Answer:
8.17.4 miles per 1 gallons 9. 2 miles per second.
Step-by-step explanation:
so you have yo divide 384 divided by 22 then boom.
Once again you have to divide 60 which is 1 hour (60 minutes is an hour) to the 32 miles. :)
Problem 8
Answer: Approximately 17.45 miles per gallon-----------------------
Explanation:
You divide the number of miles over the number of gallons to get this result
384/22 = 17.45
Another way you could think of it is to say
384 miles = 22 gallons
Then you divide both sides by 22 getting
17.45 miles = 1 gallon
Showing that 1 gallon of gas gets you roughly 17.45 miles
=============================================
Problem 9
Answer: Approximately 46.933 feet per second---------------------
Explanation:
Check out the attached diagram below. For the first column, I placed "32 miles" over "1 hour" to indicate "32 miles per hour". The second column is from the idea that 1 hour = 60 minutes. This helps us convert from hours to minutes. Note how the "hour" units cancel when we divide.
The third column helps us convert from minutes to seconds. We have the "minutes" units cancel out when they divide. It's important that one "minute" unit is on top, and the other is on the bottom. Finally, the last column helps us convert from miles to feet since 1 mile = 5280 feet.
Once this table formed, you multiply the numbers across the top to get 32*1*1*5280 = 168960
And you multiply everything along the bottom row: 1*60*60*1 = 3600
The last step is to divide the two results (top row over bottom row) getting
168960/3600 = 46.933 approximately
So 32 mph converts to roughly 46.933 ft per second.
Side note: the conversion method I used is called the "railroad method" or "railroad tracks method" as the table lines form what appears to be railroad tracks of sorts.
In the equation 2y=18, determine which property of equality will be used to isolate the variable. Choose the best answer. A. Multiplication Property of Equality B, Addition Property of Equality C. Division Property of Equality D. Subtraction Property of Equality
Answer:
(C) Division Property of Equality
Step-by-step explanation:
Looking at the equation [tex]2y=18[/tex], we see that if we want to isolate y, we need to divide it by 2 - because we're multiplying it by 2, and 2 times a number divided by 2 is just the number.
The Division Property of Equality states that if we have an equation, [tex]a=b[/tex], then [tex]a\div c = b\div c[/tex].
So, that means [tex]2y\div 2[/tex] will be equal to [tex]18 \div 2[/tex], which is 9.
Hope this helped!
Answer:
C. Division Property of Equality
Step-by-step explanation:
The equation is
2y = 18
The answer is of the form
y = a number
Now, we have 2y. We want y alone. 2y means 2 multiplied by y. Since we want y alone, to undo the multiplication of 2 and y, we need to use division. We need to divide 2y by 2. Then we also need to divide the right side by 2. Since we are using division, the answer is:
C. Division Property of Equality
Plz plz someone help me out with this
Answer:
option D
[tex]a_{1}=6561 and a_{n}=\frac{1}{3}a_{n-1}[/tex]
Step-by-step explanation:
[tex]a_{3} = 729\\\\a_{4} = 243\\\\r = \frac{a_{4}}{a_{3}}\\\\r=\frac{243}{729}\\\\r=\frac{1}{3}[/tex]
Recursive rule: Next term is obtained by multiplying (1/3) wiht the previous term
[tex]a_{n}=\frac{1}{3}*a_{n-1}[/tex]
[tex]a_{3} = \frac{1}{3}*a_{2}\\\\\\729 = \frac{1}{3}*a_{2}\\\\\\729*3=a_{2}\\\\a_{2} = 2187\\\\\\[/tex]
[tex]a_{2}=\frac{1}{3}*a_{1}\\\\\\2187=\frac{1}{3}*a_{1}\\\\\\2187*3=a_{1}\\\\a_{1}=6561[/tex]
Nancy bought 8 amusement park tickets for $82. About how much did each ticket cost?
Answer:
10.25
Step-by-step explanation:
Answer:
the answer would be 10.25
Answer it answer it answer it
Answer:
It sooo D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Solve x+y+z=10 −2x−2y−z=−32 3x−2y+2z=−8 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(12, 10, -12)
x = 12
y = 10
z = -12
Step-by-step explanation:
Let's start by picking a variable to eliminate from the three equations, since "z" is at the end, let's go with "z".
Next we'll eliminate z from two of the equations by adding them together so:
(x+y+z=10) + (-2x-2y-z=-32)
you'll get: -x-y=-22
Next we'll eliminate z from the remaining equation in the same way so:
(-2x-2y-z=-32) + (3x-2y+2z=-8)
you'll get: -x-6y=-72
We now have two new equations:
-x-y=-22
-x-6y=-72
From these let's eliminate another variable, let's go with "x" and since both "x" are negative we'll multiply one of the equations by the negative sign of the other equation so we'll end up with one positive x and one negative x, which looks like this:
-x-y=-22
x+6y=72
and when we add these two equations we get:
5y=50
Finally we can solve for y:
y=10
With the known value of y we can use y to plug into the other equations and solve for the x and z variables to get x=12, y=10, z=-12
help meeeeee plllllsssss 10pts + brainliest!!!!
Answer:
[tex]\frac{3*(8e-4f-1)}{8}[/tex]
I hope this helps. Sorry for a late response. I used
tiger-algebra.com
PEACE!☘️
Which are equivalent to Two and one-third times three-fourteenths? Check all that apply. One-half,Six-thirds times three-fourteenths, Seven-thirds times three-fourteenths, 18/42, 21/42
Answer:
Step-by-step explanation:
[tex]2\frac{1}{3}*\frac{3}{14}=\frac{7}{3}*\frac{3}{14}=\frac{1}{2}\\\\[/tex]
option 1)one- half
1/2
Option 3) Seven-thirds times three fourteenths
[tex]\frac{7}{3}*\frac{3}{14}=\frac{1}{2}\\\\[/tex]
Option 5) 21/42
[tex]\frac{21}{42}=\frac{1}{2}[/tex]
help me please I've tried for hourss
Answer:
I = BLv/R
Step-by-step explanation:
V = BLv
V = IR
Since both right sides are equal to V, set the right sides equal to each other.
IR = BLv
I = BLv/R
Perform the operation below using a number line. -7-(-8). ASAP. pleeease help.
Answer:
1
Step-by-step explanation:
Calculation steps:
-7-(-8) = ⇒ two negatives cancel and change to positive
- 7 + 8 = ⇒ 8-7 = 1
1 ⇒ answer
Which of the following is an equation of the line that passes through the point (–2, 3) and is perpendicular to the graph of the equation y = 3x – 2? A. y = –13x + 73 B. y = –13x + 113 C. y = 3x + 9 D. y = 3x – 3
Answer:
its is a
Step-by-step explanatioits n:
The equation of the line will be y = (1/3)x + ( 11 / 3 ). The correct option is B.
What is an equation of a line?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Let m be the slope of the line and c is the y-intercept of the line.
The equation of the line is given as,
y = mx + c
The product of the slopes of the perpendicular lines is equal to -1.
y = 3x – 2
m = 3
Then the slope of the perpendicular line will be -1 / 3. The equation of the line will be written as below:-
y = (-1 / 3)x + c
The line is passing through the point (–2, 3). Then calculate the value of the constant.
3 = (-1 / 3 )2 + c
c = 11 / 3
The equation of the line will be:-
y = (-1/3)x + (11/ 3)
Therefore, the equation of the line will be y = (1/3)x + ( 11 / 3 ). The correct option is B.
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You need to buy canning jar. They cost $15 a box, and you only have $150 to spend. You also have a coupon that will give you a $25 discount on your total. What is the maximum number of boxes you can buy?
Answer:
You can buy a maximum number of 11 boxes
Step-by-step explanation:
The first step is to calculate the number of boxes that you can afford with the $150 without the discount. This can simply be done by dividing $150 by $15
= 10 boxes.
The next step is to calculate the effect of the discount on the total of $150. The $25 discount will increase your average sum to $175. This extra $ 25 can afford you one more box. bringing the total number of boxes to 11.
You can buy a maximum number of 11 boxes
Students in the marching band are choosing new colors for the hats and the pants of their
uniforms. For each item, they can choose yellow (Y), green (g), or black (B). Which table
represents the sample space of choosing one color for the hat and one color for the pants?
Answer:
The sample space table is shown below.
Step-by-step explanation:
It is provided that the students has to select new colors for the hats and the pants of the marching band uniforms.
The color options for each item are:
yellow (Y), green (G), or black (B).
The sample space for the color selection of hats and pants is:
Sample Space
Hats Pants
Y Y
Y G
Y B
G Y
G G
G B
B Y
B G
B B
There are a total of 9 possible selections.
The number of the total possible selections is 9.
What is the combination?
The arrangement of the different things or numbers in a number of ways is called the combination.
It is provided that the students has to select new colors for the hats and the pants of the marching band uniforms.
The colour options for each item are:
yellow (Y), green (G), or black (B).
The sample space for the color selection of hats and pants is:
Sample Space
Hats Pants
Y Y
Y G
Y B
G Y
G G
G B
B Y
B G
B B
There are a total of 9 possible selections.
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PLEASE HELP! I will mark brainliest!
Answer:
D
Step-by-step explanation:
Instead of going through each of the table, let's create one ourselves.
So, we have the piecewise function:
[tex]f(x)=-x+8,\text{ if } x<4\\f(x)=x, \text{ if } x\geq 4[/tex]
So, let's create a table of values starting with 2 and skipping the odd numbers until 12.
2:
For 2, since 2 is less than one, plug it into the first equation. Thus:
[tex]f(2)=-(2)+8=6[/tex]
So, the first value is (2,6).
For 4, since 4 is not less than 4 but rather equal to 4, use the second equation. Thus:
[tex]f(4)=(4)=4[/tex]
The second value is (4,4).
For 6, the same thing. 6 is greater than 4 so use the second equation:
[tex]f(6)=(6)=6[/tex]
So the third value is (6,6).
And this pattern will repeat. Therefore, our table of equations is:
x | y
2 | 6
4 | 4
6 | 6
8 | 8
10 | 10
12 | 12
The choice that represents this is D. D is the correct answer.
Evaluate 6 - 2(-1) +1|-5|= 1
a.9
b.1
c.13
Answer:
c
Step-by-step explanation:
What is the product of (negative 6) (negative 7) (negative 1)?
Answer:
-42
Step-by-step explanation:
negative * negative = positive
positive * negative = negative
negative * positive = negative
(-6)(-7)(-1) =
= 42(-1)
= -42
Answer:
-42
Step-by-step explanation:
negative * negative = positive
positive * negative = negative
negative * positive = negative
(-6)(-7)(-1) =
= 42(-1)
= -42
Which expression is equivalent 4/5 - 1/3?
Answer:
7/15
Step-by-step explanation:
Well 4/5 - 1/3 = 12 / 15 - 5 / 15 which is equal to 7/15, but there aren't any expressions in your question.
Answer:
7/15
Step-by-step explanation:
4/5 - 1/3 = 12 / 15 - 5 / 15 = 7/15
Which set of side length is a Pythagorean triple? A. 2,3,13 b. 5,7,12 C. 10, 24, 29 D. 11,60,61
Answer:
B. 5,7,12 is what I got.
How to find the value of :-
[tex] \sqrt{35} [/tex]
[tex] \sqrt{2} [/tex]
What is the greatest common factor of 3x^43x 4 3, x, start superscript, 4, end superscript, 15x^315x 3 15, x, cubed, and 21x^221x 2 21, x, squared?
Answer:
3x²Step-by-step explanation:
Given three functions 3x⁴, 15x³and 21x², the greatest common factor is the greatest value that can divide through the three functions at the same time.
To get this GCF, let us divide each functions into simplest form
3x⁴ = (3 *x * x) * x * x
15x³ = 5 * (3 * x * x) * x
21x² = 7 * (3 * x * x)
It can be seen that the product in parenthesis is common to the three functions given on expanding them, hence the greatest common factor of the three functions is 3 * x * x = 3x²
Which of the following correctly uses exponents to write "6 factors of 2"? A.62 B.26 C.6 ∙ 2 D.12
Answer:
A. 6 to the Second Power.
Step-by-step explanation:
Hope it Helped!
Which of the following correctly uses exponents to write "6 factors of 2"?
2 6
6 ∙ 2
12
6 2
Answer:
First one
Step-by-step explanation:
If you mean 2 to the sixth power, then it's for sure the first one.
Answer:
2^6
Step-by-step explanation:
The ratio of adults to children on a train in 7:2. There are 245 adults on the train. Find the total number of people on the train?
Answer:
315 people
Step-by-step explanation:
Using the given ratio, we can figure out the number of children on the train by doing cross multiplication.
Let x = # of children on train.
7/2 = 245/x
7x = 490
x = 70 children
The total number of people = 70 + 245 = 315 people total
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A bag contains 7 red marbles, 8 blue marbles and 3 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red?
Answer:
7/51
Step-by-step explanation:
Assuming that the marbles are drawn without replacement, the probability of the first marble being drawn is 7/(7+8+3) which is 7/18.
The probability of the second marble being red is 6/17, as there are 6 red marbles left and 17 marbles in the bag.
We then multiply 7/18 and 6/17, getting 7/51.
A manufacturer determines that the cost of making a computer component is $4.252525. Write the
repeating decimal cost as a fraction and as a mixed number. The cost written as a fraction is???
Answer:
4 25/99 is the mixed fraction.
25/99 is the fraction
What is the answer to m^7 · m^−3?
Answer:
M^4
Step-by-step explanation:
Here use product law which state- same base power should add
M^7-3
M^4
Q1. Find y, if √12 - √147 + y√3 = 0
Q2. Without using tables or calculators, find the value of Sin45° - Cos30°
Hints: Sin45° = √2/2 Cos 30° = √3/2.
Answer:
Q1. y = 5 Q2. (√2 - √3)/2
Step-by-step explanation:
Q1
√12 - √147 + y√3 = 0
Taking -√147 and √12 to the right hand side, we have
y√3 = √147 - √12
y√3 = √(3 × 49) - √(3 × 4)
y√3 = √3 × √49 - √3 × √4
y√3 = √3 × 7 - √3 × 2
y√3 = 7√3 - 2√3
y√3 = 5√3
Dividing both sides by √3, we have
y√3/√3 = 5√3/√3
y = 5
Q2
Sin45° - Cos30°
Since Sin45° = √2/2 and Cos 30° = √3/2
Substituting these values into the equation, we have
Sin45° - Cos30° = √2/2 - √3/2
Taking L.C.M of both factors, we have
Sin45° - Cos30° = (√2 - √3)/2
The amount of money spent at the gas station varies directly with the number of gallons of gas purchased. 12 gallons of gas costs $36.00. How much would 8 gallons of gas cost?
Answer:
$24.00
Step-by-step explanation:
12 = 36
8 = x
=> Cross multiply
=> 12 * x = 36 * 8
=> 12x = 288
=> 12x / 12 = 288 / 12
=> x = 24
8 gallons of gas costs $24.00.
8 gallons of gas will cost $24.
What are the types of variation or proportion ?There are two types of variations direct variation and inverse variation.
In direct variation between two quantities if one variable increases the other also increases and vice versa.
In inverse variation of two quantities if one variable increases the other variable decreases and vice versa.
In the given question
12 gallons of gas costs $36
∴ 8 gallons of gas will cost (36 × 8)/12 gallons
= $24
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Subtract b (b²+b -7) + 5 from 3b² – 8 and find the value of expression obtained for b = -3. please explain how you got the answer
Answer:
16
Step-by-step explanation:
Subtracting the 2 expressions
3b² - 8 - b(b² + b - 7) ← distribute parenthesis
= 3b² - 8 - (b³ + b² - 7b) ← distribute parenthesis by - 1
= 3b² - 8 - b³ - b² + 7b ← collect like terms
= - b³ + 2b² + 7b - 8 ← substitute b = - 3 into the expression
= - (- 3)³ + 2(- 3)² + 7(- 3) - 8
= - (- 27) + 2(9) - 21 - 8
= 27 + 18 - 21 - 8
= 16
Please Help! 15 Points. Which of the following can be used to rewrite the expression (3)(2+c)? There are two correct answers. A. Commutative Property of Multiplication B. Associative Property of Addition C. Associative Property of Multiplication D. Commutative Property of Addition
Answers:
A. Commutative Property of Multiplication
D. Commutative Property of Addition
=======================================
Explanation:
The commutative property of multiplication is the idea we can multiply two numbers in any order. The rule is x*y = y*x
An example would be 2*3 = 3*2 since both sides result in 6.
The same applies to 3*(2+c) because it can be written as (2+c)*3. Simply flip the two factors 3 and (2+c).
--------------------
A similar idea is the commutative property of addition. This rule says that we can add two numbers in any order we want.
x+y = y+x
An example would be 7+9 = 9+7 because both sums result in 16
Using this rule, we can rewrite 2+c as c+2
Therefore 3(2+c) is the same as 3(c+2)
--------------------
We can't use any associative properties because we would need to have 3 terms being either added or 3 terms being multiplied, for associative rules to apply.
For instance 1+(2+3) = (1+2)+3 is an example of the associative property of addition. An example of the associative property of multiplication would be 3(7*9) = (3*7)*9
Simplify the expression: 4a - 3(4 - a)
Answer:
7a-12Step-by-step explanation:
[tex]4a-3\left(4-a\right)\\\\\mathrm{Expand}\:-3\left(4-a\right):\quad -12+3a\\\\=4a-12+3a\\\\\mathrm{Simplify}\:4a-12+3a:\quad 7a-12\\\\\mathrm{Simplify}\:4a-12+3a:\quad 7a-12\\\\=7a-12[/tex]