In A, traveled hours will be increased if the distance traveled is increased and hence it is in direct variation.
In B, both x and y represent the length of a table and the difference is in units only. So, it is also in direct variation.
In C, more number of $1-off coupons used, more money will be saved and hence it is also in direct variation.
In D, if the speed is increased, then the time to travel 60 miles will be decreased. Hence it is not in direct variation.
Answer:
x = time it takes to travel 60 miles, and y = speed traveled
Step-by-step explanation:
What is the perimeter of the quadrilateral 9m 5m 7m 11m
The perimeter is 32m add all sides to find perimeter
3 less than a product of two numbers
Let x= #1 number
let y= #2 number
We would get xy-3 as the answer
ab-3 is the required expression for the sentence "3 less than a product of two numbers". Here a and b are two numbers.
we need to write expression for 3 less than a product of two numbers
What is product of two numbers?The product is the multiplication of two integers.
Let a be one number
b be second number
Product of two numbers is ab.
as given 3 less than a product of two numbers
we get ab-3.
Therefore ab-3 is the required answer for 3 less than a product of two numbers.
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What’s the derivative of sin^2(cos(x^2))
Answer:
[tex]\displaystyle \frac{dy}{dx} = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sin^2 (\cos x^2)[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 2 \sin (\cos x^2) \Big( \sin (\cos x^2) \Big)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin (\cos x^2) \cos (\cos x^2) (\cos x^2)'[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -2 \sin x^2 \sin (\cos x^2) \cos (\cos x^2) (x^2)'[/tex]Basic Power Rule: [tex]\displaystyle y' = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Explain the distance formula. Then use it to calculate the distance between A(1,1) and B (7,-7)
The distance formula is given by:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
We are given two points A and B as
A(1,1) and
B(7,-7)
so we have ,
x1 = 1 , y1=1
x2= 7 and y2=-7
Plugging these in the formula we have:
[tex]d=\sqrt{(7-1)^{2}+(-7-1)^{2} }[/tex]
d=√(36+64)
d=√100
d=10
Answer: The distance between A(1,1) and B(7,-7) is 10
Answer:
d=10 units
Step-by-step explanation:
Hello.
Step 1
the formula of the distance between two points is based on the Pythagorean theorem, which states that in a rectangle :
[tex]side^{2} +side^{2}=hypotenuse^{2}\\[/tex]
Now, suppose we have two points P1(X1,Y1) and P2(X2,Y2), the distance between the two points will be the hypotenuse of our triangle, the difference in x will be the adjacent leg, and the difference in coordinates in y will be our opposite leg.
adjacent side =X2-X1
opposite side=Y2-Y1
hypotenuse=distance between P1 and P2
replacing
[tex]adjacent\ leg^{2} +opposite\ leg^{2}=hypotenuse^{2}\\(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}=(distance between\ P1\ and\ P2)^{2}\\ distance between\ P1\ and\ P2=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\\\[/tex]
we take only the positive root because it is a distance, a negative distance makes no sense
Step 2
find the distance between A(1,1) and B (7,-7) using the formula
Let
P1=A(1,1)
P2=B(7,-7)
put the values into the formula
[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\let\\\\x_{1}=1,y_{1}=1,x_{2}=7,y_{2}=-7\\d=\sqrt{(7-1) ^{2} +(-7-(1))^{2}}\\d=\sqrt{(6) ^{2} +(-8)^{2}}\\d=\sqrt{36 +64}\\d=\sqrt{100}\\ d=10[/tex]
d=10 units
Have a good day.
Angie and Kenny play online video games. Angie buys 1 software package and 3 months of game play. Kenny buys 1 software package and 4 months of game play. Each software package cost $50. If the total cost is 240, what is the cost of one month of gameplay ?
Given
Angie and Kenny play online video games
Angie buys 1 software package and 3 months of game play
Kenny buys 1 software package and 4 months of game play
Each software package cost $50
total cost is 240
Find out the cost of one month of gameplay.
To proof
let us assume that the cost of one month of game play = x
As given in the question
Angie buys 1 software package and 3 months of game play
Kenny buys 1 software package and 4 months of game play
Each software package cost = $50
Total cost =$240
Than the equation becomes
( 50 + 3x ) + ( 50 + 4x ) = 240
100 + 7x= 240
7x= 140
x = $20
The cost of one month gameplay is $ 240.
Hence proved
Find each unit rate. Round your answer to the nearest hundredth.
1.) Teresa can buy 18 golf balls for $32.99.
2.) A 15 oz bottle of juice costs $2.75.
For unit rate, divide the total dollar amounts by the amount of the item you have.
in number 1:
18 golf balls equal $32.99
so divide 32.99 by 18
32.99
18
This tells us that 1 golf ball costs roughly $1.83
2. Do the same thing except put the ounces of juice under the total cost
2.75
15
This will tell us that 1 oz of juice costs $0.18.
Since this is in word form, it is a rule in higher math to answer in the same format.
The unit rate for one golf ball is $1.83, and it costs $0.18 per ounce of juice.
Factor completely 12x4 + 6x3 + 18x2.
Prime
3(4x4 + 2x3 + 6x2)
3x2(4x2 + 2x + 6)
3x(4x3 + 2x2 + 6x)
Answer:
B)3x^2 (4*x^2 + 2x + 6)
Step-by-step explanation:
Step 1: Find the Greatest common factor of the given expression.
12x^4 + 6x^3 + 18x^2
The above expression can be written as .
= 2*2*3*x^4 + 2*3*x^3 + 2*3*3*x^2
Here 3x^2 is prime factor
Step 2: Let's take out the 3[tex]x^{2}[/tex] and write the remaining terms in the parenthesis.
= 3x^2 (2*2*x^2 + 2x + 2*3)
= 3x^2 (4x^2 + 2x + 6)
Therefore, the answer is B)3x^2 (4*x^2 + 2x + 6)
Thank you.
Write the expanded form for the decimal 24.56
Final answer:
The expanded form of the decimal 24.56 is 20 + 4 + 0.5 + 0.06, which breaks down each digit by its place value.
Explanation:
The expanded form of the decimal 24.56 is an expression that shows the value of each digit in the number. To write it in expanded form, we break down each digit according to its place value. For the number 24.56, the expanded form would look like this:
20 (which represents 2 tens, or 2 × 10)4 (which represents 4 ones, or 4 × 1)0.5 (which represents 5 tenths, or 5 × 0.1)0.06 (which represents 6 hundredths, or 6 × 0.01)Combining these values, the expanded form of 24.56 is:
20 + 4 + 0.5 + 0.06
Determine the equation of the line given by the graph.
A) y = 5/7 x − 2/3
B) y = 5/7 x − 3/2
C) y = 7/5 x − 2/3
D) y = 7/5 x − 3/2
Hello!
I was going to try to use the slope formula, and solve for the y-intercept, but the given graph is hard to distinguish accurate ordered pairs. So, we will find the equation with the graph instead.
Looking at the graph, we can see that the y-intercept is negative. Also, we can also determine that each square represents one unit. So, the y-intercept has to be -3/2 or -1.5. That removes the choices A and C because the y-intercept is in between the values of -1 and -2.
Secondly, the graph has a positive slope. Why? When the x-values increase, the y-values increase. Also, when the x-values decrease, the y-values also decrease. This tells us that the graph has a positive slope (this doesn't remove any choices, but it helps to distinguish which graph has a positive or negative slope).
Finally, we know that if the slope is greater than one, then it is steeper (m > 1). But, if it's less than one, then it becomes less steep (0 < m < 1). Looking at the graph, the graph looks relatively steep (graphing the equations y = 5/7 x - 3/2 and y = 7/5x - 3/2 can help you see the differences between them).
Therefore, the equation of the line given by the graph is choice D, y = 7/5 x − 3/2.
The equation of the line given by the graph is y = 5/7 x - 2/3 (Option A).
Explanation:The equation of the line given by the graph is y = 5/7 x - 2/3 (Option A).
To determine the equation, we look at the slope and y-intercept of the line. The slope of the line can be determined by comparing the change in y-coordinates to the change in x-coordinates between any two points on the line. In this case, the slope is 5/7. The y-intercept is the value of y when x = 0, which is -2/3 in this case.
Therefore, the equation of the line is y = 5/7 x - 2/3.
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nick can read 3 pages in 1 minute. write the ordered pairs for nick reading 0,1,2, and 3 minutes.
(0, 0) 0 pages in zero minutes.
(3, 1) 3 pages in one minute.
(6, 2) 6 pages in two minutes.
(9, 3) 9 pages in three minutes.
Solve for x.
−32>−5+9x
The inequality is
[tex]-32> -5+9x[/tex]
We need to isolate x and for that first we need to get rid of 5 by adding 5 to both sides.
[tex]-32+5 +-5+9x+5\\-27>9x\\[/tex]
Now we need to get rid of 9 and for that we divide both sides by 9 .That is
[tex]-\frac{27}{9}>\frac{9x}{9}[/tex]
[tex]-3>x[/tex]
[tex]x<-3[/tex]
Lori was paid a 15 percent commission for the home audio system that she sold. The electronics store had marked up the price of the system by 60 percent over the wholesale price of $264. How much did Lori earn for the sale of the home audio system? $15.84 $23.76 $39.60 $63.36
The wholesale price of the home audio system is = $264
The electronics store had marked up the price of the system by = 60%
So, the additional price becomes= [tex]\frac{60}{100}*264[/tex] = $158.40
Total price of the audio system now becomes = 264+158.40 = $422.40
As Lori was paid commission of = 15% on 422.40, so her commission becomes = [tex]\frac{15}{100}*422.40[/tex]
= $63.36
Hence, option D is correct.
Answer:
Lori was paid a 15 percent commission for the home audio system that she sold. The electronics store had marked up the price of the system by 60 percent over the wholesale price of $264. How much did Lori earn for the sale of the home audio system?
Answer is=$63.36
Step-by-step explanation:
I am doing a unit test on it.
3/8 into a mixed number
Answer:
296
Step-by-step explanation:
111/3 = 37
37 * 8 = 296
Hope this helps :-)
a piece of string is 3 yards long. How many 1 and a quarter yard long pieces can Julie cut from the string?
Answer:
2 pieces
Step-by-step explanation:
Julie wants to cut 1 and a quarter yard long pieces of a 3 yard string.
1 and a quarter yard = [tex]1\frac{1}{4}[/tex] yards = [tex]\frac{5}{4}[/tex] yards
= 1.25 yards
The total length of a piece of string = 3 yards
Julie can cut the number of pieces of 1.25 yards = [tex]\frac{3}{1.25}[/tex]
= 2.4 pieces
She can cut 2 pieces of 1.25 yard = 1.25 × 2 = 2.5 yard
3 yard - 2.5 yard = 0.5 yard would be leftover.
The sum of 5 consecutive integers is 110, what is the fourth number in this sequence?
The answer is: " 23 " .
→ The fourth number in the sequence is: " 23 " .
_____________________________________
Explanation:
To solve:
" x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;
in which:
"x" = The first number in these sequence;
"(x + 1 )" = the second number in the sequence;
"(x + 2)" = the third number in the sequence;
"(x + 3)" = the fourth number in the sequence;
"(x + 4)" = the fifth number in the sequence;
_____________________________________
Solve for the "fourth number in the sequence" ; or: "(x + 3)" ;
_____________________________________
Given: " x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;
↔ " x + x + 1 + x + 2 + x + 3 + x + 4 = 110 " ;
→ Solve for "x" ;
→ then, solve for "(x + 3)" ;
→ which is the fourth number in this sequence;
_____________________________________
→ " x + x + 1 + x + 2 + x + 3 + x + 4= 110 " ;
"5x + 1 + 2 + 3 + 4= 110 " ;
" 5x + 10 = 110 " ;
Solve for "x" :
Subtract "10" from EACH SIDE of the equation; as follows:
" 5x + 10 - 10 = 110 - 10 " ;
to get :
" 5x = 100 " ;
Now, divide EACH SIDE of the equation by "5" ;
to isolate "x" on one side of the equation; & to solve for "x" ; as follows:
5x / 5 = 100 / 5 ;
to get:
" x = 20 " .
_____________________________________
Now, to find the fourth number in the sequence:
→ " (x + 3) " ;
→ Substitute "20" for "x" ;
" x + 3 = 20 + 3 = 23" ;
_____________________________________
The answer is: " 23 " .
The fourth number in the sequence is: " 23 " .
_____________________________________
Let us check our work:
If there are five "5" numbers in the sequence, and "23" is the "fourth number" , then: "24" is the "fifth number" .
As such: "22" is the "third number" ; "21" is the "second number" ; and "20" is the "first number" . Is this consistent with: "x = 20" as the "first number" ? Yes!
Thus, "20 + 21 + 22 + 23 + 25 = ? 110 ? ? ;
→ 20 + 21 = 41 ;
→ 41 + 22 = 63 ;
→ 63 + 23 = 86 ;
→ 86 + 24 = 110 . Yes!
_____________________________________
Hope this answer is helpful!
Best wishes in your academic pursuits—
and within the "Brainly" community!
_____________________________________
Answer:
23
Step-by-step explanation:
Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).
Start with expressions in blue boxes:
1st column) [tex]36x+9;[/tex]
2nd column) [tex]9(4x-1)=36x-9;[/tex]
3rd column) [tex](4\cdot 9x)+(4\cdot 2)=36x+8.[/tex]
You have 6 expressions. Consider all them:
1. [tex]36x+8[/tex] - 3rd column;
2. [tex](9\cdot 4x)+(9\cdot 1)=36x+9[/tex] - 1st column;
3. [tex](3\cdot 12x)-(3\cdot 3)=36x-9[/tex] - 2nd column;
4. [tex]9(4x+1)=36x+9[/tex] - 1st column;
5. [tex]36x-9[/tex] - 2nd column;
6. [tex]4(9x+2)=36x+8[/tex] - 3rd column.
Answer:
The equivalent expressions are:
[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]
[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]
[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]
Step-by-step explanation:
Consider the provided expressions.
[tex]36x + 9[/tex]
The expression [tex]36x + 9[/tex] can be written as:
[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)[/tex]
[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]
Consider the expression [tex]9(4x-1)[/tex]
The expression [tex]9(4x-1)[/tex] can be written as:
[tex]9(4x-1)=36x-9[/tex]
Take 3 common.
[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]
Consider the expression [tex](4\cdot 9x)+(4\cdot 2)[/tex]
The expression [tex](4\cdot 9x)+(4\cdot 2)[/tex] can be written as:
Take out 4 common
[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)[/tex]
Open the parentheses.
[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]
simplify the negative square root of negative 75
he negative square root of negative 75
= - √-75
= - √(25 * 3 * i^2) ...............because i^2 = -1
= - 5i√3
The negative square root of -75 simplifies to [tex]5\sqrt{3}i[/tex] in the complex number system. 'i' is the imaginary unit, where i is the square root of -1.
Explanation:In Mathematics, we cannot take the square root of a negative number in the set of real numbers. However, we use the concept of imaginary numbers where i is the square root of -1. Therefore, to simplify the negative square root of negative 75, we begin to simplify the terms inside the square root. Negative 75 can be factored into -1 and 75. Therefore, the square root of -75 is[tex]\sqrt{75}i[/tex], where the square root of 75 can further simplifies it to[tex]5\sqrt{3}i[/tex] , making the final answer [tex]5\sqrt{3}i[/tex]
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simplify final form.
[tex]\left(\dfrac{3}{\sqrt5}\right)\left(\dfrac{4}{\sqrt3}\right)=\dfrac{3\cdot4}{\sqrt5\cdot\sqrt3}=\dfrac{12}{\sqrt{5\cdot3}}=\dfrac{12}{\sqrt{15}}\\\\=\dfrac{12\cdot\sqrt{15}}{\sqrt{15}\cdot\sqrt{15}}=\dfrac{12\sqrt{15}}{15}=\dfrac{12\sqrt{15}:3}{15:3}=\dfrac{4\sqrt{15}}{5}[/tex]
[tex]Used:\\\\\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\\\\\sqrt{a}\cdot\sqrt{a}=a[/tex]
Identify the quotient and the remainder. (24x3 − 14x2 + 20x + 6) ÷ (4x2 − 3x + 5) = Q + R 4x2 − 3x + 5
Answer:
Quotient : 6x+1
Remainder : -7x+1
Step-by-step explanation:
got it right on assignment
Using the long divison method, Therefore, remainder is calculated and quotient values are ( - 7x - 1) and 6x + 1 respectively.
Dividend = 24x³ - 14x² + 20x + 6Divisor = 4x² - 3x + 5__________| 6x + 1 - - - - - - - - - - - - Quotient
___________
4x² - 3x + 5 | 24x³ - 14x² + 20x + 6
__________|24x³ -18x² + 30x
-_______________4x² - 10x + 6
-_______________4x² - 3x + 5
___________________-7x - 1 - - - - - - - - Remainder
Therefore, remainder is calculated and quotient values are ( - 7x - 1) and 6x + 1 respectively.
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If u help me out I will give a thanks...a hot air ballon are able to fly at a very high altitudes. A world record height of 68,997 feet was set in 1988. In 2005, a new record of 68,986 feet was set. How many feet higher was the 2005 record then 1988 record?
What’s 150 divided by 180 step by step?
150 can't go into 180 equally, so the answer is 1.2
error analysis 7 3/4 divided 1/3
I don't really under stand what to do but the answer for 7 3/4 divided by 1/3 is 23 1/4.
Let me know what else is needed to figure out your question.
Using graph paper determine the line described by the given point and slope (0,0) and -2/3
Answer:
your graph is gonna have a horizontal line crossing the y axis at (0,3)
(2n-9)-5(-2.4n+4) please help!
(2n - 9) - 5(-2.4n + 4) =
The first set of parentheses is unnecessary, so we just drop them.
= 2n - 9 - 5(-2.4n + 4)
Now we distribute -5 by the second set of parentheses. Each term in the parentehses is multiplied by -5.
= 2n - 9 + 12n - 20
Now we combine like terms.
= 2n + 12n - 9 - 20
= 14n - 29
What is 4 * 492 equal to the product
Answer:
1968
Step-by-step explanation:
I use the following method when it comes about products of big numbers
I grab the longer and put on the first line, below I put the smallest number.
492
x 4
Now, it is time to distribute the product, term by term, remember that when performing a product, if the result is greater or equal than 10, you need to carry a number for the following product.
492
x 4
--------------------
19 6 8
(end) (c3) (nc)
nc means: not carrying anything since 4x2=8 and 8 <10
c3 means: carrying 3 since 4x9= 32 and 32 >10
end means: put the whole number and sum it what you were carrying. 4*4+3=19
The product 492*4=1968
The product of 4 multiplied by 492 equals 1968. To find this, we used a step-by-step approach using basic multiplication and the distributive property.
To determine the product of 4 multiplied by 492, you can execute the following steps:
First, break down the problem into smaller, manageable parts. Let's use the fact that 4 = 2 x 2.Multiply 4 by 492 directly: 4 × 492.To perform this calculation step-by-step, you can apply the distributive property: (4 × 500) - (4 × 8).Calculate each part: 4 × 500 = 2000 and 4 × 8 = 32.Subtract the second product from the first: 2000 - 32 = 1968.Therefore, 4 × 492 = 1968.
calculate the midpoint of a line segment with the endpoints 7,12 and -1,6
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have:
[tex]A(7,\ 12)\to x_A=7,\ y_A=12\\B(-1,\ 6)\to x_B=-1,\ y_B=6[/tex]
Substitute:
[tex]\dfrac{7+(-1)}{2}=\dfrac{7-1}{2}=\dfrac{6}{2}=3\\\\\dfrac{12+6}{2}=\dfrac{18}{2}=9[/tex]
Answer: (3, 9).Culinary Arts AGAIN!!! Please help me
Dived the price by the number of ounces and that should be your answer to the questions .
In a basketball game, the bulldogs make a total of 21 shots. Some of the shots are 2-pt shots while others are 3-pt shots. The bulldogs score a total of 50 points. How many 2-point and 3-point shots did they make?
Answer:
It is 8 3 pointers and 13 2 pointers
Step-by-step explanation:
8 x 3 = 24
13 x 2 = 26
24 + 26 = 50
The bulldogs made 13 2-pt shots and 8 3-pt shots.
Explanation:Let's assume that the bulldogs made x 2-pt shots and y 3-pt shots. Since each 2-pt shot is worth 2 points and each 3-pt shot is worth 3 points, we can set up the following equations: 2x + 3y = 50 (equation 1) and x + y = 21 (equation 2). To solve this system of equations, we can multiply equation 2 by 2 to get 2x + 2y = 42, and then subtract equation 1 from it. This gives us y = 8. Substituting y = 8 into equation 2, we get x + 8 = 21, which means x = 13. Therefore, the bulldogs made 13 2-pt shots and 8 3-pt shots.
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the money used in eygpt is called the pound.The exchange rate is $5 to 29 pounds. Find how many Pounds you would recieve if you exchanged $15
87 Pounds would be the correct answer I believe.
5x=29x
x=3
87 pounds
Since $5 = 29. You can multiply both 5 and 29 to get 15=87 pounds
outhside High School had a big basketball game Friday night. Six players contributed to their score. Three players scored 16 points each, 2 players made 21 points each and 1 player scored 8 points. Which expression would give you their final score?
A) (16 + 21 + 8) x 6
B) 3 x 16 + 2 x 21 +1
C) (3 x 16) + (2 x 21) + 8
D) (3 + 2 + 1) x (16 + 21 + 8)
*I hope this will help*
(3 x 16) + (2 x 21) + 8
3 people made 16, which is 48
2 made 21, making 42
and 1 made 8, making 8
The answer would be c. because there is 3 players with 16 points (3x16) and 2 with 21 points (2x21) so (3x16)+(2x21) and one player scored 8 points so (3x16)+(2x21)+8
I hope this helps have a nice day