Answer: 14
Step-by-step explanation:
First. take the prime factorization of all three numbers:
42: 21*2 ==> 3*7*2
70: 35*2 ==> 5*7*2
84: 42*2 ==> 21*2*2 ==> 3*7*2*2
Notice any common factors? That's the GCF.
GCF: 7*2=14
GCF: 14
Answer:
14
Step-by-step explanation:
The greatest number that divides 42, 70, and 84 exactly is their greatest common factor.
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The GCF of 42, 70, and 84 is 14.
The greatest number that divides 42, 70, and 84 is 14.
What is GCF?
The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a set of whole numbers. For instance, the GCF is equal to 6 for the set of numbers 18, 30, and 42.
How do I get the GCF of something?
The greatest common factor among numbers can be discovered in a number of ways.
Factoring:
List each number's factors in order to calculate the GCF by factoring. The factors that evenly divide into the number with no remainder are known as whole numbers. The GCF is the largest number that appears on each list of common factors for each number.
Example: Find the GCF of 18 and 27
The factors of 18 are 1, 2, 3, 6, 9, 18.
The factors of 27 are 1, 3, 9, 27.
The common factors of 18 and 27 are 1, 3 and 9.
The greatest common factor of 18 and 27 is 9.
Prime Factorization:
List all of each number's prime factors to determine the GCF by prime factorization. List the prime factors that each of the original numbers has in common. Include the most instances of each prime factor that each original number has in common. To find the GCF, multiply these by one another.
You'll observe that the prime factorization approach may be simpler than straight factoring as numbers grow larger.
Example: Find the GCF (18, 27)
The prime factorization of 18 is 2 x 3 x 3 = 18.
The prime factorization of 27 is 3 x 3 x 3 = 27.
The occurrences of common prime factors of 18 and 27 are 3 and 3.
So the greatest common factor of 18 and 27 is 3 x 3 = 9.
There is another method but it focuses on more complex numbers.
Hope this helps!
The area of Ivory’s scaled copy is 48 square units.
Ivory's scaled counterpart has a 48-square-unit area.
Ivory's scale factor for producing their scaled replica is;
On the graph, one interval corresponds to four units of the rectangle. This ratio is 1:4.
We can see from the provided image that the rectangle's y-axis has three intervals and its x-axis has one interval.
Now, the picture informs us that the scaled copy's area is 48 square units.
This indicates that the triangle she is attempting to depict with that graph has an area of 48 square units.
Now, if one of the graph's intervals is in units of x, then it indicates;
Y-axis: length; 3x units
size; x-axis equals x units
A rectangle's area is
based on the formula Area = Length Width, 3x [tex]\times[/tex] x = 48.
1 interval on the graph corresponds to 4 units of the rectangle because 3x2 = 48 x2 = 48/3 x2 = 16 x = 16 x = 4.
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1. Suppose a model of the fish is 10 cm and the length of a fish in real life is 140 cm. What is the scale
factor?
It is scale factor at 1/14.
What does scale factor mean?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, by increasing each side by, say, 2, we can expand the size of a rectangle with sides of 2 cm and 4 cm.
The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.
based on the information provided,
Scale Factor = Fish Model Length / Fish Length in Real Line
scale factor =10/140
=1/14
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what is the domain and range of this function?
y=|5x|-8
Answer:
Domain:
$%error%$
Range:
$%error%$
Explanation:
Both
x
and
y
belong to all the real numbers since there is no restriction on either the domain or the range.
Step-by-step explanation:
Name the angle in as many different ways as possible.
Answer:
WXZ, ZXW, 1
Step-by-step explanation:
1. Find the sum.
76,749
5 565
23
+
The sum is
(Simplify your answer. Type a whole number.)
Answer:
82,337
Step-by-step explanation:
76,749
5565
+ 23
82,337
Hope it helps!!!
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the length of a retangle is 4 times its width. The rectangles width is 8 m. What is the are of the rectangle?
The rectangle's width is 8m and the length is 4 times the width, so the length = 4 x 8 = 32m
To calculate the area of a rectangle, we take the width and multiply it with the length
A = 32 x 8 = 256m2
Can I get some help please
Step-by-step explanation:
1
A: is a function since 2 different x values can have the same y value
B: not a function since the x value 0 gives different values which makes it not a function.
C: since 4 corresponds to 2 different y values it is not a function.
D and E are not function since there are different y values for the same x value.
2: all of the answers are determined by the vertical line test.
A NOT A FUNCTION
B NOT A FUNCTION
C A FUNCTION
D UNCLEAR
E NOT A FUNCTION
hope this helps and make sure to ask any qs if you doubt anything :)
The length of a rectangle is twice the width. The area of the rectangle is 58 square units. What is the length and width of the rectangle.
The length and width of the given rectangle is 10.77 and 5.385 respectively.
According to the question statement, The length of a rectangle is twice the width and the area of the rectangle is 58 square units.
We are supposed to find the length and width of the rectangle.
Before solving this we need to know that the area of the rectangle is the product of its length and width,
Let's assume the length be "l" and width be "w"
Therefore Area = l*w
Now as length is twice the width so [tex]l=2w[/tex]
Area = [tex]58 square units[/tex]
Therefore [tex]l*w=58\\[/tex]
but [tex]l=2w[/tex]
[tex]2w*w = 58\\2w^{2}=58\\w^{2} = \frac{58}{2} \\w^{2}= 29[/tex]
[tex]w=\sqrt{29} \\w=5.385[/tex]
as [tex]l=2w[/tex]
[tex]l=2*5.385\\l=10.77[/tex]
Hence length l = 10.77 unit and width w = 5.385 unit
Area: Area is defined as the total space taken up by a 2D or a 3D surface or an object.To learn more about surface areas, click on the link given below.
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A scientist uses a submarine to study ocean life.
She begins 174 feet below sea level.
After traveling down for 15 seconds, she's 252 feet below sea level.
Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
The rate of change in the submarine's elevation in feet per second is 5.2
According to the question ,
She starts 174 feet below sea level
after 15 minutes she reaches 252 feet below sea level
distance travel in 15 minutes = [tex]\frac{252 - 174}{15}[/tex]
= [tex]\frac{78}{15}[/tex]
= [tex]\frac{26}{5}[/tex]
Round off [tex]\frac{26}{5}[/tex] = 5.2
There are certain rules to follow when rounding a decimal number. Put simply, if the last digit is less than 5, round the previous digit down. However, if it’s 5 or more than you should round the previous digit up. So, if the number you are about to round is followed by 5, 6, 7, 8, 9 round the number up. And if it is followed by 0, 1, 2, 3, 4 round the number down.
Here some Rounding Examples :
Consider the number 8.9163
8.9163 rounded to the nearest tenth is 8.9
Because 9 is followed by 1 and 1 is less than 5.
8.9163 rounded to the nearest hundredth is 8.92
Because 1 is followed by 6 and 6 is greater than 5.
8.9163 rounded to the nearest thousandth is 8.916
Because 6 is followed by 3 and 3 is less than 5.
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HELP PLS will mark brainliest
[tex](1-\frac{9x^2+4}{12x} )/(\frac{1}{3x}-\frac{1}{2} )+1[/tex]
Answer:
[tex] \frac{3x}{2} [/tex]
The students in Mr. Bishop's class have written 28 poems. They are putting their poems together to make a poetry book. They put 4 poems on each page. So far, the students have made 5 pages. How many pages do they still need to make? ____ pages
In exercises 23 and 24, find the indicated angle measures. (See photo)
Step-by-step explanation:
Just do the calculations at last by using the value of x
What is the classification for this polynomial? 6x³y³z³ + x^4y^7
A. monomial
B. binomial
C. Trinomial
help with this question please! show word needed!
Answer: u = 80° v = 25°
Step-by-step explanation:
(a) angles on a straight line = 180° - 130° = 50°
In isosceles triangle, both angles on each side is equal, so
180° - 50° - 50° = 80°
u = 80°
(b) u = (2v + 30°) because opposite angles of a parallelogram are equal.
u = 80°
80° = 2v + 30°
80 - 30 = 50
50° = 2v
25° = v
2. The equation x² + px + q = 0, where p and q are constants, has roots -3 and 5.
(i) Find the values of p and q.
(ii) Using these values of p and q, find the value of the constant r for which the equation
x² + px + q + r = 0 has equal roots.
[3]
The result are-
p = -2 and q = -15.constant r = 64.What is defined as the roots of the quadratic equation?The values of x that correspond to the given quadratic equation ax² + bx + c = 0 are known as its roots.
They are, in other words, the values of the variable (x) that satisfy the equation. The roots of such a quadratic function are indeed the x-coordinates of the function's x-intercepts.The discriminant value indicates how often roots f(x) has: - The quadratic function does have two distinct real roots if b² - 4ac > 0. The quadratic function contains a single repeated real root if b² - 4ac = 0. If b² - 4ac = 0, the quadratic function has really no true roots.For, the given expression;
x² + px + q = 0. ....... (equation 1)
where p and q are constants, has roots -3 and 5.
Part 1: solve for p and q.
Put x = -3 in equation 1.
p(-3) = (-3)² + p(-3) + q = 0
9 - 3p + q = 0 .........(equation 2)
Now, put x = 5 in equation 1.
p(5) = (5)² + p(5) + q = 0
25 + 5p + q = 0 ..........(equation 2)
Solve equation 2 and 3 by elimination method.
p = -2 and q = -15.
Part 2: Estimate the constant r.
The equation is; x² + px + q + r = 0.
Substitute the values of p = -2 and q = -15.
x² + (-2)x + (-15) + r = 0.
As, the equation given real equal roots; then,
discriminant value: b² - 4ac = 0.
Substitute the values;
(-2)² - 4×1×(-15 + r) = 0
On simplification;
4 + 60 - r = 0
r = 64.
Therefore, the value of the constant r is estimated as 64.
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900 students attend Ridgewood Junior High School. 4% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
robert spends 30.45$, before tax, at the store.
The cost of Robert purchase of books after the paid tax is $32.66.
What is defined as the percentage increase?The percentage increase would be the difference between both the final and initial values expressed as a percentage. For other sayings, it is the difference here between final and initial values divided by the original value and multiplied by 100.For the given question;
The original cost of the book purchased by the Robet = $30.45.
The tax of 7.25% is applied on the original cost of the book.
7.25% of $30.45 = (7.25×30.45)/100
7.25% of $30.45 = $2.21
The final cost of the book = original cost + tax
The final cost of the book = $30.45 + %2.21
The final cost of the book = 32.66
Therefore, the total price paid by the Robert for the book after 7.5% of the tax is applied is $36.66.
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The complete question is-
Robert spends $30.45 before tax at the bookstore. If the sales tax rate in his city is 7.25%, what is the total cost of his purchase?
Help me please, no joke answers
Answer:
Starting from the left, the points plotted are:
-√9, -1.75, -3/2, -5/3, √4
A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is _____ sampling.
A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.
What is systematic sampling?Systematic sampling is a statistical method used in survey methodology that involves selecting elements from an ordered sampling frame. An equiprobability method is the most common type of systematic sampling. The list is traversed in a circular fashion in this approach, with a return to the top once the end of the list is reached. Systematic sampling is a probability sampling method in which we randomly select one of the first k elements and then select every kth element after that. Using this method, each element in the population has a known and equal chance of being selected (also known as Epsem). As a result, systematic sampling is functionally equivalent to simple random sampling (SRS).Therefore, a probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.
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Linda built a games board in industrial arts class. The top was a rectangle of 60cm by 48cm. What was the largest size of identical felt squares she could use to cover the top exactly?
The largest size of identical felt squares that can be used to cover the top of rectangle is 5 squares of side 24cm.
The rectangle is a 2-dimensional figure with length and breadth which may or may not be same. A square is also a 2-dimensional figure with equal length of its sides.
When the dimensions of rectangle are given, it's are is given as the product of the sides of the rectangle which is given as:
Area of rectangle = Length × Breadth = 60 × 48 = 2880 cm square
The length of the square that entirely covers up the top side i.e., rectangular top can be determined by hit and trial mechanism starting from the lowest whole number in order to determine the length of largest squares of equal dimensions. Then comparing the area of the rectangular top and product of number of squares needed and area of each square, we can find the largest size of the square.
Area of square = length × length = l²
Since, Area of rectangular top = No. of squares × Area of 1 square
Therefore, 2880 = N (l²)
Putting N =1, 2, 3, 4, 5 and so on, we find that when N = 5, the value of square root of l is a perfect whole number.
Hence, 2880 = 5 × (l²)
l = √576 = 24
Thus, 5 squares of side 24cm will be used to cover the rectangular top entirely.
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So my math teacher is very specific about showing work and explaining why the answer is what it is. I'm confused quite a bit about this question.
"Given that 1 yard = 36 inches, explain how you would find the number of cubic inches in a yard"
I would assume the answer would just be 36in^3?
Answer:
There are 46,656 cubic inches in a cubic yard.
Explanation:
for an approximate result, multiply the volume value by 46660
53 + 28 help this is for my sister so she can "get" brainliets
Answer:
Alright, 53 + 28 = 81
Answer:
81
Step-by-step explanation:
A geometric sequence has these properties.
What is the 7th term of this sequence?
How is adding and subtracting
decimals similar to and different from adding
and subtracting whole numbers?
Answer:
adding decimals is different then subtracting because adding would be bigger subtracting means smaller
2|x|-9 translate 6 units up
The translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.
We are given a function:
2 | x | - 9.
A function from a set X to a set Y assigns to each element of X exactly one element of Y.
We are asked to translate the function 6 units up.
This means that we have to add 6 units to the function.
A function has been “translated” when it has been moved in a way that does not change its shape or rotate it in any way.
So, we get that:
f(x) = 2 | x | - 9 + 6
f(x) = 2 | x | - 3
Therefore, the translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.
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What is the value of y in the solution to the system of equations?
1/3x+ 1/4y=1
2x - 3y = -30
-8
-3
0 3
O 8
Answer:
y=8,x=-3
Step-by-step explanation:
1/3×+1/4y=1
lcm=12
multiply through by lcm to get equation 1
4x+3y=12
equation 2
2×-3y=-30
equation 2 by 2
using the substitution method
y=8
x=-3
Question
Find the equation of the line with slope
1/4
and y-intercept (0, -2).
Answer:
y=1/4 -2
Step-by-step explanation:
y =mx + c
m= slope
c= y-intercept
putting the valves of x and y ( 0,-2)
-2 = 1/4(0) + c
solve for C
C = -2
substituting back to the general equation of
y= 1/4x + C
y = 1/4x - 2( ans).
Randalstown Rugby Club play 20 matches and win 17 of the matches.
What percentage of the matches did Randalstown win?
Answer:
85%
Step-by-step explanation:
Total no. of matches played,
→ x = 20 matches
No. of matches they won,
→ y = 17 matches
Now the win percentage will be,
→ (y/x) × 100
→ (17/20) × 100
→ 0.85 × 100
→ 85%
Hence, the percentage is 85%.
someone help me!!!
please...
Answer:students are the independent because he will get a number of cards depending on how many students there are so its
s independent and c dependent
Step-by-step explanation:
Answer:
s = independent
c = dependent
The number of cards depends on the number of students in his class.
Hope this helps :)
solve by completing the square
2x^2-12x-20=0
The square of the equation 2[tex]x^{2}[/tex] – 12x – 20=0 is
What is a quadratic equation?
A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.
a[tex]x^{2}[/tex]+bx+c , a, b, c are integers .
formula: −b±√b2−4ac/2a
Given equation ,
2[tex]x^{2}[/tex] -12x-20=0
By comparing with the quadratic equation
Here, a=2, b= -12, c= -20.
X=−b±[tex]\sqrt{b^2-4ac}[/tex]/2a
X= -(-12) + [tex]\sqrt{(-12)2-4(2)(20)}[/tex] /2(2)
X=12+- [tex]\sqrt{144-160}[/tex]/4
X=12+- [tex]\sqrt{-16}[/tex]/4,
X=12+- (-4)/4
X=12+(-4)/4 and x=12-(-4)/4
X= 12-4/4 and x=12+4/4
X=8/4 and x= 16/4
X=2 and x= 4
Therefore, the square of the equation 2x2-12x-20=0 is x= 2 and x=4.
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