Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Answer:
Option D. {7 + i√71 / 20, 7 – i√71 / 20}
Step-by-step explanation:
10m² – 7m + 3 = 0
Using formula method, the solution to equation can be obtained as follow:
10m² – 7m + 3 = 0
Coefficient of m² (a) = 10
Coefficient of –7m (b) = –7
Constant (c) = 3
m = –b ±√(b² – 4ac) / 2a
= – –7 ±√((–7)² – 4 × 10 × 3) / 2 × 10
= 7 ±√(49 – 120) / 20
= 7 ±√(–71) / 20
Recall:
–17 = –1 × 17
Thus,
7 ±√(–71) / 20 = 7 ±√(–1 × 71) / 20
Recall:
√–1 = i
Thus,
7 ±√(–1 × 71) / 20 = 7 ± i√71 / 20
= 7 + i√71 / 20 or 7 – i√71 / 20
Therefore, the solutions to the equation are:
{7 + i√71 / 20, 7 – i√71 / 20}
Related Questions
The Yellow Cab Company charges just $1.25 per mile, but it costs $6.00 to get in the cab. Express Cab charges no fee to get in the cab, but $2.00 per mile for the ride. For what number of miles is the cost the same?
Answers
Answer: 8 miles
Step-by-step explanation:
1.25m+6=2m
--1.25m. -1.25m
6=.75
6/.75m=8 mile
s
find the volume of this cone. round to the nearest tenth. 15 m 5 m
Answers
Answer:
[tex]volume = \frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \times 3.14 \times {5}^{2} \times 15 \\ = 392.5 \: {m}^{3} [/tex]
Need help with this triangle measure please.
I also need explanation. Thank you-----
Answers
help me i been stuck for like a good 20 min
Answers
[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]
notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.
HELP In circle J with m∠HJK=126 and HJ=14 units, find the length of arc HK. Round to the nearest hundredth.
Answers
Answer: 39.79
Step-by-step explanation:
126/360 (2pi14)
During his first 20 picks from a bag of marbles, Mark chose 8 yellow marbles, 9 green marbles, and 3 blue marbles. What is the experimental probability that Mark will choose a green marble on his next pick?
please show work
Answers
Answer:
to solve this problem you have to take 9 over 20 (by assuming replacing the marbles)
9/20 is the experimental probability for a green marble to be picked
9/20 = 45%
What is the value of sin cos theta?
Answers
If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2
We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.
And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.
Given that sinθ⋅cosθ = 1/2
2(sinθ⋅cosθ) = 1 .........(1)
We know that trigonometric identity,
sin(2θ) = 2 sinθ cosθ
so equation (1) becomes,
sin(2θ) = 1
We know that sin(π/2) = 1
Comparing with equation sin(2θ) = 1 we get,
2θ = π/2
θ = π/4
Using trigonometric table,
sin(π/4) = 1/√2
and cos(π/4) = 1/√2
The value of sinθ+cosθ would be,
sin(π/4) + cos(π/4)
= (1/√2) + (1/√2)
= 2/√2
= √2
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The complete question is:
If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ
PLS HELP FAST IM BEING TIMED!!!
An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane. Which graph represents the solution to the inequality that finds the number of tickets the airline can still sell?
A number line going from 80 to 91. A solid circle is at 88. Everything to the left of the circle is shaded.
A number line going from 80 to 91. An open circle is at 88. Everything to the left of the circle is shaded.
A number line going from 80 to 91. An open circle is at 87. Everything to the right of the circle is shaded.
A number line going from 80 to 91. A closed circle is at 87. Everything to the right of the circle is shaded.
Answers
Answer:
C
Step-by-step explanation:
hope it helps
Answer:
The answer is C
Step-by-step explanation:
I keep seeing people put c so i am pretty sure that right
if you do 44 push ups in 4 minutes how many will he do in 5 minutes
Answers
Answer:
55
Step-by-step explanation: i think
Answer:
Step-by-step explanation:
it would be 55 because he does 11 each minute.
PLS HELP ME I ONLY HAV 2 MINS PLSSSSS
Answers
Answer:
- 8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
3x(x+x)−6x^2+2^2−12
=6x^2+−6x^2+4+−12
Combine Like Terms:
=6x^2+−6x^2+4+−12
=(6x^2+−6^2)+(4+−12)
=−8
DE is parallel to AC. Find the lengths of AC and AD. FAST!!!
Answers
Answer:
we have:
∆BDE is similar to ∆BAC
so their side are proportional :
BD/BD=BE/BC
2/BD=4/(6+4)
BD=2×10/4
BD=5
again
BE/BC=DE/AC
4/10=5/AC
AC=5×10/4
AC=25/2
Now,
AC=25/2 or 12.5.
AD=BA-BD=5-2=3.
is your answer.
Answer:
AC = 12.5, AD = 3
Step-by-step explanation:
A line parallel to a side of a triangle and intersecting the other 2 sides, divides those sides proportionally, that is
[tex]\frac{BD}{BE}[/tex] = [tex]\frac{AD}{CE}[/tex] , substitute values
[tex]\frac{2}{4}[/tex] = [tex]\frac{AD}{6}[/tex] ( cross- multiply )
4 AD = 12 ( divide both sides by 4 )
AD = 3
-----------------------------------------
Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is
[tex]\frac{DE}{AC}[/tex] = [tex]\frac{BD}{BA}[/tex] , substitute values
[tex]\frac{5}{AC}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )
2 AC = 25 ( divide oth sides by 2 )
AC = 12.5
The table lists recommended amounts of food to order for party guests. And are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should and order for a graduation party with drop-in guests?
Answers
To calculate the amount of food to order for the graduation party with drop-in guests, you should multiply the number of "full" guests, which is 40 + x/2, by the recommended amounts listed in the table.
To calculate the amount of food to order for the graduation party, you need to take into account the number of guests and the recommended amounts listed on the table. Since the party is for 40 guests and there will also be "drop-in" guests, you need to convert these guests into an equivalent number of "full" guests. To do this, you can divide the number of drop-in guests by 2.
So if there are x drop-in guests, the number of "full" guests will be 40 + x/2.
Now you can use this number of "full" guests to calculate how much of each food item to order. For example, if the table recommends 1/4 lb of meat per guest, you would order (40 + x/2) × 1/4 lb = 10 + x/8 lb of meat.
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Write with a single exponent:
Answers
Answer:
10^-3
10^-7
10^-8
10^-9
10^-6
Step-by-step explanation:
mark me brainliest pls
Jenny has red and white balloons. she inflates 2 red balloons for every 3 inflated white balloons. Jenny wants 20 red balloons inflated. How many total balloons will be inflated if jenny inflates the required white balloons
Answers
Answer:
50
Step-by-step explanation:
2*10=20 red
3*10=30 white
20+30=50
Answer:
50
Step-by-step explanation:
the ratio is 2:3
so every if she inflates 20 red she inflates 30 white
30 + 20 is 50
Find Arc measure of ABC
Answers
Answer:
268°
Step-by-step explanation:
[tex] In\: \odot O, [/tex] AB is diameter.
So, [tex] \widehat{AB} \:\&\: \widehat {BA}[/tex] are semicircular arcs.
[tex] \therefore m\widehat {AB} =m\widehat {BA} = 180\degree [/tex]
[tex] \because \: m\widehat {BC} = m\widehat {BA} - m\widehat {CA} [/tex]
[tex] \therefore \: m\widehat {BC} = (180-92)\degree [/tex]
[tex] \therefore \: m\widehat {BC} =88\degree [/tex]
[tex] \because m\widehat {ABC} = m\widehat {AB}+m\widehat {BC} [/tex]
[tex] \therefore m\widehat {ABC} = 180\degree+88\degree [/tex]
[tex] \therefore m\widehat {ABC} = 268\degree [/tex]
52 > 43 + w
is it a solution?
7 yes or no
4 yes or no
13 yes or no
9 yes or no
Answers
Answer: w < 9 yes
Please mark as brainlist
How do you find the missing side of a 30 60 90 triangle?
Answers
A 30-60-90 triangle is a right triangle where the three interior angles are 30°, 60°, and 90°.
Let, the shorter leg of a 30 60 90 triangle is equal to a. Then:
The second leg is equal to a√3;The hypotenuse is 2a;The area is equal to a²√3/2; andThe perimeter equals a(3 + √3).If we know the shorter leg length, we can find out that:
Longer leg= √3 times of shorter leghypotenuse= twice the shorter legIn the 30 60 90 triangles :
For angles, the ratio is 1:2:3 (30°: 60°: 90°)For sides, the ratio is 1 : √3: 2Read more about the right triangle:
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what is the volume i’m cubic inches of the rectangular prism below
Answers
Answer:
The answer would be D!
Step-by-step explanation:
Tell me if i'm wrong
**10 POINTS** probablitly for math
Answers
What is the volume of Hannah's suitcase in cubic inches?
Answers
The volume of Hannah's suitcase in cubic inches is: C: 7938.
How to find the volume?The volume can be determine using this formula
Volume = Length × Width × Depth
Where:
Length = 27 inches
Width = 21 inches
Depth = 14 inches
Let plug in the formula
Volume = 27 inches × 21 inches × 14 inches
Volume = 7,938
Therefore we can conclude that the volume is 7,938.
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(#7) A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
Answers
The ratio of surface area to volume is 6:s
What is a cube?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Given that, A cube has an edge length given by the variable “s”. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s² volume= s³
The ratio = 6s² / s³
= 6 / s
Hence, the required ratio is 6:s
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What is the Vertex of the graph?
options:
(1,1)
(-1,1)
(0,1)
(1,0)
Answers
Answer:
Step-by-step explanation:
(-1, 1): You can see that a vertical line through x = -1 is the center line (axis of symmetry) of this parabolic graph. The vertex lies 1 unit above the x-axis: y = 1.
How many pounds of walnuts that cost $0.80 per pound must be mixed
with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?
Answers
Answer:
kt 5.20 yes
Step-by-step explanation:
5.20
Step-by-step explanation:
Twelve eggs cost $2.04. How much will 18 eggs cost
Answers
Answer: $3.06
Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.
one number exceeds another by 4 and their sum is 26.find them with proper language and process.
Answers
Answer:
15 and 11
Step-by-step explanation:
First find an equation that represents this scenario.
26 = n + (n-4) works, because the sum (26) is equal to the number (n) plus the number minus 4, which is the other number.
To find both numbers, solve for n:
26 = n + (n - 4)
First, combine like terms.
26 = 2n - 4
Then, add 4 to both sides
30 = 2n
Then divide both sides by 2.
15 = n.
So the number is 15, and the other number is 15-4, which is 11.
Find the area of the figure.
8ft
8ft
6 ft
12 ft
10 ft
Answers
Answer:
46080
Step-by-step explanation:
multiply all of them
Answer: might be 150 sq ft if the problem is of the irregular figure
The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes
Answers
Answer:
55.2049%
Step-by-step explanation:
R², the coefficient of determination, is the proportion of the variation in the dependent variable that is predictable from the independent variable.
In this case, if we square our correlation coefficent r=0.743, we get R²=0.552049, which means that 55.2049% of the variation in the number of yearly boaters can be explained by differences in lake sizes
2. A recent study of 35 students determined that the mean number of hours per week they played video games was 16.6 hours. The standard deviation of the population was 2.8 hours. Find a 95% confidence interval of the population mean.
Answers
According to a recent study of 35 students,Population-wide, there was a 2.8-hour standard deviation. 16.60 is the population mean's 95% confidence interval.
What means 95% confidence interval?A Confidence Interval is a zone created using sampled data from a population (sample space) that has a fixed size and follows a specific probability distribution. The interval is built to include a selected population statistic with a certain probability. A range of values above and below the point estimate, within which the true value in the population is likely to reside with 95% confidence, is known as a 95% confidence interval. 5% of the time, the true result might not fall inside the confidence interval.A confidence interval that includes the value of no difference between treatments denotes that there is no statistically significant difference between the therapy under consideration and the control.The result is that P([sample mean] - margin of error [sample mean] + margin of error) = 0.95.To learn more about confidence interval refer to :
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The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRY! :D
Answers
The area of the floor in the scale drawing is 60 inches².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Actual rectangle:
Length = 24 feet
Width = 40 feet
Scale rectangle:
Length = 6 inches
Width = 40/4 = 10 inches
The area of the scaled rectangle.
= Length x Width
= 6 x 10
= 60 inches²
Thus,
The area of the scaled rectangle is 60 inches².
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3x^2+7x=30______________
Answers
(Hint)
by using quadratic formula we can find the value of x
3x^2+7x-30
a=3
b=7
c=-30