Answer:
True.
Step-by-step explanation:
The sum of two rational numbers is rational.
By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rational numbers produces another rational number.
it is given that 2/3, 8/d and n/39 are equivalent fractions. find the value of d and the value of n
Answer:
d = 12 and n = 26
Step-by-step explanation:
Given that the fractions are equivalent then
[tex]\frac{2}{3}[/tex] = [tex]\frac{8}{d}[/tex] ( cross- multiply )
2d = 24 ( divide both sides by 2 )
d = 12
--------------------------------------
and
[tex]\frac{2}{3}[/tex] = [tex]\frac{n}{39}[/tex] ( cross- multiply )
3n = 78 ( divide both sides by 3 )
n = 26
The fractions represent the same amount or value given that they are
equivalent.
The value of d is 12The value of n is 26Reasons:
Equivalent fractions are fractions that have equal values, therefore;
[tex]\displaystyle \frac{2}{3} = \frac{8}{d} =\frac{n}{39}[/tex]
Which by cross multiplying gives;
2 × d = 8 × 3 = 24
Therefore;
[tex]\displaystyle d = \frac{24}{2} = \mathbf{12}[/tex]
d = 12
Similarly, we have;
[tex]\displaystyle \frac{2}{3} =\frac{n}{39}= \frac{8}{d}[/tex]
Which gives;
2 × 39 = 3 × n
Therefore;
[tex]\displaystyle n = \frac{2 \times 39}{3} = \mathbf{26}[/tex]
n = 26
Learn more about equivalent fractions here:
https://brainly.com/question/13489708
Given the graph below, which of the following statements is true? On a coordinate plane, a graph shows an image with three connected lines. The first line has a negative slope and goes from (negative 5, 6) to (negative 2, 0), the second line has a positive slope and goes from (negative 2, 0) to (2, 2), and the third line has a negative slope going from (2, 2) through (4, negative 2). The graph represents a one-to-one function because every x-value is paired with only one y-value. The graph represents a one-to-one function because it is defined for all x-values. The graph does not represent a one-to-one function because it does not pass through the origin. The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
Answer:
The correct option is (D).
Step-by-step explanation:
A one-to-one function can be defined such the every value of x corresponds to exactly one value of y.
That is:
x₁ → y₁
x₂ → y₂
x₃ → y₃
.
.
.
and so on.
Consider the graph.
From the graph it can be seen that for y = 0 and y = 2 there are multiple x coordinates.
So, the graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
According to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.
Given :
On a coordinate plane, a graph shows an image with three connected lines. The first line has a negative slope and goes from (-5, 6) to (-2, 0).The second line has a positive slope and goes from (-2, 0) to (2, 2).The third line has a negative slope going from (2, 2) through (4, -2).Draw the graph of the three lines in order to determine the function is one-one function or not.
The equation of the line passing through (-5,6) and (-2,0) is given by:
[tex]\dfrac{y-6}{x+5}=\dfrac{0-6}{-2+5}[/tex]
[tex]\dfrac{y-6}{x+5}=\dfrac{-6}{3}[/tex]
[tex]y-6=-2(x+5)[/tex]
y + 2x + 4 = 0 --- (1)
The equation of the line passing through (-2,0) and (2,2) is given by:
[tex]\dfrac{y-0}{x+2}=\dfrac{2-0}{2+2}[/tex]
2y = x + 2 ---- (2)
The equation of the line passing through (2,2) and (4,-2) is given by:
[tex]\dfrac{y-2}{x-2}=\dfrac{-2-2}{4-2}[/tex]
y - 2 = -2(x - 2)
y + 2x = 6 ---- (3)
Now, with the help of these three equations, the graph of the three lines can be plotted. The Graph is attached below.
So, according to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.
Therefore, the correct option is D).
For more information, refer to the link given below:
https://brainly.com/question/12465796
Simplify to create an equivalent expression. 8−4(−x+5) Choose 1 answer: A 4x−12 B −4x−12 C 4x+13 D 4x+5
Answer:
A (4x-12)
Step-by-step explanation:
Still think of PEMDAS: 8-4(-x=5)
a) Multiply -4(-x + 5)
* -4(-x) = 4x (remember a neg x neg = pos)
* -4(5) = - 20
b) Now it reads = 8 +4x - 20
c) put all like terms together
* 8 - 20 = -12
A cylindrical water bottle with a height of 21 cm and diameter 6.5 cm is fully filled with water. Kelvin wants to pour all the water in the bottle into a cubic container. State thr minimum leght, to the nearest cm, the side of the cube.
Answer:
9 cm
Step-by-step explanation:
First, we need to find the volume of the cylindrical water bottle. The volume of a cylinder is πr²h where r = radius and h = height. In this case, r = diameter / 2 = 6.5 / 2 = 3.25 and h = 21 so the volume is π * 3.25² * 21 = 221.8125π ≈ 696.84. Let's call the length of the cubic container s. The volume of the cube (which is s³) must be at least the volume of the water bottle, therefore:
s³ ≥ 696.84
∛s³ ≥ ∛696.84
s ≥ 8.86566
The smallest integer value that satisfies this is 9 cm.
What is the range of the function represented by the table?
Answer:
The second option
Step-by-step explanation:
the range is all the y vaules
divide 68 into two parts so that the larger number exeed the smaller one by 6
Answer:
31, 37
Step-by-step explanation:
Let the smaller number be x
Therefore, longer number = x + 6
According to the given information:
x + x + 6 = 68
2x + 6 = 68
2x = 68 - 6
2x = 62
x = 62/2
x = 31
x + 6 = 31 + 6 = 37
Thus, the two parts of 68 are 31 and 37.
There are 10 blue marbles, 4 black marbles, 5 white marbles, and 6 red marbles in a box. If two marbles are drawn at random without replacement, what is the probability that both marbles removed are not blue?
Answer:
7/20
Step-by-step explanation:
10 blue marbles, 4 black marbles, 5 white marbles, and 6 red marbles = 25 marbles
25-10 = 15
There are 15 not blue marbles
P( not blue ) = not blue marbles / total = 15/25 = 3/5
keep the not blue marble
25-1 = 24 marbles left
15-1 = 14 not blue marbles
P( not blue ) = not blue marbles / total = 14/24 = 7/12
P( not blue, keep, not blue) = 3/5 * 7/12 = 21/60 = 7/20
Answer:
7/20
Step-by-step explanation:
10(blue) + 4(black) + 5(white) + 6(red) = 25(total)
25(total)-10(blue)=15(not blue)
not blue/all = 15/25 = 3/5 = probability that first marble removed are not blue
If we remove 1 marble;
25-1 = 24 (total) , 15-1=14(not blue)
second not blue/all = 14/24 = 7/12 = probability that second marble removed are not blue
probability that both marbles removed are not blue : 3/5. 7/12 = 21/60
21/60 = 7/20
Hope this helps ^-^
How do i solve this question?
Answer & step-by-step explanation:
A hot dog cart charges exactly $0.50 per hot dog. If the equation t=kh represents the total amount a customer is charged, t, for purchasing h hot dogs, what is the value of k?
Answer:
$0.50
Step-by-step explanation:
According to the information given, in the equation t=kh, t is the total amount a customer is charged and h is the amount of hot dogs purchased. So, to be able to get the total amount a customer is charged you have to multiply the amount of goods bought by the price of each good. Because of that, K would be the price per hot dog which is $0.50.
What is the simplest form of (4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x + 9)
Simplest form:
7 x^3 − 5 x^2 + x + 2
The wire supporting a 20-foot tall phone pole is attached to the top of the pole, and to the
ground 12 feet from the pole. How long is the wire?
Answer:
22.36 feet
Step-by-step explanation:
This situation forms a right triangle, where the wire is the hypotenuse
Use the pythagorean theorem to find the hypotenuse/wire length:
a² + b² = c²
20² + 12² = c²
400 + 144 = c²
544 = c²
22.36 = c
So, the wire is 22.36 feet long
what are the solutions of |3x + 2| >9?
Answer
-11/3>x>7/3
Step-by-step explanation:
|3*7/3+2|=9
|7+2|=9
|9|=9
9=9
therefore, x must be > 7/3
|3*-11/3+2|=9
|-11+2|=9
|-9|=9
9=9
therefore, x must be < -11/3
Joe’s boat rental rents paddle boats for $8.00 and the paddles rent for $5.00 for the day. If David has $45, what is the least amount of hours he could rent the paddle boat
Answer:
Well i haven't found the hours out because the problem doesn't specify how many hours you can rent the boat for. I did do the math and you can rent the boat and the paddles for 13 dollars. This means that David can rent the boat for 3 days and he will have 6 dollars left over. I hope this helped you.
Which of the following does NOT demonstrate a physical property of matter? A Salt and water combine to form a solution of salt water B Chocolate melts when it's left in the warm sun. C Batter changes to become cake when it is baked. D Water changes to water vapor when it reaches the boiling point
Answer:
b:chockelet
Step-by-step explanation:
Express the following in the usual form
(a) 6.25×10-⁵
Answer:
0.0000625
Step-by-step explanation:
[tex]10^{-5}=0.00001[/tex]
[tex]6.25*10^{-5}=6.25*0.00001=0.0000625[/tex]
Answer:
So we need to express [tex]6.25 * 10^{-5}[/tex].
What is being used here is scientific notation, and when the exponent is negative, that means the number is less than 1.
As the exponent is -5, we have to move the coma 5 positions to the left (if it was positive we would have done that put to the right), so:
[tex]6.25 * 10^{-5}=0.0000625[/tex]
If you don't understand what does it mean to move the coma to the left, see this example to understand it:
We move it one time from 6.25 --> 0.625
We move it two times from 6.25 --> 0.0625
We move it three times from 6.25 --> 0.00625
We move it four time from 6.25 --> 0.000625
What we are doing is adding 0 to the left and if the exponent was positive, we would add 0 to teh right.
So now we know that [tex]\boxed{6.25 * 10^{-5}=0.0000625}[/tex]
What is the equation of the line that passes through the point (-8,5) and has a slope of -1/4
Step-by-step explanation:
Using slope intercept for y = mx + b, substitute m = - 1/4, and (-8, 5) in for (x, y) to find the y-intercept
1
Spoints
Which is the image of vertex O after the triangle has been rotated 90 degrees counterclockwise about the origin?
6+
5
3
2
L
2
3
-653 -2.1
s! S6
o
w
s
.67
0 -1.2)
Answer:
(2, - 1 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , thus
O(- 1, - 2 ) → (2, - 1 )
The function f(x) = 4x + 30 represents the length of a rectangle. The function g(x) = x - 1 represents the width of the rectangle. Use (fºg)
(5) to determine the area of the rectangle.
04
46
O 50
O 200
Answer:
The answer is 46Step-by-step explanation:
f(x) = 4x + 30
g(x) = x - 1
In order to find (fºg)(5) first find ( f • g)(x)
To find ( f • g)(x) substitute g(x) into f(x) that's for every x in f (x) replace it with g(x)
So we have
( f • g)(x) = 4(x -1) + 30
= 4x - 4 + 30
( f • g)(x) = 4x + 26
To find (fºg)(5) substitute the value of x that's 5 into (f • g)(x)
That's
(fºg)(5) = 4(5) + 26
= 20 + 26
We have the final answer as
(fºg)(5) = 46Hope this helps you
Answer:
46
Step-by-step explanation:
Every month, Rachel gets a basic salary of $4000. He also get a bonus of $200 for each policy she sells and a bonus of $50 for each client’s complaint she resolves. Write an expression for her total salary for a month if she sells n policies and resolves x complaints.
Answer:
200n+50x+4000=Total Salary
Step-by-step explanation:
Identify the type of conic section that is represented by the equation y^2- 1 = 4(x-7). DUE IN 2 HOURS, will give BRAINLIEST! A. Circle B. Hyperbola C. Parabola D. Ellipse
Answer:
Solution : Parabola
Step-by-step explanation:
As you can see only one variable is square in this situation, so it can only be a parabola. We can prove that it is a parabola however by converting it into standard form (x - h)^2 + (y - k)^2.
[tex]y^2-1=4\left(x-7\right) = y^2-1=4\left(x-7\right)[/tex]
Respectively it's properties would be as follows,
[tex]\left(h,\:k\right)=\left(\frac{27}{4},\:0\right),\:p=1[/tex]
Under what operation are the set of integers closed? Explain your answer
Answer:
a set of integers is closed under addition, subtraction, and multiplication because when you add, subtract, or multiply any integers, the result is always an integer.
Step-by-step explanation:
Plz help ASAP WILL MARK YOU BRAINLIST IF UR ANSWER IS CORRECT Question #3
Answer: D
Step-by-step explanation:
A is a function because all quadratics are functions because it shows the graph of a parabola.
B is also a function because it is a quadratic equation
C is a function because it is a linear function
D which I don't know about doesn't looks like it represent a function.
Please help
the value -2 is lower bound for the zeros of the function below
f(x)=4x^3-12x^2-x+15
True or False
Answer:
False
Step-by-step explanation:
f(x)=4x^3-12x^2-x+15
Using synthetic division
-2 4 -12 -1 15
-8 40 -78
--------------------------
4 -20 39 -63
Since this is not zero, this is not a lower bound
Answer:
[tex]\Large \boxed{\mathrm{False}}[/tex]
Step-by-step explanation:
[tex]\sf f(x)=4x^3-12x^2-x+15[/tex]
The zeros of the function is the values at which the function crosses the x-axis.
The value -2 is not a lower bound for the zeros of the function.
(-12a^3b^5)/(4a^2b^7)
state any restrictions on the variable(s) if they exist.
PLEASE HELP (30 points)
Answer:
[tex]a\neq 0 \text{ and } b\neq 0[/tex]
Step-by-step explanation:
So we have the rational expression:
[tex]\frac{-12a^3b^5}{4a^2b^7}[/tex]
In rational expressions, the restrictions of the expression would be the zeros of the denominator Therefore, set the denominator equal to zero and solve for its zeros:
[tex]4a^2b^7=0[/tex]
Zero Product Property:
[tex]4a^2=0\text{ or } b^7=0\\[/tex]
Solve for a and b:
[tex]4a^2=0 \text{ or } b^7=0\\a\neq 0 \text{ or }b\neq 0[/tex]
Therefore, the restrictions on the variables are that a and b cannot equal zero.
HELP I NEED AN EXPLANATION IM CONFUSED |3x|>-12 is x>−4 or x<4 but I dont know how that is. I thought it was no solution.. can someone explain.
Answer:
see below (I hope this helps!)
Step-by-step explanation:
|3x| > -12
There are two cases, x is either positive (in which |3x| = 3x) or negative (in which |3x| = -3x). Therefore:
3x > -12 or -3x > -12
x > -4 or x < 4 (Remember, multiplying / dividing an inequality by a negative number flips the sign.)
Answer:
All real numbers.
Step-by-step explanation:
So we have the equation:
[tex]|3x|>-12[/tex]
Remove the absolute value bars. Definition of absolute value:
[tex]3x>(-12)\text{ or } 3x<-(-12)[/tex]
Note that we change the sign on the right because we multiplied by a negative.
Divide both sides by 3:
[tex]x>-4\text{ or }x<4[/tex]
Now, look at this inequality. This says that the solution is all the numbers to the right of -4 and all numbers to the left of 4.
I've provided a number line. The red line represents x>-4 and the blue line represents x<4.
As you can see, every value is covered both towards the left and the right.
In other words, our answer is all real numbers.
28 POINTS HELP MEA pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution
Kono divides The numerator and the denominator of 4872 by the greatest common factor to simplify the fraction in one step by what number does he divide
Complete question:
Kono divides The numerator and the denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step by what number does he divide
Answer:
2/3
Step-by-step explanation:
Given the number : 48 / 72
Obtain the greatest common factor of 48 and 72
- - - - 48 - - - - 72
- 2-- 24 - - - - 36
- 2 - 12 - - - - - 18
- 2 - 6 - - - - - - 9
- 3 - 2 - - - - - - 3
The greatest common factor of 48 and 72 is hence (2 * 2 * 2 * 3) = 24
Hence, divide both the numerator and denominator by 24 ;
Numerator = 48/24 = 2
Denominator = 72 / 24 = 3
= 2/3
4p - 3(p + 5) = 3p - 17
Answer:
p=1
Step-by-step explanation:
4p - 3(p + 5) = 3p - 17
Distribute
4p -3p -15 = 3p -17
Combine like terms
p -15 = 3p -17
subtract p from each side
p-p -15 = 3p -17-p
-15 = 2p -17
Add 17 to each side
-15+17 = 2p -17+17
2 = 2p
Divide by 2
2/2 = 2p/2
1 =p
Answer:
Need points! Give brainliest! (a useless mod deleted all my answers for no reason)
Step-by-step explanation:
4p -3p-15 = 3p-17
2 = 2p
p = 1
What is the area of the figure composed of a parallelogram, a square and a rectangle ?
Answer : The area of the figure composed of a parallelogram, a square and a rectangle is 126 in².
Step-by-step explanation :
Area of composed figure = Area of parallelogram + Area of square + Area of rectangle
First we have to calculate the area of parallelogram.
Area of parallelogram = Base × Height
Given:
Base = 10 in
Height = 3.5 in
Area of parallelogram = 10 in × 3.5 in
Area of parallelogram = 35 in²
Now we have to calculate the area of square.
Area of square = (Side)²
Given:
Side = 4 in
Area of square = (4 in)²
Area of square = 16 in²
Now we have to calculate the area of rectangle.
Area of rectangle = Length × Breadth
Given:
Length = 12.5 in
Breadth = 6 in
Area of rectangle = 12.5 in × 6 in
Area of rectangle = 75 in²
Now we have to calculate the composed figure.
Area of composed figure = Area of parallelogram + Area of square + Area of rectangle
Area of composed figure = 35 in² + 16 in² + 75 in²
Area of composed figure = 126 in²
Therefore, the area of the figure composed of a parallelogram, a square and a rectangle is 126 in².
The area of the given figure is 126in²
Composite figuresThe given figure is a composite figure composed of a parallelogram, a square and a rectangle.
Get the area of the square
Area = L²
Area of the square = 4² = 16in²
Area of the rectangle = 6 * 12.5
Area of the rectangle = 75in²
For the parallelogram:
Area of the parallelogram = Base * Height
Area of the parallelogram = 10 * 3.5
Area of the parallelogram = 35 in²
Area of the figure = 75in² + 35in² + 16in²
Area of the figure = 126in²
Hence the area of the figure is 126in²
Learn more on area of composite figures here: https://brainly.com/question/10254615
Which pairs of angles in the figure below are vertical angles?
Answer:
m∠BTD and m∠ATP
m∠ATN and m∠RTD
Answer:
ATN & RTD, BTD& ATP
Step-by-step explanation:
To find out which pairs of angles are vertical in the picture let's define it first
Vertical Angles: Opposite Angles
It can't be the first one because the angle vertical to RTP is BTN
ATN & RTD
It isn't the third option since the angle opposite to DTN is RTA
BTD& ATP