Answer:
x = 1
Step-by-step explanation:
Solve for x:
4 (2 x + 6) = 5 (x + 5) + 2
Hint: | Distribute 5 over x + 5.
5 (x + 5) = 5 x + 25:
4 (2 x + 6) = 5 x + 25 + 2
Hint: | Group like terms in 5 x + 2 + 25.
Grouping like terms, 5 x + 2 + 25 = 5 x + (25 + 2):
4 (2 x + 6) = 5 x + (25 + 2)
Hint: | Evaluate 25 + 2.
25 + 2 = 27:
4 (2 x + 6) = 5 x + 27
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
8 x + 24 = 5 x + 27
Hint: | Move terms with x to the left hand side.
Subtract 5 x from both sides:
(8 x - 5 x) + 24 = (5 x - 5 x) + 27
Hint: | Combine like terms in 8 x - 5 x.
8 x - 5 x = 3 x:
3 x + 24 = (5 x - 5 x) + 27
Hint: | Look for the difference of two identical terms.
5 x - 5 x = 0:
3 x + 24 = 27
Hint: | Isolate terms with x to the left hand side.
Subtract 24 from both sides:
3 x + (24 - 24) = 27 - 24
Hint: | Look for the difference of two identical terms.
24 - 24 = 0:
3 x = 27 - 24
Hint: | Evaluate 27 - 24.
27 - 24 = 3:
3 x = 3
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 3 x = 3 by 3:
(3 x)/3 = 3/3
Hint: | Any nonzero number divided by itself is one.
3/3 = 1:
x = 3/3
Hint: | Any nonzero number divided by itself is one.
3/3 = 1:
Answer: x = 1
show that n(n+1)(n+2) is divisible by 6
Solution
(
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula [tex]c(x)=\frac{5}{9}(x-32)[/tex]. What transformations are used in transforming the parent graph y = x, to obtain the graph of [tex]c(x)=\frac{5}{9}(x-32)[/tex]
horizontal translation
vertical compression
reflection in the x-axis
vertical translation
reflection in the y-axis
The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula . What transformations are used in transforming the parent graph y = x, to obtain the graph of blank. The answers would be:
horizontal translationvertical compressionTo obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given function of temperature is c(x) = (5/9){ x - 32}. The two graphs are plotted on the x-y plane. It is observed that y = x is transformed to the horizontal direction.
The graph of the two functions y = x and c(x) = (5/9){ x - 32 } is attached with the answer below.
Therefore, to obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.
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Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)
Answer:
The standard equation of the sphere is [tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]
Step-by-step explanation:
From the question, the end point are (3,-2,4) and (7,12,4)
Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.
The midpoint can be calculated thus
Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]
Let the first endpoint be represented as [tex](x_{1}, y_{1}, z_{1})[/tex] and the second endpoint be [tex](x_{2}, y_{2}, z_{2})[/tex].
Hence,
Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]
Midpoint = [tex](\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})[/tex]
Midpoint = [tex](\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\[/tex]
Midpoint = [tex](5, 5, 4)[/tex]
This is the center of the sphere.
Now, we will determine the distance (diameter) of the sphere
The distance is given by
[tex]d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }[/tex]
[tex]d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}[/tex]
[tex]d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}[/tex]
[tex]d = \sqrt{16 +196 + 0[/tex]
[tex]d =\sqrt{212}[/tex]
[tex]d = 2\sqrt{53}[/tex]
This is the diameter
To find the radius, r
From [tex]Radius = \frac{Diameter}{2}[/tex]
[tex]Radius = \frac{2\sqrt{53} }{2}[/tex]
∴ [tex]Radius = \sqrt{53}[/tex]
r = [tex]\sqrt{53}[/tex]
Now, we can write the standard equation of the sphere since we know the center and the radius
Center of the sphere is [tex](5, 5, 4)[/tex]
Radius of the sphere is [tex]\sqrt{53}[/tex]
The equation of a sphere of radius r and center [tex](h,k,l)[/tex] is given by
[tex](x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}[/tex]
Hence, the equation of the sphere of radius [tex]\sqrt{53}[/tex] and center [tex](5, 5, 4)[/tex] is
[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}[/tex]
[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]
This is the standard equation of the sphere
Use the number line to find 1/4+-21/8
Answer:
[tex]-\frac{19}{8}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}-\frac{21}{8}=\frac{2}{8}-\frac{21}{8}=\frac{2-21}{8}=-\frac{19}{8}[/tex]
The required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
To add fractions with different denominators, we need to find a common denominator. In this case, we can use 8 as the common denominator:
1/4 + -21/8
1/4 - 21/8
2/8 - 21/8
-19/8
-2 3/8
To represent 19/8 on a number line, we need to divide the interval between 0 and 3 into 8 equal parts, and then count 23 of these parts from 0.
The number line would look something like below as shown.
Thus, the required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.
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4.75 lbs what is the amount in grams
Radianes a grados 5 pi sobre 3
Answer:
5pi/3x180grados/piradianes
900/3=300 grados
Step-by-step explanation:
If you continue the pattern below so that you write all of the numbers in the pattern less than 500, how many even numbers will you write? 4, 9, 14, 19, 24, 29...
Answer:
I think it would be 50 even numbers
What is 10x-2(x+6)=52 ?
Answer:x=8
Step-by-step explanation:Reorder the terms:
10x + -2(6 + x) = 52
10x + (6 * -2 + x * -2) = 52
10x + (-12 + -2x) = 52
Reorder the terms:
-12 + 10x + -2x = 52
Combine like terms: 10x + -2x = 8x
-12 + 8x = 52
Solving
-12 + 8x = 52
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '12' to each side of the equation.
-12 + 12 + 8x = 52 + 12
Combine like terms: -12 + 12 = 0
0 + 8x = 52 + 12
8x = 52 + 12
Combine like terms: 52 + 12 = 64
8x = 64
Divide each side by '8'.
x = 8
Simplifying
x = 8
Answer:
x=5
Step-by-step explanation:
2.64 gallons = how many liters
Answer:
9.9924 liters
Step-by-step explanation:
there are 3.785 liters in one gallon
multiply 3.785 liters times 2.64
that comes out to 9.9924 liters
The shaded set of numbers shown on the x-axis can be expressed in interval notation as _____
This is basically saying [tex]1 \le x < 4[/tex]
The square bracket says "include this endpoint" while the curved parenthesis means "exclude this endpoint". We can tell what is included/excluded based on how the endpoint is drawn.
Open circle = exclude endpoint
Closed/filled in circle = include endpoint
Your teacher has also drawn a square bracket at the left endpoint, and a curved parenthesis at the right endpoint. This style of drawing the endpoints helps set up [1, 4). Though sometimes you might see the use of open/closed circles instead for the endpoints. I'm referring to the number line portion.
We want to express the shaded set of numbers on the x-axis with interval notation.
The interval notation is:
[1, 4)
Let's start by analyzing the graph.
We have two ends, one at x = 1, with a colored dot, which means that that value belongs to the set.
We have the other end at x = 4, with a white dot, which means that the value does not belong to the set.
Then the interval notation is:
[1, 4)
Where [] are used for colored dots.
() are used for white dots.
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An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 11 hours. If the main pump is started at 7 PM, when should the auxiliary pump be started so that the tanker is emptied by 10 PM?
Answer:
The pump should be added by 8PM
Step-by-step explanation:
An oil tanker can be emptied by the main pump in 4 hours.
An auxiliary pump can empty the tanker in 11 hours.
the main pump is started at 7 PM,and we have 10 PM - 7PM = 3 hours to empty the tank.
So we have to look for the combined rate of the both pumps .
Let's say the volume= x
Rate of first pump= x/4
Rate of second pump= x/11
The rate will be added together
Combined rate= x/11 + x/4
Combined rate= 15x/44
But they have three hours to complete their pump
15x/44 = 3
X=1.0227
The pump should be added by 8PM
Simplify the ratio 45 to 75
The GCF of 45 and 75 is 15.
So, divide both numbers by 15.
45/15 = 3
7515 = 5
Therefore, the simplified version of the ratio is 3 to 5
Best of Luck!
Question 6 of 15, Step 1 of 1
Correct
Two trucks leave a warehouse at the same time. One travels due east at an average speed of 58 miles per hour, and the other travels due west at an average speed of
65 miles per hour. After how many hours will the two trucks be 369 miles apart?
Answer:
3 hours
Step-by-step explanation:
369 divided by (58+65)
Kaleb can skateboard 75 feet in 25 seconds. How far can he skateboard in 3.25 minutes?
Answer:
585 Feet
Step-by-step explanation:
First, you have to consider how much seconds in a minute. 60.
Then, multiply 75 feet to make it match to 60 seconds. So 60/25. You get 2.4. You multiply 2.4 by 75 to get 180 feet per minute.
Finally, you multiply 180 by 3.25, as it is 3.25 minutes.
100 POINTS I NEED HELP ASAP
If h(x) = |2x-4| , find (h-7)
Answer:
The answer is 18.
Step-by-step explanation:
You just need to plug in -7 to the equation 2x-4. You get -18, but absolute value is always positive, so its 18.
The answer is 18.
Sorry no explanation im soooo sorry
Blueberries cost 4.99 a pound. Diego paid 14.95 for his blueberries. How many pounds did he buy?
Answer:
The answer is 3.
Step-by-step explanation:
The equation would be: x = 14.95 divided by 4.99, rounded to the nearest one:
14.95 divided by 4.99 = 2.99599...
Normally, I would not round the number to the nearest digit in problems like these, but 2.99599 is quite close to 3, so this might be an exception.
Anyways, that's how I got my answer.
Hope this helped.
a town has a population of 450000 people.if 60% of the population are under 25 years of age how many people in the town are 25 years old and over?
Answer:
180000
Step-by-step explanation:
100%-60%=40% - 40% of the population are above 25 years old40/100=0.4450000*0.4=180000 - There are 180000 people in the town ages 25 and up.Point B lies on segment AC . Find the length of segment BC if AB = 4 mm and AC = 4 cm.
Answer:
4cm - 4mm = 3.6 cm
So, B and C equals 3.6 cm
which of these equations or inequalities below are true 4 - 5< -2
Answer:
4-5<-2 is false it should be 4-5>-2
Step-by-step explanation:
Answer:b
Step-by-step explanation:
A train travels at a constant speed of 60.4 miles per hour for 101.5 minutes. What distance does the train cover?
Answer:
102.2 miles
Step-by-step explanation:
First, convert the minutes to hours:
101.5/60
= 1.69 hours
Multiply this by 60.4 to find how many miles it covered:
= 102.2 miles
What fraction is greater than 3/8? 1/4 7/16 1/8 3/16
Answer:
7/16
Step-by-step explanation:
3/8 = 6/16
7/16 is greater than 6/16
Hope This Helps :)
Answer:
7/16
Step-by-step explanation:
Simplified 7/16 is 3.5/8, which is more than 3/8. The rest of the answers are less than 3/8.
The distance from the green point on the parabola to the parabola's focus is
11. What is the distance from the green point to the directrix?
Focus
11
Directrix
O A. 11
B. 9.5
C. 5.5
Answer:
11
Step-by-step explanation:
sawarasenaaa kimi wa-
What is the first step to evaluate 28-64\div828−64÷828, minus, 64, divided by, 8?
Answer:
64 Divided by 8
Step-by-step explanation:
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 4x - 2
y = x + 13
A. (1, 13)
B. (0, -2)
C. (5, 18)
D. (4,-2)
Answer:
c
Step-by-step explanation:
just plug each coordinates
5=x
18=y
if its tru for both then thats the answer
Answer:
5,8
Step-by-step explanation:
y=4x-2-----(i)
y=x+13----(ii)
Equating equation i and ii we get,
[tex]4x - 2 = x + 13[/tex]
[tex]4x - x = 13 + 2[/tex]
[tex]3x = 15[/tex]
[tex]x = 3[/tex]
[tex]substitutin \: the \: value \: of \: x \: in \: equation \: (i)[/tex]
[tex]y = 4x - 2[/tex]
[tex]y = 4 \times 5 - 2[/tex]
[tex]y = 20 - 2[/tex]
[tex]y = 18[/tex]
Marks this as a brainest answer ok.
1) 6,875 28
In the problem above,
(estimate: 6,875 28 as 6,000 + 30 = 200).
After the first digit is placed in the hundreds place in the quotient and students have
divided, multiplied, subtracted, and compared, the student should bring down the 7.
Now, estimate 1270 28 and perform a second division (repeat).
1,270 28 is estimated as 1,200 + 30 = 40.
Students then divide, multiply, subtract, and compare the remainder to the divisor,
making sure it is smaller.
Finally, perform 115 -28, by estimating, dividing, multiplying, subtracting, and
comparing
After writing the remainder in the quotient, the division is complete.
What is the Quotient? Answer:
Answer:
?
Step-by-step explanation:
rochelle needs to pick a frame that measures 7 6/11 inches on each side ?
no the frame will not fit
7 6/11 =7.545454
7.545454 is larger than 7.5
Write down an expression for the nth term of the following sequence 7,16,25,34,43
Answer:
So in this sequence, we are adding by 9 in each term
So our pattern is: 7 , 7 +9 , 7 + 2(9) , 7 + 3(9) .....
hence, we can write it as: 7 + [tex]9^{n-1}[/tex] where n is the number of the term you want
Omar's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs $4.10 Omar per pound, and type B coffee costs $5.30 per pound. This month, Omar made 141 pounds of the blend, for a total cost of $640.50. How many pounds of type A coffee did he use?
Hey there! I'm happy to help!
Let's use the variables A and B to represent the number of pounds used of types A and B.
4.10A+5.30B=640.50
A+B=141
Let's rearrange the bottom equation to solve for B.
A+B=141
Subtract A from both sides.
B=141-A
We can put this value of B into the first equation to solve for the number of pounds of type A Omar used.
4.10A+5.30(141-A)=640.5
We use distributive property to undo parentheses.
4.10A+747.3-5.3A=640.5
We combine like terms.
-1.2A+747.3=640.5
Subtract 747.3 from both sides.
-1.2A=-106.8
Divide both sides by -1.2
A=89
Omar used 89 pounds of type A coffee in this month's blend.
Have a wonderful day! :D
Solve the following inequality
-x<-7
Answer:
The answer could be any number above -7.
So, it could be...
(-8)
(-9)
(-10)
etc.
Step-by-step explanation:
The bigger the negative number, the lower the value.
Angie and Kenny play online video games. Angie buys 1 software and of game play. Kenny 2 buys software and 6 months of game play. Each software package costs $50. If their total cost is $295, what is the cost of one month of game play?
Answer:$12
Step-by-step explanation:
Answer:
months of game play (m) =$11
Step-by-step explanation: