Answer:
X= 8Step-by-step explanation:
[tex]5x - 1 = 6x - 9[/tex]
Move variable to L.H.S and change its sign:
[tex]5x - 6x - 1 = - 9[/tex]
Move constant to RHS and change its sign:
[tex]5x - 6x = - 9 + 1[/tex]
Combine like terms and simplify:
[tex] - x = - 8 \\ x = 8[/tex]
Hope this helps....
Good luck on your assignment...
how to do this question plz answer
Answer:
Step-by-step explanation:
George: x
Alex: x + 12
Carl: 3(x+12)
3x+36+x+x+12= 68
5x + 48 = 68
5x = 20
x = 4; George's age
4 + 12 = 16; Alex's age
3(4+12)= 3(16)= 48; Carl's age
George to Alex: 4:16 = 1:4
Alex to Carl: 16:48= 1:3
George to Carl 4:48= 1:12
Carl to Alex: 48:16 = 3:1
which of the following represents the factorization of the binomial below? 81x^2-25y^2
Answer:
B. (9x - 5y)(9x + 5y)
Step-by-step explanation:
Rewrite the binomial as:
(9x)² - (5y)²
Apply difference of two squares formula.
x² - y² = (x - y)(x + y)
(9x)² - (5y)² = (9x - 5y)(9x + 5y)
need help with this question.
Answer:
12 and 93.
Step-by-step explanation:
Let the grandsons age be x then Mr. Roger's age = 8x - 3.
Five years ago the grandson's age was x-5 and Mr Rogers was 8x - 8 years old , so:
8x - 8 - (x - 5) = 81
8x - 8 - x + 5 = 81
7x = 81 + 8 - 5 = 84
x = 12.
So the grandson is 12 and Mt Rogers is 8*12 - 3 = 93.
what is the solution to the inequality below? 2(x-15)> x/2
Answer:
x>20
Step-by-step explanation:
2(x-15)>x/2
2x-30>x/2
Multiply both sides by 2
4x-60>x
Subtract 4x from both sides
-60>3x
-20<x
Answer: x>20
Answer:
The correct answer is x ≥ 20.
solve the equation:
x^2+3x-7=0
give your answer to 2 decimal places
Answer:
x1 = 1.54
x2 = -4.54
Step-by-step explanation:
just use calculator
An object traveled a total of 21 1/2 miles in five hours. If it traveled an equal number of miles each hour, how many miles did it travel each hour?
Answer: 4.3 miles
The decimal 4.3 is equivalent to the mixed number 4 & 3/10
=============================================================
Explanation:
Fractions are often a pain, so I find it helpful to convert to decimal form whenever possible.
1/2 = 0.5
21 & 1/2 = 21 + 1/2 = 21 + 0.5 = 21.5
21 & 1/2 miles = 21.5 miles
The object travels 21.5 miles in 5 hours. Divide the distance over the time value to get the speed (or rate). This is exactly identical to finding the number of miles traveled in one hour (since each hour the object travels the same amount of distance)
speed = distance/time = 21.5/5 = 4.3 mph
4.3 = 4 + 0.3 = 4 + 3/10 = 4 & 3/10
In my opinion, it is much easier to use decimals. Saying "the object traveled a distance of 4 & 3/10 miles" seems very clunky to me.
Therefore, each hour, the object travels 4.3 miles.
(a) P(1,0). Q(2,-5), R(-3, -5)
What triangle is this
This is a scalene obtuse triangle
An obtuse triangle is a triangle with an angle greater than 90 degrees, A scalene triangle is a triangle that has three different side lengths. You can find the side lengths(2,3,sqrt6) by plotting the triangle and using Pythagorean theorem. It is also visually clear that the triangle is obtuse if it is plotted.
Hope it helps <3
can someone help me with this question
Answer: a (see explanation below) .b.) rhombus .c) trapezoid in USA or trapezium elsewhere in the world
Step-by-step explanation:
For a.) Draw a horizontal from the bottom vertex, extending 2 units to the right. Then form a triangle by connecting a line from the right end of that line up to the right angle at the top of the original triangle
As per the given diagram
(a) represents a parallelogram not rectangle as shown in construction.
(b) Shape made by three congruent triangles on the grid below represents trapezium.
(c) Four congruent triangle in the grid below represents rhombus.
What are congruent triangles?"Two triangles are said to be congruent if the measure of all the three corresponding sides and angles of one triangle are equal to that of other triangle."
According to the question,
(a) First diagram we have to construct a triangle with given triangle in such a way it forms a parallelogram but not rectangle.
As shown in the constructed diagram.
(b) In the fourth diagram given quadrilateral having one pair of parallel line , therefore trapezium.
(c) In the second diagram all the four sides are congruent and parallel to each other and diagonals bisects each other at 90°, therefore it is rhombus.
Hence, (a) as shown in construction ,(b) trapezium and (c) rhombus is the correct answer.
Learn more about congruent triangles here
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What is the product of 6x – y and 2x – y + 2? 8x2 – 4xy + 12x + y2 – 2y 12x2 – 8xy + 12x + y2 – 2y 8x2 + 4xy + 4x + y2 – 2y 12x2 + 8xy + 4x + y2 + 2y
Answer:
(6x – y) * (2x – y + 2) =12x2 – 8xy + 12x + y2 – 2y
Step-by-step explanation:
(6x – y) * (2x – y + 2)
= 6x*(2x – y + 2) - y*(2x – y + 2)
= 12x^2 - 6xy + 12x - 2xy + y^2 -2y
= 12x^2 + 12x - 8xy - 2y + y^2
Out of the answer choices:
8x2 – 4xy + 12x + y2 – 2y
12x2 – 8xy + 12x + y2 – 2y
8x2 + 4xy + 4x + y2 – 2y
12x2 + 8xy + 4x + y2 + 2y
the second choice is a correct answer.
Answer:
Step-by-step explanation:
B. 12x2 – 8xy + 12x + y2 – 2y
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if it satisfies the given conditions.
Answer:
a
Step-by-step explanation:
find the least positive integer for which the sum of its reciprocal and 9/10 is greater than 4 times the reciprocal
Answer:
4
Step-by-step explanation:
You want the least positive integer x such that ...
1/x +9/10 > 4/x
9/10 > 3/x . . . . subtract 1/x
3/10 > 1/x . . . . .divide by 3
x > 10/3 . . . . . multiply by 10x/3
The least positive integer satisfying this requirement is x = 4.
Would someone mind explaining to me how to do this? I'm In a real crunch with this.
Answer:
first option
Step-by-step explanation:
The solution to the system of equations given graphically is at the point/s of intersection of the 2 functions.
There is only 1 point of intersection at about x = 1.5
The radius of the large sphere is double the radius of
the small sphere.
How many times is the volume of the large sphere than
the small sphere?
2
4
6
8
Answer:
8 times
Step-by-step explanation:
Volume of sphere 4/3 *pi*r^3
Let small sphere radius r1=r
So radius of large sphere R= 2r (given)
Put all valves in sphere formula and calculate
Small sphere vol v1 = 4/3*pi*r^3......... Let assume eq 1
Large sphere vol= 4/3*pi*(2r)^3
= 4/3*pi* 8r^3
Or = 8v1
substitute 4/3*pi*r^3 value from eq1
Answer:
8
Step-by-step explanation:
Given the ratio of the radii = a : b, then
ratio of volume = a³ : b³
Here the ratio of radii = 1 : 2 , thus
ratio of volume = 1³ : 2³ = 1 : 8
That is the volume of the larger sphere is 8 times the volume of smaller sphere.
Plz help I’ll mark Brainlynest
Answer:
36.00 units
Step-by-step explanation:
Lengths of horizontal and vertical segments are easily determined by subtracting coordinates or counting grid squares:
ST = 6 -1 = 5
TR = 5 -(-1) = 6
IP = 1 -(-6) = 7
PE = 2 -(-3) = 5
The lengths of the diagonal segments are found using the Pythagorean theorem. Those lengths are the root of the sum of the squares of the rise and run. As before, you can determine those from counting squares or subtracting coordinates.
RI = √(2^2 +5^2) = √29 ≈ 5.385
ES = √(3^2 +7^2) = √58 ≈ 7.616
Then the perimeter is the sum of segment lengths:
Perimeter = ST +TR +RI +IP +PE +ES
= 5 + 6 + 5.385 +7 +5 +7.616 = 36.001
Rounded to hundredths, the perimeter is 36.00 units.
Write an equation for the translation of y=|x| 2 units up
Answer:
Step-by-step explanation:
y = |x|+2 is the equation
the translation of y = |x| 2 units up
Verify the identity below with work and/ or explanation. 2gh/sin^2θ = 2gh sec^2θ/sec^2θ-1 Thanks!
Answer:
identify is verified, see work below.
Step-by-step explanation:
Verify following identity
2gh/sin^2θ = 2gh sec^2θ/sec^2θ-1
use identity 1+tan^2(θ) = sec^2(θ) on denominator of right-hand-side
right-hand side
= 2gh sec^2(θ) / (sec^2(θ)-1)
= 2gh sec^2(θ) / (tan^2(θ))
= 2gh sec^2(θ) * (cos^2(θ) / sin^2(θ) ) [note: sec^2(θ) = 1/cos^2(θ)]
= 2gh * 1 / sin^2(θ)
= 2gh / sin^2(θ)
= left-hand side
Therefore identify is verified.
solve for x 6x+238 and 3x+178 NEED HELP ASAP FIRST GETS BRAINLY
Answer:
x = -20
Step-by-step explanation:
These angles are opposite therefore they are the same angle/degree
so we can look at this problem as
6x+238=3x+178
(subtract 238)
6x=3x-60
(subtract 3x)
3x=-60
(divide by 3)
x=-20
At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture.
Answer:
We operate the principle of sets to solve the problem. We are given the number of women to be 28 and men to be 23. The intersection will be while the union of both sets will be 24. To calculate the number of women teachers attending the lecture we first sum up the number of women and men and subtract from the intersection of both sets which gives us 3. Therefore, the number of teachers that are men are 3 while the number of women teachers are 1.
Step by step explaination:
Given the following, Let the set for men be represented by MM, that of women be represented by WW and that of teachers represented by TT.
Therefore, number of men i.e n(MM)= 23,
number of women i.e n(WW)= 29
number of teachers i.e n(TT)=4
number of men or teachers i.e n(MM U TT)= 24
Therefore, we have:
n(MM U TT)=n(MM) + n(TT) - n(MM n TT)
Therefore:
n(MM n TT)=n(MM) + n(TT) -n(MM U TT)
n(MM n TT)= 23+ 4 - 24 = 3
There fore number of men that are teachers are n(MM n TT)= 3 .
Therefore, from the number of teachers n(TT)=4
the number of teachers that are men are 3 while the number of women teachers are 1.
Find the greatest common factor of 24, 36, and 48. help
Answer:
24, 36, and 48
Step-by-step explanation:
those numbers are the most high common factor of 24, 36, and 48.
Answer:
12
Step-by-step explanation:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
hopefully this helped :3
Lawrence is testing how quickly water with baking soda freezes. He adds water with baking soda to one ice tray and plain water to another ice tray. He places each tray in the freezer and records the time when each one starts to freeze. What is the treatment in this experiment?
Answer:
steps of time
Step-by-step explanation:
find the length of this
Answer:
Hey there!
We have tan 9= 21/BW
tan 9 (BW)=21
BW= 21/tan 9
BW= 132. 59
Hope this helps :)
Answer:
A- 132.59
Step-by-step explanation:
since we have to find the adjacent and already have the opposite we'll use tanθ = opp/adj
tan(9)= 21/WB
WB = 21/tan(9) (make WB the subject)
WB = 132.5887818 or 132.59
Which of the following is not a function?
A. {(4,5), (4,2), (5,4), (2,4)}
B. {(1,2), (2,3), (3,4), (4,5)}
C. {(1,2), (2,3), (3,3), (4,5)}
D. {(4,1), (5,1), (6,1), (7,1)}
Answer:
A
Step-by-step explanation:
it is A for for two outgoing (y)there is one in going(x)
Answer:
The answer is (A)
Step-by-step explanation:
Instructions: Write the explicit rule. Remember to simplify and do not put spaces in your answer. Sequence: 30,0,−30,−60,… 30 , 0 , − 30 , − 60 , … = a n = Answer
Answer:
a(n)=60-30n
Step-by-step explanation:
Equation to use:
a(n) = a(1) + d(n-1)
where a(1) is the first term, d is the common difference between terms, and n is the nth term you are trying to find.
In this case, a(1) is 30, d is -30, and n is just n.
If you plug that into the equation and use the distributive property, you would get: a(n) = 30 -30n + 30.
Adding the two 30's gets you: a(n) = 60 - 30n, which is the solution.
A ladder is 8m long. It leans against a wall with one end on the ground 6m from the wall. How far up the wall does the ladder reach?
Step-by-step explanation:
Use pythagoras theorem
a^2=b^2+c^2
a^2=64+36
a=10m
The length up to the wall of the ladder will be around 5.2915.
What is Pythagoras theorem?The Pythagoras theorem is a theorem used to find out any length of a right-angle triangle.
Pythogoroous theorem is
Hypotenuse² = base² + perpendicular²
Given that a ladder leans against a wall so the ladder will act like a hypotenuse.
Let 6m be the base then we have to find the perpendicular.
Hypotenuse² = base² + perpendicular²
perpendicular² = Hypotaneous² - base²
perpendicular = [tex]\sqrt{ (Hypotenuse)^2 - (base)^2}[/tex]
Given hypotenuse is 8m and the base is 6m.
perpendicular² = 8² - 6²
perpendicular² = 28
perpendicular = √(28) = 5.2915 hence this much be far up the wall does the ladder reach.
For more information about Pythagoras theorem.
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Help me with this please
Answer:
$2,459.21
Step-by-step explanation:
(see attached for reference)
recall that the formula for compound interest is:
A = P [ 1 + (r/n)^ (nt) ]
where,
A = Final amount ( we are asked to find this)
P = principal amount = given as $2,340
r = Annual Interest Rate = given as 5% = 0.05
n = number of times compounded in a year = 4 (compounded quarterly)
t= time = 1 year
Substituting the values into the equation,
A = P [ 1 + (r/n)^ (nt) ]
A = 2,340 [ 1 + (0.05/4)^ (4·1) ]
A = $2,459.21
The table represents the function f(x). A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 9, negative 6, negative 3, 0, 3, 6, 9. What is f(3)
Answer:
9
Step-by-step explanation:
Okay, here we have a table with the x and y columns
What we are to find is F(3)
Now this is obtainable from the table
The term f(x) equals values in the table y
We can obtain the values of y from the equation linking x to y
Now the term f(3) can be obtained by checking the value of y or f(x) that corresponds to the value 3
We can see that it is the last term on the x side that can give the value of y we are looking for
So without much further ado we can see that it is the last value on the table y we are also looking at
This equals 9
So F(3) = 9
Answer:
9
Step-by-step explanation:
Hope this helps
PLEASE HELP ME!!!
Trevor asks his bank for a loan of $22000 to add a guest
room to his house. His bank offers financing at 7.25%
compounded monthly, for a term of 5 years, payable
monthly. What is Trevor's monthly payment?
Answer:
$526.3 is the monthly payment
Step-by-step explanation:
We use the compound interest formula to calculate the total amount payable on the loan.
Mathematically;
A = P(1 + r/n)^nt
Where A is the amount to pay
P is amount borrowed = 22,000
r is interest rate = 7.25/100 = 0.0725
t is years = 5 years
n is the number of times we compound lee year = 12 times since it’s monthly
Substituting these values, we have
A = 22,000(1 + 0.0725/12)^(12)(5)
A = 22,000(1 + 0.006041666666667)^60
A = $31,578
Monthly payment is total amount/ number of months
There are sixty months in 5 years
So monthly payment is 31578/60 = $526.3
Which expression is represented by the model?
+
-X
+
O X-3
O X+3
O -x-3
O-X+3
first answer gets best marks
Answer:
-x+3
Step-by-step explanation:
3 plus signs so 1+1+1= 3
A straight line passes through the origin and has a gradient of 4. Find the equation
Answer:
y = 4x
Step-by-step explanation:
The slope is 4.
The line passes through (0, 0).
Equation of a line y = mx + b, m is the slope, and b is the y-intercept.
y = 4x + b
Put x and y as 0.
0 = 4(0) + b
0 = b
The y-intercept is 0.
The equation of the line is y = 4x.
Samad's age and his father's age
are 12 years old and 40 years old
respectively. How many years later
will Samad's father be twice as old as
Samad?
Answer:
Step-by-step explanation:
let x= time period in years between age now and when father's age=2* the samad's age
in x years father's age will be 40 + x years old
in x years samad's age will be 12+x years old
at a certain point in time, the father's age = 2*the samad's age
40+x=2*(12+x)
or, 40 +x=24 + 2x
or, 40-24 = x
x=16
test:
father=40+16=56
son=12+16=28
hence , after 16 years samad's father will be twice as old as samad