1. Suppose we have two consecutive odd integers. If the smaller one is “x” ; what would we call the large one?
2. We are told there are two consecutive odd integers and the smaller one is 12 more than one third the large one. Use the answer to problem 1 to write a clean equation then find the integers
Main Answer:1) (x + 2)
2) The numbers are 19 and 21.
Concept and definitions should be there:
An odd integer n is an integer which is not a multiple of 2 (or equivalently one more than a multiple of 2). The odd integers are ..., -5, -3, -1, 1, 3, 5, ... Every odd integer can be written in the form 2k + 1 for some unique integer k.
The product of any two odd integers is odd and the result of a division where both the dividend and the divisor are odd is odd. But the sum and difference of any two odd integers are even.
The sum and difference of an even integer and odd integer are odd. Besides 2, all prime numbers are odd. Also, odd integers are really cool
This article is a stub. Help us out by expanding it.
Given data:
1) We have two consecutive odd integers.
Solving part:
Remember that the distance between any two consecutive odd numbers is 2.
5 - 3 = 2
7 - 5 = 2
13 - 11 = 2
etc.
So if the smaller of the two odd numbers is x, then the larger one will be (x + 2).
Given that:
2) We have two consecutive odd numbers, let's write them as:
Solving part:
(2*n + 1) and (2*n + 3)
Where n is an integer number.
We know that the smaller one is 12 more than one third of the larger one, so we have:
(2*n + 1) = 12 + (2*n + 3)/3
Now we can solve this for n
2*n + 1 = 12 + (2/3)*n + 1
2*n - (2/3)*n = 12 + 1 - 1
(4/3)*n = 12
n = (3/4)*12 = 9
n = 9
Then the two consecutive odd integers are:
(2*n + 1) = (2*9 + 1) = 19
(2*n + 3) = (2*9 + 3) = 21
Final Answer:1) (x + 2)
2) The numbers are 19 and 21.
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NEEEEED HELP ASAP!!!
How do you perform the indicated operation, 8 x 10^16/4 x 10^11?
8 x 10^16/4 x 10^11
do exponents first
8 x 10,000,000,000,000,000/4 x 100,000,000,000
than multiply
80,000,000,000,000,000/4 x 100,000,000,000
than divide
20,000,000,000,000,000x 100,000,000,000
2,000,000,000,000,000,000,000,000,000
Answer this question please
Construct a frequency distribution for the data using five classes. Describe the shape of the distribution.
The data set: ages of dishwashers (in years) in 20 randomly selected households
table ( (12 6 4 9 11 1 7 8 9 8)(9 13 5 15 7 6 8 8 2 1) )
The shape of the distribution of the given data set is : Bell shaped
What is Frequency distribution ?
Frequency distribution, in statistics, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. Simple examples are election returns and test scores listed by percentile. A frequency distribution can be graphed as a histogram or pie chart.
Data: 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1
Classes = 5
Class Frequency
1-3 →3
4-6 →4
7-9 →9
10-12 →2
13-15 →2
The shape of the distribution is peak at the center and down at both the ends,
Therefore, we can say that the shape of the distribution is bell shaped.
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50 POINTS The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
A=h(a+b)/2
Solve for b.
Answer:
[tex]\mathrm{b = 2\frac{A}{h} - a}[/tex]
Translation:
Option C.
Solve for x
3x-1=11
Answer: x = 4
Step-by-step explanation:
Given:
3x - 1 = 11
Add 1 to both sides of the equation:
3x = 12
Divide both sides of the equation by 3:
x = 4
What is the value of the digit in the ones place in each number?431
Answer:
Step-by-step explanation:
400
30
1
400 FOR HUNDREDS
Two consecutive positive integers such that the square of the second integer added to 4 times the first is equal to 41
Answer:
4 and 5
Step-by-step explanation:
We need 2 positive numbers that are right beside each other, like 1 and 2. When the problem is translates into number format we get:
y^2+4x=41
x = 1st # and y = 2nd #
so if we do 4 (x) and 5 (y)
5^2+4(4)=41
the statement is true.
Find the ending
balance:
$2,500 for 25 years at
2.75% annual simple
interest
Show work
Answer:
$4,218.75
Step-by-step explanation:
The formula for computing simple interest I on a principal amount P for t years at an interest rate of R% is given by
I = Prt
The ending balance amount is found by adding the principal to the interest computed
Ending balance = P + I
Here r is the interest rate in % converted to a decimal. This is done by dividing by 100
r = R/100 = 2.75%/100 = 0.0275 per year
I = 2500 x 0.0275 x 25 = 1718.75
So interest I = $1718.75
Ending balance = $2,500 + $1718.75 = $4,218.75
I WIL VOTE BRAINLISET SOMEONE PLEASE HELP
Answer:
26.0 cm
Step-by-step explanation:
Given quadrilateral ABCD with diagonal BD forming triangles ABD and BCD, and angles A=90°, C=52°, ADB=35°, and CBD=52°, you want the length of CD to 3 significant figures.
Law of SinesThe law of sines tells you the relation between sides and opposite angles is ...
a/sin(A) = b/sin(B) = c/sin(C)
This lets us write two proportions that can be solved for the measure of CD.
In triangle ABD:
BD/sin(A) = AB/sin(D)
BD = AB·sin(90°)/sin(35°) = 12 cm/sin(35°) ≈ 20.921 cm
In triangle BCD:
CD/sin(B) = BD/sin(C)
CD = BD·sin(B)/sin(C) = 20.921 cm·sin(102°)/sin(52°) ≈ 25.969 cm
The length of CD is about 26.0 cm.
Hunter measured the middle school and made a scale drawing. The scale he used was 1 inch : 10 feet. The gym is 7 inches wide in the drawing. How wide is the actual gym?
Answer:
70 ft
Step-by-step explanation:
You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.
Scale factorEach inch represents 10 feet, so 7 inches will represent ...
7 × 10 ft = 70 ft
The gym is 70 ft wide.
__
Additional comment
You can also write and solve an equation that shows the measures are proportional:
actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)
Multiplying both sides of this proportion by 7 in, we have ...
gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft
what is the value of x?
help would be so appreciated
Answer:
x = 23
Step-by-step explanation:
The two angles are supplementary angles.
Supplementary angles sum 180°
(6x+4) + 38 = 180
6x + 42 = 180
6x = 180 - 42
6x = 138
x = 138/6
x = 23
Check:
6*23 + 4 + 38 = 180
138 + 42 = 180
Answer:
x = 23Step-by-step explanation:
We know that the sum of angles of a linear pair is always equal to 180°. These angles are also known as supplementary angles.
[tex]\bf 6x+4+38^o=180^o[/tex] (Add numbers)
[tex]\bf 6x+42=180[/tex] (Simplify)
[tex]\bf 6x+42-42=180-42[/tex](Subtract both sides by 42)
[tex]\bf 6x=138[/tex] (Simplify)
[tex]\bf \cfrac{6x}{6}=\cfrac{138}{6}[/tex] (Divide both sides by 6)
[tex]\bf x=23[/tex]
Therefore, x = 23.
_____________________
Hope this helps!
Have a great day!
Write
17/100
as a decimal number.
Answer: 0.17
Step-by-step explanation:
Plug the equation into a calculator (17 divided by 100).
You can also think of the problem like this; move both decimal places to the left twice since, in 100, there are two 0's.
17 -> 0.17
100 -> 1
This can also work with 17 and 1000, but you would have to move the decimal place three times.
17 -> 0.017
1000 -> 1
One liter of interior paint covers 100 square feet. How many gallons of paint does it take to cover 800 square meters of walls?
By doing some changes of units, we can see that we will need 22.61 gallons of paint to cover 800 square meters.
How many gallons does it take to cover 800 square meters of walls?
We know that with one liter of interior paint we can cover 100 square feet.
Remember the relation between square feet and square meeters:
1ft^2 = 0.092 m^2
Then with one liter we can cover:
100ft^2 = 100*0.092 m^2 = 9.2 m^2
So the number of liters of paint that we need to cover the 800 m^2 is given by the quotient:
L = 800m^2/9.2m^2 = 86.96
We need 86.96 liters of paint, and the relation between liters and gallons is:
1 L = 0.26 gal
Then we need:
86.96 L = 86.96*(0.26 gal) = 22.61 gal
We will need 22.61 gallons of paint to cover 800 square meters.
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1 2/3 + 3 3/4 as a fraction
Answer:
5/3 + 15/4 are the fractions
I don’t understand, can someone help me :)
I think you are supposed to add the the numbers in that row and if it's more that 18 and less that 37 that's the answer. exapmle:
2,8,3,9,5
Add those together and get 27. 27 is less than 37 and more that 18 so it would be one of the answers.
I could be wrong but I'm pretty sure that is what you do
I`m trying to figure this out. Please see question with multiple choices.
The equivalent expression of (10⁻² . 4⁵)⁻² is 10⁴ / 4¹⁰
How to find equivalent expression?We have to find the expression that is equivalent to the expression below:
(10⁻² . 4⁵)⁻².
Therefore, using the law of indices,
[tex](x^{a} )^{b} = x^{ab}[/tex]
Hence, let's find the equivalent expression by applying the laws of indices.
(10⁻² . 4⁵)⁻² = 10⁴ . 4⁻¹⁰
Also, applying the law of indices,
[tex]x^{-b} = \frac{1}{x^{b} }[/tex]
Therefore,
10⁴ . 4⁻¹⁰ = 10⁴ / 4¹⁰
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3. Log(x) +2= log(y) Which is larger x or y and by how much?
Answer:
y is 100 times larger than x===========================
Use identities[tex]log (a) + log (b) = log (ab)[/tex],[tex]a = log (10^a)[/tex],If [tex]log (a) = log (b)[/tex], then a = b.Rewrite and comparelog (x) + 2 = log (y)log (x) + log (10²) = log (y)log (x) + log (100) = log (y)log (100x) = log (y)100x = yy = 100xy is greater by 100 times
Find the value of B in the following equation if you know it
goes through the point (-4,1).
5x - 3y = B
B =
Answer:
17
Step-by-step explanation:
We can substitute x = -4 and y = 1 since the point lies on the line.
[tex]5(-4)-3(1)=B \\ \\ B=17[/tex]
Find an equation for the line which passes through (-2,8) and is perpendicular to the line containing (0,1) and (4,5).
The equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .
Let the equation of line passes through the point (-2, 8) be y = mx + b.
Where m is the slope of the line and b is the y intercept of the line.
According to the given question.
A line passes through the points (-2, 8).
And it is also perpendicular to the line containing (0, 1) and (4, 5).
Since, the line is perpendicualr to the line conatining (0, 1) and (4, 5).
So, the slope of the line whose equation is to be find is given by
m = -1/(5 - 1/4-0)
⇒ m = -1/4/4 = -1
Thereofre, the equation of line with slope -1 is
y = -1x + b
Also, it passes through (-2, 8)
So,
8 = -1(-2) + b
⇒ 8 - 2 = b
⇒ b = 6
Thereofore, the equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .
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Express 60 of its prime factors in assessing order and answer in index form
Answer:
2^2×3×5
Step-by-step explanation:
hope this works :)
Which table represents y as a function of x?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
An equation represents a represents only when there is a unique value of x for every value of y. when it represents u as a function of x.
i.e if we draw lines parallel to y axis and it cuts the curve two or more than two times at a particular value of x then it doesn't represent a function at all.
And as we can see in the given tables,
1.) 12.23 is the value of x for both 5.4 and 6.4
2.) 0.31 is the value of x for both 55 and 59
4.) 20 is the value of x for both 245 and 255
So, the only table representing y as a function of x is table 3.
Answer:
table 3 is correct i took the test
Step-by-step explanation:
Graph the function. Identify the domain and range.
each day a bobcat drinks about 3 times as much water as a canada goose drinks. how much water can a bobcat drink in 1 day?
The water that a bobcat drink in 1 day will be 3x.
How to calculate the value?Let the amount of water be represented by x.
From the information, it was stated that each day a bobcat drinks about 3 times as much water as a canada goose drinks.
Let the water that the Canada goose drank be represented as x
Therefore, the water that a bobcat drink in 1 day will be 3x.
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GIVING BRAINIEST IF CORRECT!!!!
Multiply and express in simplest radical form.
Random means by chance.
O True
O False
Answer:
True
Step-by-step explanation:
Because you never expect when something may show up once your doing something and forget about what you lost a while back. Sometimes it just pops up and we're like, "Oh that's where it was".
Can't say true or false because both can be answers in different cases, mathematically speaking you can select one thing from a set of similar things having similar chance to be selected. and again you can also select one thing at random from a set of things having different chance of being selected. in my perspective:)
and maybe the question has more chance to be false because if a statement is false at least in one case it is false.
Which fraction is greater, 35/109 or 36/104?? To explain your answer, use our definition of fraction along with reasoning other than finding common denominators, common numerators, cross-multiplying, or converting to decimals.
The fraction that is greater is 36/104 since 34.62% is greater than 32.11%
Percentages and ratioFractions are written as the ratio of two integers. For instance a/b is a fraction.
In order to determine which of the fractions is greater, we will express them as percentage as shown:
35/109 * 100
3500/109
32.11%
Similarly;
36/104 * 100
3600/104
34.62%
Hence the fraction that is greater is 36/104 since 34.62% is greater than 32.11%
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Solve for X: 4x+3x-x=-5+6x
Since the values on both sides of the expression are different, hence the equation has no solution.
Solving linear equationsLinear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b
Given the expression 4x+3x-x=-5+6x
Collect the like terms
4x+3x-x = -5+6x
4x+3x-x-6x = -5
7x - 7x = -5
Simplify
-0x = -5
0x = 5
x = 5/0
Since the values on both sides of the expression are different, hence the equation has no solution.
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The value of x is -5
What are algebraic expressions?Algebraic expressions are expressions that comprised of;
variablestermsfactorscoefficientsconstantsThey are also made of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc
Given the equation;
4x + 3x = -5 + 6x
Let's solve for x
We have;
collect like terms
4x + 3x - 6x = -5
Add or subtract like terms
7x - 6x = - 5
x = -5
Thus, the value of x is -5
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18x - 3
6 + 25x
does anyone know?