Step-by-step explanation:
The given equation is :
[tex]-2x^2+6x+1=-3x^2[/tex]
Taking all the terms to one side of the equation i.e.
[tex]-2x^2+6x+1+3x^2=0\\\\x^2+6x+1=0[/tex]
It is a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] whose solution is given by :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here, a = 1, b = 6 and c = 1
Put all the values,
[tex]x=\dfrac{-6\pm \sqrt{6^2-4(1)(1)}}{2(1)}\\\\x=-0.171\ and\ x=-5.82[/tex]
Hence, this is the required solution.
For a field trip, 848 students will be riding on 16 buses. If each bus takes the same number of students, how many students will be on each bus?
58
Answer:
53
Step-by-step explanation:
848 students/16 buses=53 students per bus
Mr. And Mrs. Smith went on vacation by car. When they began the odometer reading in the car was 28,575. When they returned the odometer reading was 29,684.
How many gallons of gas, to the nearest gallon did they use on the trip?
A
48
B
36
C.
Not enough information is given
D
26
Twice Henry's earnings increased by 10 is $253. Therefore, Henry earned $____
Answer:
121.50
Step-by-step explanation:
Let x be the earnings
2x+10 = 253
Subtract 10 from each side
2x+10-10 = 253-10
2x = 243
Divide by 2
2x/2 = 243/2
x = 121.50
What is the Surface Area of this cylinder? Round to the nearest hundredth if needed, Use 3.14 for pi
D.sqrt(2+x^/2)
Solve this question please
Answer:
Option a.
Step-by-step explanation:
By looking at the options, we can assume that the function y(x) is something like:
[tex]y = \sqrt{4 + a*x^2}[/tex]
[tex]y' = (1/2)*\frac{1}{\sqrt{4 + a*x^2} }*(2*a*x) = \frac{a*x}{\sqrt{4 + a*x^2} }[/tex]
such that, y(0) = √4 = 2, as expected.
Now, we want to have:
[tex]y' = \frac{x*y}{2 + x^2}[/tex]
replacing y' and y we get:
[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]
Now we can try to solve this for "a".
[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]
If we multiply both sides by y(x), we get:
[tex]\frac{a*x}{\sqrt{4 + a*x^2} }*\sqrt{4 + a*x^2} = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}*\sqrt{4 + a*x^2}[/tex]
[tex]a*x = \frac{x*(4 + a*x^2)}{2 + x^2}[/tex]
We can remove the x factor in both numerators if we divide both sides by x, so we get:
[tex]a = \frac{4 + a*x^2}{2 + x^2}[/tex]
Now we just need to isolate "a"
[tex]a*(2 + x^2) = 4 + a*x^2[/tex]
[tex]2*a + a*x^2 = 4 + a*x^2[/tex]
Now we can subtract a*x^2 in both sides to get:
[tex]2*a = 4\\a = 4/2 = 2[/tex]
Then the solution is:
[tex]y = \sqrt{4 + 2*x^2}[/tex]
The correct option is option a.
PLZ HELP Which of the following is a true statement?
A. Total Liabilities − Total Assets = Net Worth
B. Total Assets − Total Liabilities = Net Worth
C. Total Assets + Total Liabilities = Net Worth
D. None of these are true.
Answer:
B
Step-by-step explanation: Net worth is the total assets minus total liabilities of an individual or entity.
solve 5|x – 4| ≥ –10
Answer:
The statement is true for any value of x
Step-by-step explanation:
see the steps below:)
Answer:
No solution
Step-by-step explanation:
just trust me
13 +22
if r = -3 and s = 4
35 is the answer
have a wonderful day
A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 100 items, the defect rate is 4% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager's claim.
Answer:
The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.
Step-by-step explanation:
A manufacturer considers his production process to be out of control when defects exceed 3%.
At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So
[tex]H_0: p \leq 0.03[/tex]
At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So
[tex]H_1: p > 0.03[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.03 is tested at the null hypothesis
This means that [tex]\mu = 0.03, \sigma = \sqrt{0.03*0.97}[/tex]
In a random sample of 100 items, the defect rate is 4%.
This means that [tex]n = 100, X = 0.04[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}[/tex]
[tex]z = 0.59[/tex]
P-value of the test
The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.
Looking at the z-table, z = 0.59 has a p-value of 0.7224
1 - 0.7224 = 0.2776
The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.
A ladder is leaning against the side of a 10cm house. If the base of the ladder is a 3cm away from the house, how tall is the Ladder
Answer:
10.44cm lon
Step-by-step explanation:
Given data
Height of house= 10cm
Distance of ladder from wall= 3cm
We can apply the Pythagoras theorem to get the length of the ladder
Also, the length of the ladder is the hypothenuse
z^2= x^2+y^2
z^2= 10^2+ 3^2
z^2= 100+9
z^2= 109
square both sides
z= √109
z= 10.44cm
Hence the ladder is 10.44cm long
What is side e
Angle d and angle f
Please let me know asap
9514 1404 393
Answer:
e ≈ 9.608D ≈ 46.5°F ≈ 38.5°Step-by-step explanation:
The only given angle is between the two given sides, so the Law of Cosines must be used to find the side opposite the angle. It tells you ...
e² = d²+f² -2df·cos(E)
e² = 7² +6² -2·7·6·cos(95°) ≈ 92.321082
e ≈ 9.608
The remaining angles can be found from the law of sines.
sin(D)/d = sin(E)/e
D = arcsin(d/e·sin(E)) ≈ arcsin(7/9.608·sin(95°)) ≈ 46.5°
F = 180° -95° -46.5° = 38.5°
There are 140 balloons in a packet. The balloons are red or yellow or green or blue
Answer:
There are 35 of each color.
Step-by-step explanation:
If the number of each color is the same there are 140 / 4 = 35 balloons of each color.
Square metal plate has a density of 10.2 g/cm³ and a mass of 21.93 g
Answer:
2.15cm^3
Step-by-step explanation:
V = Mass / Density
21.93g / 10.2 g/cm^3
2.15cm^3
You want to put a 2 inch thick layer of topsoil for a new 17 ft by 30 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order
You want to walk from home to a grocery store that is3/4 miles away. You stop for a rest after 5/8 miles. How much farther do you have to walk?
Write your answer as a fraction in simplest form.
Answer:
1/8 miles
Step-by-step explanation:
You have to subtract [tex]\frac{3}{4}- \frac{5}{8}[/tex] for the answer.
First, you gotta make 3/4 have a common denominator.
To do this multiply 3/4 by 2/2 (2/2 equals one, so value isn't changed.)
and you get 6/8.
Then you can subtract 6/8 - 5/8 to get 1/8 miles.
And there's no need to simplify 1/8.
A 25/9
B 125/9
C 32
D 64
Answer:
Length = 5 feet
Breadth = (5/3) feet
Height(depth) = 2 feet
Volume of the entire tank = Length x Breadth x Height
= [tex]5 \times \frac{5}{3} \times2 = \frac{50}{3}[/tex] ----------(1)
Water is filled upto a height of (1/3) feet
Volume of water in the tank = Length x Breadth x Height
= [tex]5 \times \frac{5}{3} \times \frac{1}{3} = \frac{25}{9}[/tex] -------------(2)
Volume of space needed to be filled = (1) - (2)
= [tex]\frac{50}{3} -\frac{25}{9} = \frac{150-25}{9} = \frac{125}{9} cubic feet[/tex]
OR
Height of tank needed to be filled = 2 - (1/3) = (5/3) feet
Volume of space = Length x Breadth x Height of empty tank
= [tex]5 \times \frac{5}{3} \times \frac{5}{3} = \frac{125}{9} cubic \ feet[/tex]
What are the coordinates of the solution of these two linear equations
Answer:
(-2 -3)
Step-by-step explanation:
_____________________
what is the area of a tile floor that is 12.8 feet long and 9.5 feet wide
Answer: 121.5 ft^2
Step-by-step explanation:
Area= L x W
12.8 X 9.5
= 121.6
What is the y-value when x = 8?
14
12
10
8
2.
0 2 4 6 8 10 12 14
2 6
Answer:
4
Step-by-step explanation:
go on the x-axis where you see 8
go up until you get to the line
go toward the y-axis to the left and read ( it said 4)
Use The Divergence Theorem To Calculate The Surface Integral and Sis a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral.
Answer: hi your question is incomplete below is the complete question
Use the Divergence Theorem to calculate the surface integral S F dS with F x y z = , , and S is a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral
answer : surface integral = 384/5 π
Step-by-step explanation:
Representing the vector field as
F ( x, y , z ) = ( a^3 + y^3 ) + ( y^3 + z^3 ) + ( Z^3 + x^3 ) k
assuming the sphere ( s) with radius = 2 be centered at Origin of the vector field.
Hence the divergence will be represented as :
Attached below is the detailed solution
What is the measure of the missing angle?
Answer:
B=23.19
Step-by-step explanation:
First, find the last side of the triangle using the Pythagorean theorem.
[tex]a^{2} +b^{2} =c^{2} \\21^{2} +9^{2} =c^{2} \\441+81=c^{2} \\\sqrt[3]{58}=c[/tex]
Then, find the missing angle, lets name it B.
The angle B can be found using the inverse sine function.
B=arcsin(opp/hyp)
[tex]B=arcsin(\frac{9}{\sqrt[3]{58} } )\\B=23.19[/tex]
If 3,8,9 and x are in proportion find the value of x
Answer:
Step-by-step explanation:
since they are in continued proportion the ratio will be
3/8=9/x
do cross multiplication
8*9=3*x
72=3x
72/3=x
24=x
therefore x =24
Answer:
ans is 24
Step-by-step explanation:
soln
the 3 8 9 and x are in proportion
so 3/8=9/x
3x=72
x=72/3
x=24
which one makes a right triangle?
=======================================
Explanation:
As mentioned earlier (in a previous post) the triangle with sides 2,5,7 is not a right triangle. So we can rule out choice A.
For choice B, we have a = 6, b = 8, c = 10, and that leads to...
a^2+b^2 = c^2
6^2+8^2 = 10^2
36+64 = 100
100 = 100
The true equation at the end means the beginning equation is true as well for those a,b,c values. Therefore, we have a right triangle and the answer is choice B
Choices C and D are similar to choice A. They make a^2+b^2 = c^2 to be false.
Simplify the expression:
(2p + 1)(2) =
Answer:
4p +2
Step-by-step explanation:
(2p + 1)(2)
Distribute
2p * 2 + 1*2
4p +2
Answer:
4p+2
Step-by-step explanation:
See the steps below:)
Which choices are equivalent to the fraction below? Check all that apply.
Answer:
A, B, D, E, F
Step-by-step explanation:
48/64 can be simplified into all of them except C
PLEASE HELPPPPPP MEEEEEEE!
Answer:
124 students
Step-by-step explanation:
Girls participating in the exercise
4/15 x 285 = 76
Boys participating in the exercise
3/20 x 320 = 48
Total students participating
76 + 48 = 124
pls help!! person with correct answer will be marked brainliest
20. A, B and C start a business with a capital of Rs. 10,500. Of this Rs.4400 is contributed by A, Rs.3700 is
contributed by B and the rest by C. After 5 months C withdraws Rs.800 from the capital, while Rs.400 was
added to the capital by both A and B. At the end of the year, profit was 14% of the original capital. Find the
profit received by partner A.
O A. Rs.648.67
O B. Rs.698.77
O C. Rs.684.77
O D. Rs.668.67
Answer:
the answer to the question is A.Rs.648.67
determine the value of a cube with side length of 2 and 1/4 cm
Answer:
6 3/4 cm³
Step-by-step explanation:
I'm assuming value means volume, so if I'm wrong, let me know ;).
To find volume, you multiply length x height x width. So you multiply 2 1/4 three times.
Convert 2 1/4 to an improper fraction.
2 1/4 = 9/4
9 x 3 27
-- -- =
4 x 1 4
Now convert 27/4 to a mixed fraction.
27/4 = 6 3/4
So the volume of the cube is 6 3/4 cm³.
---
hope it helps
If Wolfgang’s Deli Shop needs 15lb of lettuce for an business, but can only use 90% due to spoilage and damage, how many lb should Wolfgang order for an evening’s business?
Answer:
13.5 pounds
Step-by-step explanation:
90% of 15 is 13.5 or if you need to round then 14 pounds of lettuce