A triangular number succession is the representation of numbers as just an ordered set of equilateral triangles. The order of these numbers is 1, 3, and 6.
What exactly is meant by triangular numbers?A triangular number is one that may be written as the sum of a initial n positive integers.
A good example of a triangular number is 6, which may be written as 1+2+3 when the first three positive integers are added together.Triangular numbers make up a sequence if one considers the sum of the first positive integer as the initial element, the sum of the first two positive integers as the second element, and so on.If a number equals that sum of such initial n positive integers, then n denotes the position of that particular triangular number with in the series.Triangular numbers can be used to create equilateral triangles.The first 3 triangular numbers are therefore 1, 3, and 6.
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Find the unit rate.
130 feet in 6.5 seconds
Answer:
20 feet per second
Step-by-step explanation:
130/6.5 = 20
someone help please
Answer:
A to #4
B to #3
C to #1
D to #2
Step-by-step explanation:
A. 7 + 3² = 16
B. 5 - 2²=1
C. 2 · 2³ = 2^4
D. 3^4/3^1=27
Is 2 a zero of the polynomial x³ 4x² 3x?
2 is not a polynomial root of [tex]x^{3} + 4x^{2} + 3x[/tex] . A polynomial is an equation that employs addition, subtraction .
what is polynomial ?A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients that uses solely the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that employs addition, subtraction, multiplication, and division of numbers to combine variables, constants, and exponents (No division operation by a variable).
given
[tex]x^{3} + 4x^{2} + 3x[/tex]
= [tex]2^{3} + 2^{2} + 3(2) = 0\\8 + 4 + 6 = 0 \\18= 0[/tex]
Consequently, 2 is not a polynomial root of [tex]x^{3} + 4x^{2} + 3x[/tex] .
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Find an ordered pair (x,y) that is a solution to the equation.
x-3y=9
(x,y)= ?
Answer:
(9,-3)
Step-by-step explanation:
Find the area of the figure.
8ft
8ft
6 ft
12 ft
10 ft
Answer:
46080
Step-by-step explanation:
multiply all of them
Answer: might be 150 sq ft if the problem is of the irregular figure
2. A computer valued at $6500 depreciates at the rate of 14.3% per year. a. Write a function that models the value of the computer. b. Find the value of the computer after 3 years
Answer:
$4088.5
Step-by-step explanation:
Given data
Price a = $6500
Rate of depreciation r= 14.3%
Time x= 3 years
The exponential function Decay is described as
y= ab^x
For decay
b= 1-r
a.
Hence the exponential function that model the value of the computer is
y=a(1-r)^x
b.
y= 6500(1-0.143)^3
y= 6500*(0.857)^3
y= 6500*0.629
y=$4088.5
Hence the value of the computer after 3 years is $4088.5
Please help me
Rachel works for a clothing store. She is paid every week plus a 10% commission on any clothes that she sells. Which of the following is true in regards to Rachel's weekly paycheck? Chose three correct answers.
1. $100 in clothing sales gives Rachel a $250 paycheck
2. $1,100 in clothing sales gives Rachel a $260 paycheck
3 $.2,200 in clothing sales gives Rachel a $370 paycheck
4. $ 4,200 in clothing sales gives Rachel a $420 paycheck
5. $10,800 in clothing sales gives Rachel a 1,230 paycheck
6. $ 16,000 in clothing sales gives Rachel a 1,450 paycheck
Answer:
2. $1,100 in clothing sales gives Rachel a $260 paycheck
3 $.2,200 in clothing sales gives Rachel a $370 paycheck
5. $10,800 in clothing sales gives Rachel a 1,230 paycheck
Step-by-step explanation:
Here is the complete question :
Rachel works for a clothing store. She is $150 paid every week plus a 10% commission on any clothes that she sells. Which of the following is true in regards to Rachel's weekly paycheck? Chose three correct answers.
1. $100 in clothing sales gives Rachel a $250 paycheck
2. $1,100 in clothing sales gives Rachel a $260 paycheck
3 $.2,200 in clothing sales gives Rachel a $370 paycheck
4. $ 4,200 in clothing sales gives Rachel a $420 paycheck
5. $10,800 in clothing sales gives Rachel a 1,230 paycheck
6. $ 16,000 in clothing sales gives Rachel a 1,450 paycheck
The equation representing Rachel's paycheck = amount she earns every month + commission
If she makes $100 in clothing sales, her paycheck = $150 + (0.1 x 100) = $160
If she makes $1100 in clothing sales, her paycheck = $150 + (0.1 x 1100) = $260
If she makes $2200 in clothing sales, her paycheck = $150 + (0.1 x 2200) = $370
If she makes $4200 in clothing sales, her paycheck = $150 + (0.1 x 4200) = $570
If she makes $10800 in clothing sales, her paycheck = $150 + (0.1 x 10800) = $1230
If she makes $16000 in clothing sales, her paycheck = $150 + (0.1 x 16000) = $1750
thus the correct options are 2,3,5
DE is parallel to AC. Find the lengths of AC and AD. FAST!!!
Answer:
we have:
∆BDE is similar to ∆BAC
so their side are proportional :
BD/BD=BE/BC
2/BD=4/(6+4)
BD=2×10/4
BD=5
again
BE/BC=DE/AC
4/10=5/AC
AC=5×10/4
AC=25/2
Now,
AC=25/2 or 12.5.
AD=BA-BD=5-2=3.
is your answer.
Answer:
AC = 12.5, AD = 3
Step-by-step explanation:
A line parallel to a side of a triangle and intersecting the other 2 sides, divides those sides proportionally, that is
[tex]\frac{BD}{BE}[/tex] = [tex]\frac{AD}{CE}[/tex] , substitute values
[tex]\frac{2}{4}[/tex] = [tex]\frac{AD}{6}[/tex] ( cross- multiply )
4 AD = 12 ( divide both sides by 4 )
AD = 3
-----------------------------------------
Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is
[tex]\frac{DE}{AC}[/tex] = [tex]\frac{BD}{BA}[/tex] , substitute values
[tex]\frac{5}{AC}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )
2 AC = 25 ( divide oth sides by 2 )
AC = 12.5
The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes
Answer:
55.2049%
Step-by-step explanation:
R², the coefficient of determination, is the proportion of the variation in the dependent variable that is predictable from the independent variable.
In this case, if we square our correlation coefficent r=0.743, we get R²=0.552049, which means that 55.2049% of the variation in the number of yearly boaters can be explained by differences in lake sizes
The table shows the amount of certain school supplies left over in the school bookstore at the end of the year.
Item Total
Pens 36
Markers 48
Erasers 24
The bookstore manager will make packages of the remaining school supplies and sell them for $5 per package. Each package will be identical and contain the same number of items, and there will be none left over. The manager wants to create the greatest number of packages possible. How much will the bookstore earn if all of the packages of supplies are sold?
Multiple choice question.
The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:
$60.
How to obtain the amount earned?Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.
The amounts of each item are given as follows:
36, 48 and 24.
Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:
36 - 48 - 24|2
18 - 24 - 12|2
9 - 12 - 6|3
3 - 4 - 2
Hence:
gcf(36, 48, 24) = 2² x 3 = 12.
Which is the number of packages. As each package sells for $5, the amount earned is given as follows:
12 x 5 = $60.
Each package is composed by:
36/12 = 3 pens.48/12 = 4 markers.24/12 = 2 erasers.More can be learned about the greatest common factor at https://brainly.com/question/219464
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PLEASE HELP ASAP. I WILL GIVE BRAINLIEST!!!
Which of the following is not an expression
A. 7 - 5x
B. 2 + 3x = 8
C. x/2 + 1
D. 2x + 6
Answer:
B) 2 + 3x = 8
Step-by-step explanation:
Option B is not an expression as expressions do not have equal signs.
NEED THIS ASAP!
(picture below)
is it
A
B
C
or D ?
(this is Fractions and Whole Numbers)
(100 Points)
Answer:
C) 4 2/3------------------------------
The product of 7/9 and 6 is:
7/9 × 6 = Simplify by cancelling 37/3 × 2 = Multiply 14/3 = Convert to mixed number4 2/3 AnswerAnswer:
[tex]\textsf{C)} \quad 4\frac{2}{3}[/tex]
Step-by-step explanation:
To find the product of two numbers, multiply them.
[tex]\implies \dfrac{7}{9} \times 6[/tex]
To multiply a fraction by a whole number, first rewrite the whole number as a fraction by dividing it by 1:
[tex]\implies \dfrac{7}{9} \times \dfrac{6}{1}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{a \times b}{c \times d}[/tex]
[tex]\implies \dfrac{7 \times 6}{9 \times 1}[/tex]
Simplify:
[tex]\implies \dfrac{42}{9}[/tex]
Reduce the fraction by dividing the numerator and denominator by the common factor of 3:
[tex]\implies \dfrac{42 \div 3}{9 \div 3}[/tex]
[tex]\implies \dfrac{14}{3}[/tex]
Divide the numerator by the denominator:
[tex]\implies 14 \div 3=4\;\rm remainder\;2[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]\implies 4\frac{2}{3}[/tex]
find the volume of this cone. round to the nearest tenth. 15 m 5 m
Answer:
[tex]volume = \frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \times 3.14 \times {5}^{2} \times 15 \\ = 392.5 \: {m}^{3} [/tex]
based on the data provided, does this algorithm run in a reasonable or unreasonable time? explain your answer
As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.
What exactly is a linear equation?A linear equation is represented by the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "simple formula with 2 factors," where both y and x are variables, is what the previous sentence was referred to as. Calculations with two variables are referred to as "bivariate linear equations." Here are a few illustrations: 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3 are the results. A mathematical equation is considered to be linear if its solution has the format y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Based on how quickly iterations rise as input increases, fair and unreasonable algorithms can be distinguished. Since the algorithm does not grow exponentially, we can infer that it completes in an acceptable amount of time.
assessing the mathematical function that represents the algorithm's growth rate when input is added;
200 = 10k, where k is the proportionality constant.
k = 200/10
k = 20
The function that represents the number of iterations is as a result:
I = input size; n = 20i; represents the number of iterations.
As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.
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What kind of triangle has sides 4 4 8?
Answer:
No triangle
Step-by-step explanation:
Since [tex]4+4=8[/tex], the side lengths fail to satisfy the triangle inequality theorem. Thus, no such triangle exists.
The area of a carpet is 180 square feet. 25% of the carpet is blue. What is the area of the blue part of the carpet?
Answer:
45
Step-by-step explanation:
b) The graph of y = x2 – 2x + 5 is
drawn on the axes on the left.
Use the graph to estimate the
values of x when y = 6.
Give your answers to 1 decimal
place.
Please Help!!!!
Answer:
[tex]x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]
Step-by-step explanation:
[tex]y = x^2-2x+5\\\\6=x^2-2x+5\\\\x^2-2x-1=0\\\\\\\frac{-b+-\sqrt{b^2-4ac} }{2a} = x\\a = 1, b = -2, c = -1\\\\\frac{2+-2\sqrt{2} }{2\\}\\\\x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]
The value of the x is -0.4 when y = 6 and the graph is drawn on the left.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The quadratic equation,
y = x² – 2x + 5
To find the value of x:
When y = 6.
So,
x² – 2x + 5 = 6
x² – 2x - 1 = 0
Comparing the quadratic equation with standard quadratic equation,
ax²+ bx +c = 0
We get,
a = 1, b = -2 and c = -1
So,
x = {-b ±√(b²-4ac)}/2a
Substituting the values,
x = (2±√8)/2
x = 1 ± √2
x = 2.41421 and x = −0.414214
And the graph is drawn on the left so x = −0.414214 = -0.4 to one decimal place.
Therefore, the value of the x is -0.4.
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if you do 44 push ups in 4 minutes how many will he do in 5 minutes
Answer:
55
Step-by-step explanation: i think
Answer:
Step-by-step explanation:
it would be 55 because he does 11 each minute.
one number exceeds another by 4 and their sum is 26.find them with proper language and process.
Answer:
15 and 11
Step-by-step explanation:
First find an equation that represents this scenario.
26 = n + (n-4) works, because the sum (26) is equal to the number (n) plus the number minus 4, which is the other number.
To find both numbers, solve for n:
26 = n + (n - 4)
First, combine like terms.
26 = 2n - 4
Then, add 4 to both sides
30 = 2n
Then divide both sides by 2.
15 = n.
So the number is 15, and the other number is 15-4, which is 11.
please answer asap if you know the answers
Step-by-step explanation:
there is nothing its just a dark screen?
PLS HELP FAST IM BEING TIMED!!!
An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane. Which graph represents the solution to the inequality that finds the number of tickets the airline can still sell?
A number line going from 80 to 91. A solid circle is at 88. Everything to the left of the circle is shaded.
A number line going from 80 to 91. An open circle is at 88. Everything to the left of the circle is shaded.
A number line going from 80 to 91. An open circle is at 87. Everything to the right of the circle is shaded.
A number line going from 80 to 91. A closed circle is at 87. Everything to the right of the circle is shaded.
Answer:
C
Step-by-step explanation:
hope it helps
Answer:
The answer is C
Step-by-step explanation:
I keep seeing people put c so i am pretty sure that right
AJLK ~ APQR. Find the value of x.
L
5
8
K
10
X
4
20
5
Р
X=
Answer:
2.5
Step-by-step explanation:
Just if you divide any to congruent sides you will find the ratio to be 2
Solve for the missing side
-4x + 5 > -5 please help me
Answer:
x<5/2
Step-by-step explanation:
hope this helps :)
Answer:
[tex]x < \frac{5}{2} [/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable. Hope it helps :)
Twelve less than 4 times a number is 20. What
is the number?
A. 2
B.4
C. 6
D.8
the correct answer is D, 8.
You have inherited land that was purchased for $30,000 in 1960. The value of the
land increased by approximately 8% per year. What is the approximate value of
the land in the year 1995?
Hint: Use the formula A=P(1+r)
Answer:
the answer is 42,000
Step-by-step explanation:
obviously because if you carry the one and than divide by the denominator, you get four oranges. and when life gives you lemons, you give it back
After Myong's cylindrical birthday cake was sliced, she received the slice at right. If her birthday cake originally
had a diameter of 14 inches and a height of 6 inches, find the volume of her slice of cake.
Answer:
97.53 in³
Step-by-step explanation:
The cylindrical birthday cake has a diameter (d) of 14 inches and a height (h) of 6 inches.
The radius of the cake (r) = diameter / 2 = 14 inches / 2 = 7 inches.
The volume of the full cake = πr²h = π(7²)6 = 924 in³
Since only a part of the cake was cut and given to Myong. The total measure of the cake is 360°, but the part given to her was 38°. Hence the volume of her slice is given as:
Volume of her slice = (38 / 360) * volume of the full cake = (38 / 360) * 924 = 97.53 in³
Volume of her slice = 97.53 in³
Twelve eggs cost $2.04. How much will 18 eggs cost
Answer: $3.06
Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.
Please help quickly! Due in 2 hours! 20pts
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answer:
1/2
Step-by-step explanation:
A line that is perpendicular to another has an opposite reciprocal slope. In this case, we can see that the slope of the given line is -2, so the perpendicular line would have a slope of 1/2.
Answer:
1/2
Step-by-step explanation:
The slope of a line perpendicular to any given line is the negative reciprocal of the given line's slope:
[tex]m_\perp = \dfrac{1}{m}[/tex]
In this problem, the slope of the given line is [tex]\dfrac{-2}{1}[/tex] (rise over run).
So, to find the slope of a line that is perpendicular to it, we simply flip the given line's slope and change its sign.
[tex]m_\perp = \dfrac{1}{2}[/tex]
So, a line which is perpendicular to the given line would have a slope of 1/2.
help me i been stuck for like a good 20 min
[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]
notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.
Someone please help me