Answer:
a) Greatest Common factor = 3
b) Greatest Common factor = x
c) Greatest Common factor = xy
Step-by-step explanation:
a)
We can write the equation "3x² - 9x + 12" into three parts and we factor them:
3x² = [tex]3\times\:x\times\:x[/tex]
9x = [tex]3\times\:3\times\:x[/tex]
12 = [tex]2\times\:2\times\:3[/tex]
Common factor = 3
b)
We can write the equation "5x² + 3x" into two parts and we factor them:
5x² = [tex]5\times\:x\times\:x[/tex]
3x = [tex]3\times\:x[/tex]
Common factor = x
c)
We can write the equation "x²y - xy²" into two parts and we factor them:
x²y = [tex]x\times\:x\times\:y[/tex]
xy² = [tex]x\times\:y\times\:y[/tex]
Common factor = xy or x ⋅ y
#1
3x²-9x+123 is common
x is not present at 12 hence it can't 3xGCF=3
#2
5x²+3xNothing common except x and 1
GCF=x#3
x²y-xy²GCF=xy
Write each expression as a single power of 10.
Answer:
Refer to below!
Step-by-step explanation (a):
[tex]\rightarrow \dfrac{10^{3} \times 10^{4} }{10^{5} } \\\\\\ \rightarrow \dfrac{10^{3 + 4} }{10^{5} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[[\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ] \\\\\\ \rightarrow \dfrac{10^{7} }{10^{5} } \\\\\\[/tex]
[tex]\rightarrow 10^{7 - 5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}] \\\\\rightarrow 10^{2}[/tex]
Step-by-step explanation (b):
[tex]\rightarrow \huge{\text{(}{10^{4} \times \dfrac{10^{12} }{10^{7} }\huge{\text{)}[/tex]
[tex]\rightarrow \huge{\text{(}{10^{4} \times {10^{12 - 7} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow \huge{\text{(}{10^{4} \times {10^{5} }\huge{\text{)}[/tex]
[tex]\rightarrow \huge{\text{(}{10^{4 + 5} }\huge{\text{)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ][/tex]
[tex]\rightarrow{10^{9} }[/tex]
Step-by-step explanation (c):
[tex]\rightarrow \huge{\text{(}\dfrac{10^{5} }{10^{3} } }\huge{\text{)}[/tex]
[tex]\rightarrow \huge{\text{(}10^{5 - 3} }\huge{\text{)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow 10^{2} }[/tex]
Step-by-step explanation (d):
[tex]\rightarrow \dfrac{10^{4} \times 10^{5} \times 10^{6} }{10^{3} \times 10^{7} }[/tex]
[tex]\rightarrow \dfrac{10^{4 + 5 + 6} }{10^{3 + 7} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \times a^{4} = a^{4 + 2} = a^{6} ][/tex]
[tex]\rightarrow \dfrac{10^{15} }{10^{10} }[/tex]
[tex]\rightarrow 10^{15 - 10} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow 10^{5} }[/tex]
Step-by-step explanation (e):
[tex]\rightarrow \dfrac{(10^{5})^{2} }{(10^{2})^{3} }[/tex]
[tex]\rightarrow \dfrac{10^{5 \times 2} }{10^{2 \times 3} } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule: }(a^{2} )^{5} = a^{2 \times 5} = a^{10} ][/tex]
[tex]\rightarrow \dfrac{10^{10} }{10^{6} }[/tex]
[tex]\rightarrow {10^{10 - 6} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using exponent rule:} \ a^{2} \div a^{4} = a^{2 - 4} = a^{-2}][/tex]
[tex]\rightarrow {10^{4}[/tex]
A video game allows players to design their own character using the following options.
Video Game Character
What is the probability of designing a female character with long, red hair?
A. 1/24
B. 1/12
C. 1/9
D. 1/4
Answer:
1/24
Step-by-step explanation:
Probability of making female character = 1/2
Probability of having long hair = 1/3
Probablity of having red hair = 1/4
Multiply all these probabilities ( 1/2 x 1/3 x 1/4) = 1/24
The probability of making a female character with long red hair in this video game is 1 in 24.
I hope this helps.
Find the value of y.
As
<IJK and <IKJ are equal measured
The triangle is isoceles
The adjacent sides of both angles are similar
Hence
IJ=IKy=21Answer:
21
Step-by-step explanation:
as angle J and angle K are equal, sides JI and IK are also equal. So y = 21
Only 16 tho!!!!!please
Answer:
(5*2) + (1/2)(2+2+2)*4)
Step-by-step explanation:
Area of Triangle = (1/2)(2 + 2 + 2 )* 4)
Area of Rectangle = 5 * 2
Total Area = (5*2) + (1/2)(2+2+2)*4)
The number 111…111 (100 ones) is multiplied by 101. The resulting number is then also multiplied by 101. The number obtained in the second step is again multiplied by 101. What is the sum of the digits of the number obtained in the third step?
Answer:
800
Step-by-step explanation:
The three multiplication steps are equivalent to multiplying by ...
101³ = 1030301
The sum of digits of the product will be the sum of digits of the partial products, since none of the digit-by-digit multiplications results in a product that is more than 10.
The sum of digits of the third product is ...
(1 × 100) × (1 + 3 + 3 + 1) = 800
PLEASE HELP ASAPP!!! (NO LINKS) WILL GIVE BRAINLIEST
Find the number of solutions of
the
equation 6x^2 + 6x + 3 = 0 by
using the discriminant.
(1 solution, 2 solutions, or no
real solutions)
Answer:
No real solutions
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]
Given equation: [tex]6x^2+6x+3=0[/tex]
[tex]\implies a=6, \quad b=6, \quad c=3[/tex]
Inputting these values into the discriminant:
[tex]\implies (6)^2-4(6)(3)=-36 < 0\implies \textsf{no real solutions}[/tex]
BRAINLIEST!!!
Given the figure below, find the values of x and z.
Step-by-step explanation:
87 and z are opposite so the are equal. The x equation is on the same line as the 87 degree angle so those 2 added together have to equal 180 so subtract 87 from 180 and get 93 and set 93 equal to 9x-87 and solve to get x=20
Answer:
=> z = 87° { vertically opposite angle }
=> 87° + (9x-87) = 180° { linear pair }
=> 87 +9x-87 = 180
=> 9x = 180°
=> x = 180/9
=> x = 20°
How do you write 9 1/10 as a decimal?) *
Answer:
Convert 9 1/10 to an improper fraction.
Decimal form
=9.1
Answer:
9.1
Convert [tex]9\frac{1}{10}[/tex] to [tex]9 + 1/10[/tex][tex]\frac{1}{10}[/tex] is the same as 1 divided by 10, which is 10, for this case 0.10Therefore, [tex]9 + 0.1 = 9.1[/tex]There are other, more complicated ways to do this, but we must start with an easier, understandable way first.
__________________________________________________________
Questions?Ask in the comments box.
The numbers represented by points w, x and y on the number line are integers.
Under which of the following conditions could the expression, x > 2, be true? Select all that apply.
Answer:
Option A) when y=6 and w= 2, Option B) when y=4 and w=-1 are the TWO correct choices.
Step-by-step explanation:
Step-by-step explanation:
https://brainly.com/question/14500266
A florist used 16 flowers to make a bouquet, including 6 lilies.
What is the probability that a randomly selected flower will be a lily?
Answer:
3/8
Step-by-step explanation:
Values we are given :
16 flowers in total6 liliesWe know that :
Probability of selecting an object from a group of items = Number of objects / Number of itemsTherefore,
Probability of selecting a lily = Number of lilies / Number of flowersP = 6/16P = 3/8In 2015, there were approximately 4, 148,000 births in a country. Find the birth rate in births per minute.
Answer:
7.89 births per minute
Step-by-step explanation:
525600 minutes in a year
4,148,000 divided by 525600 =
7.89193302892
The graph of y = StartAbsoluteValue x EndAbsoluteValue is transformed as shown in the graph below. Which equation represents the transformed function? On a coordinate plane, an absolute value function is shown. The vertex of the function is at (negative 3, negative 2). It crosses the x-axis at (negative 5, 0) and (negative 1, 0) and it crosses the y-axis at (0, 1). y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2 y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2 y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3 y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3
Using translation concepts, it is found that the equation of the transformed function is:
y = |x + 3| - 2.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The absolute value function is given by y = |x|, and has vertex at (0,0). After the transformations, the function has vertex (-3, -2), which means that:
It was shifted 3 units to the left, hence x -> x + 3.It was shifted 2 units down, hence y -> y - 2.Thus, the equation of the function is now given by:
y = |x + 3| - 2.
More can be learned about translation concepts at https://brainly.com/question/4521517
Answer:y = |x + 3| - 2.
Step-by-step explanation: B on edge
What is the equation of the following linear funchon?
Answer:
3x+8
Step-by-step explanation:
linear function formula ax+b
when x=3 3a+b=17 and when x=6 6a+b=26
3a=9 a=3,
when x=3 3.3+b=17 9+b=17 b=8
3x+8
From a barrel of colored marbles you randomly select 7 blue, 5 yellow, 8 red, 4 green, and 6 purple marbles. Find the experimental probability of randomly selecting a marble that is NOT yellow. Write your answer in simplest form.
Answer:
5/6
Step-by-step explanation:
In total there are 7+5+8+4+6=30 marbles. you need to take out the yellow marbles that you counted into the total of 30 marbles which would be 25 marble. this means that there are 25 out of 30 marble you can select that is not yellow. which gives you the probability of 25/30 simplify it to get 5/6
18. What is the value of the 5 in 256
A. 5/10
SO
B. 10/5
C. 5/100
D. 100/5
Answer:
A. 5/10
Step-by-step explanation:
Because the 5 in 256 is ine in tength's place. And 5/10 is 0.5 or 50
what's the sum of 3/8 and 1/16? a. 1/6 b. 7/16 c. 4/24 d. 1/4
Answer: B
Step-by-step explanation: 3/8 + 1/16 = 0.4375 and 7/16 = 0.4375
Answer:
b.
Step-by-step explanation:
first, you would you would find a common denominator between 3/8 and you will get 6/16. last, you would add 1/16 + 6/16 for your answer of 7/16
If a hypothesis is not rejected at the 5% level of significance, it a. will always be rejected at the 1% level b. will also not be rejected at the 1% level c. will sometimes be rejected at the 0.1% level d. will sometimes be rejected at the 1% level
Considering the p-value of the test, the correct option is:
b. will also not be rejected at the 1% level.
How do we reach the decision to reject or not reject the null hypothesis?It depends on the p-value of the test, as follows:
If the p-value is greater than the significance level, we do not reject the null hypothesis.If it is less than the significance level, we reject the null hypothesis.In this problem, the hypothesis is not rejected at the 5% level of significance, hence the p-value is greater than 0.05, which means that it will not be rejected at any level below 5% and option b is correct.
More can be learned about hypothesis tests at https://brainly.com/question/26454209
Jaydon has eaten 3.6% his 45 ounce block of chocolate
fudge. How many ounces of fudge has he eaten?
Answer:
The answer is 1.62 ounce
Step-by-step explanation:
Given;Jaydon has eaten 3.6% of his 45 ounce block of chocolate fudge.To Find;How many ounces of fudge has he eaten?Now,
3.6% of his 45 ounce
45 × 3.6 ÷ 100
162 ÷ 100 = 1.62
Thus, Jaydon has eaten 1.62 ounce block of chocolate fudge.
Teresa is loading her car with boxes that each weigh 4 3/4 pounds. If Teresa loads 9 of theses boxes find the combined weight of each box
Total weight:-
9(19/4)171/442-3/4lbs100 pts what is 2X2+6X5+8
Answer:
It's 42.
Step-by-step explanation:
Order of operations:
4+6*5+8
4+30+8
34+8
= 42
Therefore, the answer is 42.
Answer:
42
Step-by-step explanation:
Which of the following is the correct factorization of the polynomial below?
x^3 - 12
A. (x + 3)(x - 4)
B. (x - 3)(x + 4)
C. (x + 3)(x^2 - 4x + 4)
D. The polynomial is irreducible.
The sum of 4 and the product of three and a number x
Answer:
4=3+x
Step-by-step explanation:
First, let the number be x.
The product of 3 and x looks like so:-
3x
Now, add 4 (the sum of 4 and 3x):
[tex]\bigstar\sf{3x+4}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)
find the missing coordinates y+7x=1
(-1, )
(4, )
Answer:
(-1,8)
(4,-27)
Step-by-step explanation:
y+7x=1
Let x = -1 and find y
y+7(-1)=1
y -7 =1
Add 7 to each side
y-7+7 = 1+7
y = 8
(-1,8)
Let x = 4 and find y
y+7(4)=1
y +28 =1
Subtract 28 from each side
y+28-28 = 1-28
y = -27
(4,-27)
Help picture below problem 19
Answer:
9
Step-by-step explanation:
Because the 9 (by the power 12)/9 (by the power 12) becomes 9 (by the power 12) x (by the power -12). HEre 12 gets subtracted by -12 and now remains 1 so, 9 (by the power 1) is 9
Find the area of this parallelogram.
A) 20 B) 24 C) 40 D) 60
[tex]\underline{\clubsuit{\bf{Given-}}}[/tex]
Height of the Parallelogram = 4cmi.e, H = 4cm
Breadth of the Parallelogram = 10cmi.e, B = 10cm
Measure a side of the Parallelogram = 6cm.PS - Neglecting this because it is given just to puzzle us nothing else.
[tex]\underline{\clubsuit{\bf{To\:find-}}}[/tex]
the area of the Parallelogram.[tex]\underline{\clubsuit{\bf{Concept-}}}[/tex]
— Area of Parallelogram Formula
A parallelogram's area is defined as the space enclosed by two pairs of parallel lines. Since a rectangle and a parallelogram have identical properties, the area of a parallelogram equals the area of a rectangle.
— What's the procedure to find?
To find the area of the parallelogram, we have to multiply the base (denoted by B) of the perpendicular by its height (denoted by H). We should keep in mind that the base and the height of the parallelogram are perpendicular to each other, whereas the lateral side of the parallelogram is not perpendicular to the base. Thus, a dotted line is drawn to represent the height.
— Formula
Area of Parallelogram = Breadth (B) × Height (H)
[tex]\underline{\clubsuit{\bf{Solution-}}}[/tex]
Applying the formula and putting the values stated above,
[tex]\rightarrow{\sf{Area=10\times4}}[/tex]
[tex]\rightarrow{\boxed{\bf{Area=40cm^2}}}[/tex]
Hence, the area of the Parallelogram is 40cm².
HI I am 10 years old and I need help with my math homework, here's what I need help with:
Pls help me it is do today
Answer:
1 1/4
Step-by-step explanation:
Answer:
5/4 or 1 1/4
Step-by-step explanation:
1 3/4 - 2/4 = 1 1/4 or 5/4
What is the slope of
the line?
[?]
[]
Give your answer as
a fraction in simplest
form.
Answer:
slope = 3/2
Step-by-step explanation:
we rise 3 and run 2 which gives us y=3/2x
Pls help me with My math I need the ans rn, Tysm.
Answer:
35 degrees
30 degrees
what is the distance of 53 yards square
Answer:
477 square foot
Step-by-step explanation:
cause yea
A video has 25 thumbs up. What integer represents its score in points?
Answer:
25 points
Hope this helps!