Answer:
One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?
Step-by-step explanation:
Let us suppose two years ago my brother's age was x years
Then, my age was 3x
Three years from now, my brother's age will be (x +2+3) = (x+5) years
And my age will be (3x+2+3) = (3x+5) years
But it is given that i will be twice as old as my brother.
So, 2(x+5)= (3x+5)
or, x= 5 years
So my brother's present age is 5+2= 7 years
And my age is 5*3+2= 17 years
The age of the older brother is 13 and the age of the younger brother is 5.
Two simultaneous equations can be determined from this question:
y = 3x - 2 equation 1
y = 2x + 3 equation 2
Where:
y = older brother's age
x = younger brother's age
Equate equation 1 and equation 2
3x - 2 = 2x + 3
Combine similar terms
3x - 2x = 3 + 2
x = 5
Substitute for x in equation 1
3(5) - 2
15 - 2
y =13
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What is true of all multiples of 6? A. All multiples of 6 have 2 and 3 as factors. B. All multiples of 6 have 12 as a factor. C. All multiples of 6 must end in 2, 3, or 6. D. A multiple of 6 cannot have 5 as a factor.
Answer:
A
Step-by-step explanation:
Factorize the following quadratic equation u²- 12 u + 35 = 0
Answer:
X₁=7 ,X₂ = 5
Step-by-step explanation:
a= 1² b= - 12 c= 35
X =[ ( -b±√b²-4ac ) / 2a]
So, use this formula and get the answer...
Even if you use the middle term formula, you will get the same answer
The formula for the area of a triangle is a=1/2bh . If the base of the triangle is 6x units and has a height of x+3, write a simplified algebraic expression for the area of the triangle in terms of x
Answer:
a = 3x^2 +9x
Step-by-step explanation:
Put the given dimensions in the formula and simplify. The distributive property is useful.
a = (1/2)bh
a = (1/2)(6x)(x+3) = 3x(x +3)
a = 3x^2 +9x
Solve for x.
8x + 3 > 4 (1/2x – 3)
Answer:
[tex]x>-5/2[/tex]
Step-by-step explanation:
So we have:
[tex]8x+3>4(\frac{1}{2}x-3)[/tex]
First, distribute the right:
[tex]8x+3>2x-12[/tex]
Subtract 2x from both sides:
[tex]6x+3>-12[/tex]
Subtract 3 from both sides:
[tex]6x>-15[/tex]
Divide everything by 6:
[tex]x>-15/6[/tex]
Reduce:
[tex]x>-5/2[/tex]
And this is our answer :)
Everytime i try to answer the questions in the same format given it shows as unexpected character.Is there anyway i can fix this so i can submit the answers i am getting on here?
Answer:
use "Help"
Step-by-step explanation:
You need to learn how your software expects to see "infinity." It may need to be spelled out "infinity" or abbreviated "inf" or "infty".
For starters, I suggest you use the "Help" link on the page you show. If that doesn't answer the question, then consult with your instructor.
Find the distance between these points. C(0, 4), T(-6, -3) √(37) √(109) √(85)
Answer:
The answer is
[tex] \sqrt{85} [/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
C(0, 4), T(-6, -3)
The distance between them is
[tex] |CT| = \sqrt{ ({0 + 6})^{2} + ({4 + 3})^{2} } \\ = \sqrt{ {6}^{2} + {7}^{2} } \\ = \sqrt{36 + 49} [/tex]We have the final answer as
[tex] \sqrt{85} [/tex]Hope this helps you
Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}
Answer:
B {6, 6, 7}
Step-by-step explanation:
Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}
For a given triangle with 3 sides, the sun of the length of any two sides must be greater Than the third side. This can be expressed mathematically as;
Let the side be ;
x, y and z
Then:
x > (y + z) or
y > (x + z) or
z > (x + y)
For A{2,5,9}
(2 + 5) < 9 (does not meet criteria)
For B {6,6,7}
(6 +6) > 7
(7 +6) > 6
Meets all criteria
For C {6,4,2}
(4 +2) is not greater Than 6 (does not meet criteria)
For D {7,8,1}
(7 +1) is not greater Than 8 ( does not meet criteria)
According to the same report, the 28.5 million passengers in 2018 represented a 6.7% increase in cruise passengers since 2017. How many cruise passengers must there have been in 2017
Answer:
approximately 26.7 million
Step-by-step explanation:
Let x be the number of cruise passengers in 2017.
6.7% increase of x gives us 28.5 m cruise passengers in 2018.
Thus, 106.7 % of x = 28.5
[tex] \frac{106.7}{100} * x = 28.5 [/tex]
[tex] \frac{106.7x}{100} = 28.5 [/tex]
Multiply both sides by 100
[tex] \frac{106.7x}{100} * 100 = 28.5*100 [/tex]
[tex] 106.7x = 2850 [/tex]
Divide both sides by 106.7
[tex] \frac{106.7x}{106.7} = \frac{2850}{106.7} [/tex]
[tex] x = 26.7 [/tex] (approximated)
Number of passengers in 2017 must have been approximately 26.7 million
What is the value of this expression when x = -6 and ? 4(x2 + 3) − 2y
Answer:
So you kinda forgot to mention the part where y = -1/2 but the answer is 157
Step-by-step explanation:
4(x^2 +3) - 2y
replace the variables
4(-6^2 +3) - 2 (-1/2)
use PEMDAS to solve
so parenthesis first and exponents
4(6x6 +3) -2 (-1/2)
4(36 +3) -2 (-1/2) (since you multiply a - by a - you get a +)
4(39) -2 (-1/2) (again - and a - is a positive)
4(39) + 1
156 + 1
157 there it is i got a 5 of 5 on my test and have a nice day :D
The area of a square is 289 ft2. What is the length of each side?
Answer:
17 ft
Step-by-step explanation:
the area of a square is length x length, or [tex]length^{2}[/tex]
so, since you already have the area, do the opposite of squaring it, which is finding the square root.
[tex]\sqrt{289}[/tex] = 17
The length of each side of a square is [tex]17 feet[/tex] whose area is [tex]289 ft sq[/tex]. (mentioned in the question).
A square is a four-sided figure in which all sides are equal in length and the measure of each angle is [tex]90^0[/tex]. The area is defined as the space that is contained inside the closed boundary or perimeter or circumference.
We know that the
area of the square = [tex]side \times side[/tex]
[tex]289 ft sq[/tex] [tex]= side \times side[/tex]
[tex]289 = (side) ^2[/tex]
[tex]\sqrt{289 } = side[/tex]
[tex]17 = side[/tex]
Thus, the length of each side of a square consisting of an area of[tex]289 ft sq[/tex] is [tex]17 feet[/tex] .
Learn more about Square here :
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A triangle has a perimeter of 48 inches. Side B is nine inches longer than side A. The base is 7 inches more than twice side A. What are the dimensions of the triangle?
Answer:
(A, B, C) = (8, 17, 23) inches
Step-by-step explanation:
We can let A, B, and C represent the corresponding side lengths. Then we are given ...
A + B + C = 48 . . . . . . the perimeter is 48 inches
B = A + 9 . . . . . . . . . . . B is 9 inches longer than A
C = 2A +7 . . . . . . . . . . the base (remaining side) is 7 inches more than ...
Substituting for B and C in the first equation, we have ...
A + (A+9) +(2A+7) = 48
4A = 32 . . . . . . . . . . . . . . collect terms, subtract 16
A = 8
B = A+9 = 17
C = 2A +7 = 23
Side A is 8 inches, side B is 17 inches, and side C is 23 inches.
the temperature at 5:00 PM is 4 degrees. By midnight, the temperature had dropped 12 degrees. What was the temperature at midnight?
Answer:
-8 degrees
Step-by-step explanation:
4-12 = -8
It dropped 12 degrees in 7 hours.
Answer: -8°
Step-by-step explanation:
4 - 12
Oscar rode his bicycle at a rate of 9 mph and then speed up to 16 mph. he rode 30 minutes longer at 9 mph than he did at 16 mph. If he traveled a total of 22 miles, how long did he ride at the slower rate?
Answer:
t = 0.7 h
The time he rode at a slower speed is 1.2 h
Step-by-step explanation:
-The question involves algebra, to find the time the distance formula is used involving the values of distance, time and speed.
- distance = speed 1 * time 1 + speed 2 * time 2
If Oscar traveled for t minutes at 9mph and it took him 15 minutes longer than when he traveled at 16mph it means that:
speed 1 * time 1 + 30 minutes.
But 30 minutes converted to hours is 0.5 hours
22 miles = 9 * (t + 0.5) + 16 * t
22 = 9t + 4.5 + 16t
17.5 = 25t
17.5 / 25 = t
The answer is: t = 0.7
Checking the value in the equation:
22 miles = 9 * (t + 0.5) + 16 * t
22 = 9 * (0.7 + 0.5) + 16 * 0.7
22 = 9 * 1.2 + 11.2
22 = 10.8 + 11.2
22 = 22
How are you? (ignore: now for 20 more characters to meet the requirement to post this)
Answer:
lol
Step-by-step explanation:
personally... great... just mentally depressed and physically wanting to die but i guess that's great
Linda and juan went shopping. Linda spent $19 less than Juan. If we let x represent how much juan spent, write an algebraic expression for how much Linda spent
gabriela makes quilts to sell at charities. she can make 9 quilts with 36 yards of material. how many yards of material would she require for 13 quilts ?
Given the function f (x) = 5x^2 - 2 find f (-3).
Answer:
Step-by-step explanation:
5(-3)^2 - 2
5(9) - 2
45 - 2 = 43
can help me with this one?
A. 5x+9=17
B. -8x-7=15
C. 6(3×+8)=-
please send me the answer for both
Answer:
A is 1.6 and ion the other ones
FIND THE DISTANCE BETWEEN THE TWO POINTS
A(0, 0), B(6, 8)
Answer:
10
Step-by-step explanation:
Mathematical Formula: [tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
Therefore: [tex]\sqrt{\left(6-0\right)^2+\left(8-0\right)^2}[/tex]
Which = 10
What is the value of x that makes the given equation true? 4x−3=−12x+13 x=−3 x = 0 x = 1 x = 16
Answer:
The answer is C.
:)
Step-by-step explanation:
4x − 3= −12x + 13
4x + 12x = 13 + 3
16x = 16
x = 1
Answer:
X=1
Step-by-step explanation:
I took the k12 test and got it right
have a good life =D
Which two expressions , added together , form a function with the following characteristics?
-It’s range is all real numbers
- it’s graph has exactly two x-intercepts
Answer:
Options (B) and (C)
Step-by-step explanation:
We have to form a function which has following characteristics,
1). Its range is all real numbers
Which means graph of the given function starts from negative side of the y-axis (-∞) and goes towards positive direction of the y-axis (+∞).
It's a typical characteristic of odd degree polynomial/function.
2). The graph has exactly two x-intercepts.
Which means when we put f(x) = 0, we get exactly two values of x.
Therefore, function will be, f(x) = x³ + x²
Range of the function → (-∞, ∞) Or a set of all real numbers.
x-intercepts → f(x) = x³ + x² = 0
x²(x + 1) = 0
x = -1, 0
Therefore, Options (B) and (C) will be the answer.
what is 190000000000000000000999999x33
Answer:
5.7e+26
If you type in a calculator 19+19 0s + 6 9s multiplied by 3 you will get 5.7e+26.
Answer:
6.2700000 E27 (?)
Hope I helped!
Which 2 statements are true
Answer:
B
Good luck in Geometry my guy!
Can you please help me with this I’ll give you a playlist for sure it’s
Answer:
15+(-37)
initial 15
fell 37 so -37
Answer:
B, or the one labeled 15 + (-37)
Step-by-step explanation:
It starts with 15 degrees F, which is positive.
Then, you'd add -37 degrees.
Adding -37 degrees to 15 is the same as subtracting 37 from 15.
Good luck mate :)
How do you perform this: 2x+3y=25 3x+4y=22
Answer:
x = -34 , y = 31
Step-by-step explanation suing Gaussian elimination:
Solve the following system:
{2 x + 3 y = 25
3 x + 4 y = 22
Express the system in matrix form:
(2 | 3
3 | 4)(x
y) = (25
22)
Write the system in augmented matrix form and use Gaussian elimination:
(2 | 3 | 25
3 | 4 | 22)
Swap row 1 with row 2:
(3 | 4 | 22
2 | 3 | 25)
Subtract 2/3 × (row 1) from row 2:
(3 | 4 | 22
0 | 1/3 | 31/3)
Multiply row 2 by 3:
(3 | 4 | 22
0 | 1 | 31)
Subtract 4 × (row 2) from row 1:
(3 | 0 | -102
0 | 1 | 31)
Divide row 1 by 3:
(1 | 0 | -34
0 | 1 | 31)
Collect results:
Answer: {x = -34 , y = 31
2/3(6k-30)+k=100 this is the one I need help
The value of k = 20.
We have the following expression -
[tex]\frac{2}{3} (6k-30)+k=100[/tex]
We have to find the value of K.
Find the value of z → [tex]$log(2)^{z} = \pi[/tex].We have -
[tex]$log(2)^{z} = \pi[/tex]
z x log(2) = π
z = [tex]$\frac{\pi }{log\;2}[/tex]
z = 10.43
According to the question, we have -
[tex]\frac{2}{3} (6k-30)+k=100[/tex]
[tex]\frac{2}{3}\times 6[/tex](k - 5) + k = 100
4(k - 5) + k = 100
4k - 20 + k = 100
6k = 120
k = 20
Hence, the value of k = 20
To solve more questions on finding unknown variable, visit the link below-
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Both the galapagos Islands and the island of naura are on the equator, but the galapagos Islands are at 90.30 degree West whereas the island of naura is at 166.56 degree east. How far is it from galapagos Islands to naura travelling over the pacific ocean along the equator, correct to the nearest km
Answer:
11481.4875 km
Step-by-step explanation:
Given the that :
Galapagos island and Island of Naura are on the equator
Galapagos = 90.30°W
Island of Naura = 166.56°E
Ensuring same bearing is used for both :
Island of Naura = 166.56°E = (360° - 166.56°) = 193.44°W
Hence, we can calculate the difference in the bearing of both locations :
(193.44 - 90.30)°W = 103.14°
Hence the distance between Galapagos and Island of Naura along the equator is :
(Difference in bearing / total bearing) * earth's Circumference
Earth's Circumference = 40,075km
(103.14 / 360) × 40,075
0.2865 × 40,075
= 11481.4875 km
=
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
Answer:
2 works
-3 is extraneous
Step-by-step explanation:
sqrt(x + 7) - 1 = x Add 1 to both sides
sqrt(x + 7) = x + 1 Square both sides
(x + 7) = (x + 1 )^2
x + 7 = x^2 + 2x + 1 Subtract x from both sides
0 = x^2 + x + 1 -7
0 = x^2 + x - 6 This will factor
(x + 3)(x - 2) = 0 Find the values for x
x + 3 = 0
x = - 3
x - 2 = 0
x = 2
Now you must check this to see if both values work
sqrt(-3 + 7) - 1 = -3
sqrt(4) - 1 = -3
2 - 1 =? - 3
1 does not equal - 3. Therefore - 3 is extraneous. Try x = 2
sqrt(2 + 7) - 1 = 2
sqrt(9) - 1 = 2
3 - 1 = 2
2 = 2
In your own words define and give an example of Associative Property
Answer:
The associative property states that you can add or multiply regardless of how the numbers are grouped.
Step-by-step explanation:
3+4+9=9+3+4=4+9+3 etc
Form the intersection for the following sets.
R={10, 15, 20}
S = {20, 25}
R ∩S=
{10,15,25}
{10,15,20,25}
{20}
{}
Answer:
Your required answer is option is {20}.
Step-by-step explanation:
Hey, there!!
The reason for above answer is we generally find intersections among the sets by extracting the common elements of the sets.
Here,
R = {10,15,20}
S = {20,25}.
Now, 20 is common im both so,
R intersection S = {20}.
Hope it helps...