Answer:
Step-by-step explanation:
Hello,
First of all, we know that the solution of the following equation
[tex]ax^2+bx+c=0[/tex]
are
[tex]\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \ \text{ when } \Delta=b^2-4ac \geq 0[/tex]
I would suggest that you try to apply this formula first and check the solution only after you try.
Let's apply it in this case, we have:
[tex]a=4\sqrt{5} \\ \\ b=-24 \\ \\ c= -9\sqrt{5}[/tex]
[tex]\Delta=b^2-4ac=24^2+4*9*5=1296 \\ \\ \sqrt{\Delta}=36 \ \text{ and the solutions are } \\ \\ \\ x_1=\dfrac{24-36}{8\sqrt{5}}=\dfrac{-12}{8\sqrt{5}}=\boxed{\dfrac{-3}{2\sqrt{5}}} \\ \\x_2=\dfrac{24+36}{8\sqrt{5}}=\dfrac{60}{8\sqrt{5}}=\boxed{\dfrac{15}{2\sqrt{5}}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Given that Arccos (√3/2)=β, what are all the angle measurements for right triangle ABC?
Answer:
30°, 60° and 90°
Step-by-step explanation:
Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.
Note that a right angled triangle is made up of two acute angles and a right angled (90°)
Let's get one of the acute angles first
If Arccos (√3/2)=β
β = cos^-1 √3/2
β = 30°
This shows that one of the acute angles is 30°
To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.
90+30+x = 180
120+x = 180
x = 180-120
x = 60°
All the angle measurement for the right angled triangle are 30°, 60° and 90°
9. Read the following word problem, then create a linear equation to model the problem. Provide work to show how your linear equation models the problem, such as a brief description, a picture, or a table. Finally, use the linear equation you created to solve the problem.
$2400 is divided between two accounts. One account pays 2% interest, while the other account pays 3.5% interest. At the end of one interest period, the interest earned is $81. How much was invested in each account?
Answer:
$200 at 2%.
$2200 at 3.5%.
Step-by-step explanation:
Let the two amounts be x and y.
x earns 2% interest, and y earns 3.5% interest.
Since the total is $2400, then
x + y = 2400
Now we can solve for y and express the second amount in terms of x.
y = 2400 - y
The two amounts are x and 2400 - x.
In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.
2% = 0.02; 3.5% = 0.035
The x amount earns 0.02x interest.
The y amount earns 0.035y interest.
The total interest earned is the sum of the interest amounts of the two accounts.
0.02x + 0.035y
We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.
0.02x + 0.035(2400 - x) = 81
The equation above is the linear equation.
Now we solve it. Distribute on the left side.
0.02x + 84 - 0.035x = 81
Combine like terms on the left side.
-0.015x + 84 = 81
Subtract 84 from both sides.
-0.015x = -3
Divide both side by -0.015.
x = 200
$200 was deposited in the account earning 2%.
y = 2400 - x
y = 2400 - 200
y = 2200
$2200 was deposited in the account earning 3.5%.
Solve by the quadratic formula: 3x2 - 4x + 1 =0
Answer:
x=1.75
Step-by-step explanation:
3*2-4x+1=0 subtract 1 from both sides
3*2-4x=-1 multiply 3 and 2
6-4x=-1 Subtract 6 from both sides
-4x=-7 divide both sides by -4
x=1.75
If this helped, please consider giving me brainliest, it will help a lot :)
Have a good day
Use the rationalized expression from the previous question to
calculate the time, in seconds, that the cliff diver is in free fall.
Assume the acceleration due to gravity, a, is -9.8 m/s2, and the
dive distance, d, is -35 m. The negative numbers indicate the
direction is downward. Round the answer to two decimal places.
Answer:
Time taken (t) = 2.67 s (Approx)
Step-by-step explanation:
Find:
Time taken (t)
Given:
Initial velocity (u) = 0 m/s
Acceleration due to gravity(a) = -9.8 m/s²
Distance (d) = -35 m
Computation:
Using 2nd equation of motion,
d = ut + (1/2)at²
-35 = (0)t + (1/2)(-9.8)t²
-35 = -4.9 (t²)
t² = 7.1428
t = 2.6726
Time taken (t) = 2.67 s (Approx)
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use? Check all that apply.
3 x minus 3 + 4 = 2 minus x minus 3
3 x minus 1 + 4 = 2 minus x + 3
3 x minus 3 + 4 = 2 minus x + 3
3 x + 1 = negative x minus 1
3 x + 3 = negative x + 5
3 x + 1 = negative x + 5
Answer: 3 x minus 3 + 4 = 2 minus x minus 3
3 x + 1 = negative x minus 1
Step-by-step explanation:
A and D. Edge 2020
The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.
The equation is the relationship between variables and represented as[tex]y = ax +b[/tex] is an example of a polynomial equation.
Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
x = -1/2
Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.
Learn more about the equation here:
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changing fraction to percentage
Answer:
Hello There!
`~~~~~~~~~~~~~~~~~~`
You added no fraction so i thought you wanted the definition
Convert Fractions to Percents. Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.
Hope this helped you. Brainliest wouldbe nice!
What is the maximum value of the function
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]f(x)=-x^2+6x+1[/tex]
x coordinate:
[tex]\frac{-b}{2a}[/tex]
[tex]a=-1\\b=6[/tex]
[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]
y-coordinate:
[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]
Answer:
10
Step-by-step explanation:
What is P(A|B)?
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
What is P(A|B)? 
A.Not enough information
B.0.50 
C.0.10 
D.0.20
Answer:
50
Step-by-step explanation:
The value of P(A|B) = 0.50 which is correct option(B)
What is independent events?
Independent events is defined as an event that is not affected by other events.
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
P(A|B) = P(A∩B)/P(B)
P(A|B) = P(A).P(B)/P(B)
P(A|B) = P(A)
Substitute the value of P(A) = 0.50,
P(A|B) = 0.50
Hence, the value of P(A|B) = 0.50
Learn more about independent events
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please answers quick ,whats an inequality?
Answer:
Step-by-step explanation:
inequality is a equation with |x|
a inequality equation is like this..
|x|>7
Two factory plants are making TV panels. Yesterday, Plant A produced 5000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 450 defective panels
Answer:
10,000 panels
Step-by-step explanation:
A TV panel is being produced by two factory plants
Plant A produced 5000 fewer panels than plant B
Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B
a= b-5000............equation 1
5% of the panels from plant A were defective
= 5/100
= 0.05
2% of the panels from plant B were defective
= 2/100
= 0.02
The total defective panels of both plants is 450
0.05a + 0.02b= 450..............equation 2
Substitute b-5000 for a in equation 2
0.05(b-5000) + 0.02b= 450
0.05b - 250 + 0.02b= 450
Collect the like terms
0.05b+0.02b= 450+250
0.07b= 700
Divide both side by the coefficient of b which is 0.07
0.07 b/0.07= 700/0.07
b= 10,000
Hence plant B produced 10,000 panels
Find the vertex form
Hi,
[tex]y=5x^{2} +12x-2\\y=x(5x+12)-\frac{46}{5} \\y=5(x+\frac{6}{5} )^{2}-\frac{46}{5} \\[/tex]
Have a good day.
need HELP ON THIS A S AP !!!!!
Answer:
803.84yd²
Step-by-step explanation:
Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]
We are given the radius of 8 yards.
Using 3.14 for pi:
[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]
The correct answer should be 803.84yd².
Brainilest Appreciated.
Answer:
803.84 yd^2
Step-by-step explanation:
4*3.14*8^2
12.56*64
803.84
brainliest pls
hope i helped
-ZYLYNN
Part 2: describe the shape of your cross section of a slice of banana at 45° angle to a space draw picture of the sheep. Part 3: describe the shape of a cross sections if you slice banana and half with a cut perpendicular to its base draw a picture of the shape (hint remember to think of a banana a cylinder)
Answer:
Part 2:
The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points
The drawing of the angle cross section of a cylinder representing the banana is attached
Part 3:
When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle
The drawing of the perpendicular cross section of a cylinder representing the banana is
Step-by-step explanation:
HELPPPP I need help finding x a and b pleaseeee
Answer:
5x-18 this angle is equal to 92
3x+22 this angle is equal to 88
angle a=88
angle b=92
Step-by-step explanation:
set 5x-18 and 3x+22 equal to 180 and solve to get x=22. Now look for ways to fill in a and b. A is an alternate interior angle that will be equal to 3x+22
angle b will be equal to the angle 5x-18
Answer:
The value of x is22°, a is 88° and b is 92°.
Hope it helps..
What is the translation from quadrilateral EFGH to
quadrilateral E'F’G’H
Answer:
The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)
Step-by-step explanation:
The coordinates of quadrilateral EFGH are;
Point E has coordinates (-1, 1)
Point F has coordinates (0, 4)
Point G has coordinates (3, 1)
Point H has coordinates (3, 0)
The coordinates of the translation are;
Point E' has coordinates (0, -3)
Point F' has coordinates (1, 0)
Point G' has coordinates (4, -3)
Point H' has coordinates (4, -4)
The change in the y-coordinate values (y values) are;
From point E to point E', we have;
(-3 - 1) = -4 which is four units down
The change in the x-coordinate values (x values) are;
From point E to point E', we have;
(0 - (-1)) = 2 which is two units to the right
The total change in translation is [tex]T_{(2, -4)}[/tex].
HELPP PLEASE
2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options: Option A: they pay an initial fee of $30 and lunches cost $2 each Option B: shown on the graph Option C: they pay a flat fee of $70 which includes all lunches Write an equation for each option. (3 marks) Option A: Option B: Option C: b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks) Choose Option A if: Choose Option B if: Choose Option C if: 3. 4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)
Answer:
3.
A. Y = 2x + 30 (red line)
B. Y=5x (blue line)
C. Y=70 (green line)
From 0 to 10 days, choose option B (shown on graph)
From 10 to 20 days, choose option A (first option)
From 20 days and more, choose option C.
4.
surface area of label = 471.2 cm^2
Step-by-step explanation:
Q1718436 Math Camp
2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options:
Option A: they pay an initial fee of $30 and lunches cost $2 each
Option B: shown on the graph
Option C: they pay a flat fee of $70 which includes all lunches
Write an equation for each option. (3 marks) Option A: Option B: Option C:
A. Y = 2x + 30 (red line)
B. Y=5x (blue line)
C. Y=70 (green line)
b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks)
Choose Option A if: Choose Option B if: Choose Option C if:
Least cost is what is below the lowest possible line for the number of days stayed.
From 0 to 10 days, choose option B (shown on graph)
From 10 to 20 days, choose option A (first option)
From 20 days and more, choose option C.
Note that for days 10 and 20, there are two choices each.
3.
4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)
The label only covers the curved surface.
Curved surface area
= 2 pi * r * h
= 2 pi (5) * 15
= 150 pi
= 471.2 cm^2
can someone please answer this question as a simplified fraction.
Answer:
33/2
Step-by-step explanation:
6 * 11/4 = 66/4 = 33/2
In a competition, a school awarded medals in different categiories.40 medals in sport 25 medals in danceand 212 medals in music, if the total of 55 students got medals and only 6 students got medals in the three categories ,how many students get medals in exactly two of these categories?
Answer:
210
Note: this answer might be incorrect because of the value of music (212). This doesn't make logical sense.
Step-by-step explanation:
Hello,
This question can easily be solved through the use of a venn diagram.
Total number of students = 55
Number of medals in sport = 40 = A
Number of medals in dance = 25 = B
Number of medals in music = 212 = C
Number of students that got award in the three categories = (AnBnC) = 6
n(AuBuC) = 55
n(AnB) + n(BnC) + n(AnC) - 3n(AnBnC) =
n(AnB) + n(AnB) + n(AnC) -3×6 ......equation (i)
n(AuBuC) = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
Therefore,
n(AnB) + n(BnC) + n(AnC) = n(A) + n(B) + n(C) + n(AnBnC) - n(AuBuC)
n(A) + n(B) + n(C) + n(AnBnC) - n(AuBuC) - 18
40 + 25 + 212 + 6 - 55 - 18 = 210
Note: this answer might be incorrect because of the value of C (music)
What is the least number of colors you need to correctly color in the sections of the pictures so that no two touching sections are the same color?
Answer:
2
Step-by-step explanation:
Polygons on either side of a common edge need to be colored differently, so 2 colors are needed, as a minimum. Polygons of the same shape do not share an edge, so all can be colored the same color.
Type the correct answer in each box. Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes. (graph below) The function with the lowest output values as x approaches infinity is ____ . The function with the greatest output values as x approaches infinity is ____ .
As x approaches infinity,
The function with the lowest output is graph A
The function with the greatest output is graph B
===========================================================
Explanation:
As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.
The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.
Answer: The function with the lowest output values as x approaches infinity is Graph A.
The function with the greatest output values as x approaches infinity is Graph B.
Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!
Which expression is equivalent to -80
Answer:
what expressions?
Step-by-step explanation:
Dale is in a ski rental shop trying to decide which equipment to rent for the day. The shop offers 4 kinds of skis and 3 kinds of poles. A helmet is always a good idea, and the shop has 8 different helmets available. How many different sets of ski equipment can Dale rent? sets
Answer:
96
Step-by-step explanation:
Simply multiply all the numbers together.
4 * 3 = 12
12 * 8 = 96
There are 96 possible combinations.
If this helped, please mark brainliest :D
Answer: 12 poles and 16 helmets
Step-by-step explanation:
3+4 =8
-4= -4
1.7
James bought 12 cookies and ate 3 of them. He ate ____% of the cookies. (Make sure to enter the answer using numbers only. Do not enter special characters such as the percent symbol.)
Answer:
25Step-by-step explanation:
Total cookies = 12
Ate = 3 cookies
Now,
Percentage of the cookies that James are:
[tex] \frac{3}{12} \times 100 \: percent[/tex]
Calculate:
[tex] = 25 \: percent[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
answer is 25
Step-by-step explanation:
Prove that. 1-sin2A=2sin^2(45-A)
Answer:
Proved
Step-by-step explanation:
2 sin square( 45°-A)
(therefore;
by trigonometry ratios
sin45°=1)
=2sin2(1-A)
=2sin(1-A)
=1+sin2A
hence proved
I HOPE THIS WILL HELP YOU
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Tysm
The registrar keeps an alphabetical list of all undergraduates, with their current addresses. Suppose there are 10,000 undergraduates in the current term. Someone proposes to choose a number at random from 1 to 100, count that far down the list, taking that name and every 100th name after it for the sample.
a) Is this a probability method?
b) Is it the same as simple random sampling?
c) Is there selection bias in this method of drawing a sample?
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
Following are the description of the given points:
(a) This is a system of probability, which possibility occurs inside an intended manner whenever they choose this specific point of origin from 1 to 100 with no one reserve the possibility about who gets throughout the survey.
(b) Its method is different from the random sampling technique with the base available. For example, two individuals whose names identical to both the list have no chance to join within the survey.
(c) its sample is objective to its everyone can enter the test in equal measure.
What is the length of AC?
Please help me ASAP!!!
Answer:
a
Step-by-step explanation:
PLEASE HELP!!!
A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.
Image attached
Answer: C
explanation: a p e x
Explanation:
Start with the template they give, which is y = ax+b. From here, replace 'a' with -2.9 and b with 13.5 to get the answer y = -2.9x + 13.5
The r and r^2 values aren't used to form the regression line. Instead, they are ways to see how good a fit we have. Since r is fairly close to -1, this means we have a really strong negative correlation. All of the points are close or around the same straight line with a negative slope (that slope being -2.9).
Write an expression for the volume and simplify your answer. 3x x+1 x+4
Answer:
volume=3x³+15x²+12x
Step-by-step explanation:
v= l*w*h =(3x )(x+1) (x+4)
v=3x(x²+5x+4)
volume=3x³+15x²+12x
Find the area of equilateral triangle with side a.
Answer:
[tex]\frac{\sqrt{3} }{4} a^2[/tex]
Step-by-step explanation:
To find the area of an equilateral triangle, we can apply a formula.
[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]
[tex]A= area\\s=side \: length[/tex]
The side length is given a.
Plug a in the formula as the side length.
[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]
Answer:
3 square root over 4 a square
Step-by-step explanation:
Help please!!! Thanksss
Answer:
6:00 p.m.
hope this helps :)