Solving Quadratic Equations
Directions: Solve the following quadratic equations using the quadratic formula. Show your work
and all answers must be in simplest radical form.
I
a. x2 - 2x - 15 =0
b. x2 + 8x - 10 =0
Answer:
a) x= 5 or x= -3
b) x = -4 + [tex]\sqrt{26}[/tex] or -4 - [tex]\sqrt{26}[/tex]
Step-by-step explanation:
a) [tex]x^{2}[/tex] - 2x - 15 =0
x = [tex]\frac{-(-2) +\sqrt{(-2)^{2} - 4(1)(-15)}}{2(1)}[/tex] or [tex]\frac{-(-2) -\sqrt{(-2)^{2} - 4(1)(-15)}}{2(1)}[/tex]
x= 5 or x=-3
b) [tex]x^{2}[/tex] + 8x - 10 =0
x = [tex]\frac{-(8) +\sqrt{(8)^{2} - 4(1)(-10)}}{2(1)}[/tex] or [tex]\frac{-(8) -\sqrt{(8)^{2} - 4(1)(-10)}}{2(1)}[/tex]
x = -4 + [tex]\sqrt{26}[/tex] or -4 - [tex]\sqrt{26}[/tex]
A swimming pool measures 10 feet by 8.5 feet by 5 feet. How many cubic feet of water will the swimming pool hold?
Answer:
425 Cubic Feet
Step-by-step explanation:
Cubic feet is volume meaning that in order to find the volume you must multiply the length, width and the height. The answer is 425
The swimming pool will hold 425 cubic feet of water.
What is the volume of a rectangular prism?The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.
To find the volume of the swimming pool in cubic feet, we need to multiply the length, width, and height of the pool:
The volume is calculated as,
Volume = length x width x height
Volume = 10 ft x 8.5 ft x 5 ft
Volume = 425 cubic feet
Therefore, the swimming pool will hold 425 cubic feet of water.
To know more about volume follow
brainly.com/question/24284033
#SPJ3
The set of data below represent the number of runs scored by a youth baseball team over the course of a season.
Team: 4, 8, 5, 12, 3, 9, 5, 2 Which set of statements about the data is true?
1)Mean < Standard Deviation
2)First Quartile < Standard Deviation
3)Median > Mean
4)Mean > Standard Deviation
The correct answer will be option (3) Median > Mean
ConceptFirst we will find the mean, median and standard deviation of given dataAfter finding mean, median and standard deviation we will compare them to find the correct answerHow to solve this problem?The steps are as follow:
The runs scored by youth baseball team over the course of a season is : 4, 8, 5, 12, 3, 9, 5, 2Mean is given as follow:[tex]x \: = \frac{4 + 8 + 5 + 12 + 3 + 9 + 5 + 2}{8} \\ x = 6[/tex]
So the mean will be 6Arranging the given observation 2,3,4,5,5,8,9,12To find the median the total number observation is 8 which is even so formula to find median will be:[tex][tex]m = \frac{ { (\frac{n}{2}) }^{th} obs + ( { \frac{n}{2} + 1)}^{th} obs }{2} \\ m= \frac{ { (\frac{8}{2}) }^{th} obs + ( { \frac{8}{2} + 1)}^{th} obs }{2} \\ m= \frac{ { (4) }^{th} obs + ( { 5)}^{th} obs }{2} \\ m= \frac{ { 5} + 5}{2} \\ m = 5[/tex][/tex]
So the correct answer will be option (3) Median > Mean
Learn more about mean and median here:
https://brainly.com/question/13741558
#SPJ2
Please help will give brainliest
Answer:
For one I think the answer is 14 and my brothers name is ethan!
Step-by-step explanation:
Chanasia buys a plastic bucket. The bucket weighs 460 g. The label on the bucket says made with 20% recycled plastic. How many grams of recycled plastic are used to make Chanasia’s bucket?
Answer:
92
Step-by-step explanation:
20% of 460 is 92 so it would be 92
PLLLZZ HHEELLPPP! QUESTION IS BELOW!
Answer:
32°Step-by-step explanation:
The two given angles are complementary, it means they add to 90°Find x:
2x + 10 + x + 8 = 903x + 18 = 903x = 72x = 24Find Y:
m∠Y = x + 8 = 24 + 8 = 32°Please please help me
Type the expression that results from the following series of steps:
Start with x, subtract 6, then times by 3.
Answer:
(x-6)3
hope it helps
A principal wants to find out if her school needs more bike racks. A survey is taken of 30 students who ride the bus. Why might the sample be biased? Describe in words how a sample could have been done that is more representative of the entire school.
Answer:
The students who ride the bus most likely won't use the bike racks so it doesn't impact them and they probably don't know if they need more bike racks.
Step-by-step explanation:
Help please 10 points
Answer:
200
Step-by-step explanation:
basically, all you have to do is plug in 30 for n. You would get -3 + 7(30-1), and then you would get -3 + 7 x 29, and then you would get -3 + 203, and the final answer would be 200
Select the zeros of the function
Answer:
Zeroes are where y=0 (x-intercepts)
I think they are expressed as just the x values since the y value can only be zero, but I could be wrong
the zeroes are at x=-6 and x=-2
so (-6, 0) and (-2, 0)
Question 2
Write true or false for each of the following
statements:
2.1
1 is the smallest uneven prime number
Answer:
false, 1 is not the smallest uneven prime number as it is not a prime number, prime numbers have 2 and only 2 factors whereas 1 only has 1 factor, as well as this, you can have negative prime numbers
Answer:
False one is not the smallest uneven prime number
Please please help help me please please ASAP ASAP please
Answer:1.b 2.i think 5x5 3.a
Step-by-step explanation:
there your ANWERS
It’s not 12 but what goes on the green box?
Answer:
9
Step-by-step explanation:
Use exponential rules: add the exponents when multiplying, subtract the exponents when dividing.
Answer:
3^9
Step-by-step explanation:
- Rewrite the division as a fraction. 3^8x3^3/3^2
- Multiply
3^8 by 3^3 by adding the exponents.
3^11/3^2
- Cancel the common factor of 3^11 and 3^2
3^9
Evaluate.
2(4 what is the correct answer?
Answer:
16
Step-by-step explanation:
2^4= 2 x 2 x 2 x 2 =16
Select the best term from the box to complete the sentence.
A three-dimentional figure having length, width, and height is called a ___?___
You do not list what the choices are but it can be one of these:
A solid figure
A space figure
Can someone explain the answer?
Write a linear equation in slope- intercept form given 2x +5y =35
Answer:
(0,−7)
Explanation:
To find the y-intercept of an equation, set x equal to 0 and solve: In the case of 2x−5y=35, let's replace all instances of x in the equation with 0 and solve for y: 2(0)−5y=35−5y=35−5y−5=35−5
y=−7
Thus, the y-intercept is at (x y)=
(0,−7).
helppp pleaseee :)))
Answer:
1)
Y-intercept: -3
Slope: 2
Equation: y = 2x - 3
Step-by-step explanation:
I just answered one since it was only for 5 points. :)
find the slope and y intercept for this problem: -2y= -16x+8
Answer:
Step-by-step explanation:
The slope intercept form of a line is y=mx+b where m=slope and b=y intercept so we can solve for y from what you were given.
-2y=-16x+8
y=8x-4
So the slope is 8 and the y intercept is -4.
If you can answer BOTH CORRECTLY you'll get brainliest
Answer:
Sorry the pictures re not clear. Could u zoom in? :)
A company manufactures computers. Function N represents the number of components that a new employee can assemble per day. Function E represents the number of components that an experienced employee can assemble per day. In both functions, t represents the number of hours worked in one day.
N(t)=50t/t+4
E(t)= 70t/t+3
Which function describes the difference of the number of components assembled per day by the experienced and new employees?
A. D(t)= 10t(2t+13)/t+3
B. D(t)= 10t(2t+13)/ (t+4)(t+3)
C. D(t)= 10t(2t-13)/t+4
D. D(t)=10t(2t-13)/ (t+4)(t+3)
The difference of the number of components assembled per day by the experienced and new Employees is : D(t)= 10t(2t+13)/ (t+4)(t+3)
Here we perform subtraction :
D(t) = N(t) - E(t)
N(t) = 50t / (t+4)
E(t) = 70t / (t+3)
The difference :
D(t) = E(t) - N(t)
D(t) = [70t / (t+3)] - [50t / (t+4)]
The L.C.M of (t+3) and (t+4) is (t+3)(t+4)
[70t(t+4)] - [50t(t+3)] / (t+3)(t+4)
70t² + 280t - [50t² + 150t] / (t+3)(t+4)
[70t² + 280t - 50t² - 150t] / (t+3)(t+4)
20t² + 130t / (t+3)(t+4)
D(t) = 10t(2t + 13) / (t+3)(t+4)
The difference of the number of components assembled is : D(t)= 10t(2t+13)/ (t+4)(t+3)
Learn more : https://brainly.com/question/1166214
Answer:b
Step-by-step explanation:
plato
What is 1,872,521 rounded to the nearest thousand?
Answer:
1,873,000
Step-by-step explanation:
Answer:Rounded to the nearest thousand is the 4th number. Since the 3 numbers past the 2 is over 500, the rounded number would be 1,873,000.
Step-by-step explanation:Have a great day
Eric has a bag of carrots that weighs 3 pounds. He separates the carrots equally into 10 containers. How many pounds are in each container?
Answer:
3/10 pounds
Step-by-step explanation:
Distribute 3 pounds equally into 10 containers so it is 3/10 pounds in each container.
A spinner used in a board game is divided into 8 equally sized sectors. Three of these sectors indicate that the player should move his token forward on the board, two of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board. The total area of the sectors that do not allow the player to move his token is 35.9 inches squared. What is the radius of the spinner
Answer:
5.52 inch
Step-by-step explanation:
Recall :
Area of Sector : θ/ 360 * πr²
Sectors that do not allow movement : (8-3-2) = 3
Total sectors = 8
θ/ 360 = 3/8 ; Area = 35.9
Radius = r
35.9 = 3/8 * π * r²
35.9 / (3/8 * π) = r²
30.472866 = r²
r = √30.472866
r = 5.52 inch
The radius of the spinner is 5.520 inch whose [tex]\frac{3}{8}[/tex] sector area is 35.9 inches square.
It is given that the spinner used in a board game is divided into 8 equally sized sectors. three sectors indicate that the player should move his token forward on the board, two sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board and its area of the sector is 35.9 inches square.
It is required to find the radius of the spinner.
What is the area of the sector?The region enclosed by the two radii of a circle and the arc is known as a sector's area. In other words sector area is a portion of the circle's area.
We know the formula of sector area (A):
[tex]\rm A= \frac{\theta}{360 \°} \pi r^2[/tex] Where 'r' is the radius of the circle and [tex]\rm \theta[/tex] is in degree
The remaining sectors = ( Total sectors - Three sectors - Two sectors)
= ( 8 - 3 - 2) ⇒ 3 sectors indicate the player do not move his token
Total sector = 8
[tex]\rm \frac{\theta }{360 \° } = \frac{3}{8} \ when \ A = 35.9 \ inches^2[/tex]
Putting these values in the above formula, we get:
[tex]\rm 35.9 = \frac{3}{8} \pi r^2\\\rm 35.9\times 8 = 3\pi r^2\\\rm 287.2 = 3\pi r^2\\\\\rm \frac{287.2}{3} = \pi r^2\\\\\rm 95.733= \pi r^2\\\rm 30.4728 = r^2[/tex]Where [tex]\rm \pi[/tex] = 3.14159
[tex]\sqrt{30.4728} = r\\\rm 5.520= r \\\rm or = 5.520 \ inch[/tex]
Thus, the radius of the spinner is 5.520 inch.
Learn more about the area of sectors here:
https://brainly.com/question/15849991
Pls help me and thank youuu
Answer:
x = 1
Step-by-step explanation:
14 -4x = 10
-4x = -4
x = 1
Answer:
x=1
Step-by-step explanation:
2×7=14
2×2=4
4×1=4
14-4=10
How many degrees is angle x?
Answer
127
Step-by-step explanation:
First add 42 and 85. Then do 180-(42+85) to get w. Then do 180-w to get x as a line always equals 180
why is it important to know the shape of the base of the pyramid
Answer:The pyramid had sloping sides so that the dead pharaoh could symbolically climb to the sky and live forever. The pyramid represented the rays of the Sun I hope this helps
Step-by-step explanation:
Ed has $5.06.
He finds $1.03.
About how much $ does he have now?
Answer:
Ed now has $6.09
Which is NOT true about the transformation below?
A. The orientation of the figure stayed the same.
B. The transformation is a reflection.
C. The two figures are congruent.
D. The pre-image is in Quadrant I.
Answer:
D IS THE ANSWER
Step-by-step explanation:
I THINK ITS B
Answer:
B
Step-by-step explanation: