the coeffient of d^2
.. d = √147.06 in ≈ 12.13 in . . . . . . . . take the square root
The diameter of the base would need to be about 12.13 inches.
An American car company has designed a new high fuel efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency in SI units. What is the fuel usage rate in kilometers per liter?
Answers
Cheryl falkowski has a collection of silver spoons from all over the world. she finds that she can arrange her spoons in sets of 77 with 44 left over, sets of 88 with 33 left over, or sets of 1515 with 1414 left over. if cheryl has fewer than 200 spoons, how many are there?
Answers
.. 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, 179, 194 (separated by 15)
Modulo 8, these numbers are
.. 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2
This reduces the numbers of interest to those that are 3 modulo 8:
.. 59, 179 (separated by 8*15 = 120)
Looking at these modulo 7, we have
.. 3, 4
pinpointing 179 as the number of spoons in Cheryl's collection.
_____
The attachment shows a solution via graphing calculator. We simply added the absolute values of the differences of the remainders from the desired values and looked for where that sum was zero. This method, too, pointed to 179 as the solution to the problem.
Steven has 14 steel balls of equal weight. If he puts 9 of them in one pan of a pan balance and the rest along with a weight of 20 grams in the other pan, the pans balance each other. What is the weight of one steel ball?
Answers
4x = 20
x = 20/4 = 5
each one weighs 5 grams
Answer:
Step-by-step explanation:
A basketball player makes 40% of his shots from the free throw line. suppose that each of his shots can be considered independent and that he throws 3 shots. let x = the number of shots that he makes. what is the probability that he makes 2 shots or less?
Answers
_____
P(≤2) = 1-P(3) = 1-(0.4)^3 = 1 -0.064 = 0.936
Using the binomial distribution, it is found that there is a 0.936 = 93.6% probability that he makes 2 shots or less.
-------------------
For each throw, there are only two possible outcomes. Either the player makes it, or he misses it. The probability of making a throw is independent of any other throw, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this question:
The player makes 40% of the shots, thus [tex]p = 0.4[/tex]3 shots, thus [tex]n = 3[/tex]The probability of making 2 or less is the probability that he does not make all of them, that is:
[tex]P(X < 3) = 1 - P(X = 3)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.4)^{3}.(0.6)^{0} = 0.064[/tex]
[tex]P(X < 3) = 1 - P(X = 3) = 1 - 0.064 = 0.936[/tex]
0.936 = 93.6% probability that he makes 2 shots or less.
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Brett is making a fruit salad. The recipe calls for 1
1
2
cups of apple,
3
4
cup of oranges, and
2
3
cup of grapes. How many cups of fruit salad will Brett’s recipe make
Answers
[tex]\boxed{ 1\frac{1}{2}+ \frac{3}{4} + \frac{2}{3} = 2 \frac{11}{12} }[/tex]
She would then have to use only (2)11/12 of fruit.
Evaluate these quantities.
a.−17 mod 2
b.144 mod 7
c.−101 mod 13
d.199 mod 19
Answers
-17/2 = 8.5 2*.5 =1
a. 1
-144/7 = -20 5/7 . 4/7 *7 = 4
b. 4
-101/13 =
c. 3
199/19=
d.9
The modulo operator determines the remainder of a division operation. For the given expressions, the results are a. 1, b. 4, c. 2, d. 6
Explanation:The question is asking to evaluate several expressions using the modulo operation. Modulo is a mathematical operation that finds the remainder or signed remainder of a division, after one number is divided by another (called the modulus). Here's how we can solve each:
a. −17 mod 2 = 1 (Because when -17 is divided by 2, the remainder is 1) b. 144 mod 7 = 4 (Because when 144 is divided by 7, the remainder is 4) c. −101 mod 13 = 2 (Because when -101 is divided by 13, the remainder is 2) d. 199 mod 19 = 6 (Because when 199 is divided by 19, remainder is 6)Learn more about Modulo Operation here:https://brainly.com/question/36617304
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Find the sum of the first 30 terms of the sequence. a_(n)=4n+1
Answers
a(n)=4n+1
To find the sum of the first n terms of an arithmetic series
use the formula
Sn=n(a1 + an)/2
a1--------------> is the first term
an--------------> is the last term
n--------------- > is the number of terms
we have that
a1------------> 4*(1)+1=5
a30----------> 4*(30)+1=121
n------------- > 30
S30=30*(5 + 121)/2=1890
the answer is 1890
Officer Brimberry wrote 8 tickets for traffic violations last week, but only 7 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.
Answers
Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels. She then found 1 dime and 1 nickel. How many dimes and nickels does Jessie have in all?
Answers
So, Jessie made 7 stacks of dimes and 8 stacks of nickels.
Each stack of dimes has 6 dimes.
Each stack of nickels has 5 nickels. Multiply:
6 × 7 = 42
8 × 5 = 40
Then she finds another dime and another nickel.
42 + 1 = 43
40 + 1 = 41
43 + 41 = 84
ANSWER:
Jessie has 43 dimes, 41 nickels, and 84 coins in all.
NEED HELP ASAP:
Suppose you pay $24 for a pair of shoes that has been discounted 20%. What is the original price of the shoes? Show how you identify what you are looking for, set up an equation, arrive at your answer, and check your work. Then clearly state your answer.
Answers
x = original price before discount
y = price after discount (before taxes)
y = 80% of x
y = 0.80*x
24 = 0.80*x
24/0.80 = x
30 = x
x = 30
The original price of the shoes was $30
Determine (without solving the problem) the maximal interval in which the solution of the given initial value problem is guaranteed to exist: ???????? ′ + tan(????) ???? = sin(????) , ????(????) = 6.
Answers
Find the orbital period (in years) of an asteroid whose average distance from the sun is 10 au.
Answers
The orbital period (in years) of an asteroid whose average distance from the sun is 10 AU is 212314723 years.
What is Orbital period ?
Orbital period of a body is the the time taken by a body to cover one circular path around the central object under whose influence it is following circular path.
Given is a asteroid moving around the sun.
Mean distance from the Sun [x] = 10 AU = 1.496 x 10¹² m.
Assume that the time period of the asteroid is T.
The formula to calculate the orbital period around the sun is -
T²/ R³ = 4π²/GM[s]
Where -
R is the mean distance from sun.
G is the universal Gravitation constant.
M[s] is the mass of Sun.
Substituting the values, we get -
T² = (1.496 x 10¹² x 4 x 3.14 x 3.14)/(6.673 x 10⁻¹¹ x 1.98 x 10³⁰)
T² = (59 x 10¹²)/(13.2 x 10⁻¹⁹)
T² = 4.45 x 10 x 10³⁰
T² = 44.5 x 10³⁰
T = √44.5 x √10³⁰
T = 6.7 x 10¹⁵ seconds
In years, the time period will be -
T = 212314723 years (approx.)
Therefore, the orbital period (in years) of an asteroid whose average distance from the sun is 10 AU is 212314723 years.
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A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 2025 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?
Answers
Let's assume a the number of miles done by the 1 vehicule (35 mi/gal)
2025-a is the number of miles done by the 2nd vehicule (20 mi/gal)
[tex] \dfrac{a}{35} + \dfrac{2025-a}{20} =75\\\\ 4a+(2025-a)*7=10500\\\\ -3a=10500-7*2025\\\\ 3a=-3675\\\\ a=1225(miles)\\\\ [/tex]
The gas consumption of the 1 vehicule is 1225/35=35 (gallons)
The gas consumption of the 2 vehicule is 75-35=40 (gallons)
write the equation of the line with the following chracteristics
perpendicular to y=1/2x+3 through (9,1)
Answers
1/2 → opposite sign is (-) reciprocal is (2) → slope of ⊥ = -2
Now let's find the b → by substituting the values for y, m, and x in y = mx + b
1 = -2(9) + b
1 = -18 + b
19 = b
The equation is y = -2x + 19
or 2x + y = 19
8x-2=46 what is this
Answers
Divide 8: x=6
If you need me to explain message me
Hope this helps
The heights of fully grown English oak (also known as Brown oak) trees are normally distributed with a mean of 95 feet and a standard deviation of 10 feet. What proportion of fully grown English oak trees are taller than 110 feet?
Answers
z = (x - μ) / σ
μ = 95
σ =10
z = (110-95) / 10
= 1.5
the probability z>1.5 using the standardization table = 0.0668
P(z > 1.5) = 0.0668
Final answer:
Using the z-score calculation and the standard normal distribution, approximately 6.68% of fully grown English oak trees are taller than 110 feet.
Explanation:
To find the proportion of fully grown English oak trees taller than 110 feet, given that the heights are normally distributed with a mean of 95 feet and a standard deviation of 10 feet, we first calculate the z-score for a height of 110 feet. The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value of interest (110 feet), μ is the mean (95 feet), and σ is the standard deviation (10 feet).
By substituting the given values: z = (110 - 95) / 10 = 1.5. This z-score represents the number of standard deviations 110 feet is above the mean. To find the proportion of trees taller than 110 feet, we consult the standard normal distribution table or use a calculator that provides the area to the right of the z-score, which corresponds to the proportion we seek.
The standard normal distribution table or a calculator shows that the proportion of the area under the curve to the right of a z-score of 1.5 is approximately 0.0668.
Thus, about 6.68% of fully grown English oak trees are taller than 110 feet.
How many solutions are there to the system of equations graphed below if the lines are parallel
Answers
Sorry, this is a general answer. I could not view the graph below...
Answer:
Zero
C is the correct option.
Step-by-step explanation:
In the given graph, the given lines are parallel to each other and hence never intersect.
Now, we know that the intersection point (s) of two curves gives us the solution.
Here the lines are parallel to each other and hence do not intersect each other.
Thus, there would not be any intersection point.
Hence, the system of equations has no solution.
C is the correct option.
Which line is parallel to line r?