Answer:
121 is a rational number because it can be expressed as the quotient of two integers: 121/ 1
Step-by-step explanation:
The number 121 is not a irrational number
How to determine the type of the numberFrom the question, we have the following parameters that can be used in our computation:
The number 121
When evaluated, we have
The number 121 = 121
The above number is represented by the quotient of 2 integers
using the above as a guide, we have the following:
We can conclude that the number is a rational number
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the mean of the values in a data set is a. If each of the values in the data set were multiplied by 7, what would be the mean of the resulting data?
Answer:
Mean of resulting data = 7 times mean of original data=7a
Step-by-step explanation:
Given that all values in a data set are multiplied by 7. to find the mean of the new set.
Let {x1,x2....xn} be the original data set.
The mean of this data set a= [tex]\frac{x1+x2+...+xn}{n}[/tex]
Now multiply all values by 7
New data set
= {7x1, 7x2...7xn}
Sum of these = 7(x1+x2+..+xn) = 7 times sum of original data set
No of element = n for both the sets
Hence new mean = 7 * mean of original set.=7a
in other words, if the mean of the values in a data set is a. If each of the values in the data set were multiplied by 7, new mean would be 7a.
Answer:
It’s 7a
Step-by-step explanation:
Simplify the given expression below (1+2i) times (5-3i)
Answer:
11 + 7i
Step-by-step explanation:
(1 + 2i)(5 - 3i)
= 1(5 - 3i) + 2i(5 - 3i)
= 5 - 3i + 10i - 6i^2
Note i^2 = -1 So we have:-
5 + 7i + 6
= 11 + 7i (answer).
The expression (1+2i) times (5-3i) simplifies to -1 + 7i by using the distributive property for multiplication over addition and remembering that i squared equals -1.
Explanation:The expression (1+2i) times (5-3i) is a function of two complex numbers. To simplify this, you would use the distributive property for multiplication over addition.
The first step is to distribute each component of the first number against each component of the second number. (1 * 5 + 2i * -3i) + (1 * -3i + 2i * 5)
Next, we perform the multiplications and simplify, bearing in mind that i squared is -1. This gives us (5 - 6) + (-3i + 10i)
So the simplified expression is -1 + 7i.
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which of the following statements is true about the triangles below
Answer: SAS, Triangle JKN and LKM are congruent by SAS
Step-by-step explanation: Vertical angles are equal, so the triangles are congruent by SAS.
The given triangles congruent by SAS congruency . Option D is correct.
What are triangles?A 2 dimensional figure bounded by 3 sides is called a triangle. Sum of all the angles of the triangle in 180°.What are congruent triangles?Triangles having same shape and size are called congruent triangles.There are five types of congruencies, SAS, AAS, SSS, ASA, RHSWhat are vertically opposite angles?The angles opposite each other when two lines cross are called vertically opposite angles.
How to know which of the given statements is true about the triangles?Considering Δ JKN and Δ LKM
JK = LK (given)
∠JKN = ∠LKM (vertically opposite angles)
KN = KM (given)
So Δ JKN and Δ LKM are congruent by SAS congruency .
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what is 12 1/4 simplifying
Answer:
12.25 or 49/4
Step-by-step explanation:
12.25 is the decimal version because 1/4 is equal to 0.25 as a decimal and then add the 12 on.
13/4 is the improper fraction. To get an improper fraction, you multiply the main number (12) by the denominator (4) this gives you 48. Then, you have to add your numerator (1), leaving you with 49 over 4.
The value of the mixed fraction number 12 ¹/₄ will be 12.25.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The mixed fraction number is given below.
⇒ 12 ¹/₄
Convert the mixed fraction number into a decimal number. Then we have
⇒ 12 ¹/₄
⇒ 12 + ¹/₄
⇒ 12 + 0.25
⇒ 12.25
The value of the mixed fraction number 12 ¹/₄ will be 12.25.
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How do I order rational and irrational numbers from least to greatest
Answer: Rational numbers are any numbers that can be expressed by a fraction with integers in both the numerator and the denominator. The amount of time and paper it takes to put them into an increasing line depends on how many numbers there are and how big of a range they have.
1.Rewrite improper fractions
An improper fraction is a fraction with a bigger numerator than denominator. These numbers can be difficult to compare. For example, numbers such as 26/7, 31/9, 12/5, 8/3 and 22/13 do not have an obvious highest or lowest term. Rewrite improper fractions as mixed numbers or as numbers with decimals. To turn an improper fraction into a decimal, divide the numerator by the denominator. If the denominator is large or a prime number greater than five, use a calculator. For example, divide the numbers 26/7, 31/9, 12/5, 8/3 and 22/13 to create 3.71, 3.44, 2.4, 2.67 and 1.69.
2.Find the highest and lowest terms
Figure out where your number line starts and ends. Put the lowest term on the far left and the highest term on the far right. Remember, negative numbers are lower than positive numbers, and the greater a negative number's distance from zero, the lower it is.
3.Mark benchmark terms
Draw a line extending through your lowest and highest points. Figure out some major points between these values and mark them on your line. For example, if your lowest number is negative 25 and your highest number is 50, find where zero and 25 would be. Mark these as benchmarks or guides.
4.Fill in the remaining numbers
Using your guides, fill in the rest of the numbers. Start with the lowest values on the left and work your way up.
Rational and irrational numbers can be ordered from least to greatest by converting them into decimal forms. Once in decimal form, they can be compared and ordered just like regular real numbers.
Explanation:To order rational and irrational numbers from least to greatest, first you need to understand what these numbers are. Rational numbers are numbers that can be expressed as a ratio of two integers, while irrational numbers cannot be expressed as such ratio and their decimal expansions are non-repeating and non-terminating.
If you are given both rational and irrational numbers, you can start by converting all of the numbers to decimal form if they are not already. Then, you can simply order them from least to greatest, just like how you order regular real numbers.
For example, if you are given the numbers 3/2, √2, and 1. You would convert 3/2 to 1.5 and approximate √2 as 1.414. Then you would order them as 1 (1.0), √2 (1.414), and 3/2 (1.5).
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Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1
[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]
From Left side:
[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)[/tex]
[tex]\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}[/tex]
NOTE: sin²θ + cos²θ = 1
[tex]\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{2}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}[/tex]
[tex]\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}[/tex]
[tex]\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]
Left side = Right side so proof is complete
Answer:
\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}
From Left side:
\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)
\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}
NOTE: sin²θ + cos²θ = 1
\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}
\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}
\dfrac{2}{sin^2\theta-cos^2\theta}
\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}
\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}
\dfrac{2sec^2\theta}{tan^2\theta-1}
Left side = Right side so proof is complete
Step-by-step explanation:
43.586 to the nearest hundredth place
Answer: 43.59
Step-by-step explanation:
The hundredth place is two points after the decimal, so it is where the 8 is.
When the number to the right of it is 5 or higher you round it up.
Answer:
43.59
Step-by-step explanation:
tens ones . tenths hundredths thousandths
4 3 5 8 6
We want to round the 8 so we look at the 6.
Since 6>=5 we round the 8 up
43.59
Can you help me with numbers 14 and 15. Thank you!!!!
Answer:
14th answer is [tex]x=\sqrt{288} \\ x= -\sqrt{288}[/tex]
15th answer is [tex]xy^{2} \sqrt{5}[/tex]
Step-by-step explanation:
14)
triangle is a right triangle, the legs will have the same measure
let the legs be x
x^2 + x^2 = 24^2
2x^2 = 576
x^2 = 288
[tex]x=\sqrt{288} \\ x= -\sqrt{288}[/tex]
15)
[tex]area of the circle[/tex][tex]=\pi r^{2}[/tex]
[tex]5x^{2} y^{4} \pi =\pi r^{2} \\ r^{2} =5x^{2} y^{4} \\ r\sqrt{5x^{2} y^{4} } \\ r=\sqrt{5} xy^{2}[/tex]
Which of the following is necessary when proving that the opposite sides of a parallelogram are congruent
ANSWER:
To prove that opposite sides of a parallelogram are congruent, we have to prove that the quadrilateral is a parallelogram.
The ways to prove that a quadrilateral is a parallelogram include:
- a quadrilateral with parallel opposite sides
- a quadrilateral with congruent opposite angles
- a quadrilateral with diagonals that bisect each other
Answer:
alternate interior angles of congruent
opposite sides are parallel
Step-by-step explanation:
ap3x
Which of the following functions is graphed below?
Answer:
y = abs (x-5) -4
Step-by-step explanation:
We are shifting the absolute value function
f(x) = |x| to
g(x) = | x +h| + k
where h is a shift left if h > 0
right if h < 0
and k is a shift up if k> 0
down if k< 0
Since the graph is shifted down and to the right
k is <0 and h < 0
where k = -4 and h=-5
Of fabric costs $5.00 per yard, how much will 7/8 yards cost?
Answer: It would be $4.38
Step-by-step explanation: If you divide the $5 by .8 it will give you what 1/8 of it would be then you multiply it by 7 to get the 7/8 of it.
How do you say the number .0088?
I think it's Ten thousandths, zero eighty-eight.
I'm not too sure on this, but hopefully i helped you.
All of the following are equivalent except
4 · y
4 + y
4y
(4)(y)
Answer:
4+y
Step-by-step explanation:
4 · y
4 + y
4y
(4)(y)
All of these are multiplication except 4+y
What is the solution to the system of equations below?
y= -1/3x+6 and x = –6
(–6, 8)
(–6, 4)
(8, –6)
(4, –6)
Final answer:
The solution to the system of equations is (-6, 8), found by substituting x = -6 into the first equation and simplifying to find the value of y.
Explanation:
The solution to the system of equations y= -1/3x+6 and x = -6 can be found by substituting the value of x from the second equation into the first equation. Here's how it's done:
Substitute x into the first equation: y = -1/3(-6) + 6.
Simplify the equation: y = 2 + 6.
Add the numbers to find the value of y: y = 8.
Therefore, the solution to the system of equations is the point (-6, 8).
Try to determine how much money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickel on day three and so on. what type of process would you use?
Answer:
In a 28 day month 20 dollars and 30 cents
Step-by-step explanation:
1+2+3+4+5+6+7......
Answer*5=Cents
If cents equal to or greater than 100 than = dollar
$30 money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickels on day three, and so on.
What is arithmetic series?The arithmetic series is a series in which the numbers are in the order of some common difference. The difference between any two consecutive numbers is constant.
[tex]a_n = a_1 + (n -1)d[/tex]
you would be using a be using the [tex]a_n = a_1 + (n -1)d[/tex] meaning that it's the previous entry plus the different process.
[tex]a_n = a_1 + (n -1)d[/tex]
[tex]a_{30} = .05 + (30-1).05[/tex]
[tex]a_{30}[/tex] = $29.10
Thus, $30 money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickels on day three, and so on.
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700 – 35w = 450 + 15w
Answer:
5
Step-by-step explanation:
700-35w=450+15w
Subtract 15 from -35
700-50w=450
Subtract 700 from 450
-50w=-250
divide -250 by -50w
answer is 5
[tex]700-35w=450+15w\qquad\text{subtract 700 from both sides}\\\\-35w=-250+15w\qquad\text{subtract 15w from both sides}\\\\-50w=-250\qquad\text{divide both sides by (-50)}\\\\\boxed{w=5}[/tex]
Explain how you can use a table of values, an equation, and a graph to determine whether a function represents a proportional relationship.
Answer:
From the table: you have to have the same increment for the x values and the same increment for the y values. Doesn't have to be the same increment for both x and y values.
From an equation: the exponent of the x and y should be 1. The equation should be a line equation.
From a graph: the graph should be a continuous straight line.
Step-by-step explanation:
Below is a double bar graph indicating the number of left handed students and right handed students in Mr. Jude's class. The bar graph shows the results in terms of boys versus girls. Use the graph to determine the difference between the number of right handed and left handed students in Mr. Jude's class. Type a numerical answer
Answer:
13 more right handed students PLEASE GIVE BRAINLIEST
Step-by-step explanation:
left handed
3 boys + 4 girls = 7 left handed students
right handed
9 boys + 11 girls = 20 right handed students
20 - 7 = 13 more right handed students
Answer: 13 more right handed girls and boys.
Hope this helped and also please give brainlist really need it need 2 more if you do me as one only need one more and I need them before the end of toaday.
If (x)=x^2+2x-5. What is f(a+1)
Answer:
a^2+4a-2
Step-by-step explanation:
f(x)= x^2+2x-5
f(a+1) = (a+1)^2 + 2(a+1) -5
= a^2 + 2a + 1 + 2a +2 -5
=a^2+4a -2
on the first day of the month, john counted his money and found he had $28.35. since then l, he has revived an additional $17.26 from the jobs he does after school. how much money does he have now?
Answer:
$45.61
Step-by-step explanation:
1) On the first day of the month, John counted his money and found he had $28.35
2) He has received an additional $17.26
so
to find the total money he has now sum the two quantities
$28.35 + $17.26 = $45.61
therefore
the answer is
$45.61
4m4 - 8m3 - 7m) + (4m4 - 7m2 - 5m
Answer:
8m^4 -8m^3 -7m^2 -12 m
Step-by-step explanation:
(4m^4 - 8m^3 - 7m) + (4m^4 - 7m^2 - 5m)
I like to line them up vertically. I put 0 in the spots to keep them lined up
4m^4 - 8m^3 +0m^2 -7m
+4m^4 +0m^3 - 7m^2 - 5m
--------------------------------------------
8m^4 -8m^3 -7m^2 -12 m
[tex](4m^4-8m^3-7m)+(4m^4-7m^2-5m)\\\\=4m^4-8m^3-7m+4m^4-7m^2-5m\qquad\text{combine like terms}\\\\=(4m^4+4m^4)-8m^3-7m^2+(-7m-5m)\\\\=\boxed{8m^4-8m^3-7m^2-12m}[/tex]
Jack earns $50 for washing cars on the weekdays He makes an average of $4.25 in tips per hour right the function of Jacks earnings and solve
for how much you make after six hours
Answer:
Function: y= $4.25x + $50; After 6 hours: $25.50
Step-by-step explanation:
Answer:
Joe would make $75.50 after 6 hours.
Step-by-step explanation:
A function for this would be m = 50 + 4.25t. The $50 is the one time thing. We must multiply the tips by 6. 4.25 * 6 = 25.50. 50 + 25.50 is 75.50.
PLS I NEED HELP!!!!!
Amy’s room is 12 feet long X 10 feet wide. She plans to purchase carpet for the entire room. The carpet costs $25 per square meter. What will be the total cost of the new carpet to the nearest cent?
Calculate total area:
12 x 10 = 120 square feet
Convert square feet to square meters:
1 square foot = 0.0929 square meters
120 x 0.0929 = 11.1484 square meters
Total cost = 11.1484 x 25 = $278.71
Write the equation of a line in slope intercept form that has a slope of 6 and has a y-intercept of ½.
Answer:
y=[tex]6x+ \frac{1}{2}[/tex]
Step-by-step explanation:
m=6
yint=1/2
y=mx+b
when x=0 y=1/2
1/2=6(0)+b
b=1/2
y=[tex]6x+ \frac{1}{2}[/tex]
The equation of the line in slope-intercept form is y = 6x + 1/2, where the slope is 6 and the y-intercept is 1/2. The slope of 6 means that for every increase of 1 in the x-axis, the y-axis will increase by 6.
Explanation:The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is 6 and the y-intercept is 1/2, the equation of the line is y = 6x + 1/2.
The slope of 6 means that for every increase of 1 in the x-axis, the y-axis will increase by 6.
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Find the common ratio of the sequence. 3, 9, 27, 81, . . . 6 –6 3
Answer:
The common ratio is 3
Step-by-step explanation:
To determine the common ratio, we take the second term and divide by the first term
9/3 =3
To verify this we take the third term and divide by the second term
27/9 = 3
Select the two figures that are similar to the 5 by 5 figure that is shown.
Answer:
the blue and the pink
Step-by-step explanation:
help me hurry can someone these equations
f(x) + n - move the graph n units up
f(x) - n - move the graph n units down
n · f(x) - stretch by n in the y-direction
1/n · f(x) - compress by n in the y-direction
-------------------------------------------------------------------------
First:
[tex]A)\ y=x^2\\\\B)\ y=x^2-4\\\\C)\ y=x^2-2\\\\D)\ y=x^2+2\\\\E)\ y=x^2+4[/tex]
Second:
[tex]A)\ y=x^2\\\\K)\ y=4x^2\\\\L)\ y=2x^2\\\\M)\ y=\dfrac{1}{2}x^2\\\\N)\ y=\dfrac{1}{4}x^2[/tex]
Parallelogram ABCD has vertices at A(2,-3), B(8,-6), Cl14,-3), and D(8,0)
IF THE FOLLOWING STATEMENTS ARE TRUE, WHAT KIND OF PARALLELOGRAM IS THIS
The lengths of two consecutive sides are equal.
The slopes of two consecutive sides are not opposite reciprocals.
A) rectangle
B) square
C)rhombus
D) not enough info
Answer:
The correct option is C.
Step-by-step explanation:
The vertices of ABCD are A(2,-3), B(8,-6), C(14,-3), and D(8,0).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of sides are
[tex]AB=\sqrt{(8-2)^2+(-6+3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
[tex]BC=\sqrt{(14-8)^2+(-3+6)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
[tex]CD=\sqrt{(8-14)^2+(0-3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
[tex]AD=\sqrt{(8-2)^2+(0+3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]
Since length of all sides are equation therefore the given parallelogram cannot be a rectangle.
Slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of AB is
[tex]m_1=\frac{-6-(-3)}{8-2}=\frac{-3}{6}=\frac{-1}{2}[/tex]
Slope of BC is
[tex]m_2=\frac{-3-(-6)}{14-8}=\frac{3}{6}=\frac{1}{2}[/tex]
Since the slopes of two consecutive sides are not opposite reciprocals, therefore the given parallelogram is a rhombus. Option C is correct.
Find the coordinates of the midpoint of the segment whose endpoints are H(6,4) and K(2,8).
Answer:
The midpoint is (4,6)
Step-by-step explanation:
When we have 2 points, we can find the midpoint by using the formula
midpoint = (x1+x2)/2, (y1+y2)/2
= (6+2)/2, (4+8)/2
= (8/2), 12/2
= 4,6
the value of square root -9 is not -3 because ___
Final answer:
The square root of -9 is not -3 but 3i, indicating the need for complex numbers to describe the square root of negative numbers, with 'i' denoting the imaginary unit.
Explanation:
The value of the square root of -9 is not -3 because the square root operation defined for real numbers does not apply to negative numbers in the same way. Instead, when dealing with the square root of a negative number, we enter the realm of complex numbers.
A complex number is a combination of a real part and an imaginary part. The square root of -1 is defined as i, the imaginary unit. Therefore, the square root of -9 is correctly expressed as 3i, not -3. This is a critical distinction because the result provides a basis for complex arithmetic, expanding the scope of mathematical operations into the complex plane.
Complex numbers and imaginary numbers are fundamental in various fields of science and engineering, particularly in situations involving quadratic equations with no real roots or in the analysis of electrical circuits. Recognizing the utility of the imaginary unit, i, allows for solving equations that otherwise would not have solutions within the set of real numbers.