The factors of the expression 42 - 12 are 2(21 - 6), 3(14 - 4), 6(7 - 2).
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, We have to factor 42 - 12.
Now, Factors of 12 are 1, 2, 3, 4, 6 and 12.
Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
Common factors of 12 and 42 are 2, 3 and 6.
So, 42 - 12.
= 2(21 - 6).
= 3(14 - 4).
= 6(7 - 2).
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The factored form of the expression 42 - 12 using the GCF is 6(7 - 2).
To factor the expression 42 - 12 using the greatest common factor (GCF), we need to find the largest number that divides both 42 and 12.
First, let's find the prime factorization of both numbers:
42 = 2 x 3 x 7
12 = 2 x 2 x 3
Now, let's find the common factors:
The common factors are 2 and 3.
Next, let's determine the GCF by multiplying the common factors:
GCF = 2 x 3 = 6
Finally, we can factor out the GCF from the expression:
42 - 12 = 6 x (7 - 2)
Therefore, the factored form of the expression 42 - 12 using the GCF is 6(7 - 2).
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The sum of two numbers is 58 and the difference is 8. What are the numbers?
Larger Number:
Smaller Number:
How can you tell the diffrence between horizontal and vertical translation in an equation?
Helppp mee quickkkkk pleasee Im struggling!
Answer:
y= -3/1 plus 5
Step-by-step explanation:
correct me if im wrong u can just write -3 instead of -3/1
a store sells tiles for $3.80 per square feet and an additional fee is $200 to install it what is the independent and dependent variable?
Answer:
i tkinhk it 1.30
Step-by-step explanation:
Toy shop purchases 125 identical stuffed animals for total cost of 312.50 thousand for seven dollars each what is the percent markup
Answer:
0.4
Step-by-step explanation:
por que tienes que aser una division
Real World Systems
1. Members of a drama club spend $795 on T-shirts and sweatshirts for a play. They purchase 20 more T-shirts than
sweatshirts. They buy T-shirts for $12 each and sweatshirts for $25 each.
How many T-shirts do the drama club members buy?
A
15 T-shirts
B.
21 T-shirts
с
22 T-shirts
D.
35 T-shirts
I need help please I have to finish this
Answer:
x = 80 degrees
y = 25 degrees
Step-by-step explanation:
First find angle BCA.
We know a line is 180 degrees, and angle BCD is 130. So 180-130 = 50 degrees for angle BCA.
Since it is isosceles (two lines on both sides of triangle ABC) this means the bottom two angles are the same. Now we know the two angles to find missing angle X.
50+50+ x = 180 degrees
x= 180 - 100 = 80 degrees
Next we know triangle BCD is isosceles, so angle BDC and angle CBD are the same. We know the third angle is 130 degrees.
So 180 - 130 = 50 degrees split between two angles that are the same. So one angle is 50/2 = 25 degrees.
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What is the probability of picking a purple marble and spinning green?
Use the following situation to answer the next 2 questions: A manufacturer claims that a particular car will get at least 50 miles per gallon on the highway. The researchers of a consumer-oriented magazine believe this claim is too high and plan a test with a simple random sample of 30 cars. Assume the population standard deviation for individual cars is 2.3 miles per gallon. The researchers found the sample mean to be 49 miles per gallon, and they decided on using a = 0.05. (Hint: H n SD = H. Find the value of the test statistic. A.-2.38 B.-1.645 C.-0.43 D. 0.0087 E. 2.38 What is the conclusion of the hypothesis test? There evidence to reject the manufacturer's claim because sufficient:________A. Is not; 49 miles per gallon is too close to the claimed 50 miles per gallon B. Is not; the p-value of 0.0087 is less than the significance level C. Is; the sample mean is less than the claimed mean D. Is; the p-value of 0.0087 is less than the significance level E. Is; the p-value of 0.0174 is less than the significance level
Answer:
First question
The correct option is A
Second question
The correct option is E
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 50 \ mpg \ (miles \ per \ gallon )[/tex]
The sample size is n = 30
The population standard deviation is [tex]\sigma = 2.3 \ miles[/tex]
The sample mean is [tex]\= x = 49 \ mpg[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 50 \ mpg[/tex]
The alternative hypothesis is [tex]H_a : \mu < 50 \ mpg[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 49 - 50 }{ \frac{2.3}{ \sqrt{30 } } }[/tex]
=> [tex]t = -2.38[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
[tex]df = 30 - 1[/tex]
[tex]df = 29[/tex]
Generally from the student t distribution table the probability corresponding to -2.38 to the left at a degree of freedom of [tex]df = 29[/tex] is
[tex]p -value = P( t < -2.38 ) = 0.0174[/tex]
From the value obtained we see that
[tex]p-value < \alpha[/tex] hence
The decision rule
Reject the null hypothesis
The conclusion is
There evidence to reject the manufacturer's claim because the p-value of 0.0174 is less than the significance level E
What is the length of x?
Answer:
The length of 'x' is 4
Step-by-step explanation:
We can use the pythagorean theorem to solve this.
The pythagorean theorem is:
[tex]a ^{2} + b^{2} = {c}^{2} [/tex]
[tex]a ^{2} + b^{2} = c^{2} \\ {3}^{2} + {b}^{2} = 5^{2} \\ 9 + {b}^{2} = 25 \\ \frac{ - 9 \: \: \: \: \: \: \: \: = - 9}{b ^{2} = \sqrt{16} } \\ b = 4[/tex]
Therefore x = 4
What is the value of x in the equation below?
⅗ = x/30
A. 6
B. 9
C. 10
D. 18
Answer:
D. 18
Step-by-step explanation:
3÷5=0.6
0.6×30=18
x=18
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Answer:
The value of x in the equation below is 18.
Step-by-step explanation:
We can use proportions to solve this. Cross-multiply then divide.
[tex] \frac{3}{5} = \frac{x}{30} \\ \\ \frac{5x}{5} = \frac{90}{5} \\ \\ x = 18[/tex]
Find the value
of
(3x + 3y)^2
If xy = =-2 and x^2+y^2=5
Step-by-step explanation:
9x^2 + 9y^2 + 18xy
9(5)+18(-2)
45-36
9
Landon bought a tray of plants for $8.15. There were 16 plants in the tray. If Landon only bought 1 plant, about how much would it have cost?
Each side of a square is (7 + 3x) units. Which is the perimeter of the square?
Answer:
28+12x
Step-by-step explanation:
The perimeter of a square is 4s where s is the side lenght. In your case s is 7+3x so the perimeter will be (28+12x).
Which expression is equivalent to 24 - (-6)?
Choose 1 answer:
--6-24
B
24 + (-6)
24 + 6
6 - 24
look at the picture
Answer:
c
Step-by-step explanation:
Find the square
X^2+2x=35
Answer:
x=-7,5
Step-by-step explanation:
Rewrite 8.24 × 10^6 in standard notation.
824,000
8,240,000,000
82,400,000
8,240,000
Answer:
The last choice 8,240,000.
Step-by-step explanation:
The exponent 6 tells us there are 6 digits after the first digit (8).
Answer is 8,240,000
Solve the following equation for f. Be sure to take into account
whether a letter is capitalized or not.
9 = Gf
Answer:
f is equal to 3 which means g is also equal to 3
Step-by-step explanation:
Which quote from Little Women best exemplifies the theme of making sacrifices for genuine love?
Answer:
"’I don't want a fashionable wedding, but only those about me whom I love, and to them I wish to look and be my familiar self.’"
Step-by-step explanation:
Answer:
the one above my answer is correct
Step-by-step explanation:
Wall-mart had a laptop for $500. Best Buy was selling the same laptop for 15% more. What is price of the laptop at Best Buy?
Answer:
575
Step-by-step explanation:
15% of 500 = 75
500 + 75 = 575
Answer:
$425
Step-by-step explanation:
500*0.15=75
500-75=524
bacteria is produced in a lab. the number of bacteria, as a function of time, is modeled by y=3(2)x
Answer:
The function is nonlinear .
Step-by-step explanation:
This is a non linear function.
Need help on 3 please help thank you so much I appreciate
Answer: Interesting question bro
Step-by-step explanation:
Put these fractions in order of size, smallest to largest.
7/10
2/3
4/5
11/15
Answer:
11/15 7/10 4/5 2/3
Step-by-step explanation:
the bigger the fraction the smaller the number
Indicate the answer choice that best completes the statement or answers the question.
The table shows the cost of long distance calls as a function of the number of minutes used. Is the cost a linear or nonlinear function of the
number of minutes used? Explain.
Number of Minutes 40 |80 120 160 1200
Cost (S)
14.00 8.00 12.00 16.00 120.00
Answer: hold on you didn’t give enough info for this to make sense
Step-by-step explanation:
Please help! Linear Equation word problems using the Ax + By = C form!
Answer:
1. T = 5x + 3y
2. 16 tomatoes.
Step-by-step explanation:
1. Determination of the linear expression.
Let x represent the number of pumpkin.
Let y represent the number of tomato.
Let T represent the total sales made from selling the pumpkins and tomatoes.
From the question,
1 pumpkin = $ 5
Hence,
x pumpkin = 5x
1 tomatoe = $ 3
Hence
y tomatoes = 3y
Therefore, the total sales (T) made from selling the pumpkin and tomatoes will be:
T = 5x + 3y
Where:
T is the total sales made from selling the pumpkin and tomatoes.
x is the number of pumpkin.
y is the number of tomatoe
2. Determination of the number of tomatoes sold.
Total cost (T) = $ 98
Number of pumpkin (x) = 10
Number of tomatoe (y) =?
T = 5x + 3y
98 = 5(10) + 3y
98 = 50 + 3y
Collect like terms
98 – 50 = 3y
48 = 3y
Divide both side by 3
y = 48/3
y = 16
Therefore, 16 tomatoes was sold.
Order the numbers from least to greatest 3/7, 5/9, 43%
Answer:
The answer is 3/7, 43%, 5/9
Answer:
3/7.43%, 5/9
Step-by-step explanation:
3/7, 43/100,5/9
3/7, .43, 59
Triangle A'B'C' with coordinates of A' (-6,2)
Answer: (A), (B) and (E).
Step-by-step explanation: Given that ΔA’B’C’ with coordinates of A(-6,2),B’(-4,2), and C’(-6,-2) is the image of ΔABC after a translation of (x-3,y+2). We are to find the possible coordinates for the original vertices of ΔABC.
For vertex A, we have
So, the coordinates of vertex A are (-3, 0).
For vertex B, we have
So, the coordinates of vertex B are (-1, 0).
For vertex C, we have
So, the coordinates of vertex C are (-3, -4).
Translate the product of 8 and the quotient of 6 and x into an algebraic expression
Answer:
3 x
x + y
Step-by-step explanation:
(think about it with a horizontal line between the two numbers)
When using fractions and whole numbers turn the whole numbers into fractions like ---> 3/1
and if their like 3 5/6 (for example) you would multiply the denominator by the whole number ---> 3*6=18 then add what's on the numerator with it. so 18+5=23 which would make it 23/6
Just some tips for making it easier!
Hope it helps! :)
given f(x)=x(x-3)+4 what is the derivative of f at a?
[tex]f(x) = {x}^{2} - 3x + 4 \\ \frac{d}{dx} ( {x}^{2} - 3x + 4) \\ g(x) = 2x - 3[/tex]
Let g(x) = f'(x)
Substitute a in x, therefore the answer is.
[tex]g(a) = 2a - 3[/tex]
— Note that it'd be better to use f'(a) or y' instead. For this one, I let g(x) equal the derivative of f(x) —
