Answer:
{4, 20}
Step-by-step explanation:
x2 − 24x = −80
divide -24 by 2 and square result get 144
x^2 - 24x + 144 = -80 + 144
(x - 12)^2 = 64
x - 12 = root (64)
x = 12 + 8 or x = 12 - 8
x = 20 or 4
The solution set of the considered quadratic equation x^2 − 24x = −80 is given by: Option B: {4,20}
What is completing the squares method for solving the quadratic equations in one variable?The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.
The quadratic equation would look something like:
(px + q)^2 = s
where p, q and s are some constants.
We do so, so that we can then use square root and some other operations to get the variable 'x' on one side of the equation, and all the constants on the other side, being solution of the considered quadratic equation.
Expressing the quadratic equation in such form converts the form of the equation which contains 'x' with different powers in different term to a form which contains 'x' single time.
What is the expansion of square of sum of two terms?Suppose that two terms are 'a' and 'b'.
Then, their sum's square is expanded as:
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
For this case, the equation considered is :
[tex]x^2 -24x = -80[/tex]
Comparing the left side with [tex]a^2 + 2ab + b^2[/tex], we see that we can use a = x.
Let we try to make the considered equation look more like the equation [tex]a^2 + 2ab + b^2[/tex] .
[tex]x^2 -24x = -80\\x^2 -2(12)x = -80\\x^2 -2(12)x + 12^2 -12^2 = -80\\x^2 -2(12)x + 12^2 = -80 + 12^2 = 64\\[/tex]
Now, we can use [tex](a+b)^2 = a^2 + 2ab + b^2[/tex] for the left sided expression, as shown below:
[tex]x^2 -2(12)x + 12^2= 64\\\\(x-12)^2 = 64[/tex]
Taking square root, we get:
[tex]\sqrt{(x-12)^2} = \sqrt{64}\\\\(x-12) = \sqrt{(\pm 8)^2} = \pm 8\\or\\\\x = 12 \pm 8\\x = 12+8, x = 12-8\\x = 20, x = 4[/tex]
Thus, the solution set of the considered quadratic equation x^2 − 24x = −80 is given by: Option B: {4,20}
Learn more about completing the squares method here:
https://brainly.com/question/16800259
#SPJ2
Solve the four problems below. Which of the following problems can be solved by finding ? 3 divided by 1/2
a. Shauna buys a three-foot-long sandwich for a party. She then cuts the sandwich into pieces, with each piece being 1/2 -foot long. How many pieces does she get?
b. Phil makes 3 quarts of soup for dinner. His family eats half of the soup for dinner. How many quarts of soup does Phil's family eat for dinner?
c. A pirate finds three pounds of gold. In order to protect his riches, he hides the gold in two treasure chests, with an equal amount of gold in each chest. How many pounds of gold are in each chest?
d. Leo used half of a bag of flour to make bread. If he used 3 cups of flour, how many cups were in the bag to start?
Answer:
[tex](a)=6\\(b)=1\ \frac {1}{2}\\(c)=1\ \frac {1}{2}\\d=6[/tex]
Step-by-step explanation:
(a)
3 ft long when divided into half ft each will be
3ft ÷1/2 ft
We change the ÷ to × then the second part is reciprocated hence
3ft÷1/2= 3ft×2/1=6 pieces
(b)
The question requires us to get the differences. Initially, Phil makes 3 quarts of soup but the family takes only half of the original quantity to mean Phil remains with the other half.
Therefore, half of 3 is 3×1/2=3/2= 1.5 or 1 1/2
(c)
Hiding 3 pounds of gold into two equal sections means 3 is divided by 2
3÷2=1.5 or 1 1/2
(d)
If half, 0.5 represent 3 cups then full quantity represent x
0.5=3 cups
1=x
By cross multiplication
1*3/0.5=6
What is the rest plz help me
''Complete the following pattern: 2, 4, 8, 16, 32, ___.''
Answer:
64
Step-by-step explanation:
32*2 = 64
Answer:
it will be 48
Step-by-step explanation:you have to multiply each number by 2
The sum of the present ages of a father and his son is 80 years. When the
father's age was equal to the present age of the son, the sum of their ages
would be 40 years. Find their present ages.
Answer:
Father=60
Son=20
Step-by-step explanation:
Let the father's age be x
Let the son age be y
Present age of them
X+y=80...(1)
Since the father's age equals to the present age of the son
Y+y=40
2y=40....(2)
Make y the subject of formula by dividing both sides by 2
Y=20
Substitute the value for x into (1)
20+x=80
Substrate 20 from both sides
X=60
Therefore the father's age is 60 and the son's age is 20
Put these in order from least to greatest 1/2, 1/3, 2/5, 0.6 , o.3
Answer:
0.3, 1/3, 2/5, 1/2, 0.6
Step-by-step explanation:
Answer:
ok first lets make them all decimals
1/2=0.5
1/3= 0.3333333
2/5= 0.4
ok now we got 0.5, 0.33333, 0.4, 0.6, 0.3,
now lets also add zeros to the back to make it a more clear picture
0.50, 0.33, 0.40, 0.60, 0.30 ok now put the in order
0.30 , 0.33, 0.40, 0.50, 0.60
Step-by-step explanation:
A relative frequency table is made from data in a frequency table.
Relative Frequency Table: A 4-column table with 3 rows. The first column has no label with entries likes S, T, total. The second column is labeled U with entries 26%, 21%, 47%. The third column is labeled V with entries 42%, k, 53%. The fourth column is labeled total with entries 68%, 32%, 100%.
What is the value of k in the relative frequency table? Round the answer to the nearest percent.
2%
11%
20%
33%
Answer:
k = 11 let me know if you don't understand how I got this.
Step-by-step explanation:
I'm gonna write it out
U V total
S 26 42 68
T 21 k 32
Total 47 53 100
So, you want to look at the column and row labeled total, this is the key. for the row total, it sums up everything in the column above it. so for the u column, the total value is 47 while the two values above it are 26 and 21. These two values sum to 47. This is the same for all other columns, and you can use the same reasoning with the total column as well summing rows.
This gives you two ways to solve for k. either 21 + k = 32 or 42 + k = 53. Either way gets you the answer k = 11
The value of k in the relative frequency table is 11%.
What is relative frequency?The ratio of the frequency of a particular event in a statistical experiment to the total frequency.
U V total
S 26 42 68
T 21 k 32
Total 47 53 100
As, when we add the column data 26+ 21 = 47 which shows that the total consist of sum of column data.
So,
21 + k = 32
k = 11
Learn more about relative frequency here:
https://brainly.com/question/16832475
#SPJ5
If $500 yields $51.76 in simple interest over 7yrs, what is the annual rate? Answer need to be rounded to the nearest thousandth
The annual rate of interest is 1.479%.
Step-by-step explanation:
Given,
Principle (P) = $500
Interest (I) = $51.76
Time (T) = 7 years
To find out the rate of interest (R).
Formula
Simple interest (I) = [tex]\frac{PTR}{100}[/tex]
According to the problem,
[tex]\frac{PTR}{100}[/tex] = 51.76
or, R = [tex]\frac{51.76X100}{PT}[/tex]
or, R = [tex]\frac{51.76X100}{500X7}[/tex]
= 1.4788 = 1.479% (approx)
Answer:
1.5%
Step-by-step explanation:
Principal, P = $500
Simple interest S.I. = $51.76
Period, T = 7 years
Simple interest = P*R*T / 100
Let's make rate, R the subject of formula
R = 100 * S.I. / P * T
Slot in the respective values
R = 100 * 51.76 / 500 * 7
R = 1.5%
26 Points!!! Select True or False for each equation.
Answer:
The first one is true, meanwhile the second is false!
Step-by-step explanation:
The first one both simplify to -3.
The second one, -6/-2 ( fraction ) simplifies to positive 3 because dividing or multiplying by 2 negative numbers cancels out the negative sign.
Hope it helps!
Answer:
1) True
2) False
Step-by-step explanation:
- 6/2 = -3
Solve for h
35=1/2h (5+2)
Answer:
10
Step-by-step explanation:
35= 1/2h(7)
1/2 of 7 is 3.5
3.5(10)=35
h=10
Answer:
Solve for h
35=1/2h (5+2)
Multiply (5+2) by 1 divided by 2, then we have
7/2h= 35
cross multiply
35 x 2h= 7
70h= 7
divide both sides by 70
h= 7/70
h= 1/10
Step-by-step explanation:
Solve the system of equations.
- 5x – 3y - 9 = 0
4x – 187 - 54 = 0
Answer:
Step-by-step explanation:
Solve simultaneously
-5x-3y=9
4x-187-54=0
4x=241
x=60.25
To get y
Substitute for x in equal one
-5(60.25)-3y=9
-301.25-3y=9
-3y=9+301.25
-3y=310.25
y=-103.4
Complete the statements about the two cones. The volumes of the cones are equal when . If a > b, then the cross-sectional area of cone A is the cross-sectional area of cone B at every level parallel to their respective bases.
Answer: a=b , greater than
Step-by-step explanation:
Answer:
B and C
Step-by-step explanation:
Y= -x + 5; (2,),(5,),(0,)
Answer:
(2,3) (5,0) (0,5)
Step-by-step explanation:
Plug the x values into the equation to find your y value.
Exterior angles of a triangle...help?
Answer:
Angle 4 is the exterior angle
Step-by-step explanation:
Exterior mean "outside"
Angle 4 is the only angle outside of the triangle
resolva a questão a seguir 18x -43= 65
Answer:
6
Step-by-step explanation:
18x - 43 = 65
move the 43 over by adding since it's being subtracted
18x = 108
divide by 18 to get x by itself
x = 6
Answer:
x=6
Step-by-step explanation:
According to the question
18x-43=65
Let's add 43 to both sides
18x=65+43
18x=108
Divide both sides by 18
x=6
Therefore x=6
If the base of a prism has an area of 24 m2
and the prism has a height of 7 m, what is the volume
of the prism?
A. 168 m3
B. 31 m3
C. 1176 m3
D. Not enough information.
DONT SCROLL
To find the volume of a prism, you multiply the area of its base by its height. Thus, the volume of a prism with a base area of 24 m² and a height of 7 m is 168 m³.
Explanation:The subject of this question is Mathematics, more specifically, geometry. The question wants to find the volume of a prism. The formula for finding the volume of a prism is Base Area x Height. In this case, the base area of the prism is given as 24 m², and the height is given as 7 m.
We use the formula: Volume = Base Area x Height which translates to Volume = 24 m² x 7 m= 168 m³. So the answer is 168 cubic meters, which corresponds to option A.
Learn more about Volume of a prism here:https://brainly.com/question/22147194
#SPJ12
Which is a Linear Equation?
A. Y=3-2x
B. Y= -7x^2
C. Y=2-3x^2
D. Y=-7×^3
Answer:
(A)
Step-by-step explanation:
A linear equation can be written in slope intercept form, [tex]y=mx+b[/tex].
X must be in it's first power in a linear equation. X being in any other power will result in a curved line.
This eliminates B, C and D already. X is not in it's first power in the given three options.
The best option is A.
please help with this question its in the picture :)
2.75 cups of water mixed with 3.5 cups of pancake mix will make 19 pancakes. How much water is needed if there is only 1.5 cups of pancake mix left?
Answer:
You would need .75 cups of water (or 3/4 cups) if there is only 1.5 cups of pancake mix left
Step-by-step explanation:
So the ratio of water to pancake mix is 2.75 : 3.5 (which makes 19 pancakes)
To get from 3.5 cups of pancake mix to 1.5 cups of pancake mix you would subtract 2 cups. Since this is a ratio, you would not only subtract 2 cups from the pancake mix, but also from the water. 2.75 - 2 = .75 Therefore, you would need .75 cups of water (or 3/4 cups) if there is only 1.5 cups of pancake mix left. Hope this helps!
Answer:
1 5/28 cups of water
Step-by-step explanation:
Water : pancake mix
2.75 : 3.5
X : 1.5
2.75/X = 3.5/1.5
X = 2.75 × 1.5/3.5
X = 33/28 or 1 5/28 cups
Let f(x) = 8x + 5 and g(x) = -2x - 4 Find the value of f(2) + g(5) *
Answer: lock down
Step-by-step explanation: f(x)= 8x2 + 5=21--> f(x)=21
g(x)= -2x5 - 4=-14--> g(x)=-14
f(2)+g(5) = 7
Step-by-step explanation:
Given,
f(x) = 8x+5
g(x) = -2x-4
To find f(2)+g(5)
Now,
f(2) means putting the value of x = 2 in f(x)
g(5) means putting the value of x = 5 in g(x)
f(2) = 8(2)+5 = 21
g(5) = -2(5)-4 = -14
Hence,
f(2)+g(5) = 21-14 = 7
6 times ( negative 1 )
Answer: -6
Step-by-step explanation:
Liz flips a coin 50 times. The coin lands heads up 20 times and tails up 30 times. Complete each statement. The theoretical probability of the coin landing heads up is ______. Based on Liz’s results, the experimental probability of the coin landing heads up is_____. The theoretical probability is than the experimental probability in this experiment________.
Answer:
50% or 50/100 or 25/50 40% or 40/100 or 20/40MoreStep-by-step explanation:
The theoretical probability is more than the experimental probability in this experiment
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the number of times the coin is flipped be n = 50
And , the number of times the heads is shown = 20 times
The number of times the tails is shown = 30 times
The theoretical probability of a coin being head or tail P ( A ) = 50 %
So , the experimental probability of being a head is P ( B ) = 20/50
P ( B ) = 40/100 = 40 %
Therefore , P ( A ) > P ( B )
Hence , theoretical probability is more
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ3
Answer please and explain I’m having some trouble
Answer:
A
Step-by-step explanation:
The end behaviour as x gets larger and positive ( right- hand end )or larger and negative ( left- hand end )is determined by the term of the greatest degree.
For p(x) that is 4[tex]x^{8}[/tex], with
• Even degree (8) and positive leading coefficient (4), then
as x → ∞ , p(x) → ∞ and
as x → - ∞ , p(x) → ∞
How many pounds are in
8 kilograms? 1 kg = 2.2 lbs
8 kg = [?] lbs
Answer:
17.6 lbs
Step-by-step explanation:
1kg=2.2lbs
Multiply each side by 8
8kg=17.6 lbs
Given that there are 1 kilogram in 2.2 pounds. By unitary method, we can say that 8 kilograms are equal to 17.6 pounds.
Unitary method is the method of solving problems wherein you first find the value of one item, then to find value of k items, multiply value of one item by k.
The given question is about establishing a relationship between measurement units kilogram and pound with their units being kg and lbs respectively.
Given in the question,
1 kg = 2.2 lbs
8 kg = 8 * 2.2 lbs = 17.6 lbs
Implying that 8 kilograms are equal to 17.6 pounds.
Learn more about unitary method here
brainly.com/question/28276953
#SPJ2
what is the perimeter of this tile 10 in 8 in 6 in
Answer:
24 inches
Step-by-step explanation:
To find perimeter, simply add all the side lengths
10 + 8 + 6 = 24in
Thank me later :)
What, approximately, is the mean weight for babies born
during this two-month period?
As a nurse in a maternity ward, you are tracking the
weights of newborn babies. In the month of August, 360
babies are born, with a mean weight of 8.1 pounds. In the
month of September, 291 babies are born, with a mean
weight of 7.8 pounds.
7.83 pounds
7.93 pounds
7.95 pounds
7.97 pounds
7.99 pounds
Final answer:
The approximate mean weight for babies born during the two months of August and September is calculated using a weighted average, and it is approximately 7.97 pounds.
Explanation:
To find the mean weight of the babies born during the two months, we can use the weighted average formula which takes into account the different numbers of babies born in each month and their respective mean weights.
The formula for the weighted mean is as follows:
Weighted mean = (Sum of weights × their respective frequencies) / (Total sum of frequencies)
Calculate the total weight for August: 360 babies × 8.1 pounds = 2916 pounds.Calculate the total weight for September: 291 babies × 7.8 pounds = 2269.8 pounds.Add the weights from both months: 2916 pounds + 2269.8 pounds = 5185.8 pounds.Add the number of babies from both months: 360 babies + 291 babies = 651 babies.Divide the total weight by the total number of babies: 5185.8 pounds ÷ 651 babies = approximately 7.97 pounds.Therefore, the approximate mean weight for the babies born during August and September is 7.97 pounds.
Using a 16-sided number cube, what is the probability that you will roll a multiple of 4 or an odd prime number? The number 1 isn't an odd prime. Round to three decimals.
A. 0.625
B. 0.250
C. 0.563
D. 0.688
================================================
Explanation:
E = event space
E = set of outcomes we want to happen
E = rolling a multiple of 4 or rolling an odd prime number
E = {4,8,12,16 3,5,7,11,13}
n(E) = number of items in set E
n(E) = 9, (four multiples of 16+five ways to roll odd prime number)
-----
S = sample space
S = set of all possible outcomes (whether we want them to happen or not)
S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}
n(S) = number of items in set S
n(S) = 16
-----
P(E) = probability of event space occurring
P(E) = probability of rolling a multiple of 4 or rolling an odd prime number
P(E) = n(E)/n(S)
P(E) = 9/16
P(E) = 0.5625
P(E) = 0.563
HELP ASAP WORTH 30 PTS!!!!!!!!!!!
True or False? The higher the Mean Absolute Deviation (MAD) is of a set of data, the closer the data is grouped.
Answer:
FALSE=Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set.
Step-by-step explanation:
Which of the given points would be in a table generated by the equation below?
pm + gy = 5
А. (0, 9)
B. (0, й)
C. , о)
D. (2 , 0)
What is the length of the third side of the window frame below
15
27
25
32
Answer:
25
Step-by-step explanation:
What is the area of this irregular figure knowing that the formula for the area of a rectangle is l x w.
Answer:
35
Step-by-step explanation:
5+5+10+3+2+7+3=35
Answer:
The area is 42
Step-by-step explanation:
First you have to divide the figure into three rectangles
The first one has
Lenght=10
Width=5-2=30
Area=l x w=10x30=30
The other two are equivalent in lenght and width that means that if if we find the area of one we must multiply by 2 to find the other.
Rectangles 2 and 3
Lenght=3
Width=2
Area of one of them=3x2=6
Both rectangles=6x2=12
Now, we add everything up
Total Area=12+30=42
Remove all perfect squares from inside the square root.
\sqrt{108a^6}=
Answer:
[tex]y = 6\cdot a^{3}\cdot \sqrt{3}[/tex]
Step-by-step explanation:
The following expression is needed to be solved:
[tex]y = \sqrt{108\cdot a^{6}}[/tex]
The solution is done by means of algebraic handling:
[tex]y = \sqrt{2^{2}\cdot 3^{2}\cdot 3 \cdot a ^{6}}[/tex]
[tex]y = 6\cdot a^{3}\cdot \sqrt{3}[/tex]