can someone please help it’s for dance class not mathematics
Does every quadratic equation have at
least one real solution? Explain. (1 point)
A. Yes. When the discriminant is zero, there is exactly one solution. When the discriminant is not zero, there are two unique solutions.
B. No. When the discriminant is greater than zero, there are no real solutions.
C. Yes. When the discriminant is zero, there are two unique solutions. When the discriminant is not zero, there is exactly one solution.
D. No. When the discriminant is less than zero, there are no real solutions.
Answer:
D. No. When the discriminant is less than zero, there are no real solutions.
Step-by-step explanation:
We have to notice that quadratic equations are second order polynomials whose standard form is:
[tex]y = a\cdot x^{2}+b\cdot x + c \cdot x[/tex], [tex]\forall \,a,b,c\,\in\,\mathbb{R}[/tex]
The factorized form of this polynomial is:
[tex]y = (x-r_{1})\cdot (x-r_{2})[/tex]
Where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the quadratic equation, which may be real or complex.
If we equalize [tex]y[/tex] to zero and make algebraic handling, we can get the value of each root anatically by the Quadratic Formula:
[tex]r_{1,2} = \frac{-b\pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
Where [tex]b^{2}-4\cdot a\cdot c[/tex] is known as the discriminant. Then, we should remember the following rules:
i) If discriminant is greater than zero, then the quadratic equation has two different real roots.
ii) If discriminant is zero, then the quadratic equation has two equal real roots.
iii) If discriminant is less than zero, then the quadratic function has two complex roots.
In consequence, we came to the conclusion that statement is false, as quadratic equation have all roots real or all complex, but not one real and the other complex.
In a nutshell, the correct answer is D.
A football kicker boots the ball from the 15 yard line to the 35 yard line. The equation can be modeled by the the following: y = - .054(x - h)(x - k).....where h and k are where the football lands (x-intercepts). What was the maximum height that the football reached?
Answer:
The maximum height that the football reached = 5.4 yards (16.2 feet)
Step-by-step explanation:
The initial location of the ball = 15 yard line
The final location of the ball = 35 yard line
The equation of the ball's motion can be modeled as follows;
y = -0.054·(x - h)·(x - k)
Where;
h and k are the x-intercepts which are the points where the ball lands or where the ball is in contact with the ground
Given that the kicker kicks the ball from the ground on the 15 yard line and the ball lands on the ground at the 35 yard line, we can write
h = 15 yard line
k = 35 yard line
Therefore;
y = -0.054·(x - 15)·(x - 35) = -0.054·x² + 2.7·x-28.35
The maximum height is found by differentiating the function with respect to x and equating the result to 0 as follows;
d(-0.054·x² + 2.7·x-28.35)/dx = 2.7 - 0.108·x = 0
x = 2.7/0.108 = 25
Therefor, at the maximum point, we have;
x = 25
∴ y = -0.054·(25 - 15)·(25 - 35) = -0.054×10×(-10) = 5.4
The maximum height that the football reached = 5.4 yards = 16.2 feet.
In the quadratic formula, −b±b2−4ac√2a, what is b2−4ac called?
Answer:
Step-by-step explanation:
In the quadratic formula x = -b±√b²-4ac/2a, the expression b²-4ac inside the square root is called the discriminant. The discriminant is the function that determines the nature of the roots of the equation even without the constant a, b and c
If b²-4ac > 0, the roots of the equation will be real and distinct
If b²-4ac < 0 the roots of the equation will be complex number
If b²-4ac = 0 the roots of the equation will be real and the same
PLEASEEEE help me on 3 4 & 5. it’s due before midnight
Answer:
See below
Step-by-step explanation:
When changing from scientific notation to standard, you want to look at the exponent.
If exponent is positive, move decimal that many times to the right.
If negative, move to the left.
7.875 x 10^4
Exponent is positive so move to the right.
78750
4.53 x 10^-4
Exponent is negative so move to the left.
0.000453
8.9 x 10^-7
Exponent is negative so move to the left
.00000089
-3(-9v – 4) – 2(v – 2)
Answer:
V= -8/29
Step-by-step explanation
-3(-9v-4), -3 makes -9 and -4 positive cause neg times neg equals a positive
same goes for -2(v-2) so your new equation is 27v+12-2v+4
minus 12 from both sides which gives you -8 and add 2v on both sides which gives you 29v and you divided the two new numbers and you get -8/29
Micheal is 5 years older than Rui Feng and Vishal is thrice as old as Micheal if Rui Feng is p years old, find i) Michael's present age, ii) Vishal's present age, ii) the sum of there age in 6 age years time, iv) the sum of their ages 3 years ago.
Answer:
Michael's present age = p + 5
Michael's present age = 3p + 15
Sum of there ages 6 year age = 5p + 38
Sum of there ages 3 year ago = 5p - 11
Step-by-step explanation:
Assume;
Age of Rui Feng = x
Age of Micheal = x + 5
Age if Vishal = 3[x+5]
Given:
Age of Rui Feng = P
Computation:
Michael's present age = Age of Rui Feng + 5
Michael's present age = p + 5
Vishal's present age = 3[p + 5]
Michael's present age = 3p + 15
Sum of there ages 6 year age = [p + 6] + [p + 5 + 6] + 3[p + 5] + 6
Sum of there ages 6 year age = 5p + 38
Sum of there ages 3 year ago = [p - 3] + [p + 5 - 3] + 3[p + 5] - 3
Sum of there ages 3 year ago = 5p - 11
i’m not sure about this please help
Answer:
3
Step-by-step explanation:
Evaluate x/4 + 6 (x - 12) where x = 12:
x/4 + 6 (x - 12) = 12/4 + 6 (12 - 12)
Hint: | Reduce 12/4 to lowest terms. Start by finding the GCD of 12 and 4.
The gcd of 12 and 4 is 4, so 12/4 = (4×3)/(4×1) = 4/4×3 = 3:
3 + 6 (12 - 12)
Hint: | Look for the difference of two identical terms.
12 - 12 = 0:
6×0 + 3
Hint: | Any number times zero is zero.
0×6 = 0:
0 + 3
Hint: | Simplify the expression.
Write 3 + 0 as 3:
Answer: 3
The answer is three.
Explanation:
x/4 = 12/4 = 3. 6(x-12) = 6(12-12) = 6(0) = 03+0=3Evaluate g(x) = 4 – 3x when x
= -3, 0, and 5.
What is the perimeter of a triangle with the following side lengths?
Side 1=22x-17
Side 2=-15x+12
Side 3=-3x-5
Answer:
p=22x-17-15x+12-3x-5
4x-10
Step-by-step explanation:
hope it is helpful for you if it is follow me
If you and a friend each toss two pennies at the same time, what is the probability that all four pennies will be tails?
A. 1/2
B. 1/4
C. 1/8
D. 1/16
E. 1/32
Answer:
1/16
Step-by-step explanation:
Probability helps us to know the chances of an event occurring. The probability that all four pennies will be tails is (1/16).
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of a penny getting a tail is 0.5 or (1/2), therefore, the probability of four penny getting a tail can be written as,
[tex]\rm Probability = \dfrac14 \times \dfrac14 \times \dfrac14 \times \dfrac14 = \dfrac1{16}[/tex]
Hence, the probability that all four pennies will be tails is (1/16).
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(-2m^3n^4)^x=-8m^9n^12
Answer:
[tex]6m^{2} - 5mn - 6n^{2}[/tex]
Step-by-step explanation:
I hope this helps you :)
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she rose 24.2 feet. How many feet had she been below sea level, if she was 0.5 feet below sea level after she rose?
Answer:
She was initially at a depth of 24.7 feet before she rose
Step-by-step explanation:
To get her initial depth, we need to understand how many feet she sank and rose.
Let us say she was initially at a depth which we can call = x feet.
After 10 minutes she rose for 24.2 feet.
This means her new depth will be x - 24.2 ft.
We are also told that this new depth is actually 0.5 feet below sea level.
This means
x - 24.2 = 0.5
Now that we have this equation we can simply make x the subject of the formula and solve for x
x = 24.2 + 0.5 = 24.7
She was initially at a depth of 24.7 feet before she rose
Answer:
24.7
Step-by-step explanation:
Add 24.2 and 0.5
-what is the solution to this equation -16x=80
Answer:
-5
Step-by-step explanation:
You divide 80 by -16
Felicia took out a $5,000 loan to buy a car. If the interest is compounded annually at a rate of 11%, how much will she pay in all?
PLEASE HELP
Answer: 550
Step-by-step explanation: 5,000x11%=550
20=10-2y+4+4y what does y equal
Answer:
y = 3
Step-by-step explanation:
[tex]10-2y+4+4y+20[/tex]
Combine like terms
[tex]2y+14=20[/tex]
Move all terms not containing y to the right side of the equation.
[tex]2y=6[/tex]
Divide both sides by 2
y = 3
Plz mark me brainliest!
It's ok if u don't...lol
I hope this helped!!
CAN SOMEONE HELP ME PLEASE???
Answer:
[tex]x^3[/tex]
Step-by-step explanation:
To find the greatest common factor of a set of numbers, we need to find the greatest number, that when it's used as a divisor for all the numbers, returns an integer value.
We have the numbers [tex]x^3, x^6,[/tex] and [tex]x^9[/tex].
Exponent rules tell us that [tex]a^b \div a^c = a^{b-c}[/tex].
This means that each of these values must be raised to the power of three. Therefore, each of them can be divided by [tex]x^3[/tex].
[tex]x^3 \div x^3 = 1[/tex]
[tex]x^6 \div x^3 = x^3[/tex]
[tex]x^9 \div x^3 = x^6[/tex]
So [tex]x^3[/tex] is the GCF.
Hope this helped!
Factor 15 + 50.
5(10 + 3)
5(3 + 10)
3(5 + 25)
10(5 + 5)
Answer:
B
Step-by-step explanation:
So we have the expression:
[tex]15+50[/tex]
Since 5 goes into both 15 and 50, we can factor out a 5. First, rewrite the numbers as:
[tex]5(3)+5(10)[/tex]
Factor out the 5:
[tex]=5(3+10)[/tex]
So, our answer is B
And we're done!
the sum of 32 and w
Please help ASAP
Answer:
Verbal expression; The sum of thirty -two and a number w
Algebraic expression ;32+w
Step-by-step explanation:
Explanation:
10. Jack and Jill were working on their homework together but ended up with two different
answers to the same problem. The problem asked for a new line, parallel to y=2x+3, and
containing the point (-2,-2). Who got the problem correct? Explain your reasoning?
Jack:
y-2 = 2(x - 2)
y-2 = 2x - 4
y = 2x - 2
Jill:
y + 2 = 2(x + 2)
y + 2 = 2x + 4
y = 2x + 2
Answer:
Explanation:
Step-by-step explanation:
Hey there!
Firstly we need to find an equation of the line passing through point (-2,-2).
Now,
The equation of a st.line passing through point (-2,-2) is,
[tex](y - y1) = m1(x - x1)[/tex]
Now, putting the values,
[tex](y + 2) = m1(x + 2)[/tex]
It is first equation.
Now, another equation is,
y= 2x+3
Comparing, the equation with y = mx+c.
slope (m2)= 2
As per the condition of parallel lines,
m1=m2= 2
Putting, the values of m1 in equation (i)
(y+2)= 2(x+2)
y= 2x+2....is the equation.
Therefore, Jill's equation is correct answer.
Hope it helps...
y=1\2x+3. y=5. pls help solve by substitution .
Answer:
x=4
Step-by-step explanation:
y=1/2x+3....equation 1
y=5....equation 2
Sub equation 2 in 1:-
5=1/2x+3
2=1/2x
x=4
Donovan spent 2/15 hour walking to the mailbox, 1/6 hour walking to the library, and 2/10 hour walking to the park. Which took Donovan the longest amount of time to walk to? Explain.
Answer:
The walk to the park took the longest amount of time
Step-by-step explanation:
In this question, we want to find the location that took Donovan the longest amount of time to work.
We should recall that an hour is 60 minutes
So time spent walking to the mailbox would be 2/15 * 60 = 8 minutes
Time spent walking to the library would be 1/6 * 60 = 10 minutes
Time spent walking to the park = 2/10 * 60 = 12 minutes
So as we can see, the distance taking the longest amount of time to walk is the Park which took a total of 12 minutes
What is the length of
BD with endpoint B(1,4)
and midpoint T(4,6)?
Thank you in advance!
Answer:
2√13
Step-by-step explanation:
B(1,4) T(4,6) what is BD
find BT
d=√(x2-x1)²+(y2-y1)²
d=√(4-1)²+(6-4)²
d=√3²+2²
d=√9+4
d=√13 this is haf the distance
BD=2d=2√13
A line segment is also a line but a line with finite length and fixed endpoints. The length of BD is 2√13 units.
What is the length of any line on the graph?The distance or length of any line on the graph,
d = √[(x₂- x₁)² + (y₂- y₁)²]
where,
d = distance/length of the line between points 1 and 2,
(x₁ , y₁) = coordinate of point 1,
(x₂ , y₂) = coordinate of point 2,
Given the coordinate of B and T as (1,4) and (4,6), respectively. Therefore, the length of BT can be written as,
Length of BT = √[(x₂- x₁)² + (y₂- y₁)²]
= √[(4 - 1)² + (6 - 4)²]
= √[(3)² + (2)²]
= √(9 + 4)
= √13
Now, we can write the length of BD as the sum of BT and TD,
BD = BT + TD
Since T is the midpoint of BD, therefore, it will divide it into two equal parts, therefore, we can write,
BD = BT + BT
BD = 2(BT)
BD = 2√13
Hence, the length of BD is 2√13 units.
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-8.68 divided -0.024
Answer:
-8.704
Step-by-step explanation:
hav a great day
Answer:
1085/3 = 361.7
Step-by-step explanation:
Expand −8.68/0.024 ≈361.666666667 by multiplying both numerator and the denominator by 1000.
8680/-24 ≈361.666666667
Reduce the fraction −8680/24≈361.666666667 to lowest terms by extracting and canceling out −8.
1085/3≈361.7
Lua has a red ribbon that is 2 1/12 inches long she has a blue ribbon that is 4 times as many inches long. how many inches long is the blue ribbon
Answer:
The length of the blue ribbon is approximately 8.333 inches
Step-by-step explanation:
The given information are as follows;
The given length of the red ribbon = 2 1/12 inches
The length of the blue ribbon is given as 4 × The length of the red ribbon
Therefore;
The length of the blue ribbon = 4 × 2 1/12 inches = 25/3 inches = 8 1/3 inches
The length of the blue ribbon = 8 1/3 inches ≈ 8.333 inches.
Answer:
8 1/3 inches
Step-by-step explanation:
I
1
The square root of 5 will be classified as what according to the real
number system?
*
Real, irrational
Real, rational, integer
real, rational, integer, whole number
real, rational, integer, whole number, natural number
real, rational, irrational, integer, whole number, natural number
Answer:
irrational number
Step-by-step explanation:
The square root of 5 belongs to a long list of irrational algebraic number. It has been categorized in such list because the square root of 5 cannot be expressed as a fraction and has an infinite number of
Compare your response to the sample response. Which of these did your response include? Check all of the boxes that apply.
[] The real number is on the number line, but the complex number is in the complex plane.
[] Both are distances.
[] Both are positive values.
[] The distance formula or the Pythagorean theorem is used to calculate the absolute value of a complex number.
Answer:
A,B,C: The real number is on the number line, but the complex number is in the complex plane.
Both are distances.
Both are positive values.
Step-by-step explanation:
took the test
Answer:
1, 2, and 3
Step-by-step explanation:
i needdd helppppppp plsss
Answer:
3
Step-by-step explanation:
3 - 6 = -3Plug -3 in: [tex]-\frac{12}{-3} + (-1)^{3}[/tex] Simplify the fraction. Two negatives equal a positive. It should now look like this: [tex]\frac{12}{3} + (-1)^{3}[/tex] Simplify even more. Divide 12 by 3, and change -1 to a positive by removing the plug sign: [tex]4 - 1^{3}[/tex] [tex]1^{3} = 1[/tex] Plug 1 in: 4 - 14 - 1 = 3I hope this helps!
Can you help me translate into equations plssssss!!
1. Five more than twice a number is 7.
2. Fourteen more than three times a number is 2.
3. Seven less than twice a number is 5.
4. Two more than four times a number is -10.
6. Eight less than three times a number is – 14.
6. Three more than the quotient of a number and 2 is 7.
7. The product of a number and 4 plus 2 is 14.
8. Eight less than the quotient of a number and 3 is 5.
9. The difference of twice a number and 3 is II.
10. The sum of 3 times a number and 7 is 25.
Answer:
1 is 5+2a =7 and 2is 14+3a=3 and 3 is 7-2a=5
Answer:
1. 2x+5=7
2. 3x+14=2
3. 2x-7=5
4. 4x+2=-10
6. 3x-8=-14
6. (x/2)+3=7
7. 4x+2=14
8. (x/3)-8=5
9. 2x-3=11
10. 3x+7=25
want to make confetti. In order to get the right balance of ingredients for their tastes they bought 2 pounds of paper hearts at $ 3.42 per pound comma 2 pounds of sparkling stars for $ 3.93 per pound comma and 5 pounds of shiny coils for $ 2.53 per pound. Determine the cost per pound of the confetti.
Answer:
$3.039
Step-by-step explanation:
Step 1
They bought 2 pounds of paper hearts at $ 3.42 per pound
1 pound = $3.42
2 pounds =
2 × $3.42
= $6.84
2 pounds of sparkling stars for $ 3.93 per pound
1 pound of sparking stars = $3.93
2 pounds =
$3.93 × 2
= $7.86
5 pounds of shiny coils for $ 2.53 per pound.
1 pounds of shiny coils = $2.53
5 pounds =
5 × $2.53
= $12.65
Step 2
We find the total cost of the materials
Total cost of Materials that make up the confetti = Cost of paper heart + Cost of sparkling stars + Cost of shiny coils.
= $6.84 + $7.86 + $12.65
= $27.35
Step 3
Total pounds of materials bought = 2 pounds + 2 pounds + 5 pounds
= 9 pounds
Step 4
The cost per pound of confetti = Total cost of the materials bought/ Total pounds of materials
= $27.35/9
= $3.0388888889
Approximately ≈ $3.039
The cost per pound of the confetti = $3.039
The cost per pound of the confetti is $3.04
Total cost :Given that, they bought 2 pounds of paper hearts at $ 3.42 per pound.
The cost of 2 pounds of paper hearts is, [tex]=2 *3.42=6.84[/tex]
the 2 pounds of sparkling stars for $ 3.93 per pound
The cost of 2 pounds of sparkling stars is, [tex]=$3.93 * 2=7.86[/tex]
the 5 pounds of shiny coils for $ 2.53 per pound.
The cost of 5 pounds of shiny coils is, [tex]=5 * $2.53=12.65[/tex]
Total cost of confetti is,
[tex]= $6.84 + $7.86 + $12.65=27.35[/tex]
Total pounds of materials bought ,
[tex]=2+2+5=9pounds[/tex]
The cost per pound of confetti is,
[tex]=\frac{27.35}{9}=3.04[/tex]
The cost per pound of the confetti is $3.039
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