Using the least common factor, it is found that it would take 90 minutes for both boys to return to the starting point at the same time.
How do we find the least common factor of two amounts?To find the least common factor, we factor the numbers by prime factors, and then multiply these factors.
The lcm represents the periodicy, that is, when two periodic amounts will be at the same value.
In this problem, the periods are of 15 minutes and 18 minutes, hence:
15 - 18|2
15 - 9|3
5 - 3|3
5 - 1|5
1 - 1
Hence:
lcm(15,18) = 2 x 3 x 3 x 5 = 90.
It would take 90 minutes for both boys to return to the starting point at the same time.
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Points R(-6,-5),S(-2,-5) and T(-2,n) are plotted in the coordinate plane. The distance between points R and S is half the distance between points S and T. The value of n could be blank or blank.
The square of the distance between two points is the sum of the squares of the difference between two coordinates. The value of n can be -13 or 3.
What is the distance between two points?The distance between two points is given by the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
As it is given that the distance between points R and S is half the distance between points S and T.
[tex]2(RS) = ST[/tex]
Now, the distance between RS can be written as,
[tex]RS=\sqrt{[-6-(-2)]^2+[-5-(-5)]^2}\\RS = \sqrt{(-6+2)^2+(0)^2}\\RS = \sqrt{16}\\RS = \pm 4[/tex]
Further, we can write,
[tex]2(RS) = ST\\\\2(\pm 4) = \sqrt{[-2-(-2)]^2+[-5-n]^2}\\\\\pm 8 = \sqrt{(0)^2+(-5-n)^2}\\\\\pm 8^2=(-5-n)^2\\\\\pm8=(-5-n)\\\\[/tex]
When the value of 8 is positive,
[tex]+8+5=-n\\\\13=-n\\\\n=-13[/tex]
When the value of 8 is negative,
[tex]-8+5=-n\\\\-3=-n\\\\n=3[/tex]
Hence, the value of n can be -13 or 3.
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Pls help I need this
Step-by-step explanation:
I hope this helps, you take the substitution and put it in where the variable once was in parenthesis, then you let them interact as the vaiable onece was but now you can solve because you know the value.
oder number to least to greatest 1/8 ; 2/5 ; 3/4
Answer:1/8, 2/5 3/4
Step-by-step explanation: you can turn each into decimal
0.125, 0.4 and 0.75
Answer:
[tex]\dfrac{1}{8} < \dfrac{2}{5} < \dfrac{3}{4}[/tex]
Step-by-step explanation:
[tex]\text{You can rewrite the fractions as}\\\\\dfrac 18=\dfrac{5}{40}\\\\\\\dfrac 25 = \dfrac{16}{40}\\\\\\\dfrac 34 = \dfrac{30}{40}\\\\\\\text{So,} ~\dfrac{5}{40} < \dfrac{16}{40} < \dfrac{30}{40}[/tex]
PLEASE HELP !!! FIND THE SLOPE OF THE LINE
Slope=1
Solution:There are several ways to find the slope. Here's one of them:Pick two points on the line, plug them into the slope formula and simplify.I chose the following points: (-1, 0) and (0, 1)Plug them into the formula:[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex][tex]\displaystyle\frac{1-0}{0-(-1)} =\frac{1}{0+1} =\frac{1}{1}=1[/tex]Hope it helps.
Do comment if you have any query.
Answer: Slope=1
Step-by-step explanation:
A country pledges to reduce its annual CO2
emissions by 5% per year. If the emissions in
2022 are 6,080 Mt (metric megatons), what are
the maximum allowable emissions in the year
2029?
A country pledges to reduce its annual CO₂ emissions by 5% per year, the maximum allowable emissions in the year 2029 is, 4245.89 Mt
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
Given that,
A country pledges to reduce its annual CO₂ emissions by 5% per year
The emissions in 2022 are 6,080 Mt
The maximum allowable emissions in the year 2029 = ?
In 2022 CO₂ emission = 6,080 Mt
5% reduces next year
So, In 2023
CO₂ emission = 6080(1 - 0.05)
In 2024
CO₂ emission = 6080(1 - 0.05)(1 - 0.05)
So after 7 years in 2029
CO₂ emission = 6080(1 - 0.05)⁷
= 4245.89
Hence, the maximum permissible emission is 4245.89 Mt
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2/5+7/20 can y’all help me
Answer:
3/4
hope this helps. have a nice day :>
3. A square pyramid has a base with a side length
of 3 ft and lateral faces with heights of 2 ft. What
is the lateral area of the pyramid?
The lateral area of the pyramid is 15!
How do I solve 20x + 21??
Answer:
Step-by-step explanation:
20x+21=0
20x=-21
x=-1.05
What is x and y? 2x-2y=-4 2x+y=11 Is there infinitely many solutions, 1 solution, or no solution? solve by elimination.
Let's solve your system by substitution.
2x−2y=−4;2x+y=11
Rewrite equations:
2x+y=11;2x−2y=−4
Step: Solve2x+y=11for y:
2x+y=11
2x+y+−2x=11+−2x(Add -2x to both sides)
y=−2x+11
Step: Substitute−2x+11foryin2x−2y=−4:
2x−2y=−4
2x−2(−2x+11)=−4
6x−22=−4(Simplify both sides of the equation)
6x−22+22=−4+22(Add 22 to both sides)
6x=18
6x/6 = 18/6
(Divide both sides by 6)
x=3
Step: Substitute3forxiny=−2x+11:
y=−2x+11
y=(−2)(3)+11
y=5(Simplify both sides of the equation)
Answer:
x=3 and y=5
Which statement is true about the factorization of 30x2 40xy 51y2? the polynomial can be rewritten after factoring as 10(3x2 4xy 5y2). the polynomial can be rewritten as the product of a trinomial and xy. the greatest common factor of the polynomial is 51x2y2. the greatest common factor of the terms is 1.
The statement that is true about the trinomial is the greatest common factor of the terms is 1.
What is a trinomial?A trinomial is a polynomial with three terms or monomials.
To know which statements about the polynomial are true, let's check each of the statements individual.
A.) The polynomial can be rewritten after factoring as [tex]10(3x^2+4xy+5y^2)[/tex]
Since the product of 5 and 10 is equal to 50, the third term is 51. Therefore, the statement about the polynomial is false.
B.) The polynomial can be rewritten as the product of a trinomial and xy.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
C.) The greatest common factor of the polynomial is 51x2y2.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
D.) The greatest common factor of the terms is 1.
As all the greatest common factors of the terms are completely different, therefore, the only common factor between the three terms will be 1.
Hence, the statement that is true about the trinomial is the greatest common factor of the terms is 1.
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Answer:
Step-by-step explanation:The statement that is true about the trinomial is the greatest common factor of the terms is 1.
What is a trinomial?
A trinomial is a polynomial with three terms or monomials.
To know which statements about the polynomial are true, let's check each of the statements individual.
A.) The polynomial can be rewritten after factoring as
Since the product of 5 and 10 is equal to 50, the third term is 51. Therefore, the statement about the polynomial is false.
B.) The polynomial can be rewritten as the product of a trinomial and xy.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
C.) The greatest common factor of the polynomial is 51x2y2.
All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.
D.) The greatest common factor of the terms is 1.
As all the greatest common factors of the terms are completely different, therefore, the only common factor between the three terms will be 1.
Hence, the statement that is true about the trinomial is the greatest common factor of the terms is 1.
Which number is equivalent to 3.4/3.2?
A. 2
B. 9
C. 81
D. 729
Answer:
1.0625
Step-by-step explanation:
3.4 divided by 3.2 = 1.0625 Did you enter your Q and A correctly ?
A botanist is using two types of plants for an experiment. she writes inequalities to model the constraints on the number of each type of plant she can use. she uses linear programming to find the vertex of the feasible region that results in the minimum value, in dollars, of the cost function. if that vertex is (5, 39), what do the coordinates represent? buying five of one type of plant and 39 of the other type of plant results in the lowest cost. buying five of each type of plant costs $39, which is the lowest possible cost. the lowest possible cost of the plants is $5, which occurs when 39 of each type of plant are bought. the lowest possible cost of the plants is $5, which occurs when a total of 39 plants are bought.
The coordinates represent the numbers of plants of each type she can use and minimize the cost
Let x be the number of plants of one type.
y be the number of plants of the other type.
What is the meaning of the vertex of the feasible region?
The optimal solutions will occur at one or more of the extreme points this is the vertices of the feasible region.
We have, The vertex of the feasible region that results in the minimum value of the cost function is (5,39).
That means buying 5 of one type of plant and 39 of the other type of plant results in the lowest cost.
Thus the coordinates represent the numbers of plants of each type she can use and minimize the cost.
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Answer:
Buying five of one type of plant and 39 of the other type of plant results in the lowest cost.
Step-by-step explanation:
Sarah deposited $920 into a savings account 6 years ago. The account earns 7 --% interest, compounded annually. How much 3 interest has she earned? Answer in dollars and round to the nearest cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$920\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases}[/tex]
[tex]A=920\left(1+\frac{0.07}{1}\right)^{1\cdot 6}\implies A\approx 1380.67~\hfill \underset{earned~interest}{\stackrel{1380~~ - ~~920}{\approx 460.67}}[/tex]
Delta math: Angle Terminology with Equations
Answer:
m∠A = 139°
Step-by-step explanation:
First we must know that
Supplementary angles equal to 180 degree.
Since we know that supplementary angles equal to 180 degree we can solve now:
Putting m ∠A and m ∠ B together and put the = 180
( 7x - 15 ) + ( 2x - 3 ) = 180
Now solving for x:
( 7x - 15 ) + ( 2x - 3 ) = 180
9x - 18 = 180
9x - 18 + 18 = 180 + 18
9x = 198
9x/9 = 198/9
x = 22
Hence, Angle A will have a measure of 7x - 15 which means 7 × 22 -15 = 154 - 15 = 139°
m∠A = 139°
The measure of Angle B will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°
m∠ B = 41°
139 + 31= 180
[RevyBreeze]
Supplementary angles have sum 180°
7x-15+2x-3=1809x-18=1809x=198x=198/9x=22m<A
7(22)-15=154-15139By definition, theoretical probability is equal to:
A.
No. Of favorable outcomes
Total no. Of possible outcomes
B.
No. Of total outcomes
Total no. Of impossible outcomes
No. Of total outcomes
C.
Total no. Of possible outcomes
D.
No. Of possible outcomes
Total no. Of favorable outcomes
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The Correct choice is A
Theoretical probability is defined as number of favorable outcomes out of Total possible outcomes.
That is :
[tex]\qquad \tt \dashrightarrow \: \dfrac{ \texttt{No. of favorable outcomes}}{ \texttt{Total number of possible outcomes}}[/tex]
By definition, Theoretical probability is equal to,
⇒ Number of favorable outcomes / Total no. of possible outcomes.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
To find the definition of Theoretical probability.
Now, We know that;
Theoretical probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
Hence, By definition, Theoretical probability is equal to,
⇒ Number of favorable outcomes / Total no. of possible outcomes.
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Please help me with this!!! (Please no scams or fake answers)
Step-by-step explanation:
maybe if i reply I'll get points or whatever
7th grade math escape room: geometry Math in the Midwest 2019
An example of 7th grade geometry Math in the Midwest 2019 is Puzzle: Simplify -5 + 8 - 7.
What is geometry ?Geometry is known to be an aspect of mathematics that deals with the study of sizes, positions of angles, and others.
To simply the above, -5 + 8 - 7, follow the rule of BODMAS. and thus: we solve for addition before subtraction.
= -5 + 8 = 3
3 - 7 = -4
Therefore the simplified form of -5 + 8 - 7 is -4
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Thank you for answering this question.
Note the rules
a^m×a^n=a^m+n(a^m)^n=a^mn[tex]\\ \rm\Rrightarrow \dfrac{7^{12}7^9}{(7^6)^3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{7^{21}}{7^{18}}[/tex]
[tex]\\ \rm\Rrightarrow 7^3[/tex]
[tex]\\ \rm\Rrightarrow 729[/tex]
Two times the sum of four times a number plus six is the same as five less than twice the same number what is the number?
Answer:
[tex]\frac{-17}{6}[/tex]
Step-by-step explanation:
Let x be the number we want to find.
First we analyze the given informations
Info 1 : Two times the sum of four times a number plus six
We translate this statement (info 1) mathematically as : 2×(4x + 6)
Info 2 : five less than twice the same number
We translate this statement (info 2) mathematically as : 2x - 5
Info 1 is the same as Info 2 ⇔ 2×(4x + 6) = 2x - 5
2×(4x + 6) = 2x - 5
⇔ 8x + 12 = 2x - 5
⇔ 8x - 2x = -5 - 12
⇔ 6x = - 17
⇔ x = -17/6
See the picture below.
Answer:
in photo
Step-by-step explanation:
remember you still need to round it to 2 decimal places!!
Find the distance between the points ( – 4,8) and ( – 4, – 5)
Answer:
they are 13 points away from eachother
Step-by-step explanation:
count up or down then left or right
Answer:
13 units.
Step-by-step explanation:
Distance = √[(x2-x1)^2 + (y2-y1)^2] where (x1,y1) and (x2,y2) are the 2 points
So here the distance = √(-4 - -4)^2 + (8 - -5)^2)
√(0 + 13^2)
= 13
4. Romeo paid $380.75 in car repairs. The sales tax rate is 8%. What is the
total Romeo paid to repair his car?*
[tex][text]\orange{ \rule{100pt}99999pt}[/tex]
120 students were surveyed about which vegetable is their favorite.
Answer:
48 Students
Step-by-step explanation:
It is given that the total number of students is 120, and to find the amount of students that chose carrots or potatoes as their favorite vegetable multiply the percentage by 120 and add. 120 * .1 = 12. 120 * .3 = 36. 36 + 12 = 48.
Answer:
48 Students
Step-by-step explanation:
Please, Please, Please Help MEE!! ASAP!
1a. 35
b. 17.5
c. 3.5d
2. $4.5
rewrite the function in an equivalent form the would reveal the vertex of the function f(x)=x^2+8x+6
Answer:
f(x)=(x+4)-10
Step-by-step explanation:
Since the function f(x)=x^2+8x+6 is in standard form, you need to find the axis of symmetry using the formula -b/2a, and then plug the value back into the original equation to find the vertex.
The vertex is (-4, -10)
Using this information, we can rewrite the equation in vertex form (f(x=a(x-h)+k), where (h, k) is the vertex.
The equation we rewrite is f(x)=(x+4)-10
Nicole bought a meal in a town that has no sales tax. She tips 20%. Select all meals Nicole could buy with less than $16 total.
A-$12. 36
B-$12. 50
C-$13. 00
D- $14. 79
E- $14. 99
Answer:
I'm missing some information... but I'll answer the question regardless
x=the cost of the meal
1.2x≤$15
divide both sides by 1.2
x≤$12.5
In short, this means that Nicole can buy anything that costs $12.50 or less.
I need this answered please
Answer:
80 yds^2
Step-by-step explanation:
A=2(wl+hl+hw)=2·(2·2+9·2+9·2)=80
The product of two rational numbers is 6 If one of them is 8 find the other numbers
Answer:
3/4
Step-by-step explanation:
8x = 6
x = other number = 6/8 = 3/4
A dime has a radius of 8.5 millimeters. Find the circumference of a dime to the nearest tenrh
What is 112.491 written in word form?
Answer:
112.491 = one hundred twelve and four hundred ninety-one
thousandths.
Step-by-step explanation: