[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
Sum of three consecutive odd integers = [tex]27[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The values of the three integers.
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
Let us assume the three consecutive odd integers to be [tex]x[/tex], [tex](x+2)[/tex] and [tex](x+4)[/tex].
As per the condition, we have
[tex]Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27[/tex]
[tex]➺ \: x + (x + 2) + (x + 4) = 27[/tex]
[tex]➺ \: x + x + 2 + x + 4 = 27[/tex]
Now, collect the like terms.
[tex]➺ \: (x + x + x) + (2 + 4) = 27[/tex]
[tex]➺ \: 3x + 6 = 27[/tex]
[tex]➺ \: 3x = 27 - 6[/tex]
[tex]➺ \: 3x = 21[/tex]
[tex]➺ \: x = \frac{21}{3} \\[/tex]
[tex]➺ \: x = 7[/tex]
Therefore, the three consecutive odd integers whose sum is [tex]27[/tex] are [tex]\boxed{ 7 }[/tex], [tex]\boxed{ 9 }[/tex] and [tex]\boxed{ 11 }[/tex] respectively.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]⇢ 7 + 9 + 11 = 27[/tex]
[tex]⇢ 27 = 27[/tex]
⇢ L. H. S. = R. H. S.
[tex]\sf\blue{Hence\:verified.}[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
One-third of a number is 8 less than the number itself
Answer:
let the number be x
[tex] \frac{1}{3} x = x - 8 \\ x = 3(x - 8) \\ x = 3x - 24 \\ 3x - x = 24 \\ 2x = 24 \\ x = 12[/tex]
Answer:
x=12
Step-by-step explanation:
1/3 of 12 is 4 which is 8 less then 12 :))))))
Hope this helps <3
Elliot is 2 times as old as Tanya. 10 years ago, Elliot was 4 times as old as Tanya. How old is Elliot now?
Answer:
Step-by-step explanation:
To solve this, we are going to make an age table:
Age Now Age 10 years ago
Tanya
Elliot
Filling the in the Age Now column comes from the first sentence. If Elliot is 2 times Tanya's age and we don't know Tanya's age, then Tanya's age is x and Elliot's age is 2x:
Age Now Age 10 years ago
Tanya x
Elliot 2x
Filling in the Age 10 years ago column simply requires that we take their ages in the Age Now column and subtract 10 from each age:
Age Now Age 10 years ago
Tanya x x - 10
Elliot 2x 2x - 10
Since the question is How old is Elliot now based on the fact that 10 years ago....blah, blah, blah, we are using the ages in the 10 years ago column to write our equation. It says:
10 years ago, Elliot was 4 times as old as Tanya. Translated into mathspeak:
2x - 10 = 4(x - 10) and
2x - 10 = 4x - 40 and
-2x = -30 so
x = 15. That means that Elliot is 30 and Tanya is 15
Someone, please help
Timothy has 72 coins, consisting of quarters, dimes, nickels, and 8 pennies. Samantha comes and takes all of his quarters, takes 3 of his dimes, takes 2 of his nickels, and leaves him with one penny, leaving him with 45 coins. What is the value of quarters that Samantha took?
72 - 45 = 27
Samantha took 27 coins. She took 3 dimes, 2 nickels and all but 1 penny, so 7 pennies. This is 12 coins. The rest must be quarters. 27 - 12 = 15 quarters.
15 x 0.25 = 5.25
The value of the quarters that Samantha took is $3.75.
Hope this helps!
15. Mary was given data comparing students’ mark in math class and the number of classes missed. She plotted the data on the graph below and drew a line of best fit. Do you agree with Mary’s drawing of the line of best fit? Justify your answer
What is the smallest prime number that is also a factor of 27 and a multiple of 3?Please explain why this or that is the answer.
Answer:
To be fair I believe it's 3 because 27/3=9 and 3x1=3
10 fewer than the difference of 8 and w! Please helpppppppp!!!!!!!! get 5 stars and brainly and heart!!!!!!!
Answer:
(8-w) -10
Step-by-step explanation:
fewer than comes after
difference of 8 and 2
(8-w)
10 fewer than
(8-w) -10
Answer:
(8 - w) - 10
Step-by-step explanation:
10 fewer than the difference of 8 and w.
-10
fewer means that we are taking away something, so it is minus.
8 and w (difference)
and is a word that adds something, but we have to pay attention to the difference. that means -.
8 - w
Put parenthesis around it so we know it is 8 and w that seperates from the (10 fewer).
(8 - w)
add - 10 at the end
(8 - w) - 10
Given the preimage and image, find the dilation scale factor
Answer:
it should be 2 as your answer
write a function g whose graph represents a horizontal shrink by a factor of 1/2 of the graph f(x)= |2x| +4
The function g is:
[tex]g(x) = |4x| + 4[/tex]
----------------------
Horizontally shrinking a function f(x) by a factor of [tex]\frac{1}{a}[/tex] is equivalent to finding f(ax).
----------------------
In this question, the function is:
[tex]f(x) = |2x| + 4[/tex]
Horizontally shrinking by a factor of [tex]\frac{1}{2}[/tex] means that [tex]a = 2[/tex], so:
[tex]g(x) = f(ax) = f(2x) = |2(2x)| + 4 = |4x| + 4[/tex]
Thus, the function g is:
[tex]g(x) = |4x| + 4[/tex]
A similar question is given at https://brainly.com/question/20379647
help me with the question of O.math
Answer:
24
Step-by-step explanation:
2*1+1+2*2+1+2*3+1+2*4+1=24
Identify the equation of the circle that has its center at (7, -24)
and passes through the origin.
Answer:
(x-7)²+(y+24)² = 625
Step-by-step explanation:
A circle with center (h, k) and radius r can be represented as
(x-h)²+(y-k)² = r²
We know the center and one point, and need to find the radius. The radius is equal to the distance from the center to any point on the circle. Therefore, we need to find the distance from the center to the point on the circle (in this case, the origin) to obtain the radius.
The distance formula for points (x₁, y₁) and (x₂, y₂) is √((x₁-x₂)²+(y₁-y₂)²). Note that x₁ and x₂ (as well as y₁ and y₂) are interchangeable but x₁ and y₁ or x₂ and y₂ are not.
Our distance between (7, -24) and the origin is
√((x₁-x₂)²+(y₁-y₂)²) = √((7-0)²+(-24-0)²)
= √625
= 25
Therefore, the radius is 25 and our equation is
(x-7)²+(y-(-24))² = (x-7)²+(y+24)² = 25² = 625
Guided Practice
Find the first, fourth, and eighth terms in the sequence.
an=−5 · 3n−1a subscript n baseline equals negative 5 times 3 superscript n minus 1 baseline
A.
–15; –405; –32,805
B.
5; 135; 10,935
C.
–5; –135; –10,935
Answer:
C.
–5; –135; –10,935
Step-by-step explanation:
Answer:
C. -5; -135, -10,935
Step-by-step explanation:
...............................................................................................................................................
X
45°
454
Find the value of x.
A.
B.
3.2
2
C. 3√2
D. 33
Save and Fyit
(10x²+19x+6) ÷(5x+2)
Answer:
2x + 3
Step-by-step explanation:
(10x² + 19x + 6) ÷ (5x + 2) =
= (10x² + 15x + 4x + 6) ÷ (5x + 2)
= [5x(2x + 3) + 2(2x + 3)] ÷ (5x + 2)
= [(5x + 2)(2x + 3)] ÷ (5x + 2)
= 2x + 3
Answer:
2x+3 is your answer
Which of the following is equivalent to 0.00451?
A. 4.51x10^-3
B. 45.1x10^-3
C. 0.451x10^-3
D. 4.51x10^-2
Step-by-step explanation:
0.00451
[tex] = \frac{451}{100000} [/tex]
[tex] = \frac{4.51}{1000} [/tex]
[tex] = \frac{4.51}{ {10}^{3} } [/tex]
[tex] = 4.51 \times {10}^{ - 3} (option \: a)(ans)[/tex]
The required scientific notation is A. 4.51x10⁻³ is equivalent to 0.00451. It's in scientific notation where 4.51 is between 1 and 10, and -3 is the exponent representing the decimal shift.
In scientific notation, a number is written in the form of "a × 10ⁿ" where "a" is a number between 1 and 10 (including 1 but excluding 10), and "n" is an integer exponent.
The goal is to represent the number in a more compact form using powers of 10.
0.00451
To express this in scientific notation, we need to find "a" and "n" such that "a × 10ⁿ" equals 0.00451.
The option A, 4.51 × 10⁻³ is the correct choice because:
"a" is 4.51, which is between 1 and 10.
"n" is -3, as we are shifting the decimal point three places to the left to convert 0.00451 to 4.51 × 10⁻³.
Therefore, 0.00451 is equivalent to scientific notation option A. 4.51 × 10⁻³, which is option A.
learn more about scientific notation here
brainly.com/question/19625319
#SPJ3
Relationship between q and t pleaseeee helppppp
Step-by-step explanation:
it is simple.
there is a constant speaking time of 25 minutes.
the duration of the meeting is the speaking time plus the question answering time.
so,
q = 1 means t = 25 + 1 = 26
q = 2 means t = 25 + 2 = 27
q = 3 means t = 25 + 3 = 28
q = 8 means t = 25 + 8 = 33
Aman age is 2 times of his son's age after 5 years sum of their age will be 70 find their present age
Answer:
aman's son's age = 20
aman's age = 40
Step-by-step explanation:
let aman's son's age be x
aman's age = 2x
2x+5+x+5 = 70
3x+10=70
3x = 60
x = 20
2x = 40
which one of the following is not true about a rectangle? A. all its angels are right angels B. its opposite angels are equal C.opposite sides are parallel D. all its sides are equal
Answer:
I am not sure but it may be option c .
Step-by-step explanation:
I chose option c because in parallelogram the opposite sides are parallel .
A man makes a profit of 15%6y selling an article for Rs 2500. For what price should he sellituto make a profit of 38%
Find the price before the 15% profit:
2500 / 1.15 = 2173.91
Now multiply the original cost by 1 + 38%:
2173.91 x 1.38 = 2999.99
Answer: 2.999.99 ( may need to round to 3,000)
not sure how to solve this
Answer:
x=11
Step-by-step explanation:
(x+7)×7=6×(6+15)
or, 7x+49=6×21
or, 7x=126-49
or, 7x=77
or, x=11
The library has 2,730 books. If each shelf can hold 30 books, how many shelves will the library need to hold all of its books?
Answer:
2730÷30=91
Step-by-step explanation:
take the number of books and divide it by the number of books each shelve can hold and ull get ur answer
Ajay is researching how the population of his hometown has changed over time. Specifically, he learns his hometown had a population of 20{,}00020,00020, comma, 000 in 199019901990, and that the population has since increased by about 8\%8%8, percent every 333 years.
Ajay predicts that his town can only support a population of 50{,}00050,00050, comma, 000. Ajay is relieved to see that population has not exceeded 50{,}00050,00050, comma, 000 ttt years after 199019901990.
Write an inequality in terms of ttt that models the situation.
Answer:
Could you Write the question more clearly?
Step-by-step explanation:
The graph below shows the amount of money a store earns for selling T-shirts.
у
T-shirt Sales
100
80
60
Money Earned
(dollars)
40
20
0
4
24
8 12 16 20
Number of T-shirts Sold
What is the unit rate of the graph?
Answer:
Whattt pls draw the graph.. And it will show the us the rate
A square has a perimeter of of 28 m. What is the length of each side
Answer:
a square has 4 sides therefore the formula for perimeter of a square would be 4a where a is the number of sides. in this case, we want to know the length of each side so we divide total length (28) by number of sides which is 4 and we get 7m
Answer:
the side lengths of a square are equal. Second, know that the sum of all 4 side lengths gives us the perimeter.
Given the quadratic equation (x + p)²=49,where p is a constant,find the values of p if one of the roots of the equation is 4.
Pls help me,will mark as the brainliest.
Answer:
-11, 3
Step-by-step explanation:
We know one of the roots are
[tex](x+ 4) {}^{2} = 49[/tex]
[tex]x + 4 = - 7[/tex]
[tex]x + 4 = 7[/tex]
[tex]x = - 11[/tex]
or
[tex]x = 3[/tex]
which choice is equivalent to the expression below? 7x√2 - 4√2 + x√2
A. 6x√2 - 3√2
B. 5x^2√2
C. 3x√2
D. 8x√2 - 4√2
Answer:
D
Step-by-step explanation:
[tex]8x \sqrt{2} - 4 \sqrt{2} [/tex]
what is the answer to -22/9r = 11/9
Answer:
2
Step-by-step explanation:
for this question you've to cross multiply
-22/9r=11/9
99r=-198
then you divide both sides by 99 inorder to remain with r on one side
99r/99=198/99
r=2
I hope this helps
The side lengths of a 30-60-90 triangle are in the ratio 1: V3 : 2. What is
sin 30°?
Answer:
A
Step-by-step explanation:
side opposite to smallest angle is smallest=1
Hypotenuse=2
sin 30=1/2
What is the value of the expression below when z=6
z²+3z-3
Answer:
51 I hope it will help you
Step-by-step explanation:
mark me as a brainlist answer
Answer:
51
Step-by-step explanation:
Plug in z
(6)^2 + 3(6) - 3
36+18-3
54-3= 51
Attached Math question document. Find the value to complete this calculation.
To find the missing value divide both sides by -7:
28/-7 = 4
The missing value is 4
Answer= -4
Step-by-step explanation:
negative × negative = positve. therefore if 7×4=28 , then -7×-4=28
A business made a profit of $44,000 in 1991. Then its profits decreased by 5% each year for 4
years. Find its profit in the year 1995.
Answer:
= profit in the year 1995 are $880,000
