The greatest common factor (GCF) of the monomials [tex]34a^2b[/tex] and [tex]24a^5b^2[/tex] is [tex]2a^2b[/tex]. This is found by determining the GCF of the coefficients and the lowest exponent for each common variable.
To find the GCF of two monomials, we need to find the common factors for the coefficients, and then the lowest exponent for each variable that appears in both terms. The coefficients of the given monomials are 34 and 24. The GCF of these numbers is 2.
Next, look at the variables:
For a, the lowest exponent in both terms is a2
For b, the lowest exponent is just b (since one term is b, and the other is b2)
Therefore, the GCF of [tex]34a^2b[/tex] and [tex]24a^5b^2[/tex] is [tex]2a^2b[/tex].
Round 2.767.545 to the nearest ten
To round 2.767.545 to the nearest ten, we look at the digit in the tens place (4) and the following digit (5). Since the following digit is 5, we round up, resulting in 2.767.550.
When rounding 2.767.545 to the nearest ten, we must focus on the digit in the tens place and the digit that comes immediately after it. In this case, the digit in the tens place is 4, and the one following it is 5. According to the standard rules for rounding numbers, if the first dropped digit is 5 or higher, we round up. Thus, rounding 2.767.545 to the nearest ten, we get 2.767.550.
Mrs.Magdalino kept records on how much she spent on gasoline and the maintenance of her car. She found that it cost $485 to drive 500 miles in a month. Find the cost per month.Write a rule to describe the cost c for gasoline and the maintnance of a car as a function the number of miles m the car is driven.
Cost per mile = [tex]\frac{cost}{number of miles}[/tex]
[tex]= \frac{485}{500}[/tex]
= 0.97
Now,
c - cost for gasoline and maintenance and
m - number of miles traveled
Hence, the required expression is c = 0.97m.
Which sum is rational?
A. π + 18
B. √25 + 1.75
C. √3 + 5.5
D. π + √2
Answer:
B. √25 + 1.75
Step-by-step explanation:
A. π + 18 = 21.14159265..
B. √25 + 1.75 = 6.75
C. √3 + 5.5 = 7.2320508...
D. π + √2 = 4.55580..
Rational numbers are any fractions, integers, terminating decimals, or repeating decimals.
Option B will be a rational number while options A, C and D will be irrational numbers.
What is a rational number?A number that can be written in p/q form where q≠0 is called a rational number.
An irrational number is non-terminating and non-repeating in nature.
For example, π is an irrational number because
π =3.1415926535897.....................that is non-terminating and non-repeating and can never be written in p/q form
Similarly, a non-perfect-square number written inside a root is also an example of an irrational number.
A) π + 18
π is an irrational number while 18 is a rational number so the sum of irrational and rational will be an irrational number.
B) √25 + 1.75
√25 = 5 i.e. a rational number
1.75 is a rational number
Rational + Rational = Rational
5+1.75 = 6.75
6.75 is a rational number.
C) √3 + 5.5
√3 is an irrational number so √3 + 5.5 is an irrational number.
D) π + √2
π is an irrational number so π + √2 is an irrational number.
Hence, Option B will be a rational number while options A, C and D will be irrational numbers.
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how do you write 996 as a fraction, mixed number, or whole number in simplest form?
To convert a mixed number to its lowest form, one needs to change the mixed number into an improper fraction and then reduce this improper fraction to the lowest possible fraction. To do these conversions, one needs to perform a few calculations. One also has to understand the definitions of "mixed number," "improper fraction" and "proper fraction."
A proper fraction is a fraction that has a lower number in the numerator and a higher number in denominator, such as the fraction three-fourths. An improper fraction is the inverse of this, which entails the higher number in numerator and lower number in the denominator, like 5/3. A mixed number is a whole number with a fraction, such as 1 3/4.
To convert the mixed number 1 3/4, one has to multiply the denominator 4 by the whole number 1 that gives 4, add this 4 to the 3 in the numerator to get 7 and place 7 over the denominator to find the improper fraction 7/4. In this case, this is the lowest form for this mixed number. However, if the mixed number is 6 4/6, then this converts to the improper fraction 40/6. One can divide the numerator and denominator of 40/6 by 2 to find that 20/3 is the lowest form for the mixed number 6 4/6.To convert a mixed number to its lowest form, one needs to change the mixed number into an improper fraction and then reduce this improper fraction to the lowest possible fraction. To do these conversions, one needs to perform a few calculations. One also has to understand the definitions of "mixed number," "improper fraction" and "proper fraction."
996/1
thats all i know hope this helps
In which number is the digit 7 ten time larger than it is in the number 794
7,381 is the answer.
A washer and a dryer cost $800 combined. The washer costs $50 less than the dryer. What is the cost of the dryer?
800-50=750 so 750+50=800 the dryer maybe go be 750
When a washer and a dryer cost $800 combined. The washer costs $50 less than the dryer the cost of the dryer is $425.
Let's assume the cost of the dryer is "D" dollars.
According to the given information, the washer costs $50 less than the dryer, so the cost of the washer would be "D - $50" dollars.
Now, we know that the combined cost of the washer and dryer is $800, so we can set up an equation:
Cost of washer + Cost of dryer = $800
(D - $50) + D = $800
Now, let's solve for the cost of the dryer (D):
2D - $50 = $800
Add $50 to both sides:
2D = $850
Now, divide by 2 to solve for D:
D = $850 / 2
D = $425
So, the cost of the dryer is $425.
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Which of the following options have the same value as 10%, percent of 33? Choose 3 answers: (Choice A) 0.1 x (Choice B) 10 x 33 (Choice C) 1/10 x 33 (Choice D) 0.1 x 33
Answer:
C D AND E
Step-by-step explanation:
I AM SMART!!!
To find the value that is equivalent to 10% of 33, you can use the formula (10/100) x 33. Simplified, this is (1/10) x 33. The options that have the same value as 10% of 33 are Choice A (0.1 x 33), Choice C (1/10 x 33), and Choice D (0.1 x 33).
Explanation:To find the value that is equivalent to 10% of 33, we can use the formula:
10% of 33 = (10/100) x 33.
Simplifying this, we get:
10% of 33 = (1/10) x 33.
So, the options that have the same value as 10% of 33 are Choice A (0.1 x 33), Choice C (1/10 x 33), and Choice D (0.1 x 33).
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A shelf holds 2 cans of tomato soup, 8 cans of vegetable soup, 1 can of chicken noodle soup, and 8 cans of potato soup. Without looking you grab one can of soup. What's the probability that it's potato soup?
You have an 8 out of 19 chance to grab a potato soup.
The probability of randomly selecting a can of potato soup from the shelf of 19 cans is 8/19. This situation involves the concept of probability in mathematics where you divide the number of favorable outcomes by the number of total outcomes.
Explanation:The subject of the question is probability, which falls under the broader category of mathematics. The question is about finding the probability of selecting a can of potato soup from a shelf.
If we look at this question in terms of probability,
we first identify the total number of outcomes, which refers to the total number of cans on the shelf. There are 2 cans of tomato soup, 8 cans of vegetable soup, 1 can of chicken noodle soup, and 8 cans of potato soup, giving us a total of 19 cans.
The desirable outcomes are the number of cans of potato soup, which is 8.
The probability of an event is given by the ratio of the number of favorable outcomes to the number of total outcomes. In this instance, the probability of pulling out a can of potato soup is therefore 8/19.
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Find the slope of the line passing through the points (2, 7) and (-1, 4).
Hello!
Step-by-step explanation:
[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{4-7}{(-1)-2}=\frac{-3}{-3}=1[/tex]
Slope is 1.
Final answer is 1.
*The answer must have a positive sign.*
Hope this helps!
Thanks!
Have a nice day! :)
:D
-Charlie
The slope of the line passing through the point (2, 7) and (-1, 4) exists 1.
How to find the slope of the line?Let the two points are (2, 7) and (-1, 4).
The slope of a line that passes through the points be [tex]$\left(x_{1}, y_{1}\right)$[/tex] and [tex]$\left(x_{2}, y_{2}\right)$[/tex] exists given by
[tex]$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$[/tex]
[tex]$x_{1}=-1, y_{1}=4$[/tex] and
[tex]$x_{2}=2, y_{2}=7$[/tex]
Now, substitute the above values in the slope formula.
[tex]$&m=\frac{7-4}{2-(-1)} \\[/tex]
[tex]$&=\frac{7-4}{2+1}=\frac{3}{3}[/tex]
Slope m = 1
Hence, the slope of the line passing through the point exists 1.
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i need to know the expression for the verbal phrase :
the quotient of fifteen and the product of two times x
15 ÷ 2 . X =
There's the expression
Help!!!!!!!!!!!!!!!!!!
You enter a relay race. To start, you must run 20 yards to Checkpoint A. You then must turn and run 12 yards to Checkpoint B. Last, you must turn and run back to the starting line. What is the distance from Checkpoint B to the starting line? THANKS :)
Final answer:
To find the distance from Checkpoint B to the starting line, we add the distances from Checkpoint B to Checkpoint A and then double that sum.
Explanation:
To find the distance from Checkpoint B to the starting line, we need to add the distances from Checkpoint B to Checkpoint A and then double that sum. Let's calculate it step by step:
Distance from starting line to Checkpoint A: 20 yards
Distance from Checkpoint A to Checkpoint B: 12 yards
Total distance from starting line to Checkpoint B: 20 + 12 = 32 yards
To find the distance from Checkpoint B to the starting line, we double the distance from starting line to Checkpoint B: 2 × 32 = 64 yards
Therefore, the distance from Checkpoint B to the starting line is 64 yards.
I’m trying to correct this problem but I don’t know how can someone help me
Remark
It is not a straight line distance from the park to the mall. None of the answers give you that result. And if you know what displacement is, none of the answers are really displacement either. The distance is sort of a "as the crow flies." distance. There's a stop off in the middle of town.
Method
You need to use the Pythagorean Formula twice -- once from the park to the city Center and once from the city center to the mall.
Distance from the Park to the city center.
a = 3 [distance east]
b = 4 [distance south]
c = ??
c^2 = 3^2 + 4^2 Take the square root of both sides.
c = sqrt(3^2 + 4^2)
c = sqrt(9 + 16) Add
c = sqrt(25)
c = 5
So the distance from the park to the city center is 5 miles
Distance from City center to the mall
a = 2 miles [distance east]
b = 2 miles [distance north]
c = ??
c^2 = a^2 + b^2 Substitute
c^2 = 2^2 + 2^2 Expand this.
c^2 = 4 + 4
c^2 = 8 Take the square root of both sides.
sqrt(c^2) = sqrt(8)
c = sqrt(8) This is the result
c = 2.8
Answer
Total distance = 5 + 2.8 = 7.8
what equation equals 12 with at least fractions or decimals involved
Examples of fraction equations that equal 12:
13/2 + 11/2 = x
x = 12
---------------------------------------------------------------------------------------------------------------------
14/4 + 34/4 = x
x = 12
---------------------------------------------------------------------------------------------------------------------
Examples of Decimal equations that equal 12:
9.37 + 2.63 = x
x = 12.00
---------------------------------------------------------------------------------------------------------------------
5.85 + 6.15 = x
x = 12.00
---------------------------------------------------------------------------------------------------------------------
hope this helps
~Rise Above the Ordinary
Final answer:
To solve for 12 involving fractions or decimals, divide 0.40 into both sides of the equation and multiply both sides by 12.
Explanation:
Here are several equations that involve fractions or decimals and equal 12:
1. 12 = 12 (This is a simple example with no fractions or decimals, but it satisfies the condition of equaling 12.)
2. 11.5 + 0.5 = 12 (This uses two decimals to reach 12.)
3. 12/1 = 12 (This uses a fraction, specifically 12 divided by 1, which equals 12.)
4. 6 2/3 = 12 (This uses a mixed number, which combines an integer and a fraction, to equal 12.)
5. 12 x 1/1 = 12 (This shows how multiplying 12 by 1 (written as a fraction) still results in 12.)
These are just a few examples, and there are countless other equations you can create that involve fractions, decimals, or both and still equal 12.
Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. Use the drop-down menus to identify the steps Lorne used to find the difference. 1. (–3x3 + 5x2 + 4x – 7) + (–6x3 + 2x – 3) 2. (–3x3) + 5x2 + 4x + (–7) + (–6x3) + 2x + (–3) 3. [(–3x3) + (–6x3)] + [4x + 2x] + [(–7) + (–3)] + [5x2] 4. –9x3 + 6x + (–10) + 5x2 5. –9x3 + 5x2 + 6x – 10
Answer:
[tex]-9x^3 + 5x^2 + 6x-10[/tex]
Step-by-step explanation:
Lorne subtracted [tex]6x^3 - 2x + 3[/tex] from [tex]-3x^3 + 5x^2 + 4x - 7[/tex]
We need to subtract [tex]6x^3 - 2x + 3[/tex]
[tex]-3x^3 + 5x^2 + 4x - 7 - (6x^3 - 2x + 3)[/tex]
Multiply negative sign inside the parenthesis
[tex]-3x^3 + 5x^2 + 4x - 7 -6x^3 +2x - 3[/tex]
Now combine like terms to simplify it
[tex]-3x^3-6x^3 + 5x^2 + 4x+2x - 7 - 3[/tex]
[tex]-9x^3 + 5x^2 + 6x-10[/tex]
Answer:
the guy above me is wrong
Step-by-step explanation:
1-c
2-d
3-b
4-a
i did this n got em right hope it helps :)
Graph the image of this figure after a dilation with a scale factor of 1/2 centered at the point (2, 2) .
Answer:
(1, 3), (0, 6) and (-2, 5)
Step-by-step explanation:
First we will translate the image 2 left and 2 down to account for moving the center of dilation (2, 2) away from the origin:
(0, 4)→(-2, 2)
(-2, 10)→(-4, 8)
(-6, 8)→(-8, 6)
Next we apply the scale factor of 1/2:
(-2, 2)→(-1, 1)
(-4, 8)→(-2, 4)
(-8, 6)→(-4, 3)
Lastly we translate the figure back 2 right and 2 up:
(-1, 1)→(1, 3)
(-2, 4)→(0, 6)
(-4, 3)→(-2, 5)
Solve the compound inequality. Graph your solution using a number line. Please help.
4+k>3 or 6k<-30
Thanks!
Answer:
(-∞,-5)∪(-1,∞)
Step-by-step explanation:
1. You have the compound inequality given in the problem above:
[tex]4+k>3[/tex] or [tex]6k<-30[/tex]
2. First, you must solve for [tex]k[/tex], as following:
[tex]4+k>3\\k>3-4\\k>-1[/tex]
[tex]6k<-30\\k<\frac{-30}{6}\\k<-5[/tex]
3. Then, the solution is:
(-∞,-5)∪(-1,∞)
5. You can pose the solution in the number line, as it is shown in the graph attached.
Find the slope of the line. A.-4, B.4, C. 1/4, D. -1/4
The slope of a line passing through two points is found by taking the change in y-coordinates divided by the change in x-coordinates. For the given points (1, 0.1) and (7, 26.8), the slope is approximately 4.45.
Explanation:The slope of a line passing through two points can be found using the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
Given the points (1, 0.1) and (7, 26.8), the change in y-coordinates is 26.8 - 0.1 = 26.7 and the change in x-coordinates is 7 - 1 = 6. Substituting these values into the formula, we get:
slope = 26.7/6
slope ≈ 4.45
Frank drove 320 km in 4 hours. What was his average speed?
Answer: 80
Step-by-step explanation:
You know frank drove 320 in 4hr so you do 320 divide by 4 and u get 80
If x varies inversely as y and directly as t, and x = 12 when t = 10 and y = 25, find y when x is 6 and t = 3. 9 3/5 15 166 2/3
answer : 15
x varies inversely as y and directly as t
We use formula [tex]x = \frac{kt}{y}[/tex]
x varies inversely as y so we divide by y
x varies directly as t so we multiply x
k is the constant of proportionality
Lets find out k using the given values
x = 12 when t = 10 and y = 25
[tex]x = \frac{kt}{y}[/tex]
[tex]12 = \frac{k*10}{25}[/tex]
Multiply by 25 on both sides
300 = 10k (divide by 10)
So k = 30
Lets find y when x is 6 and t = 3. we got k = 30
[tex]6 = \frac{30*3}{y}[/tex] (cross multiply)
6y = 90 (divide by 6 )
[tex]y = \frac{90}{6} =15[/tex]
The value of y = 15
Answer:
15
Step-by-step explanation:
If x varies inversely as y and directly as t, and x = 12 when t = 10 and y = 25, find y when x is 6 and t = 3.
166 2/3
9 3/5
15
what is the surface area of a box that is 2 in long, 3 in wide, and 1.5 in tall
Can someone please help me!
[tex]5^{-2}[/tex]
In order to do this problem, you must know how to do exponents. You take 5 and divide it by -2. Then your answer is 0.04 or 1/25!
Hope this helped. :)
Simplify the expression.
7d + 12 – 4d – 3
19d – 7
3d + 9
12d
3d2 + 9
Sorry I'm confused XP
Maybe 12d?
Answer:
3d+9
Step-by-step explanation:
7d + 12 − 4d − 3 = 7d + 12 + − 4d + − 3
Combine Like Terms:
= 7d + 12 + − 4d + − 3
= (7d + − 4d) + (12 + − 3)
= 3d + 9
Hope this helps :-)
The simplified value of the given expression is 3d+9
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 7d + 12 − 4d − 3, we need to simplify it,
7d + 12 − 4d − 3
Combine Like Terms:
= 7d + 12 + − 4d − 3
= (7d + − 4d) + (12 + − 3)
= 3d + 9
Hence, the simplified value of the given expression is 3d+9
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Please help me with this! Worth 10 pts
D
convert 7 [tex]\frac{4}{5}[/tex] to a decimal = 7.8
compare 7.8, 7.6, 7.41
listing from least to greatest
7.41, 7.6, 7 [tex]\frac{4}{5}[/tex]
What does counterexample mean
an example that opposes or contradicts an idea or theory.
Final answer:
A counterexample is an example that disproves a statement or argument by showing that the conclusion can be false even when the premises are true. This concept is widely used in philosophy to test and refine arguments and definitions.
Explanation:
A counterexample is a specific case or example that refutes a general assertion or proposition. In philosophical reasoning and critical thinking, counterexamples hold particular significance as they can demonstrate the invalidity of an argument. The argument may have premises that are all true, but the conclusion drawn from these premises is shown to be false through the counterexample. Philosophers often use this method to refine definitions, understand the essence of concepts, and advance epistemological theories about knowledge and justification. Furthermore, it is a useful practice to generate counterexamples in order to test the validity of our own beliefs and arguments.
To identify counterexamples, one must consider a statement or argument and then conceive of a scenario where despite the premises being true, the conclusion does not follow. This act of finding counterexamples is critical for ensuring the soundness of deductive reasoning and often leads to the revision or abandonment of flawed concepts or arguments.
PLZ HELP 90 PTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Graph f(x)=−0.25x+4. Use the line tool and select two points to graph the line.
We need to graph ⇒⇒⇒ f(x) = - 0.25 x + 4
the given equation represents a linear equation, we need just 2 points to graph it
At x = 0 ⇒⇒⇒ f(x) = -0.25 * 0 + 4 = 4
At x = 4 ⇒⇒⇒ f(x) = -0.25 * 4 + 4 = 3
The attached figure represents the table and the graph of the given function.
Answer:
this equation represents a linear equation, you just need 2 points to graph it
At x = 0 to f(x) = -0.25 * 0 + 4 = 4
At x = 4 to f(x) = -0.25 * 4 + 4 = 3
Hope this helps. :)
In a study of 300 pregnant women with good to excellent health diets, 95% had babies in good or excellent health. How many women in this group had babies in good or excellent health?
For this question, just multiply the number (300) by the percent (.95)
Your answer is 285 women
To determine the number of women with babies in good or excellent health, we multiply the total number of women (300) by the percentage of women with healthy babies (95%). We find that 285 out of the 300 women had babies in good or excellent health.
Explanation:In the study mentioned, it is stated that 95% of pregnant women with good to excellent health diets had babies in good or excellent health. The total number of women considered in this study is 300. To calculate the exact number of women who had babies in good or excellent health, we can apply the concept of percentage which means 'per 100'. So, 95% of 300 women equals (95/100)*300 = 285 women. Therefore, out of 300 women, 285 women had babies in good or excellent health.
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Find the range of the function for the given domain. f(x) = 2x - 7 ; {-2, -1, 0, 1, 2}
The domain is a discrete set. So we will have a discrete range.
The range is a set containing:
f(-2)=-11
f(-1)=-9
f(0) = -7
f(1) = -5
f(2) = -3
Range = {-11,-9,-7,-5,-3}
Final answer:
The range of the function f(x) = 2x - 7 for the domain {-2, -1, 0, 1, 2} is found by substituting the domain values into the function, resulting in the range {-11, -9, -7, -5, -3}.
Explanation:
The student is asking to find the range of a given function f(x) = 2x - 7 for a specific domain. The domain provided is {-2, -1, 0, 1, 2}. To find the range, we substitute each value from the domain into the function and calculate the corresponding output values.
For x = -2, f(x) = 2(-2) - 7 = -4 - 7 = -11For x = -1, f(x) = 2(-1) - 7 = -2 - 7 = -9For x = 0, f(x) = 2(0) - 7 = 0 - 7 = -7For x = 1, f(x) = 2(1) - 7 = 2 - 7 = -5For x = 2, f(x) = 2(2) - 7 = 4 - 7 = -3Therefore, the range for the given domain is {-11, -9, -7, -5, -3}.
When 8668/25+4141/9-5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of that mixed number?
Answer:
Fractional part of the mixed number is [tex]\frac{23}{45}[/tex].
Step-by-step explanation:
First we have to simplify the given expression,
[tex]\frac{8668}{25} +\frac{4141}{9} -\frac{5533}{25}[/tex]
=[tex]\frac{(8668*9)+(4141*25)-(5533*9)}{25*9}[/tex]
=[tex]\frac{(8668-5533)*9+(4141*25)}{25*9}[/tex]
=[tex]\frac{(3135*9)+(4141*25)}{25*9}[/tex]
=[tex]\frac{28,215+103,525}{225}[/tex]
=[tex]\frac{131,740}{225}[/tex]
=[tex]\frac{26,348}{45}[/tex]
=[tex]585.51111[/tex]
Now we have to take the whole number that we get by dividing numerator by denominator,
It is 585
Now we have to find the remainder after taking the numerator,
[tex]26,348-(585*45)=23[/tex]
Now we represent the whole number and the fraction of remainder together as a mixed number.
[tex]585\frac{23}{45}[/tex]
Therefore, fractional part of the mixed number is [tex]\frac{23}{45}[/tex].
whats between 5 and 10?
There are an infinite amount of numbers between 5 and 10 if you consider decimal positions.
However, if you're referring to whole numbers (example: 5, 25, 200, etc)
There are 4 numbers between 5 and 10:
6, 7, 8, and 9.