What is the complete factorization of 8x2 − 8x + 2?
A. 2(4x − 1)2
B. 8(x − 1)(x + 1)
C. 2(2x − 1)2
D. 2(x − 2)(x + 2)
Answer:
Step-by-step explanation:
8x^2 - 8x + 2
2(4x^2 - 4x + 1)
2(2x - 1)(2x - 1) or 2(2x - 1)^2
answer is C
The complete factorization of [tex]8x^2 - 8x + 2[/tex] will be [tex]2(2x-1)^2[/tex] .
What is factorization ?Factorization is a process consists of writing a number or another mathematical object as a product of several factors solving it into other factors.
We have,
[tex]8x^2 - 8x + 2[/tex]
Using the mid term splitting method;
[tex]=8x^2-4x-4x+2[/tex]
[tex]=4x(2x-1)-2(2x-1)[/tex]
[tex]=(4x-2)(2x-1)[/tex]
[tex]=2(2x-1)(2x-1)[/tex]
[tex]=2(2x-1)^2[/tex]
So, the factorization of the given expression is given in option [tex](c)[/tex] i.e. [tex]2(2x-1)^2[/tex] .
Hence, we can say that the complete factorization of [tex]8x^2 - 8x + 2[/tex] will be [tex]2(2x-1)^2[/tex] .
To know more about factorization click here
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In a library, there are 12 books in each of the 4 shelves but then Jamie takes away 3 books. Choose the correct expression and evaluation
Answer:
I think Thts the answer
Step-by-step explanation:
(12x4)-3
In ASTU, S = 3.8 inches, t = 9.8 inches and u=9.6 inches. Find the measure of ZU to
the nearest 10th of a degree.
Answer: 75.8
Step-by-step explanation:
100 points---please help
"Ay, marry, will I join with you all," quoth the Tinker, "for I love a merry life, and I love thee, good master, though thou didst thwack my ribs and cheat me into the bargain. Fain am I to own thou art both a stouter and a slyer man than I; so I will obey thee and be thine own true servant."
So all turned their steps to the forest depths, where the Tinker was to live henceforth.
What universal theme does this excerpt represent?
A. Money is everything.
B. Rebels inspire loyalty.
C. Obedience is better than rebellion.
D. Cheating will get you everywhere.
Answer:
a: everything is money
don't mind this it just said I need to write more to turn it in
Bryce tried to solve an equation step by step.
8
3
+3)
5
3
3
8
5
3c + -
Step 1
3
3
13c
Step 2
1
©
3
Step 3
Find Bryce's mistake.
Plz help i am really confused
Answer:
sorry im confused too . i would help you but I don't know what they are asking sorry
Someone plz help it’s due in 3 minutes
Answer:
Yes
Step-by-step explanation:
Because as you look closer to this question, you will notice, their the same questions but the denominator is just switched around.
Hope this helped!
Answer:
Both products are equals
Step-by-step explanation:
The rule:
(a/b) × (c/d) = (a*c) / (b*d)
then:
According to the rule, numerators are multiplied by numerators and denominators by denominators. In this exercise the numerators are the same as the denominators, so the result of both products is the same.
4a^2b^2,12ab^2,-8a^2b
(SAT Prep) Find the value of x.
Answer: x=40°
Step-by-step explanation:
The two triangles are congruent (I think it’s called the interior angle proof) so the bottom right angle is also 65°. All angles in a Triangle equal 180°, so 180-(75+65)=40
Answer:
huh
Step-by-step explanation:
just multi ply its not hard
The square of a number plus the number is 12. Find the number(s).
Answer:
n= -4, 3
Step-by-step explain
n^2 + n = 12
n^2 + n - 12 = 0
n^2 + 4n - 3n - 12 = 0
n(n+4) -3(n+4) = 0
(n-3) (n+4) = 0
n-3 = 0 = n=3
n+4 = 0 = n=-4
Plzz helpp I’ll mark brainiest
Answer:
Ben $19 Amy $22
Step-by-step explanation:
$10+ ($3*3)=$19
$13+($3*3)=$22
Help me please if you can!
Don't guess!
Answer:
17 R 25
Step-by-step explanation:
long division. 17(15) is 510. 535-510 is 25, which is the remainder.
Make d the subject of the formula h =d/3 +2
Choose the correct answer
1. ______is the ratio of 300 to 100.
a) 3 : 1 b) 1 : 3 c) 300 : 1 d) 100 : 3
2. If the weight of 20 books is 80Kg, then the weight of 1 book is..
a) 4 Kg b) 20 Kg c) 40 Kg d) 8 Kg
3. An equivalent ratio of 3 : 2 is
a) 3 : 4 b) 6 : 4 c) 9 : 4 d) 3 : 6
4. The middle terms of 3:15 = 21:105 are.
a) 3 and 15 b) 21 and 105 c) 3 and 21 d) 15 and 21
5. Which of the following is not proportional?
a) 8 : 4 :: 8 : 16 b) 4 : 8 :: 8 : 16 c) 16 : 8 :: 8 : 4 d) 8 : 16 :: 4 : 8
6. If two ratios are equal, then they are in ____________
7. The ratio of 20 boys to 15 girls is _____________
8. Express the following ratios in the simplest form.
a) 14 to 42 b) 56 to 80
9. Check whether the following are in proportion or not.
a) 4, 6, 8, 12. b) 15, 45, 5, 25.
10. If the cost of 6 cans of Juice is ₹ 210, then what will be the cost of 4 Juice?
11. Taniya earns ₹ 150,000 and saves ₹ 50,000. Find the ratio of
a) Her earning to her expenditure b) Her earning to her savings
12. Find the ratio of 15 cm to 2 meters.
Answer:
1) A, 2) A, 3) B, 4) D, 5) A, 6) proportion, 7) 4 : 3, 8) a) The simplest ratio of 14 : 42 is 1 : 3, b) The simplest ratio of 56 : 80 is 7 : 10, 9) a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units, b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series, 10) 4 cans of juice cost 140, 11) a) 3 : 2, b) 3 : 1, 12) The ratio of 15 centimeters to 2 meters is 3 : 40.
Step-by-step explanation:
1) The ratio is determined by following operation:
[tex]x = \frac{300}{100}[/tex]
[tex]x = \frac{3}{1}[/tex]
3 : 1 is the ratio of 300 to 100. (Answer: A)
2) The weight of 1 book is found by the total weight of books divided by the total amount of books, that is:
[tex]x = \frac{80\,kg}{20}[/tex]
[tex]x = 4\,kg[/tex]
The weight of 1 book is 4 kilograms. (Answer: A)
3) The equivalent ratio of 3 : 2 is found by multiplicating both numerator and denominator by a given positive number:
[tex]x = \frac{3\times 2}{2\times 2}[/tex]
[tex]x = \frac{9}{4}[/tex]
An equivalent ratio of 3 : 2 is 6 : 4. (Answer: B)
4) The middle terms of ratio correspond with the denominator of the ratio on the left and the numerator of the ratio on the right. Hence, the middle terms of 3 : 15 = 21 : 105 are 15 and 21. (Answer: D)
5) 8 : 4 is not proportional to 8 : 16, since both numerators and denominators are not multiplied by the same number. That is:
[tex]x = \frac{8\times 1}{4\times 4}[/tex]
[tex]x = \frac{8}{16}[/tex]
8 : 4 :: 8 : 16 is not proportional. (Answer: A)
6) If two ratios are equal, then they are in proportion. That is:
[tex]a \,:\,b \,::c\,:\,d[/tex], where [tex]r = \frac{c}{a} = \frac{d}{b}[/tex], [tex]\forall\,r > 0[/tex].
If two ratios are equal, then they are in proportion. (Answer: proportion)
7) The ratio of 20 boys to 15 girls is derived of 20 divided by 15 until a denominator of the least integer is found by simplifying the fraction:
[tex]\frac{20}{15} = \frac{4}{3}[/tex]
The ratio of 20 boys to 15 girls is 4 : 3. (Answer: 4 : 3)
8) Express the following ratios in the simplest form:
a) [tex]\frac{14}{42} = \frac{7}{21} = \frac{1}{3}[/tex].
The simplest ratio of 14 : 42 is 1 : 3.
b) [tex]\frac{56}{80} = \frac{28}{40} = \frac{14}{20} = \frac{7}{10}[/tex]
The simplest ratio of 56 : 80 is 7 : 10.
9) When a series is in proportion, it must be in increasing or decreasing order at constant rate.
a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units.
b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series.
10) We determine the cost of 4 cans of juice by simple rule of three:
[tex]x = \frac{4\,cans}{6\,cans}\times 210[/tex]
[tex]x = 140[/tex]
4 cans of juice cost 140.
11) a) The ratio of her earning to her expenditure is:
[tex]x = \frac{150000}{150000-50000}[/tex]
[tex]x = \frac{3}{2}[/tex]
The earning to expenditure ratio is 3 : 2.
b) The ratio of her earning to her savings is:
[tex]x = \frac{150000}{50000}[/tex]
[tex]x = 3[/tex]
The earning to savings ratio is 3 : 1.
12) 1 meter equals 100 centimeters. Then, the given ratio is:
[tex]x = \frac{15\,cm}{200\,cm}[/tex]
[tex]x = \frac{3}{40}[/tex]
The ratio of 15 centimeters to 2 meters is 3 : 40.
Melanie has a bag that contains orange chews, cherry chews, and peach chews. She performs an experiment. Melanie randomly removes a chew from the bag, records the result, and returns the chew to the bag. Melanie performs the experiment 61 times. The results are shown below: A orange chew was selected 38 times. A cherry chew was selected 5 times. A peach chew was selected 18 times. Based on these results, express the probability that the next chew Melanie removes from the bag will be peach chew as a decimal to the nearest hundredth.
Answer:
0.30
Step-by-step explanation:
Given that:
Total number of trials = 61
Number of orange chews = 38
Number of cherry chews = 5
Number of peach chews = 18
Probability that next chew removed will be a peach chew ;
This is an experimental probability problem ;
Using the relation :
Experimental probability of A;
Number of successes (A) / total number of trials
Hence, Probability that next chew removed will be a peach chew ;
Experimental probability of peach chew :
Number of trails = 61 ; number of successes (peach chew) = 18
P(peach chew) = 18 / 61
P( peach chew) = 0.2950819
= 0.30 ( nearest hundredth)
Suppose that the functions g and h are defined for all real numbers x as follows.
8(x)=x+5
h(x) = 3x+4
Write the expressions for (g+h)(x) and (g-h)(x) and evaluate (g•h)(-2).
Valentino's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.
Type of Crust Number Sold
Thin crust 338
Thick crust 331
Stuffed crust 164
Pan style 192
Based on this information, of the next 4000 pizzas he sells, how many should he expect to be stuffed crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Answer: Number of pizzas out of 4000 that is expected to be pan size
= 4000 * 168 / (326 + 309 + 247 + 168)
= 640
Suppose a chemist combines a 25% acid solution and a 50% acid solution to make 40 L of 45% acid solution. How many liters of each solution did she use? Use the blanks below to fill in your numerical answers.
Answer:
The number of liters for :
Acid solution a = x = 8 liters
Acid solution b = y = 32 liters
Step-by-step explanation:
Let us represent:
The number of liters for :
Acid solution a = x
Acid solution b = y
Suppose a chemist combines a 25% acid solution and a 50% acid solution to make 40 L of 45% acid solution.
x + y = 40 ...... Equation 1
x = 40 - y
25% × x + 50% × y = 45% × 40
0.25x + 0.5y = 18...... Equation 2
We substitute, 40 - y for x in Equation 2
0.25(40 - y)+ 0.5y = 18
10 - 0.25y + 0.5y = 18
- 0.25y + 0.5y = 18 - 10
0.25y = 8
y = 8/0.25
y = 32 Liters
Solving for x
x = 40 - y
x = 40 - 32
x = 8 Liters.
Hence:
The number of liters for :
Acid solution a = x = 8 liters
Acid solution b = y = 32 liters
HELP!!! 25 POINTE AND BRAINLIEST!! a local cafe sells 7,200 cold beverages in the month of july. over the next six months, the number of cold beverages decreases at an average rate of 750 cups per month. During the same time frame, the number of hot beverages sold is represented by the equation y=900x + 3,300 where the number of hot beverages, y, is a function of x, the number of months after july.
A. what is the rate of change of cold beverages sold per month? hot beverages?
B. which rate of change is greater? what does it mean?
Answer: a. The rate of change of cold beverages: -750 cups/month
The rate of change of hot beverages: 900 cups/month
b. The rate of change of hot beverages is greater (900 > -750). It means that the number of hot beverages sold increases at a rate of 900 cups every month.
Step-by-step explanation:
a. The question says that "the number of cold beverages decreases at an average rate of 750 cups per month". This indicates that the rate of change of cold beverages is -750 cups/month. Why negative? Remember that it decreases, not increases.
Then let's look at the equation given for the sale of hot beverages:
y=900x + 3,300
The slope of the equation is 900, which is also the rate of change. So the rate of change of hot beverages is 900
To determine the point at which medians of a triangle intersect one another, it is necessary to determine the equations of the lines for two
medians. The coordinates of which two points are used in the calculation of the equation for a given median?
A. the perpendicular bisector of one side and its intersection with a second side
B. the midpoint of one side of a triangle and the midpoint of a second side
C. one vertex of a triangle ahd the point of intersection of the angle bisector and the opposite side
D. one vertex of a triangle and the midpoint of its opposite side
PLEASE PLEASE PLEASE HELP TEACHER NEEDS THIS BY THE END OF THE DAY ITS FOR 20PTS
Jacob studied on 3 different nights during the work week. He also put in an extra 45 minutes during the weekend. If Jacob studied the same amount of time each night during the week and 45 minutes on the weekend, how long did he study s each night during the week?
a. Write a 2-step equation that can be used to solve for the time Jacob studied each night.
Answer:
I think its 7x+45=3 but im not 100% positive
Answer:
what she said bc i got it right
Step-by-step explanation:
Vinny took some pictures. He printed 28 of them. He has 36 left to print. How many pictures did he take?
Answer:
64 pictures
Step-by-step explanation:
36 + 28 = 64 pictures
Answer:
36+28=64
Step-by-step explanation:
that should be right
5/6-1/9=?/?-?/? =13/18
Me pueden ayudar por favor
Answer:
Más información por favor
Step-by-step explanation:
v = u + at
u = 2 and a= -5 and t= 1/2
work out the value of v
Step-by-step explanation:
v=u+at
v=2+(-5)1
2
v=2-2.5
v=-0.5m/s²
hope it helps.
Answer:
[tex]v = u + at \\ v = 2 + ( - 5)( \frac{1}{2} ) \\ v = 2 + \frac{( - 5)}{2} \\ v = \frac{4 + ( - 5)}{2} \\ v = \frac{ (- 1)}{2} \\ v = - 0.5 \: m {s}^{ - 1} [/tex]
-0.5 m/s is the right answer.Write 2/3 and 3/4 as equivalent fractions using a common denominator.
Answer:
8/12 and 9/12
Step-by-step explanation:
What is the absolute value of the integer –12
Which two expressions are equivalent?
5^2= (-5)^2
true or false
Select all the equations that match the diagram.
plz answer only if correct :))
(this is trig.ratios) in
Answer:
39
Step-by-step explanation:
Since you want to find the variable x all you have to do is simple subtraction.
The two numbers (61 and 22). Subtract those numbers and you get 39. Now it wants you to round to the jearest hundredth but there is no hundreds place so we can round to the nearest tenth. Which would be 30! Hope it helped... :)!
bye