-6.75 is a rational number.
Let us understand about natural, whole, integer, rational, and irrational numbers one by one.
Natural number:
Natural numbers are numbers that start from 1 and end at infinity. These are non-negative numbers.
Whole number:
Whole numbers are numbers that start from 0 and end at infinity.
We can also natural numbers including 0 is known as whole numbers.
These are non-negative numbers.
Integer:
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Rational number:
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Also, the decimal representation of the rational number is terminating and recurring.
Irrational number:
An irrational number is a number that can not be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Also, the decimal representation of the irrational number is non-terminating and non-recurring.
The given number is -6.75.
The decimal form is terminating.
So, it is a rational number.
Thus, -6.75 is a rational number.
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find the product(x+2)(y^2+2y-12)
Answer::
[tex]=xy^2+2xy-12x+2y^2+4y-24[/tex]Explanation:
Given the expression:
[tex]\mleft(x+2\mright)\mleft(y^2+2y-12\mright)[/tex]First, distribute the left bracket:
[tex]=x\mleft(y^2+2y-12\mright)+2\mleft(y^2+2y-12\mright)[/tex]Next, open the bracket:
[tex]=xy^2+2xy-12x+2y^2+4y-24[/tex]What are the all the expressions that are equivalent to 3 3/4
Exit Ticket : Submit on Schoology Write an equations that represents the proportional relationship between the time in class x and the number of pages y. Hotebo... Create a table & graph to represent the proportional relationship. 5/29/21 Liana takes 2 pages of notes during each hour of class.
Given that;
Liana takes 2 pages of notes during each hour of class.
To write a proportional relationship, let x represent the time in class and y represent the number of pages.
[tex]y=kx[/tex]according to the question, the constant of proportionality is equal to 2. ( 2 pages per hour).
So, the equation becomes;
[tex]y=2x[/tex]Therefore, an equation to represent the proportional relationship is;
[tex]y=2x[/tex]We can represent the equation on the graph as;
We can also represent it on the table as;
[tex]\begin{gathered} x\text{ y} \\ 1\text{ 2} \\ 2\text{ 4} \\ 3\text{ 6} \\ 4\text{ 8} \\ 5\text{ 10} \end{gathered}[/tex]Where x is in hours and y is in pages.
3. In the figure below, XU is the midsegment of TVW and is parallel to VW, determine the length of XU. (3 points) 11x + 2 U 10x + 16
If XU is the midsegment of TVW, then, it is necessary that:
(11x + 2)/(10x + 16) = 1/2
multiply the previous equation by 10x + 16:
11x + 2 = 1/2(10x + 16)
11x + 2 = 5x + 8 subtract 5x and 2 both sides
11x - 5x = 8 - 2
6x = 6
x = 6/6
x = 1
THe length of XU is:
XU = 11x + 2 = 11(1) + 2
XU = 13
JJ decides to leave a tip that is 15% of the original price for his meal. How much should he leave as tip for the $5.50 cheeseburger and $2.50 milkshake? Express your answer to the hundredths place.
JJ should leave $1.20 as a tip for the meal.
What is a tip?Gifts or amounts offered for services provided or expected.Below are some of the most common ways to calculate a tip:Method 1: Hover over the decimal point on your bill total and double the number.Method 2: Double the tax amount on the invoice.Method 3: Double the Input Tax Invoice, then shift the decimal point by one place.Some places add a tip to the bill, so check your bill carefully.For waiters in sit-down restaurants, the tip is 15-20% of the bill before tax.
According to the question:
Tip = 15% of the original priceTip = 15 % × $8Tip = $1.20Therefore, JJ should leave $1.20 as a tip for the meal.
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Find the equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)
Solution
Since it is a perpendicular bisector, hence point M is the midpoint
[tex]\begin{gathered} \therefore Mid\text{ point AB}=(\frac{-2+5}{2},\frac{7+2}{2}) \\ mid\text{ point=(}\frac{3}{2},\frac{9}{2}) \end{gathered}[/tex]Slope
[tex]\text{Slope (m)=}\frac{2-7}{5--2}=-\frac{5}{7}[/tex]Since they are perpendicular
[tex]\begin{gathered} m_1\times m_2=-1 \\ -\frac{5}{7}\times m_2=-1 \\ m_2=\frac{7}{5} \end{gathered}[/tex]The equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)
[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-5=\frac{7}{5}(x-2) \\ y-5=\frac{7}{5}x-\frac{14}{5} \\ y=\frac{7}{5}x-\frac{14}{5}+5 \\ y=\frac{7}{5}x+\frac{11}{5} \end{gathered}[/tex]The final answer
[tex]y=\frac{7}{5}x+\frac{11}{5}[/tex]I need help with this problem. the answer i got was that there is no solution. is that correct?
Explanation:
To solve the equations by Elimination we can multiply the first equation by -2.5 as follows:
[tex]\begin{gathered} (2x+8y=6)\cdot(-2.5) \\ -2.5\cdot2x-2.5\cdot8y=-2.5\cdot6 \\ -5x-20y=-15 \end{gathered}[/tex]Now, we can add this equation to the second equation as follows:
- 5x - 20y = - 15
5x + 20y = 15
0 + 0 = 0
0 = 0
When we get 0=0, the system has infinite solutions
So, this system has solutions with the form:
(x, y) where 2x + 8y = 6
It also means that both equations, 2x + 8y = 6 and 5x + 20y = 15 are equivalent equations and the solutions of the first one are also the solutions of the second one.
Janelle plays on her community basketball team, the Raging Rabbits. During their big game against the Porcupines, the Rabbits score 35 points in the first half. They add to their score in the second half. In all, the Rabbits score 90 points. Use an equation for to find the number of points the Rabbits score in the second half.
Answer:
90-35=x 90-35=55
Step-by-step explanation:
To find your value of X, subtract your score of the first half from your total score.
Toby buys a new iPhone for a price of $599. What is the total amount his credit card is charged if the sales tax is 7%?
Answer:
$640.93
Step-by-step explanation:
Convert 7% into a decimal
7% = 0.07
Multiply that by $599 to get the sales tax
599(0.07) = $41.93
Add that with the $599
599 + 41.93
= $640.93Toby's credit card will get charged $640.93.
12. What is the slope using the following points?
(12, 4) and (14, 6)
m= 1
m= 2
m=-1
m= -1
m= 10/26
Answer:
hope it helps
Step-by-step explanation:
A rock is thrown vertically from the ground with a velocity of 28 meters per second, and it reaches a height of -5.2t2 + 28.6t + 4 after t seconds. How many seconds after the rock is thrown will it reach maximum height?
After 2.75 seconds of motion in the upward direction, the stone will reach maximum height.
What is the general equation of a parabola?The general equation of a parabola is given by y = a(x – h)² + k or
x = a(y – k)² + h. Here (h, k) denotes the vertex
We have a rock which is thrown vertically from the ground with a velocity of 28 meters per second, and it reaches a height of -5.2t² + 28.6t + 4 after t seconds.
We have -
y = - 5.2t² + 28.6t + 4
dy/dx = - 10.4t + 28.6
For maximum height -
dy/dx = 0
- 10.4t + 28.6 = 0
28.6 = 10.4t
t = 28.6/10.4
t = 2.75 seconds
Therefore, after 2.75 seconds of motion in the upward direction, the stone will reach maximum height.
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-3, -6, -12, -24,.... Next 3 2, 4, 8-12, -6, -3-48, -96, -192 -36, -48, -60
We can see that the ratio between consecutive numbers is
[tex]\frac{-6}{-3}=\frac{-12}{-6}=\frac{-24}{-12}=2[/tex]this means that, the nex number is
[tex]\begin{gathered} -24\cdot2=-48 \\ \text{and next} \\ -48\cdot2=-96 \\ \text{and finally} \\ -96\cdot2=-192 \end{gathered}[/tex]Hence, the answer is -48, -96, -192
Solve each system of equations by SUBSTITUTION. Clearly identify your solution.5x + 3y = 15) (x - 6y = 3
x = 3, y = 0
Explanation:5x + 3y = 15 ...equation 1
x - 6y = 3 ...equation 2
Using substitution method:
We can use any of the variables to work out the substitution method
let's make x the subject of formula in equation 2:
x - 6y = 3
x = 3 + 6y ...equation 3
Now we substitute 3+6y for x in equation 1:
5(3+6y) + 3y = 15
Expand the paranthesis:
15 + 30y + 3y = 15
collect like terms:
30y + 3y = 15 - 15
33y = 0
Divide both sides by 33:
33y/33 = 0/33
y = 0
We substitute 0 for y in any of the equation:
Using equation 2:
x - 6(0) = 3
x - 0 = 3
x = 3
Use the diagram below to find the area of the shaded sector
SOLUTION
We need to get the slopes of the lines A and B.
Slope of A considering the points (-4, 3) and (0, 0) which is at the origin, we have
[tex]\begin{gathered} m=\frac{0-3}{0-(-4)} \\ m=\frac{-3}{4} \\ m=-\frac{3}{4} \end{gathered}[/tex]Since line B is a horizontal line, the slope is 0.
angle between two slopes is given as
[tex]\begin{gathered} tan\theta=|\frac{m_2-m_1}{1+m_1m_2}| \\ where\text{ }\theta\text{ is the angle between them and } \\ m_1\text{ and m}_2\text{ are slopes of the line } \end{gathered}[/tex]So, we have
[tex]\begin{gathered} tan\theta=|\frac{m_2-m_1}{1+m_1m_2}| \\ tan\theta=|\frac{0-(-\frac{3}{4})}{1+0(-\frac{3}{4})}| \\ tan\theta=|\frac{\frac{3}{4}}{1}| \\ tan\theta=|\frac{3}{4}| \\ tan\theta=\frac{3}{4} \\ \theta=tan^{-1}\frac{3}{4} \\ \theta=36.86989 \\ \theta=36.87\degree \end{gathered}[/tex]Hence the angle between A and B is 36.87 degrees
Area of a sector is given as
[tex]A=\frac{\theta}{360\degree}\times\pi r^2[/tex]Note that the radius r is the length of line B, which is 5 units. So, the area becomes
[tex]\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ A=\frac{36.87}{360}\times\pi\times5^2 \\ A=8.04376\text{ units}^2 \end{gathered}[/tex]Hence the answer is 8.04 square units. The last option is the answer
i need help on this answer
The correlation coefficient "r" can take values from -1 to 1
If the correlation coefficient is less than zero, r < 0, the correlation will be considered negative.
If the correlation coefficient is greater than zero, r > 0. the correlation will be considered positive.
A correlation coefficient equal to zero, r = 0, then there is no correlation between both variables.
If the absolute value of the coefficient is less than 0.35: 0 < | r | < 0.35 → you can say that the correlation between the variables is weak or low.
If the absolute value of the coefficient is between 0.35 and 0.38: 0.35 < | r | 0.65 → you can say that the correlation between both variables is moderate.
If the absolute value of the coefficients is greater than 0.66: | r | > 0.66 → you can say that there is a strong/ high correlation between the variables.
If the absolute value of the coefficient is greater than 0.90: | r |>0.90 → You can conclude that the correlation between both variables is very high or marked.
To be able to classify the type of correlation, the first step is to calculate the correlation coefficient between both variables. You can do that manually using the formula:
[tex]r=\frac{\Sigma x_1x_2-\frac{(\Sigma x_1)(\Sigma x_2)}{n}}{\sqrt[]{\lbrack\Sigma x^2_1-\frac{(\Sigma x_1)^2}{n}\rbrack\lbrack\Sigma x^2_2-\frac{(\Sigma x_2)^2}{n}\rbrack}}[/tex]First, let's determine the sums
X₁: Height (in)
[tex]\begin{gathered} \Sigma x_1=20+30+40+40+70+90 \\ \Sigma x_1=290 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_1=20^2+30^2+40^2+40^2+70^2+90^2 \\ \Sigma x^2_1=17500 \end{gathered}[/tex]X₂: Length (in)
[tex]\begin{gathered} \Sigma x_2=18+16+15+16+9+4 \\ \Sigma x_2=78 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_2=18^2+16^2+15^2+16^2+9^2+4^2 \\ \Sigma x^2_2=1158 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x_1x_2=(20\cdot18)+(30\cdot16)+(40\cdot15)+(40\cdot16)+(70\cdot9)+(90\cdot4) \\ \Sigma x_1x_2=3070 \end{gathered}[/tex]There are 5 ordered pairs, so the sample size is n=6
Replace every value on the formula:
[tex]\begin{gathered} r=\frac{3070-\frac{290\cdot78}{6}}{\sqrt[]{\lbrack17500-\frac{290^2}{6}\rbrack\lbrack1158-\frac{78^2}{6}\rbrack}} \\ r=\frac{3070-3861}{\sqrt[]{3483.33\cdot144}} \\ r=-0.99 \\ \end{gathered}[/tex]The correlation coefficient is r= -0.99
→ r is a negative value, which means that the correlation between the height and length of the rectangles is negative
→ the absolute value of the coefficient is greater than 0.90; | r | =0.99, so the correlation between both variables can be considered as a strong correlation
You can say the there is a strong negative correlation between both variables (option F)
Factor the expression using the GCF.
60−36
Answer:
12
Step-by-step explanation:
12x3=36, 12x5=60 shazam
the lengths of the upper end lower bases of a trapezoid are 6 centimeters and 10 centimeters respectively, and the distance between them is 15 centimeters. what is the area of the trapezoid
Given data:
The upper end length of the trapezoid is: a=6 cm
The lower end length of the trapezoid is: b=10 cm
The height of the trapezoid is: h=15 cm
The expression to calculate the area of the trapezoid is,
[tex]A=\frac{1}{2}\times h\times(a+b)[/tex]Substitute vall known values in the above expression.
[tex]\begin{gathered} A=\frac{1}{2}\times15\times(6+10) \\ =\frac{1}{2}\times15\times16 \\ =\frac{240}{2} \\ =120cm^2 \end{gathered}[/tex]Thus, the area of the trapizoid is 120 square centi meter.
probe algebraically that. (2n+1)^2-(2n+1) is an even number.
(2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
How to simplify an expression?
Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When we combine like terms in an expression and, if necessary, solve all of the specified brackets, we are only left with unlike terms in the simplified expression that cannot be further reduced.
What is an even number?
An even number is any number that can be divided by 2 precisely. The last digit of an even number is always one of the following: 0, 2, 4, 6, or 8. Even numbers can include 2, 4, 6, 8, 10, 12, and 14. These are even numbers because they are simple to divide by two. It is important to remember that 2 is the smallest positive even natural number.
Given, the equation under consideration is y = (2n + 1)² - (2n + 1)
Upon simplifying and solving for y, we have:
y = (2n + 1)² - (2n + 1) = 4n² + 4n + 1 - 2n - 1 ⇒ y = 4n² + (4n - 2n) + (1 - 1)
⇒ y = 4n² + 2n + 0 ⇒ y = 2 (2n² + n) --(i)
On carefully analyzing (i), we can affirm that y is divisible by 2, thus confirming that (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
Therefore, (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
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I need help check the picture
The value that does not belong in the domain of the set is 7 and the value that does not belong in the range of the set is 10.
Given set of values:-
{(2,7), (8,12), (5,9), (10,15)}
Domain : {2,5,7,8,10}
Range: {7,9,10,12,15}
We have to determine the numbers which do not belong in the domain and range of the relation.
We know that in a set of values (x,y) , x is the part of the domain and y is the part of the range.
Hence, the domain of the relation is given by:-
{2,8,5,10}
The range of the relation is given by:-
{7,12,9,15}
Hence, 7 does not belong to the domain of the set and 10 does not belong to the range of the set.
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can someone turn 5x + 20y = 500 into slope intercept form
Answer:
y=-1/4x+25
Step-by-step explanation:
Answer: y=-1/4x + 25
Step-by-step explanation: If you don't understand how i got this remember the formula
y = mx + b
Good luck!
what is 95% of 40?part. ___ = ___. percentwhole. 100 percent
1) According to that table we can write:
40-------100
x-------95
100x = 40*95
x= 38
2) So filling in we have:
Cross multiplying it we can find that 38 is 95% of 40.
Jan takes her three children and two neighbor's childrento a matinee. All of the children are under age 13. Writan expression for the total cost of admission. Howmuch in all did Jan pay for admission?(Matinee: 3$)
There are 6 people going to the movie
Jan, her 3 children, 2 neighbor children
(1+3+2)
Each costs 3 dollars to get in
Total cost = number of people * cost
Total cost = (1+3+2) * 3
= 6*3
= 18
TIME REMAINING56:5412.Which points are reflections of each other across both axes?Ty24-2(-2.8) and (2. -8)(-7 -1) and (-7. 1)(5.-6) and (-5, -6)NelSubSave and ExitMark this and return
a point is reflected against both axes when the two signs of the point are opposite
for example the reflexion against both axes for the point(-2,8) is (2,-8)
among the options there is none that meets this condition
For each ordered pair, determine whether it is a solution to 4x + 5y = -13.
(-7,4)
(8,- 9)
(-1, -2)
(6, 3)
Is it a solution ?
Answer:
4x-5y=-13. 4x−5y=−13 4 x - 5 y = - 13.
Step-by-step explanation:
Step 1. Solve the equation for y y . Tap for more steps.
what is the slope of the line that passes through the points (-4,2) and (-5,0). answer in simplest form
The line which passes through (-4,2) and (-5,0) has a slope of 2.
Let,
[tex](x_{1},y_{1})[/tex] = (-4,2)
[tex](x_{2},y_{2})[/tex] = (-5,0)
If the points are equal to each other, their x-coordinates are equal to each other:
[tex]x_{1}[/tex]=-4
[tex]x_{2}[/tex]=-5
If the points are equal to each other, their y-coordinates are equal to each other:
[tex]y_{1}[/tex]=2
[tex]y_{2}[/tex]=0
The slope, m is the steepness of a line and it is measured as the ratio of the change in vertical distance, rise over the change in horizontal distance, run.
The slope of the line, m:
m = ([tex]y_{2}[/tex]-[tex]y_{1}[/tex])/([tex]x_{2}[/tex]-[tex]x_{1}[/tex])
m=(0-2)/(-5-(-4))
m=(-2)/(-1)
m=2
The slope of the line for the two points is 2.
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Enter the answer in the space provided.
Consider the figure.
142
68
N
Enter the measure of anglez, in degrees, in the space provided.
Step-by-step explanation:
as simple as it sounds, we need to do a few steps to actually get the result.
first the outer angle 142° and the corresponding inner angle in the triangle are a linear pair of angles, and together they have 180°.
so, the inner angle is 180 - 142 = 38°.
then, remember, the sum of all angles in a triangle is always 180°.
so, the third inner angle is 180 - 38 - 68 = 74°
now, this third inner angle is with z (the corresponding outer angle) again a linear pair (sum 180°).
so,
z = 180 - 74 = 106°
Im doing a practice assignment and im not the best at word problems Im not understanding the question
A sample statistic is is any quantity from the sample of a population.
We can see in the last option, that from the population (total of subjects of study) Kaisa, selected 84 of the total students. This fits in to the definition of sample statistic.
Thus, the correct option is the last one.
If cos B = 7/8, then what is the positive value of tan 1/2 B, in simplest radical formwith a rational denominator?
Let us use the rule of the double of the angle
Since
[tex]\cos B=2\cos ^2\frac{B}{2}-1[/tex]Substitute cos B by 7/8
[tex]\frac{7}{8}=2\cos ^2\frac{B}{2}-1[/tex]Add 1 to both sides
[tex]\begin{gathered} \frac{7}{8}+1=2\cos ^2\frac{B}{2}-1+1 \\ \frac{15}{8}=2\cos ^2\frac{B}{2} \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{\frac{15}{8}}{2}=\frac{2\cos ^2\frac{B}{2}}{2} \\ \frac{15}{16}=\cos ^2\frac{B}{2} \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{\frac{15}{16}}=\cos \frac{B}{2} \\ \cos \frac{B}{2}=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]let us find sin B
Since
[tex]\sin ^2\frac{B}{2}+\cos ^2\frac{B}{2}=1[/tex]Then
[tex]\sin ^2\frac{B}{2}+\frac{15}{16}=1[/tex]Subtract 15/16 from both sides
[tex]\begin{gathered} \sin ^2\frac{B}{2}+\frac{15}{16}-\frac{15}{16}=1-\frac{15}{16} \\ \sin ^2\frac{B}{2}=\frac{1}{16} \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sin \frac{B}{2}=\sqrt[]{\frac{1}{16}} \\ \sin \frac{B}{2}=\frac{1}{4} \end{gathered}[/tex]Since
[tex]\tan \frac{B}{2}=\frac{\sin \frac{B}{2}}{\cos \frac{B}{2}}[/tex]Then
[tex]\begin{gathered} \tan \frac{B}{2}=\frac{\frac{1}{4}}{\frac{\sqrt[]{15}}{4}} \\ \tan \frac{B}{2}=\frac{1}{\sqrt[]{15}} \end{gathered}[/tex]The value of tan(1/2 B) is
[tex]\frac{1}{\sqrt[]{15}}\times\frac{\sqrt[]{15}}{\sqrt[]{15}}=\frac{\sqrt[]{15}}{15}[/tex]Solve for x. Enter the solutions from least to greatest.
(x-7)²-25= 0
lesser =
greater x =
The values for the lesser and greatest are:
-14 and 0
Step 1: Define
(x + 7)² - 49 = 0
Step 2: Solve for x
Add 49 to both sides: (x + 7)² = 49
Square root both sides: x + 7 = ±7
Subtract 7 on both sides: x = -7 ± 7
Evaluate: x = -14, 0
Step 3: Check
Plug in x values into original equation to verify they are a solution.
x = -14
Substitute in x: (-14 + 7)² - 49 = 0
Add: (-7)² - 49 = 0
Exponents: 49 - 49 = 0
Subtract: 0 = 0
Here we see that 0 does indeed equal 0.
∴ x = -14 is a solution of the equation
x = 0
Substitute in x: (0 + 7)² - 49 = 0
Add: 7² - 49 = 0
Exponents: 49 - 49 = 0
Subtract: 0 = 0
Here we see that 0 does indeed equal 0.
∴ x = 0 is also a solution of the equation.
Hence we get the required answer.
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what 6y=3x-9, in the simplest form
Answer: x=2y+3
Step-by-step explanation:
Switch around the 6y
3x-9=6y
Add 9 to both sides
3x-9+9=6y+9
3x=6y+9
Divide everything by 3
x=2y+3