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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Which of the following is equivalent to the expression 1/2x+4x-1/2x+60?
Answer:
4(x + 15)
Step-by-step explanation:
1/2x - 1/2x = 0
You're then left with 4x + 60
Factor out the 4 and you get 4(x + 15)
Answer: ITS C.
Step-by-step explanation: It’s not B I took the test and put C and got it right
which graph best represents y= -x^2*6x-1
Answer:
c is the correct answer
Step-by-step explanation:
Answer:
Correct Answer is B
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (−3,−10)
Focus: (−3,−[tex]\frac{39}{4}[/tex])
Axis of Symmetry: x = −3
Directrix: y = −[tex]\frac{41}{4}[/tex]
x y
-5 -6
-4 -9
-3 -10
-2 -9
-1 -6
9. 16 is 40% of what number? If necessary, round to the nearest tenth. A 40.0 B 0.4 C 640.0 D 6.4
Answer:
A
Step-by-step explanation:
16 x 100 = 1600
1600 / 40 = 40.0
Answer:
A. 40.0
Step-by-step explanation:
What is the 21st term of the sequence with a1 = -6 and d = 4?
choices-
74
70
78
-40
Answer:
[tex]\boxed {\boxed {\sf 74}}[/tex]
Step-by-step explanation:
The nth term of an arithmetic sequence can be found using the following formula.
[tex]a_n=a_1+(n-1)d[/tex]
Where n is the term, a₁ is the first term, and d is the common difference.
We want to find the 21st term, we know the first term is -6, and the common difference is 4.
[tex]n= 21\\a_1= -6 \\d=4[/tex]
Substitute the values into the formula.
[tex]a_{21}=-6+(21-1)4[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Solve inside the parentheses.
[tex]a_{21}=-6+(20)4[/tex]
Multiply 20 and 4.
[tex]a_{21}= -6+80 \\[/tex]
Add -6 and 80.
[tex]a_{21}=74[/tex]
The 21st term of the sequence is 74
Answer:
SoluTion :-Here we will use the formula
[tex] \tt \: a_n \: = a_1 +( n - 1)\: \times d[/tex]
[tex] \tt\: a_{21} = −6+(21−1)4[/tex]
By using PEMDAS
[tex] \tt \: a_{21} = - 6 + (20)4[/tex]
[tex] \tt \: a_{21} \: = - 6 + 80 = 74[/tex]
[tex] \huge \tt \bigodot \: \: 74[/tex]
El tripe de a edad de pedro mas 2 es igual a la edad actual de pedro mas 6. ¿Cuál es la edad actual de pedro?
Answer: Pedro tiene 2 años.
Step-by-step explanation:
Definamos la variable P como la edad de Pedro.
Sabemos que " El triple de la edad de pedro, más 2, es igual a la edad actual de pedro más 6"
Esto se escribe como:
3*P + 2 = P + 6.
Para encontrar la edad de Pedro, tenemos que resolver esa ecuación.
Para hacerlo, el primer paso es llevar todos los términos con "P" al lado izquierdo, y los términos sin "P" al lado derecho.
3*P - P = 6 - 2
2*P = 4
Ahora podemos dividir por 2 en ambos lados:
2*P/2 = 4/2
P = 2
Entonces podemos concluir que Pedro tiene 2 años.
The value of y varies directly with x, and y =-10 when x=40, identify the value of y when x =-5
Answer:
I think that answer is 5 or 35
what
is 20 times 50 divided by 9009 added by 10101010 and subtracted by 675098
...
Answer:
9425912.111
Step-by-step explanation:
Answer:
9425912.111
Step-by-step explanation:
4.5÷6=
estimate the quotient
Answer:
0.75 - 0.8
Step-by-step explanation:
4.5/6 = 0.75
The closest number to round 0.75 to is 0.8
We are given the expression:
4.5 / 6
Simplifying the given expression:
We can rewrite 4.5 as 4/10:
[tex]\frac{45}{10}*\frac{1}{6}[/tex]
Since 45 and 6 have a common factor: 3
[tex]\frac{3*15}{10}*\frac{1}{3*2}[/tex]
The 3 in the numerator and the denominator will cancel out:
[tex]\frac{15}{10}* \frac{1}{2}[/tex]
We know that 15/2 is 7.5
[tex]\frac{7.5}{10}[/tex]
0.75
Hence, the quotient of the expression: 4.5/6 is 0.75
A truck driver is able to move 48 kg in 20 weeks. Find the unit rate of how many kilograms the truck driver is able to move per week. Round to the nearest tenth.
Answer:
2.4 kg/week
Step-by-step explanation:
(48 kg)/(20 weeks) = 2.4 kg/week
Wayne has a recipe on an index card with a length of 3 inches and a width of 5 inches. He wants to enlarge to 15 inches long. How wide will the enlargement be?
A 9 inches
B 13 inches
C 25 inches
D 45 inches
Answer:
a) 9 inches
is correct answer for you
Answer:
C, 25
Step-by-step explanation:
3 x 5 = 15
5 x 5 = 25
Gary's pay is $15 per hour. He receives a 6% pay raise.
Which method can Gary use to correctly calculate his new hourly pay rate?
Choose Yes or No for each method.
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The calculation can be done by any method that adds 6% of the original salary to the original salary. That's equivalent to multiplying the original salary by 1.06 or 106%. The attachment shows some possibilities.
Answer:
_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_
Step-by-step explanation:
A 500 yard train travels at a constant speed. A motorcyclist rides at a constant speed on the highway parallel to the train tracks. The motorcyclist starts at the rear of the train and drives to the very front of the train, and then falls back to the rear of the train. As the motorcycle completes this cycle, the train travels 1200 yards. How far did the motorcyclist travel?
Answer:
120/2 = x/5....120 miles to 2 hrs = x miles to 5 hrs
cross multiply
(2)(x) = (120)(5)
2x = 600
x = 600/2
x = 300....the motorcyclist would travel 300 miles in 5 hrs
or u could do it this way..
120/2 = 60 miles per hr
60 * 5 = 300 miles
Step-by-step explanation:
AJKL and ALMN are shown.
Answer:
mLNM=63
Step-by-step explanation:
triangle JKL is isocelese so mKJL and KLJ are the same
180-72=108
108/2=54
so both mKLJ and mMLN are equal
and since triangle LMN is an isoceles then mLNM and mLMN are equal to each other
so 180-54=126
126/2=63
mLNM=63
18
Write an equation in POINT-SLOPE FORM for the line that has a slope of
1
5
and passes through (1,-2).
Could someone please answer this I will give a brainless if answer correctly and explained
Answer:
SSS
Step-by-step explanation:
The SSS theorem is the side-side-side theorem. Basically, since all three sides from one triangle is congruent to the corresponding sides of the other triangle, then the triangles have to be congruent. There are other theorems such as the SAS theorem (side-angle-side), but since the question only give us the fact that the sides are congruent, its SSS. Sorry, I hope this is good enough. XD
CAN YALL PLEASE HELP ME ❗️❗️❗️PLEASEEE
Answer:
1) intersection of both lines is the solution: (-3, 1)
2) y = -1/6x + 1 will produce a perpendicular line and intersect at only one point (slopes of 6 and -1/6 are opposite and reciprocal, thereby producing perpendicular lines)
3) 'b' can be any value except 1
Step-by-step explanation:
The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 degrees. The tree stands 20 ft off the hill. How high is the top of the tree from the base of the hill?
Answer:
Approximately [tex]101\; \rm ft[/tex] (assuming that the height of the base of the hill is the same as that of the observer.)
Step-by-step explanation:
Refer to the diagram attached.
Let [tex]\rm O[/tex] denote the observer.Let [tex]\rm A[/tex] denote the top of the tree.Let [tex]\rm R[/tex] denote the base of the tree.Let [tex]\rm B[/tex] denote the point where line [tex]\rm AR[/tex] (a vertical line) and the horizontal line going through [tex]\rm O[/tex] meets. [tex]\angle \rm B\hat{A}R = 90^\circ[/tex].Angles:
Angle of elevation of the base of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].Angle of elevation of the top of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].
Let the length of segment [tex]\rm BR[/tex] (vertical distance between the base of the tree and the base of the hill) be [tex]x\; \rm ft[/tex].
The question is asking for the length of segment [tex]\rm AB[/tex]. Notice that the length of this segment is [tex]\mathrm{AB} = (x + 20)\; \rm ft[/tex].
The length of segment [tex]\rm OB[/tex] could be represented in two ways:
In right triangle [tex]\rm \triangle OBR[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].In right triangle [tex]\rm \triangle OBA[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].For example, in right triangle [tex]\rm \triangle OBR[/tex], the length of the side opposite to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex] is segment [tex]\rm BR[/tex]. The length of that segment is [tex]x\; \rm ft[/tex].
[tex]\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}[/tex].
Rearrange to find an expression for the length of [tex]\rm OB[/tex] (in [tex]\rm ft[/tex]) in terms of [tex]x[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}[/tex].
Similarly, in right triangle [tex]\rm \triangle OBA[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}[/tex].
Equate the right-hand side of these two equations:
[tex]0.810\, x \approx 0.649\, (x + 20)[/tex].
Solve for [tex]x[/tex]:
[tex]x \approx 81\; \rm ft[/tex].
Hence, the height of the top of this tree relative to the base of the hill would be [tex](x + 20)\; {\rm ft}\approx 101\; \rm ft[/tex].
find the measure of the line segment TR
9514 1404 393
Answer:
24
Step-by-step explanation:
The product of lengths from the point where the secants meet to the near and far circle intersection points is the same for both secants.
RQ·RC = RS·RT
8(27) = (3x)(8x)
9 = x^2 . . . . . . . . . divide by 24
3 = x
Then the length of interest is ...
TR = 8x = 8·3
TR = 24
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during and are as follows: Season: 75 79 80 78 76 74 76 78 Season: 72 71 76 78 86 81 72 80 a. Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years. Mean 77 Standard deviation 2.07 Mean 77 Standard deviation 5.26 b. What is the primary difference in performance between and
Answer:
Explained below.
Step-by-step explanation:
The scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida are,
Season 1: {75, 79, 80, 78, 76, 74, 76, 78}
Season 2: {72, 71, 76, 78, 86, 81, 72, 80}
(a)
Compute the mean and standard deviation of the golfer's scores as follows:
Season 1:
[tex]\bar x_{1}=\frac{1}{n_{1}}\sum x_{1}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]
[tex]s_{1}=\sqrt{\frac{1}{n-1}\sum(x_{1}-\bar x_{1})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 30}\\\\=2.0702\\\\\approx 2.07[/tex]
Season 2:
[tex]\bar x_{2}=\frac{1}{n_{2}}\sum x_{2}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]
[tex]s_{2}=\sqrt{\frac{1}{n_{2}-1}\sum(x_{2}-\bar x_{2})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 194}\\\\=5.26444\\\\\approx 5.26[/tex]
(b)
The primary difference in performance between the two seasons is:
[tex]\text{Diff} = \bar x_{2}-\bar x_{1}\\\\=5.26-2.07\\\\=3.19[/tex]
Plzz help me thank you
Answer:
A
Step-by-step explanation:
A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least seven years. A survey of companies reported in the Wall Street Journal found a sample mean tenure of years for CEOs with a standard deviation of years. a. Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. - Select your answer - - Select your answer - b. Assume companies were included in the sample. What is the -value for your hypothesis test
Complete question is;
A shareholders’ group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least seven years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x¯ = 7.27 years for CEOs with a standard deviation of s = 6.38 years (The Wall Street Journal, January 2, 2007).
a. Formulate hypotheses that can be used to challenge the validity of the claim made by
the shareholders’ group.
b. Assume 85 companies were included in the sample. What is the p-value for your hypothesis
test?
Answer:
A) Null hypothesis: H0: μ ≥ 7
Alternative hypothesis: μ < 7
B) p-value = 0.3488
Step-by-step explanation:
A) We are told that the shareholders group claimed that the mean tenure for a chief executive office (CEO) was at least seven years.
Thus, defining the hypothesis, we have;
Null hypothesis: H0: μ ≥ 7
Alternative hypothesis: μ < 7
B) Sample mean: x¯ = 7.27 years standard deviation: s = 6.38 years
Sample size = 85
Formula for the test static is;
t = (x¯ - μ)/(s/√n)
t = (7.27 - 7)/(6.38/√85)
t = 0.39
From online p-value from t score calculator attached using: t = 0.39, DF= 85 - 1 = 84, significance value = 0.05, one tail, we have;
p-value = 0.3488
What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?
Answer:
33Step-by-step explanation:
The nth term of a geometric sequence is expressed as;
Sn = a(r^n - 1)/r - 1
a is the first term of the sequence
r is the common ratio
n is the number of terms
From the sequence;
a = 3
r = -6/3 = 12/-6 = -2
n = 5 (since are looking for the sum of first five terms)
Substitute into the formula;
S5 = 3((-2)^5 - 1)/-2 - 1
S5 = 3(-32-1)/-3
S5 = 3(-33)/-3
S5 = -(-33)
S5 = 33
Hence the sum of the first five terms of the sequence is 33
Graph the line whose y-intercept is 2 and whose x-intercept is -5
Answer:
y=2/5x + 2
Step-by-step explanation:
find slope by using formula between these two points: (0,2) and (-5,0); then put into slope-intercept form (y=mx+b)
In 1863, President Abraham Lincoln gave his famous Gettysburg Address. It starts, “Four score and seven years ago....” Four score and seven is equal to 87. How many years are in a score? What year was President Lincoln referring to?
Answer: There are 20 years in a score. The year he is talking about is 1776
Step-by-step explanation:
NEED HELP WITH THIS PLEASE
Answer:
-25 + 75 = 50
Step-by-step explanation:
Since we don't know the value of the bar, we will call it x.
-25 + x = 50
Add 25 to both sides to find the value of x.
x = 75
You can also double check this answer by doing simple math.
-25 + 75 = 50
help please I'm lost
Answer:
translation
W(-10, 0)
X(-10, -8)
Y(-18, -4)
Z(-14, 8)
dilation
W(-8, 16)
X(-8, 0)
Y(-24, 8)
Z(-16, 32)
Step-by-step explanation:
In translation, all you are doing is taking each point and subtracting 6 from the x, and subtracting 8 from the y. The point of W is (-4, 8). Thus you do (-4 - 6 , 8-8) and you get the new point (-10,0). Repeat this for all the others.
In dilation you are multiply both x and y by 2. For point W you do (-4*2, 8*2) to get the new point (-8, 16). You repeat this for the remaining points.
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A snail takes 24 min to travel 5 ft. At this rate, how many inches does the snail travel every hour?
Answer:
150 in
Step-by-step explanation:
Antonio completed the right column of the table to help him find the sum of 2/9 and 1/5. In which step did his first error occur?
Answer:
Step 1
Step-by-step explanation:
His first error occurred in step 1.
The common denominator of [tex] \frac{2}{9} [/tex] and [tex] \frac{1}{5} [/tex] is 45, and not 14.
Common denominator of both fractions, is a number of which both 9 and 5 are its factor. That is, it is a common multiple of 9 and 5.
45 can be divided by 9 without remainder. Also 45 can be divide by 5 without a remainder.
45 would make both fractions common not 14.
Rewrite 105,000 in scientific notation.
Answer options are in pic below
Answer:
the answer is the third option (C)
Please help me pleasee!
Answer:
3) (4, 2)
Step-by-step explanation:
The point of intersection of the lines is the solution. That point is (4, 2).
Answer: 3) (4, 2)
Answer:
the answer is the third one (4, 2)
Step-by-step explanation:
the solution to a system of equations is always where they intersect. in this case, the two lines intersect at (4, 2), which means that the solution is (4, 2).
hope this helped!! :D