To find which expression must be an odd integer when m + 1 is even, we analyze each option using substitution. The only option that results in an odd integer is 2m + 1.
If m + 1 is an even integer, then m must be an odd integer. Let's analyze each option to see which one of them must be an odd integer:
(A) m - 1: Since m is odd, subtracting 1 from an odd number will result in an even number. Therefore, (A) m - 1 is not an odd integer.(B) 2m - 2: If we substitute an odd integer for m, we get (2 * odd) - 2, which simplifies to an even number. Thus, (B) 2m - 2 is not an odd integer.(C) 2m + 1: Substituting an odd integer for m gives (2 * odd) + 1, which simplifies to an odd number. Therefore, (C) 2m + 1 is an odd integer.(D) 2m + 2: If we substitute an odd integer for m, we have (2 * odd) + 2, which simplifies to an even number. Hence, (D) 2m + 2 is not an odd integer.Therefore, the answer is (C) 2m + 1 as it is the only option that must be an odd integer.
Learn more about Odd and Even Integers here:https://brainly.com/question/35543948
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Final answer:
Option C, which is 2m + 1, must be an odd integer if m + 1 is an even integer because adding 1 to any even integer results in an odd integer.
Explanation:
Given that m + 1 is an even integer, we can determine which of the other expressions would therefore be an odd integer. We know that any even integer can be written in the form 2k, where k is an integer, because even integers are multiples of 2. Similarly, odd integers can be written as 2k + 1, where k is also an integer.
Given the options:
A: m - 1, if m + 1 is even, then m is odd, and subtracting 1 from an odd number results in an even number, so this option is not correct.B: 2m - 2, this is clearly even because it is a multiple of 2 regardless of the value of m, so this option is not correct.C: 2m + 1, if m is odd (since m + 1 is even), this will result in an odd number, so this option is correct.D: 2m + 2, like option B, this is also clearly even, so this option is not correct.Therefore, the answer is C: 2m + 1.
What is true about triangle ABC. Select three options
Answer: The answer is sin A = cos C
Step-by-step explanation: sin A = cos C
Answer:
It should be A, B, C
Step-by-step explanation:
Find the range of the data sources: 83,77,88,93,97,79,94,80,97,81
Let r = range
Range = biggest value minus smallest value
r = 97 - 77
r = 20
Answer:
Range 20
Step-by-step explanation:
First put all the numbers in order from least to greatest
77,79,80,81,83,88,93,94,97,97
To find range you subtract the largest number from the smallest number.
So 97 - 77 = 20
The range is 20
Hope This Helps!! :}
What are the factors of x^2 - 81
(X + 9)(x -9)
(x-9)(x -9)
(x + 3)(x - 27)
Prime
Answer:
A. x-9 and x+9 because these are perfect squares. 9 times -9 is -81. x times x is x^2. 9 + -9 is 0
A 279-foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is as long as the second. How long is each piece of rope?
Step-by-step explanation:
Let's say x is the length of the first piece.
The second piece is 2x.
The third piece is 2x.
So the total length is:
x + 2x + 2x = 279
5x = 279
x = 55.8
That means 2x = 111.6.
So the first piece is 55.8 feet, the second piece is 111.6 feet, and the third piece is also 111.6 feet.
Answer:
Piece 1 : 55.8 ft
Piece 2: 111.6 ft
piece 3: 111.6 ft
Step-by-step explanation:
From the question we can see that the total length of the rope is 279 ft and as mentioned it is cut into three pieces. Since the first piece has no length we can give it a variable of x . Piece two is twice as long as piece one, so we can give it a value of 2x . Lastly, piece three is the same as piece two, so it would also be 2x.
So we can now say the following:
[tex]x + 2x + 2x = 279ft[/tex] .... now we can solve for x.
[tex]5x = 279[/tex]
[tex]x = 55.8 ft[/tex]
So we can see that piece one is 55.8 ft long . Now we can use this value to find pieces two and three.
[tex]2x = P2[/tex]
[tex]2(55.8) = P2[/tex]
[tex]111.6 = P2[/tex]
So pieces two and three are 111.6 ft long
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
The function below represents the annual interest Victoria earns on a savings account. Identify the term that represents the amount of money originally deposited in the account.
f(x) = 300(1 + 0.03)x
300
1
0.03
x
Answer:
[tex]\$300[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value ( value of the function when the value of x is equal to zero)
b is the base
r is the rate
b=1+r
we have
[tex]f(x)=300(1+0.03)^{x}[/tex]
therefore
The term that represents the amount of money originally deposited in the account is the initial value
For x=0
substitute
[tex]f(0)=300(1+0.03)^{0}[/tex]
[tex]f(0)=\$300[/tex]
Answer:
The correct option is 1.
Step-by-step explanation:
The function is
[tex]f(x)=300(1+0.03)^x[/tex]
We need to find the term that represents the amount of money originally deposited in the account. It means we need to find the initial amount.
Substitute x=0 in the given function, to find the initial value of the function.
[tex]f(0)=300(1+0.03)^(0)[/tex]
[tex]f(0)=300(1)[/tex]
[tex]f(0)=300[/tex]
The term 300 represents the amount of money originally deposited in the account. Therefore the correct option is 1.
What is the median of this distribution?
Answer:
4
because if you cross off one number at a time from each side you are left with 2 number 4s and 4+4/2=4
Solve for x -2x + 5 <7
Answer:
[tex]\large\boxed{x>-1}[/tex]
Step-by-step explanation:
In this question, we're trying to solve for x.
In other words, we're going to need to get x by itself in order to get our answer for the inequality.
Solve:
[tex]-2x + 5 <7\\\\\text{Subtract 5 on both sides to get -2x by itself}\\\\-2x<2\\\\\text{Divide both sides by -2}\\\\\text{Since you're dividing by a negative, the} < \text{will flip to} >\\\\x>-1[/tex]
When you're done solving, you should get x > -1
This means that when you solve for x, you should get x > -1
I hope this helped you out.Good luck on your academics.Have a fantastic day!anyone willing to help out really quick?^^
Answer:
15.86 inches
Step-by-step explanation:
Area of rectangle = length times width
l = ∛81 inches
w = 3 2/3 inches
= l x w
= ∛81 x 3 2/3
= 15.86 inches
Max saved some money by buying a book of 10 movie passes rather than individual tickets.Howcan he figure out how much money he saved?
What is the slope of the line through (-7, -2) and (-6, 7)?
Make sure to explain your answers, please!
{No spam answers, please! Thank you!}
Answer:
[tex]\displaystyle =9[/tex]
Step-by-step explanation:
The slope formula is
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle y_2=7\\\displaystyle y_1=(-2)\\\displaystyle x_2=(-6)\\\displaystyle x_1=(-7)[/tex]
[tex]\frac{7-(-2)}{(-6)-(-7)}=\frac{9}{1}=9[/tex]
Therefore, the slope is 9, and the correct answer is 9.
Hope this helps!
3 integers less than 25 range of 10 mean of 13
Answer:
8, 13, 18
Step-by-step explanation:
If we want the mean to be 13, and there are 3 integers, that means the sum of all 3 integers must be 39. I started at 13 and counted 5 up and 5 down, which already makes sure of the range and the mean is 13 (since it's balanced with 13 being the middle), therefore, 13+5 is 18, 13-5=8.
LOOK AT PICTURE PLEASE ANSWER ASAP parabola directrix focus and vertex
Answer:
[tex]y = - \frac{3}{20} {x}^{2} [/tex]
Step-by-step explanation:
The given parabola has focus at:
[tex](0, - \frac{5}{3} )[/tex]
and directrix at
[tex]y = \frac{5}{3} [/tex]
This is a vertical parabola that opens downwards.
The equation is of the form;
[tex] {x}^{2} = - 4py[/tex]
p is the distance from the vertex to the directrix.
Since the vertex is at the origin, we have
[tex]p = \frac{5}{3} [/tex]
We plug this value into the equation to get:
[tex] {x}^{2} = - 4( \frac{5}{3} )y[/tex]
[tex] {x}^{2} = - \frac{20}{3} y[/tex]
We solve for y to obtain:
[tex]y = - \frac{3}{20} {x}^{2} [/tex]
The 3rd option is correct.
what are solutions to the quadratic equation 2x^2+6x-10=x^2+6
Answer:
x = -2 or x = 8Step-by-step explanation:
[tex]2x^2+6x-10=x^2+6\qquad\text{subtract}\ x^2\ \text{and 6 from both sides}\\\\x^2+6x-16=0\\\\x^2+2x-8x-16=0\\\\x(x+2)-8(x+2)=0\\\\(x+2)(x-8)=0\iff x+2=0\ \vee\ x-8=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x-8=0\qquad\text{add 8 to both sides}\\x=8[/tex]
Answer:
2 and -8
Explanation is Apex
Write an equation: 1/5 of a shipment of books weights 25 pounds
To find the total weight of the shipment where [tex]\frac{1}{5}[/tex] weighs 25 pounds, we use the equation [tex]\frac{1}{5}[/tex]W = 25 and solve for W, leading to a total weight of 125 pounds.
The question is asking us to write an equation that represents the situation where [tex]\frac{1}{5}[/tex] of a shipment of books weighs 25 pounds.
To find the total weight of the shipment, we should set this up as an equation where the total weight of the shipment is represented by W. Since [tex]\frac{1}{5}[/tex] of the shipment weighs 25 pounds, we can write the equation as [tex]\frac{1}{5}[/tex] W = 25.
To find the weight of the whole shipment, we need to multiply both sides of the equation by 5, which will give us
W = 125 pounds.
When converting units such as pounds to ounces, we use the unit equivalence 1 pound = 16 ounces.
If the weight of the books needed to be in ounces, we could convert 125 pounds by multiplying
125 x 16 = 2000 ounces
Write the equation that contains the point (3, -9), and in which the graph of the line has a slope of 4 in slope-intercept form.
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-9})~\hspace{10em} slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-3) \\\\\\ y+9=4x-12\implies y=4x-21[/tex]
There are 32 more apple than oranges in a box. 3/5 of the oranges and 1/3 of the apples are overripe. If the number of overripe apples and the number of oranges is the same, how many pieces of overripe fruit are there?
The answer is:
There is a total of 48 overripe fruit.
Why?To calculate the number of pieces of overripe fruit we have, we need to write two equations to create a relationship between the number of apples and oranges.
Let be "x" the number of oranges, so:
[tex]Oranges=x\\Apples=x+32[/tex]
Now, we know that 3/5 of the oranges and 1/3 of the apples are overripe, so:
[tex]OverripeApples=\frac{1}{3}(x+32)\\\\OverripeOranges=\frac{3}{5}(x)[/tex]
Then, we have a condition that states that the number of overripe apples and overripe oranges is the same, so:
[tex]\frac{1}{3}(x+32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(x)+\frac{1}{3}(32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3}{5}(x)-\frac{1}{3}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3x*3-1*x}{15}=\frac{9x-5*x}{15}=\frac{4x}{15}[/tex]
[tex]\frac{32}{3}=\frac{4x}{15}[/tex]
[tex]\frac{32*15}{3}=4x[/tex]
[tex]\frac{480}{3}=4x[/tex]
[tex]160=4x[/tex]
[tex]\frac{160}{4}=x[/tex]
[tex]40=x[/tex]
Therefore, we have that there are 40 oranges and 72 apples (40+32).
Now, calculating the number of overripe oranges and apples, we have:
[tex]OverripeApples=\frac{1}{3}(72)=24\\\\OverripeOranges=\frac{3}{5}(40)=24[/tex]
Hence, we have that there are 24 pieces of overripe oranges and 24 pieces of overripe apples. It means that there is a total of 48 overripe fruit.
Have a nice day!
Write a numerical expression for each verbal phrase? How many more pencils Chet has than Benito if Benito has ten pencils and Chet has seventeen pencils
Answer:
-10 + 17 [OR 17 - 10]
Step-by-step explanation:
To find out how MANY MORE of something someone has THAN the other, you use the operation of deduction [subtraction].
I am joyous to assist you anytime.
Answer:
Chet has 7 more pencils than Benito.
Step-by-step explanation:
We have to Write a numerical expression for each verbal phrase:
Number of pencils Benito has = 10
Number of pencils Chet has = 17
The number of more pencils Chet has than Benito is = [tex]17-10=7[/tex]
Therefore, Chet has 7 more pencils than Benito.
What number :Increased by 130% is 69 ?
130% as a decimal is 1.3
Divide 69 by 1.3:
69 /1.3 = 53.076923
Round the answer as needed
To find the original number that increased by 130% equals 69, we divide 69 by 2.30, which reveals that the original number is 30.
The student is asking how to find a number that, when increased by 130%, results in 69. To solve this problem, let's represent the original number as x. The increase by 130% of the original number would be x + 1.30x (which equals 2.30x), and this sum is equal to 69. To find x, we divide 69 by 2.30:
x = 69 / 2.30
We calculate this as:
x = 30
Therefore, the number which when increased by 130% equals 69 is 30.
Which of the following values is a solution for the inequality statement? Select all that apply. 11 > a/4 -16 55 -150 210 -78 108
Answer:
55, -150, -78
Step-by-step explanation:
The given inequality is:
[tex]11>\frac{a}{4}-16[/tex]
Adding 16 to both sides, we get:
[tex]11+16>\frac{a}{4}-16+16\\\\ 27>\frac{a}{4}[/tex]
Multiplying both sides by 4, we get:
[tex]27 \times {4}>\frac{a}{4} \times 4\\\\ 108>a[/tex]
Hence, the solution to the inequality is 108 > a or this can be written as a < 108
This means, the values less than 108 are a solution of the given inequality. 108 is not a part of the solution as the inequality symbol says less than 108.
Among the given options following are the values that are less than 108 and thus will satisfy the inequality:
55, -150, -78
The average of a set of 5 numbers is 44. If the number 50 is added to the set, what is the new average?
Answer:
45
Step-by-step explanation:
Um, If we say that all the numbers are 44, and now we add 50, then we will get 270. Find the mean of 270. We get 45.
Final answer:
To find the new average after adding 50 to a set of 5 numbers with an average of 44, multiply the average by the number of elements, add the new number, then divide by the total number of elements to get the new average of 45.
Explanation:
The average of a set of 5 numbers is 44. To find the sum of the original set, multiply the average by the number of elements: 44 x 5 = 220. When 50 is added, there are now 6 numbers in the set. To find the new average, divide the new sum (220 + 50 = 270) by the total number of elements (6) to get 45 as the new average.
20 points!!!
If two lines are perpendicular to the same line are they perpendicular to each other?
Answer:
no
Step-by-step explanation:
Answer:
Step-by-step explanation:
depending on the space you're considering, it would be SOMETIMES true. But usually, the 2 lines would be parralel.
What i'm saying is, that in an euclidian space, the 2 lines would be parallel. In another kind of space, the two lines could be anything...
for example: look at how longitude and lattitude are represented on a globe : they are "lines"... 2 sets of perpendicular lines...
Now look at what happens in the poles : all lines intersect! (therefore, they're not parallel, and not necessarily perpendicular either)
A patient’s weight is recorded as 75 kilograms. How many pounds does the patient weigh?
Answer:
165.347 pounds ..
Step-by-step explanation:
The weight of patient is given in kilograms which is
W = 75 kilo grams.
In order to convert the weight into pounds we have to multiply or divide 75 with some number.
There are 2.20462 pounds approximately in one kilogram.
So the weight in pounds will be:
Weight in pounds = 75 * 2.20462
= 165.3465 pounds
= 165.347 pounds ..
The domain of r:(3,-2)(1,2)(-1,-4)(-1,2)
Answer:
domain {-1,1.3}
Step-by-step explanation:
The domain is the input values, or in this case the first or x values
domain {3,1,-1,-1}
We do not put the same value twice
domain {3,1,-1}
We like to put them in numerical order
domain {-1,1.3}
What is the vertex and the equation of the axis of symmetry of the graph of y=x^2-6x-7
for a vertically opening parabola, its axis of symmetry will come from the x-coordinate of its vertex, thus
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{-6}{2(1)}~~,~~-7-\cfrac{(-6)^2}{4(1)} \right)\implies (3~~,~~-7-9)\implies (3~~,~~-16) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=3}~\hfill[/tex]
I Need Help!! Answer Please!!
Answer:
50 degrees
Step-by-step explanation:
all inside angles in every triangle can be added up to equal 180 degrees.
this is a right angle, so one has to be 90 degrees
on the bottom right it's marked 140 degrees on the outside, in order to find the inside angle, you need to subtract 140 from 180, which gives you 40 degrees
180-90=90
90-40=50
so the answer is 50
if that's not clear enough leave a comment, hope this helps!
Answer:
50°
Step-by-step explanation:
Inside angles of a triangle = 180°
The triangle shown is a right triangle.
Therefore, it is 90°
180 - 90 = 90
90 - 40 = 50
Answer = 50°
Rational numbers do NOT include:
infinite decimals
repeating decimals
terminating decimals
Answer:
Infinite decimals that do not repeat.
Step-by-step explanation:
Repeating decimals can be as fractions where the top and bottom are integers.
Examples: .3333333333333333333333333333333.... can be written as 1/3.
or .19191919191919191919..... can be written as 19/99.
Terminating decimals can also be written as fractions where the top and bottom are integers.
Examples: .11=11/100 or .161=161/1000
Any number that can be written as a fraction where the top and bottom are integers (bottom integer not 0)
is a rational number.
Repeating decimals are infinite. So what I think they mean by infinite here is numbers like [tex]\pi[/tex] or [tex]\sqrt{2}[/tex]. There are not rational. They cannot be written as a fraction where the top and bottom are integers.
Answer:
Rational numbers do NOT include:
infinite decimals
Step-by-step explanation:
- (1-7x) -6 (-7-x) = 36
Solving for x:
Start by distributing the numbers outside the parentheses to inside the parentheses:
-1 + 7x + 42 + 6x = 36
Now combine like (similar) terms:
13x + 41 = 36
Subtract 41 from both sides:
13x = -5
Divide both sides by 13:
x = [tex]-\frac{5}{13}[/tex]
Therefore, x = [tex]-\frac{5}{13}[/tex].
Hope this helps! :)
Find the area of the rhombus. (4)
Answer:
24 cm2 is the answer or option d
Step-by-step explanation:
Hair color. |. Clothing
Brown. I Dress
Black. I Jumpsuit
Blonde. I Pajamas
Red. I Jeans
The table above shows hair colors and clothing available at a doll shop. How many different combinations of hair color ND clothing are there?
Answer:
16 possible hair/clothing combinations
Step-by-step explanation:
1) Brown-dress; 2)Brown-jumpsuit; 3)Brown-pajamas ; 4)Brown-Jeans; 5)Black-Dress; 6)black jumpsuit; 7)black pajamas; 8)black jeans; 9)blonde dress; 10)blond jumpsuit; 11)blonde pajamas; 12)blond jeans; 13)red dress; 14)red jumpsuit; 15)red pajamas; 16)red jeans
Or just multiply 4x4 because there were four of each.
what is the inverse of the function f(x)=2x+1
Answer:The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2
Step-by-step explanation: