Yes, the product of an integer and a natural number will always be an integer.
A natural number refers to a whole number that does not have any kind of fraction or decimal. Some examples of natural numbers are 1, 2, 3, 4, and so on. Zero is not a natural number.
Integers refer to all numbers that can be positive and negative. It should not have a fractional part or a decimal part in the number. Integers can be depicted by the positive or the negative sign. Zero is an integer.
Whenever we are multiplying a natural number with an integer, we are ultimately getting the result as a positive number, negative number, or zero. Thus, it will become an integer.
Example 1: We can take the natural number 10 and the integer -5. Its product will be -50. Thus, it is an integer.
Example 2: We can take the natural number 16 and the integer 0. Its product will be 0. Thus, it is an integer.
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Determine whether the graph represents a function. Explain
Evaluate each expression for the given value of the variable. 5c³ - 6c√-2 c ; c=-5
The value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] at c = -5 is [tex]5(-125 +6\sqrt{10})[/tex] .
An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).
For Example , 2c+5x+6 is an algebraic expression.
In the given expression
[tex]=5c^{3} -6c\sqrt{-2c}[/tex]
Substituting the value of c = -5 .
We get ;
[tex]=5(-5)^{3} -6(-5)\sqrt{-2(-5)}[/tex]
[tex]=5(-125) +30\sqrt{-2(-5)}\\ \\ =-625 +30\sqrt{10}[/tex]
taking 5 common from both the terms
[tex]=5(-125 +6\sqrt{10})[/tex]
Therefore , the value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] is [tex]5(-125 +6\sqrt{10})[/tex].
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Evaluate each finite series for the specified number of terms. 80-40+20- . . . ; n=8
Answer:
The value of the given series is 49.75
Step-by-step explanation:
This is a problem from geometric progression ,
As we know the formula for geometric progression is aₙ = a₁ r ⁿ⁻¹
Where , a₁ is the first term and r is the ratio , and n is the number of terms.
Ratio is , 40/80 = 1/2
Here , a₄ = 80 . (1/2)⁴ ⁻ ¹ = 80 / 8 = 10
a₅ = 80 . (1/2)⁵ ⁻ ¹ = 80 / 16 = 0.5
a₆ = 80 . (1/2)⁶ ⁻ ¹ = 0.25
a₇ = 80 . (1/2)⁷ - ¹ = 0.125
a₈ = 80 . (1/2) ⁸ ⁻ ¹ = 0.625
Now the series can be written as .
80-40+20- 10 + 0.5 - 0.25 + 0.125 - .625 = 49.75
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I need help with both question pls
Answer:
0.03x+0.05=1.50
Hopely this can help you
Step-by-step explanation:
What number is represented by
(a) 6 tens 7 ones
The number is represented by 6 tens 7 ones 67 .
2-digit ranges square measure the amounts that have 2 digits and that they begin from the amount ten and end wise the number ninety nine.They can't begin from zero as a result of therein case it'll be thought of as a single-digit range. The digit on the tens place will be any range from one to nine.Let the unit's place digit be " x " and ten's place digit be " y ".
Two digit number is given by = 10 y + x .....(1)
It is given that 6 tens 7 ones.
Putting x = 6 and y = 7 in equation (1) , we get
10(6) + 7 = 60 + 7
= 67
Hence , the number is 67 .
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Find the first five terms of each sequence. an =5 n-3
The first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
According to the question.
We have a formula or a rule for finding the terms of a sequence i.e.
an = 5n -3.
The first term of the sequnence an = 5n - 3 is given by
a(1) = 5(1) -3 = 5 -3 = 2
The second term of the sequence an = 5n - 3 is given by
a(2) = 5(2) - 3 = 10 - 3 = 7
The third term of the sequence an = 5n -3 is given by
a(3) = 5(3) - 3 = 15 - 3 = 12
The fourth term of the sequence an = 5n - 3 is given by
a(4) = 5(4) - 3 = 20 - 3 = 17
The fifth term of the sequence an = 5n - 3 is given by
a(5) = 5(5) - 3 = 25 - 3 = 22
Hence, the first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
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What is the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15,-5)?
y=3/5x-20
y=-3/5x+20
y=5/3x-20
y=-5/3x+20
Answer: Option (4)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we want to find is -5/3.
Of the options, the only one that satisfies this is choice 4.
Help please need it for rn
Check the picture below.
In a rectangle, the width is 1 feet shorter than the length. The area of the rectangle is 30 square feet. Find the length of the rectangle.
(ANSWER ASAP EXTRA POINTS)
Suppose you turn the water on in an empty bathtub with vertical sides. After 20 s , the water has reached a level of 1.15 in. You then leave the room. You want to turn the water off when the level in the bathtub is 8.5 in. How many minutes later should you return? (Hint: Begin by identifying two terms of an arithmetic sequence.)
I should return after 7.7 minutes later to bathtub.
What is bathtub?You want to turn the water off when the level in the bathtub is 8.5
66/8.5
7.7 minutes
A bathtub is a long, typically rectangular container that you sit in to bathe your body after filling it with water.
Let's start with the truth: Showers are cleaner than baths. Showers spray polluted water out of sight while distributing water evenly over your body.
Actually, there is nothing that sets one apart from the other. All of them include jets, bubbles, and frequently different colored lights and other decorations. They are all sizable hot water containers. Overall, the terms "whirlpool bath," "Jacuzzi," and "hot tub" all refer to the same thing.
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Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.
Answer:
22 divided by 2 equals 11, so each shirt at store one, you are getting for $11. Store 2 is having a sale of 10% off 12.99 is 11.69, so each shirt is $11.69. So, Store 1 is a better deal.
Step-by-step explanation:
Answer:
1.38$
Step-by-step explanation:
QUESTION
Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.
EXPLANATION
store one 2 shirts 22$
store 2 1 shirt 12.99/10=1.30 so 12.99-1.30=11.69x2=23.38
23.38-22=1.38
NEED THIS NOW DONE CORRECTLY
The figure shows three quadrilaterals on a coordinate grid:
B and C are similar and also congruent.
A and B are similar but not congruent.
A and B are similar and also congruent.
A and C are similar but not congruent.
Step-by-step explanation:
A and B are similar but not congruent
similar=same shape
congruent=same shape and same size
in exercises 1-4, find m 1 and m 2. Tell which theorem you use in each case.
Answer:
m1 = 122°
m2= 58°
Step-by-step explanation:
M1 is an alternate interior angle, of 122°, which means that that angle is also 122°.
The line with m1 and m2 added together equal 180°, so we can subtract 122 from 180 to find m2.
180-122= 58
(02.02 LC)
If f(x) is the total cost, in dollars, of x brownies, which of the following statements best describes the meaning of f(4) = 10?
a
The total cost of 2 brownies is $4.
b
The total cost of 4 brownies is $2.
c
The total cost of 4 brownies is $10.
d
The total cost of 10 brownies is $4.
The total cost of 10 brownies is $4 is the statement that best describes the meaning of f(4) = 10, if f(x) is the total cost, in dollars, of x brownies.
What is a function?In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are widespread in mathematics and are required for the formulation of physical relationships in the sciences. The present concept of function was initially proposed in 1837 by the German mathematician Peter Dirichlet.
If a variable y is so closely tied to a variable x that whenever a numerical value is assigned to x, there is a rule that determines a unique value of y, then y is said to be a function of the independent variable x.
As we can see it is mentioned that f(x) = total cost = f(4)
So only option d. has 4 as total cost, that why d is the right option and statement as follows The total cost of 10 brownies is $4.
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y-2=¼(x+5) into slope-intercept form?
The slope intercept form is y = 1/4x + 13/4
The general expression for slope intercept form is given as follows
y = mx + c
where, m = slope of the line
c = intercept
We have been given the equation that is,
y – 2 = 1/4(x+ 5)
We will solve this step by step to convert it into the general form that is,
y – 2 = 1/4(x+ 5)
y – 2 = 1/4x + 5/4
y = 1/4x + 5/4 + 2
y = 1/4x +13/4
which is in the general form of y= mx + c where m = 1/4 and c = 13/4
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Lisa wants to buy some new shirts are her favorite store. Each shirt costs $15 and she wants to buy a pair of shoes that are $35. Lisa only has $137 to
spend
Let S represent the number of shirts that Lisa buys
Which inequality describes this scenario?
O 137 < 158 +35
O 137 > 158 +35
O 137 >_ 158 +35
O 137 <_158 +35
The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let s represent the number of shirts that Lisa buys. Lisa only has $137 to spend, therefore:
15x + 35 ≤ 137
The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137
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if the lenght and breadth of the rectangular sheet of paper is 49 1/2 cm and 23 1/2 cm repsectivly . Find its perimeter
Answer: 146 cm
Step-by-step explanation:
A simple way to find the perimeter of a rectangle is to double both sides and add them.
(49.5 * 2) + (23.5)
= 99 + 47
= 146
Suppose B is the midpoint of -AC . Use the given information to find the missing measure. A B=6 y-14, B C=10-2 y, A C= ?
If AB = 6y - 14, BC = 10 - 2y then the value of AC = 8.
What is meant by midpoint?
In geometry, the midpoint is the point in the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid. It cuts the segment in half.
Given: AB = 6y - 14, BC = 10 - 2y
Since B is the midpoint of AC, AB = BC then
6y - 14 = 10 - 2y
Add 14 on both sides of the equation, and we get
6y - 14 + 14 = 10 - 2y + 14
6y = - 2y + 24
Add 2y on both sides of the equation
6y + 2y = - 2y + 24 + 2y
simplifying the above equation, we get
8y = 24
y = 24/8
y = 3
Substitute the value of y in AC then we get
AC = 2(6(3) - 14)
= 2(4)
AC = 8
Therefore, the value of AC = 8.
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Evaluate 6(x-5) at x=8
Answer:
18
Step-by-step explanation:
Substitute x with 8 :
6(8-5) =
8-5 = 3
6(3) = 6 × 3 = 18
Therefore 18 is our final answer
Hope this helped and have a good day
Hey there!
6(x - 5)
= 6(8 - 5)
= 6(8) + 6(-5)
= 48 - 30
= 18
OR EVEN:
6(x - 5)
= 6(8 - 5)
= 6(3)
= 18
18 = 18
Therefore, your answer should be:
18
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A. Solves each equation by extracting square root.
1.) x² = 16
2.) x² = 49
3.) x² = 128
4.) x² = 108
5.) x² = 121
6.) x²-169 = 0
7.) x²-80=0
8.) x²-63=0
9.) 5x2 – 125 = 0
10.) 3x²-132-0
1,2,5 square root both sides
47simplify into 8 root 2simplify into 6 root 311add 169 to both sides and square root to get 13add 80 to both sides and simplify into 4 root 5add 63 to both sides and simplify into 3 root 7add 125 to both sides, divide both sides by 5, x^2=25, square root, x=5add 132 to both sides, divide by 3, x^2=44, square root simplified is 2 root 11
Find the coordinates of point P on →AB that partitions the segment into the given ratio AP to PB .
a. A(0,0), B(0,6), 2 to 1
The point P which partitions the line segment AB have coordinates as P(0,3)
Line Segment is a line which joins together two points to form a straight line. It can be extended in either side.
It is given that,
A line segment AB having coordinates such as A(0,0) and B(0,6) respectively
The line segment AB is partitioned by a given point P in two minor line segments AP and PB
We need to find, the coordinates of the partitioning point i.e. P
The given formula will be used,
The coordinates of the point P = ([tex]\frac{x1+x2}{2}[/tex], [tex]\frac{y1 + y2}{2}[/tex])
Now, x1 = 0, x2 = 0, y1 = 0, y2 = 6
Putting values in the formula, we get
([tex]\frac{0+0}{2}[/tex], [tex]\frac{0+6}{2}[/tex])
(0,3)
Hence, the point P which partitions the line segment AB have coordinates as P(0,3)
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Here is a distribution of quiz scores for a statistics course: 87, 91, 74, 73, 80, 84, 68, 75 what is the standard deviation?
The standard deviation is 7.35.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79
Determine the difference between each value and the mean and then square the result:
(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)² + (84- 79)² + (68 - 79)² +( 75- 79) ²
64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432
Determine the mean of the sum of the squared differences and then find the square root of the mean:
√432 / 8 = 7.35
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Use this activity to explain how the AA criterion for triangle similarity follows from the definition of similarity in terms of dilations. (Hint: Use parallel lines)
The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.
What is a triangle similarity criterion?
According to the Angle-Angle (AA) criterion, two triangles are considered comparable if "two angles of one triangle are respectively equivalent to two angles of another triangle."
What distinguishes AA similarity from AAA similarity?
The total number of angles in a triangle is 180. Therefore, the third angle of a triangle will automatically become equal if two of its angles are equal. Triangles are related because of the AA resemblance. Three angles should equal the other triangle in AAA.Learn more about Angle-Angle-Side (AAS)
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What are the solutions of the quadratic equation x²-20=8 x ?
F. 2,10
G. 20,1
H. -1,20
J. -2,10
The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
The given quadratic equation is [tex]x^{2}[/tex] - 20 = 8 x . To get the solutions of the given quadratic equation we need to simplify the quadratic equation. The step wise simplification of the given quadratic equation is,
[tex]x^{2}[/tex] - 20 = 8 x
[tex]x^{2}[/tex] - 8x -20 =0
on breaking -8x in two parts as -10x + 2x , we will get
[tex]x^{2}[/tex] -10x + 2x -20 = 0
x (x - 10) + 2 (x - 10) = 0
On taking (x-10) as common, we get
(x-10) (x+2) = 0
x = -2 , 10
The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
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What is the sum of the solutions of |3|y-4| = 9 and |y-4|=3 ?
The sum of the solutions are 32/3.
The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.
Example: 100 mod 9 equals 1
Because 100/9 = 11 with a remainder of 1
Another example: 14 mod 12 equals 2
Because 14/12 = 1 with a remainder of 2
12-hour time uses modulo 12 (14 o'clock becomes 2 o'clock)
It is where we end up, not how many times around.
|3y-4|=9
3y-4=9 or 3y-4=-9
3y=13 or 3y=-5
y=13/3 or y-5/3
|y-4|=3
y-4=3 or y-4=-3
y=7 or y=1
The solutions are y=13/3, y=-5/3, y=7, y=1
Hence the sum of the solutions are 32/3.
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If mA = 29° and m/B= 29°, then mZA = m/B represents the property of what?
The statement, m∠A ≅ m∠B, represents the congruence property.
What is the Congruency Property of Equality?The congruency property of equality states that if two angles have measures that are equal to each other, then both angles are said to be congruent to each other.
Given that:
The measure of angle A = 29 degrees
The measure of angle B = 29 degrees.
Since both angles have the same measure, then both angles are congruent to each other.
Therefore, the statement, m∠A ≅ m∠B, represents the congruence property.
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−
6
x
−
4
≤
2
(
x
−
10
)
Answer:
x > 2
Step-by-step explanation:
because , you have to use inverse operation to check your answer .
-6x-4< 2x-20
-6x-4+4<2x-20=4
-6x<2x-16
-6x-2x<2x-16-2x
-8x<-16
(-8x)(-1)>(-16)(-1)
8x>16
8x/8 > 16/8
x>2
what number is the square root of 78 in between of
Answer:
the square root rounded up is around 8
Step-by-step explanation:
because if the 5 is not beside the number it rounds down and the number was 3 so its 8
Simplify each expression.
-35 / (-5)
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
The simplified expression of -35 / (-5) is 7.
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Let the given expression be -35 / (-5) then
-35 / (-5) = -35/-5
simplifying the above equation, we get
= 35/5
= 7
Therefore, the value of -35 / (-5) is 7.
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Complete the square. x² -5 x+ ____
The full quadratic expression is expressed as follows:
x² - 5x + 6.25
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:
(a - b)² = a² - 2ab + b²
x² - 5x + ?
x² = a²5x = 2abb = ?5x = 2xb
2b =5
b = 5/2
Let's complete the square
x² - 5x + (5/2)²
x² - 5x + 25/4
x² - 5x + 6.25
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