Answer:
The difference quotient is 4.
Step-by-step explanation:
Given that:
[tex]g(x) = 4x - 1[/tex]
To find:
Difference quotient = ?
where [tex]h \neq 0[/tex]
Solution:
Formula for Difference quotient is given as:
[tex]\dfrac{g(x+h)-g(x)}{h}[/tex]
First of all, let us find out [tex]g(x+h)[/tex]
Replacing [tex]x[/tex] with [tex]x+h[/tex]
[tex]g(x+h) = 4(x+h)-1 \\\Rightarrow g(x+h) = 4x+4h-1[/tex]
Now,
[tex]g(x+h)-g(x) = (4x+4h-1 )-(4x-1)\\\Rightarrow g(x+h)-g(x) = 4x+4h-1 -4x+1\\\Rightarrow g(x+h)-g(x) = 4h[/tex]
Putting the above value in:
[tex]\dfrac{g(x+h)-g(x)}{h} = \dfrac{4h}{h}[/tex]
We are given that, [tex]h \neq 0[/tex]
[tex]\therefore \dfrac{4h}{h} = 4[/tex]
So, the difference quotient is 4.
There are 65 children in a form 1. There are 15 more boys than girls. What is
the ratio of boys to girls, in its simplest form?
Answer:
8:5
Step-by-step explanation:
there are 25 girls, and 40 boys, so you find the common factor between them,which is 5 and divide each number by 5.
25/5=5 girls
40/5=8 boys
so the ratio of boys to girls is 8:5
Alan buys 5.3 ounces of sour patch kids candy. After sharing with his friends he returns to buy an additional 6.75 ounces. How many ounces did he buy in all?
Answer:
Alan buys 12.05 ounces of sour patch kids candy in all.
Step-by-step explanation:
We are given that Alan buys 5.3 ounces of sour patch kids candy. After sharing with his friends he returns to buy an additional 6.75 ounces.
And we have to find the total ounces he buys in all.
As we know that for finding the total quantity or amount, we will use addition for calculating it.
Firstly, Alan buys = 5.3 ounces of sour patch kids candy
Additional ounces of sour patch kids candy Alan buys = 6.75
So, the total ounces of sour patch kids candy he buys in all = 5.3 + 6.75
= 12.05 ounces
Hence, he buys 12.05 ounces in all.
f(x) =x^2 +4x-60 and g(x) =x-6, find (f•g) (x) and express the result in standard form
Answer:
[tex](f o g)(x) = f(g(x))\\ = f(x-6)\\ = (x-6)^{2} +4(x-6)-60\\ = x^{2} -12x+36+4x-24-60\\ = x^{2} -8x-48\\ = (x-12)(x+8)[/tex]
Step-by-step explanation:
how do u solve for 16=17-t
Answer:
t = 1
Step-by-step explanation:
16=17-t
Subtract 17 from each side
16-17=17-17-t
-1 = -t
Multiply each side by -1
1 = t
Answer:
move 17 to the other side and subtract it from 16 leaving u with -1=-t and the divide it by -1 leaving you with t=1
Step-by-step explanation:
please help :) Kiran explores the growth of a plant in natural light, then repeats the experiment with the same plant type but different colored filters. A. asking a question B. performing an investigation C. collecting data D.providing explanations E. communication results
Answer:
Its c
Step-by-step explanation:
I answered this same question Heh. Its c because you have to collect the data in order to record the growth of each plant.
how do i solve (−7z 4 )(7z)
Answer:
-49z^5
Step-by-step explanation:
(−7z^ 4 )(7z)
Multiply the numbers together
-7*7 = -49
Add the exponents
z^4 * z = z^4 * z^1 = z^(4+1) = z^5
Put back together
-49z^5
The square of 1 3/4 is
Answer:
169/16
Step-by-step explanation:
13/4
what is a square at first
a square is the result of multiplying a number by itself
so the square of 13 will be 169
and the square of 4 will be 16
so easy...bingo
Question 2 (10 points)
(01.03 MC)
A plane can fly 11 miles per minute. The plane will fly 6 trips, and each trip is 500 miles. How many hours will the plane fly?
Answer:
4hrs 33mins
Step-by-step explanation:Speed = 11m/min
Total distance=500miles*6=3000miles
Total time= 3000miles/11m/min=273minutes = 4hrs 33mins
It costs Doug $30 to set up a cupcake stand. He charges $2 for every cupcake he sells. If Doug makes $48 of profit in one day, how many cupcakes does he sell? 14 cupcakes 24 cupcakes 12 cupcakes 39 cupcakes
Answer:
It is 39 cupcakes.
Since he charges $2 per cupcake (39), it is 78.
He makes profit so subtract 30 from 78 and you get $48.
Answer:
39
Step-by-step explanation:
how to find the 30th term in a sequence
Answer:
just use the formula
an=a+(n-1)dHelp help help help help
lets say for the first transformation x=1 and y=2
the transformation results in quadrant 2 (originating in quadrant 1) telling us it was a 90° counter-clockwise turn
for the second transformation we can let x=3 and y=4
transformation 2 results in quadrant 3 (originating in quadrant 1) telling us it was a 180° counter-clockwise turn
HOPE THIS HELPS!!!! :)
<333333333
9.356, 9.543, 9.376, 10.459
Arrange the terms in ascending order.
9.356 , 9.376 , 9.543 , 10.459
The mean of a set of numbers is the sum divided by the number of terms.
9.6835
Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
9.4595
help me its my math....
If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
Since one alternate interior angle measures 60 degrees,
the other alternate interior angle must also measure 60 degrees.
find the measure of angle b
Answer:
119 degrees
Step-by-step explanation:
as the straight line has an angle of 180 degrees and we already know that a part of it is 61 degrees so we just subtract 61 from 180 and the answer we receive is 119
Simplify (-5) ^3 125 -15 15 -125
Answer:
=−17265
Step-by-step explanation:
(−5)3(125)−1515−125
=−17265
Answer:
-125
Step-by-step explanation:
HAVE A GREAT DAY EVERYONE...what value of (m) makes this equation true
Answer:
-71
Step-by-step explanation:
(M+3)/4=-17
M+3=-17*4
M+3=-68
M=-68-3
M=-71
Hi pls help if you’re good at trigonometrytysm
Answer:
a = 80
b = 310
c = 96
Step-by-step explanation:
1)
20 + a + a = 180
2a + 20 = 180
2a = 160
a = 80
2)
180 - 65 - 65 + b = 360
b + 50 = 360
b = 310
3)
52 + c + 32 = 180
c + 84 = 180
c = 96
Anyone know how to do this?
Answer:
120, 68, 72, 36, 32, 41, 31 (Left to right, top to bottom)
Step-by-step explanation:
When looking at the tree, we start from left to right. That means the numbers on the left are larger and get smaller as we move to the right. The very first one on the left is 120 since there are 120 in the theater.
We know that 72 are female so we can put that in the lower bubble of the second column. From this information, we can find the # of males.
140-72=68. We can put 68 in the upper bubble of the second row.
We can first finish the male side with ice cream. We know 36 purchased ice cream which goes in the top bubble on the right. Now we subtract to find the remainder. 68-36=32. 32 goes right below 36
Now we go to the female side. 41 bought ice cream. This goes in the one 3rd down on the right. 72-41=31. 31 goes right below 41
Answer:
There are 120 people (both male and female)
48 male = 36 bought ice cream
12 without an ice cream
72 female = 41 bought ice cream
31 without ice cream
Hope it helps :>
A 3 L bottle of oil costs $36 and contains 12 cups. Dinesh puts 1 cup of oil, 10 garlic gloves and 1 cup of lemon juice in each batch of hummus recipe that he makes. Dinesh makes 5 batches of hummus. What is the total cost of oil that he uses in the 5 batches of his recipe?
Answer:
$15
Step-by-step explanation:
Let's start by figuring out how much 1 cup of oil costs.
12 cups of oil is 36$
Let's set up a proportion.
12/36=1/x
Cross Multiply
12x=36
Divide both sides by 12.
x=3
1 cup of oil is $3.
Dinesh makes 5 batches of hummus, and each batch requires 1 cup of oil.
5*1=5
This means he needs 5 cups of oil.
5*3=15
He used $15 worth of oil in the 5 batches of his recipe.
However, since it is impossible to buy 5/12 bottles of oil, he would have needed to spend $36.
please help I need it urgently
Answer:
240m²
Step-by-step explanation:
1/2bh
1/2(16)(30)
240m²
The utility industry had 428.5 thousand jobs in 2010 and is expected to decline at an average rate of 3 thousand jobs per year from 2010 to 2020. Assuming this holds true, what will be the utility’s percent change from 2010 to 2020?
Answer:
Utility's percent Change from 2010 to 2020 = 7%
Step-by-step explanation:
Jobs available at the utility industry in 2010= 428.5 thousand
Average rate of decline = 3 thousand
Years between 2010 and 2020
Utility's percent Change from 2010 to 2020 = Total change in jobs / jobs in 2010 × 100
Total change in jobs:
There are 10 years between 2010 and 2020
Jobs decline at an average of 3 thousand per year
Total change in jobs= 10 years × 3 thousand
= 30 thousand
Utility's percent Change from 2010 to 2020 = Total change in jobs / jobs in 2010 × 100
= 30 thousand / 428.5 thousand × 100
= 0.07 × 100
= 7%
Utility's percent Change from 2010 to 2020 = 7%
Four students each wrote an equation. Which two students wrote equations that have no solution?
Answer:
Beto and Mark
Step-by-step explanation:
To know which of the equations written by the four students has no solution, let's try to solve each.
Beto's equation:
[tex] 3m = 3m + 5 [/tex]
[tex] 3m - 3m = 3m + 5 - 3m[/tex]
[tex] 0 = 5 [/tex] (This is incorrect. 0 ≠ 5. This is not a solution)
Lila's Equation:
[tex] 9r + 4 = 4 + 9r [/tex]
[tex] 9r + 4 - 9r = 4 + 9r - 9r [/tex]
[tex] 4 = 4 [/tex] (this is correct)
Mark's equation:
[tex] 6 - n = -n + 2 [/tex]
[tex] 6 - n + n = -n + 2 + n [/tex]
[tex] 6 = 2 [/tex] (incorrect. 6 ≠ 2)
Wanda's Equation:
[tex] 8u - 2 = 2u + 8 [/tex]
[tex] 8u - 2 + 2 = 2u + 8 + 2 [/tex]
[tex] 8u = 2u + 10 [/tex]
[tex] 8u - 2u = 2u + 10 - 2u [/tex]
[tex] 6u = 10 [/tex]
[tex] \frac{6u}{6} = \frac{10}{6} [/tex]
[tex] u = \frac{5}{3} [/tex]
If you plug in the value of u into the original equation, the equation would be balanced. Therefore, this is a solution.
Beto and Mark we equations that have no solution.
Which of the following is equivalent to 2x2 + 9x + 9?
(x - 3)(2x - 3)
(x + 3)(2x + 3)
(x - 9)(2x - 1)
(x + 9)(2x + 1)
Answer:
(x+3)(2x+3)
Step-by-step explanation:
Factor:
2x^2+9x+9
=(2x+3)(x+3)
Answer:
(x + 3)(2x + 3)
Step-by-step explanation:
Sum = 9
Product = 2*9 = 18
Factors = 6 ,3
2x² + 9x + 9 = 2x² + 6x + 3x + 3 * 3
= 2x ( x + 3) + 3( x + 3)
= (x +3)(2x + 3)
30 x + 7 (3 - 4 x) =
Answer:
I'm a bit rusty. But try 58x +21
Hope I helped you.
1) what is the answer to 2^-2x2^-4
Answer:
[tex]\frac{1}{64}[/tex]
I hope this helps!
Answer:
1/64
Step-by-step explanation:
mentally calculated
no explanation
PLEASE HELPPP WILL GIVE BRAINLIEST As the students were approaching the park, they noticed a huge tower that was just being completed. Lucas and Jacob were part of the group responsible for looking at advertising. They couldn't help but to think that one of the main attractions of the park would be the ride involving this tower. It was a bright, sunny day. As they got off the bus, they collected the mathematical materials provided by their teacher. These materials included: pencil, paper, eraser, calculator, measuring tape, a clinometer (a tool used to measure vertical angles). They walked through the park until they reached the shadow of the tower. They looked up and couldn't believe how high it was.
Explain how the height of the tower might be calculated from the materials they have, using similar triangles.
If they are going to advertise the height of the tower in a brochure that is being created, they want to be sure of their answer. Describe how they could use the materials they have and trigonometry to determine the height of the tower.
Answer:
a) By multiplying the length of the shadow of the tower to the ratio of the height of the exposed pencil placed in the ground to the length of the pencil's shadow the height of the tower can be found
b) Height of the tower = Level to which the clinometer was raided + length of the shadow of the tower × tan (Angle of elevation of the top of the tower)
Step-by-step explanation:
a) The steps to measure the length of height of the tower using similar triangles are as follows;
Whereby the ground over which the tower is located is flat, place the pencil in the ground and ensure that it is upright and standing on its own
1) Measure the length of the shadow of the pencil
2) Measure the height of the exposed (above the ground) pencil
3) Find the ratio of the height of the exposed pencil to the length of the pencil's shadow
4) Measure the length of the shadow of the tower
5) Multiply the length of the shadow of the tower to the ratio of the height of the exposed pencil to the length of the pencil's shadow to find the height of the tower
b) To measure the height of the tower by trigonometry and the materials they have, we have;
1) Measure the length of the shadow of the tower using the measuring tape. Record the length as l
2) From the end of the length of the shadow of the tower, measure the angle of elevation of the top of the tower using the clinometer. Record the angle of elvation as θ
3) Measure the distance from the ground the clinometer was raised to measure the height of the shadow and record it as H₁
The height of the tower can then be found by the following formula;
Height of the tower, h = H₁+ length of the shadow of the tower × tan(θ)
h = H₁ + l × tan(θ)
equivelnt to 3(4h+2k)
Answer:
I would assume it would be 12h+6k
Answer:
Step-by-step explanation:
Use distributive property
a(b+c) = a*b + a*c
3(4h + 2k) = 3*4h + 3 *2k
= 12h + 6k
How many real number solutions does the quadratic below have? y=2x^2-10x+6
Answer:
2 real number solutions.
Step-by-step explanation:
You check the value of the discriminant b^2 - 4ac.
Here it = (-10)^2 - 4*2* 6)
= 100 - 48
= 52. (Positive)
This means that it has 2 real number solutions.
If the discriminant = 0 it has one real number solution and if negative it has no real number solutions.
Answer:
i think its 2 real number
Step-by-step explanation:
Take the equation 103=-7(x+8)+7(x+7). Jamie says this equation has no solution. Mick says it does. Who is correct? Why?
[tex] 👋 [/tex] Hello ! ☺️
Step-by-step explanation:
[tex] 103 = - 7(x + 8) + 7(x + 7) [/tex]
[tex] 103 = - 7x - 56 + 7x + 49 = 0x + 7 [/tex]
0x= 7 => x ∉ |R
[tex]\boxed{\color{gold}{S = ∅}} [/tex]
Jamie is right.
* Any number multiplied by 0 gives 0.
Stephen and Aaron solved the same equation using two separate methods
BUT WHERE IS EQUATIONS. THEN HOW CAN I HELP YOU.???