The smallest integer is 4.
How to calculate the value?Let the numbers be x, x+1 and.x + 2.
Therefore, the expression will be:
x + x + 1 + x + 2 = x(x + 2) - 9
3x + 3 = x² + 2x - 9
Collect like terms
x² + 2x - 9 - 3x - 3
x² - x - 12 = 0
x² -4x + 3x - 12
x(x - 4) + 3(x - 4)
x - 4 = 0
x = 0 + 4 = 4
The smallest number is 4.
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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.
How many gallons are left in the tank when the car has traveled the following distances on the highway?
90 miles
Answer:
13 gallons
Set It UpIf the car is able to travel 30 miles per gallon and has a 16-gallon fuel tank, its total fuel efficiency is found by evaluating the product of the two factors.
Therefore, we can multiply 30 by 16 and find the total mileage that the car is equipped to travel:
[tex]30\times16=480[/tex]
SolveNow, assuming that the car has a full tank of gas, it travels 90 miles on the highway. We can find out the remaining fuel efficiency by subtracting 90 miles from the maximum fuel efficiency:
[tex]480-90=390[/tex]
Then, since the car can travel 30 miles per gallon, divide this fuel efficiency by 30 miles to find the remaining gallons in the tank:
[tex]\displaystyle \frac{390}{30} = 13[/tex]
Final Answer[tex]\boxed{\bold{13 \ gallons}}[/tex]
A jug of juice has 8 cups of pineapple juice and 3 cups of orange juice. Write the ratio of number of cups of pineapple juice to total number of cups of juice in three different ways.
Answer:
8 : 3, 8/3, and "8 to 3"
Please help!!! I really need this!!! It's piecewise functions......
well, let's take a peek at the graph, hmmm it has a straight line from the origin to (5,10), and then another straight line from (5,10) to (10,5) and then another one from there up to (20,5).
well, let's simply get the equations for each of those lines then
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{2}(x-\stackrel{x_1}{0})\implies \boxed{y = 2x} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{5}}} \implies \cfrac{ -5 }{ 5 }\implies -1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-1}(x-\stackrel{x_1}{5}) \\\\\\ y-10=-x+5\implies \boxed{y=-x+15} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{20}-\underset{x_1}{10}}} \implies \cfrac{ 0 }{ 10 }\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{0}(x-\stackrel{x_1}{10})\implies y-5=0\implies \boxed{y=5}[/tex]
so then hmmm let's use those, we know how f(x) is moving now, so
[tex]\stackrel{y}{f(x)}= \begin{cases} 2x&x\geqslant 0\\\\ -x+15&x\leqslant 10\\\\ 5&x\leqslant 20 \end{cases}[/tex]
23. SALES TAX You buy a jacket, and the sales tax is 6%. The total cost is $79.49.
Find the cost of the jacket before the tax.
The Cost of jacket before tax is 74.73.
According to the statement
We have to find that the cost of jacket.
So, For this purpose, we know that the
The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.
From the given information:
the sales tax is 6%. The total cost is $79.49.
Then the real cost is :
Real cost = 6% of the $79.49
Then
solve it
tax amount applied on the jacket = 6/100*79.49
tax amount applied on the jacket = 0.06*79.49
tax amount applied on the jacket = 6/100*79.49
tax amount applied on the jacket = 4.76
Then
Cost of jacket before tax = 79.49 -4.76
Cost of jacket before tax = 74.73.
So, The Cost of jacket before tax is 74.73.
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Lori ran 5 ½ miles Monday, 6 %4 miles Tuesday, 4½ miles Wednesday, and 234 miles on
Thursday. What is the average number of miles Lori ran? Write your answer as an improper
fraction.
19 miles the average number of miles Lori ran.
Miles Lori ran on Monday = 5 ½ = 11/2
Miles Lori ran on Tuesday = 6 ¼ = 25/4
Miles Lori ran on Wednesday = 4½ = 9/2
Miles Lori ran on Thursday = 2¾ = 11/4
Total miles she ran = sum of 4 days runs
= 11/2 + 25/4 + 9/2 + 11/4
= 22/4 + 25/4 + 18/4 + 11/4
= [tex]\frac{22 +25+18+11}{4}[/tex]
= 76/4 miles or 19 miles
How to calculate average number?By combining a set of integers and then dividing by their count, the average number—also known as the arithmetic mean—is created. For instance, the sum of 2, 3, 3, 5, 7, and 10 is equal to 30 divided by 6, which equals 5.
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In an arithmetic sequence, the first term is 8, the common difference is 3 and the last term is 68.
a How many terms are there in this sequence?
b Find the sum of all the terms of the sequence.
Answer: a. 21 terms
b. 798
Step-by-step explanation:
a. 68-8=60 ==> difference between 1st and last term
60/3=20 ==> number of terms after the first term
20+1=21 terms ==> total number of terms
b. Find the mean of the terms first:
(68+8)/2= ==> the mean of all terms in a sequence is equal to the mean of the first and last term
76/2=38
38*21=798 ==> add the mean 21 times to get the total sum since there are 21 terms in the sequence.
K What is 0.288 rounded to the neare hundredth? 0.288 20
Answer: 0.29
Step-by-step explanation:
= 0.288
8>5
= 0.29
PLEASE HELP FAST! 35 PTS!!
Justify each step by identifying the property used.
[tex]t+5(t+1)=t+(5t+5)[/tex]
[tex]=(t+5t)+5[/tex]
[tex]=(1t+5t)+5[/tex]
[tex]=(1+5)t+5[/tex]
[tex]=(6t+5)[/tex]
The algebraic properties used in the steps are the distribution property, the associative property, the identity property, and the distribution property
How to justify each step by identifying the property used?The first step in the equation is given as:
t + 5(t + 1) = t + (5t + 5)
The distribution property states that
a(b + c) = ab + ac
So, the property used in t + 5(t + 1) = t + (5t + 5) is the distribution property
Next, we have:
t + 5(t + 1) = (t + 5t) + 5
The associative property states that
a + (b + c) = (a + b) + c
So, the property used in t + 5(t + 1) = (t + 5t) + 5 is the associative property
Next, we have:
t + 5(t + 1) = (1t + 5t) + 5
The identity property states that
a * 1 = a
So, the property used in t + 5(t + 1) = (1t + 5t) + 5 is the identity property
Next, we have:
t + 5(t + 1) = (1 + 5)t + 5
The distribution property states that
a(b + c) = ab + ac
So, the property used in t + 5(t + 1) = (1 + 5)t + 5 is the distribution property
Lastly, we have the solution
(6t + 5)
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What is the value of the expression below after it has been simplified completely?
-3 1/2 - 4.75
Answer:
1.25
Step-by-step explanation:
. determine whether each of the following statement is true or false: a) x ∈ {x} b) {x} ⊆{x} c) {x} ∈{x} d) {x} ∈ {{x}}
(a) True, x is an element of the set {x}
(b) True, the set {x} is a subset of itself.
(c) False, x is an element of {x}, but the set {x} is not an element of {x}.
(d) True, the set {x} is an element of the set {{x}}.
What do you mean by the element of the set?The numbers 1, 2, 3, and 4 are the elements of set A, as indicated by the formula A=1,2,3,4. Subsets of A are collections of components from A, like 1, and 2. Sets may also function as elements.
Consider the set B=1,2,3,4 as an example. B's constituent parts are not 1, 2, 3, or 4. Instead, there are just three components of B: the numbers 1 and 2, as well as the set "3, 4."
A set's components can be anything. For instance, the set "C=red, blue, green" contains the colors red, green, and blue as its constituents.
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A mother is choosing which baby foods to serve her infant. A jar of meat has 2g of protein and 34 calories. A jar of vegetables has 1g of protein and 17 calories. How much of each will she need to serve to get 5g of protein and 120 calories?
A mother will need 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories.
Given that, a mother is choosing which baby foods to serve her infant. A jar of meat has 2g of protein and 34 calories. A jar of vegetables has 1g of protein and 17 calories. Now , we have to calculate how much she will be needed if she wants to serve 5g of protein and 120 calories respectively.
So, let's proceed to solve this question.
For 5g of protein she will be needed 2 jars of meat having 2g protein and 1 jar of vegetables which has 1g protein, then total protein will be equals to 5g.
5g of protein = 2 x A jar of meat + 1 x A jar of vegetables
For 120 calories, she will be needed 3 jars of meat and 1 jar of vegetable then it comes out to be 119 calories approximately equals to 120 calories.
So, 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories.
Therefore, 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories is the required answer.
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I need help asap!! (Fractions)
Answer:
b 2 2/9
Step-by-step explanation:
As we know
6×2/3 = {6×3+2}/3
=> 20/3
20/3 is the walk for 3 days
by unitary method
Walk of one day should be
20/3×3
20/9 = 2×2/9 miles per day
Answer:
2 2/9 miles per day
Step-by-step explanation:
If she walked 6 2/3 miles in 3 days, then she walked 1/3 of 6 2/3 miles in 1 days.
We need to find 1/3 of 6 2/3 miles.
1/3 of 6 2/3 =
= 1/3 × 6 2/3
= 1/3 × (6 + 2/3)
= 1/3 × 6 + 1/3 × 2/3
= 2 + 2/9
= 2 2/9
landon elliot fumigates rooms and charges $21.95 per room. on monday, he fumigated 3 rooms in one house, 2 in another, and 4 in a third.
The total charge for the rooms will be $197.55.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
The charge for one room = $21.95
Total number of rooms = 3+2+4=9 rooms
Total charges for the room= Charge for one room × total number of room
Substitute the values:-
The total charge for the room = 21.95 × 9 = 197.55
Hence, the total charge for the room is 197.55
The complete question is given below:-
Landon Elliot fumigates rooms and charges $21.95 per room. on Monday, he fumigated 3 rooms in one house, 2 in another, and 4 in a third. find his total charges.
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6. Thirty-five more than .8 times a number is the
same as 43 less than the
product of -7 and the
number.
The value of the given number is -10.
Here, we are given that Thirty-five more than 0.8 times a number is the same as 43 less than the product of -7 and the number.
Let the number be x
0.8 times x = 0.8
35 more than 0.8x = 35 + 0.8x
Thus, our left hand side of the equation is 35 + 0.8x
Now, the product of -7 and x = -7x
43 less than -7x = -7x - 43
Thus, we get the following equation-
35 + 0.8x = -7x - 43
we can solve this equation to find the value of x-
0.8x + 7x = -43 - 35
7.8x = -78
x = -78/ 7.8
x = -1/ 0.1
x = -10
Thus, the value of the given number is -10.
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Can Someone help me?
Step-by-step explanation:
first- b
swcond- a
third- c
Rose has 1 3/4 cups of powdered sugar. she sprinkles 1/3 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies. how much sugar does rose sprinkle on the brownies?
0.58 or more than half of sugar is sprinkled by rose on the brownies.
How much sugar does rose sprinkle on the brownies?
Given,
Rose has 1 3/4 cups of powdered sugar.
1/3 of the sugar sprinkled on lemon cookies
Therefore'
1 3/4 = (4*1+3) / 4
= 7/4
1/3 of the sugar sprinkled on lemon cookies
= 1/3 (7/4)
= 7/12
= 0.58 or more than half of sugar is sprinkled by rose on the brownies.
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Help, I've been stuck on these questions for an hour!
Explanations would be helpful, please!
Answer:
A. 3005
B. 3110
C. 1016.67
Step-by-step explanation:
A. Inital means occuring at the beginning. So the month they got the account, the value is around 3005. Every tick mark on the y-axis represents 30.
B. Like I said, every tick mark represents 30, so on the x-axis, the line between 6 and 8 is 7. go up towards where the line is, and that equals 3110.
C. I really haven't learned about rate of interest yet, but I tried my best to figure it out. I found out that for every month, you get 1016.67 value of interest.
What is the
y-value of the
of the
solution
system?
y = 5x + 3
y = 7x-3
Answer:
y is about equal to -4.692
Step-by-step explanation:
What is the slope of the line that passes through the points (6, -5)(6,−5) and (6, -4)(6,−4)? Write your answer in simplest form.
When graphed, one point is on top of the other, creating a vertical line. This could either be ∞ or -∞ .
A cartoon of 2 dozen eggs includes 3 with cracks. how many eggs without cracks can be expected in 6 dozen eggs?
If a cartoon of 2 dozen eggs includes 3 with cracks, then the number of eggs without cracks in 6 dozen eggs can be expected to be 63.
A dozen abbreviated as doz is a batch of 12. So in this situation, one dozen refers to 12 eggs. Therefore the number of eggs in 2 dozen will be equal to,
1 dozen = 12 eggs
2 dozen = 12x2= 24 eggs.
Therefore, a cartoon of 24 eggs includes 3 with cracks.
Similarly, 6 dozen is equal to,
1 dozen = 12 eggs
6 dozen = 12 x 6 = 72 eggs
We can determine the number of eggs with cracks by using an algebraic expression,
24 eggs include 3 eggs with cracks
72 eggs include: x eggs with cracks
x = 72×3 ÷ 24
x = 216 ÷ 24 = 9 eggs with cracks.
Therefore the number of eggs without cracks can be calculated by the subtraction of total eggs from the eggs with cracks.
Eggs without cracks= 72 - 9 = 63 eggs.
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The lengths of the three sides of a triangle (in feet) are consecutive even integers. If
the perimeter is 96 feet, find the value of the shortest of the three side lengths.
A cube-shaped planter has a volume of 729 in.³. What is the length of the planter?
Answer:
9 inches
Step-by-step explanation:
To find the volume of a cube, you could cube the side length, simplified as x³.
x³ = 729
x = 9
9 inches
Hope this helps! :)
Simplify each part of the expression using the laws of exponents.2^7/2^5+(4^5)^0+3^-1
What laws or properties did you use to simplify each part? What is the value of the expression?
Answer:
5.333333333333
Step-by-step explanation:
1. 2^7 &2^7 have the vase, by subtracting their power, the result is 4.
2. (4^5)^0=1
3. 3^-1=0.3333333
4 finally by adding each values in above steps
What is the answer to this problem?
Answer: 3
Step-by-step explanation:
A/B
30/10 = 3
There are a children in the class, and b of them are girls. How many boys are in the class?
Number of boys = a - b
Step-by-step explanation:Number of children in the class = a
Number of girls in the class = b
Number of boys = Total - Girls
a - b
The volume of a prism is given by the formula V=lwh , where l is the length, w is the width, and h is the height of the prism.
a. Solve the formula for h .
Answer:
[tex] \sf \large \: h = \frac{v}{lw} [/tex]
Step-by-step explanation:
Let's solve for h.
v=lwh
Step 1: Flip the equation.
hlw=v
Step 2: Divide both sides by lw.
hlw/lw = v/lw
h= v/lw
describe the given set with a single equation or with a pair of equations. the plane through the point parallel to a. the xy-plane b. the yz-plane c. the xz-plane
Equations for the set of the plane through the point [tex](x_0,y_0,z_0)[/tex] and parallel to:
a. xy-plane is [tex]z=z_0[/tex] b. yz-plane is [tex]x=x_0[/tex] c. xz-plane is [tex]y=y_0[/tex]
The given set is the plane through the point [tex](x_0,y_0,z_0)[/tex] parallel to:
a. xy-plane b. yz-plane c. xz-plane
Equation of the plane parallel to a plane containing a vector [tex]\vec r[/tex] through the point [tex](x_0,y_0,z_0)[/tex] is [tex](\vec r-(x_0,y_0,z_0)) .\vec n=0[/tex] ,where [tex]\vec n[/tex] is the normal to the plane and [tex]\vec r =x\vec i +y\vec j +z\vec k[/tex].
a. Plane through [tex](x_0,y_0,z_0)[/tex] and parallel to the xy-plane is,
[tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec k[/tex] = 0
⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec k=0[/tex]
⇒ [tex]z-z_0 =0[/tex]
⇒ [tex]z=z_0[/tex] is the equation of the plane through [tex](x_0,y_0,z_0)[/tex] and parallel to xy-plane.
b. Plane through [tex](x_0,y_0,z_0)[/tex] and parallel to the yz-plane is,
[tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec i[/tex] = 0
⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec i=0[/tex]
⇒ [tex]x-x_0 =0[/tex]
⇒ [tex]x=x_0[/tex] is the equation of the plane through [tex](x_0,y_0,z_0)[/tex] and parallel to yz-plane.
c. Plane through [tex](x_0,y_0,z_0)[/tex] and parallel to the xz-plane is,
[tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec j[/tex] = 0
⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec j=0[/tex]
⇒ [tex]y-y_0 =0[/tex]
⇒ [tex]y=y_0[/tex] is the equation of the plane through [tex](x_0,y_0,z_0)[/tex] and parallel to xz-plane.
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Identify all the possible proper subset relationships that
occur among the following sets.
the subsets in this case are:
C ⊆ BC ⊆ AB ⊆ AHow to identify the subsets?Remember that for two sets A and B, we say that A is a subset of B if and only if all the elements of A also are elements of B.
In this case, we have 3 sets:
A = {3n| n ∈ N}B = {6n| n ∈ N}C = {12n| n ∈ N}We can rewrite these ones as:
A = {3n| n ∈ N} = {3, 6, 9, 12, 15, 18, ...}B = {6n| n ∈ N} = {6, 12, 18, ...}C = {12n| n ∈ N} = {12, 24, 36, ...}Here we can see that all the elements in C also belong in B and also belong in A, and all the elements in B also belong to A, then the subsets are:
C ⊆ B
C ⊆ A
B ⊆ A
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Simplify the expression 4( m - 2 ) + 3m
Answer:
7m-8
Step-by-step explanation:
distribute 4 through the parentheses
4m-8+3m
collect like terms
7m-8
Answer:
7m-8
Step-by-step explanation:
So to simplify this expression, you would need to do distributive property.
4(m-2)
(4*m) + (4*-2)
4m-8+3m
7m-8
So your simplification is 7m-8
Help pls. Fill in the blanks that are circled. I'll mark as brainlist!!
Answer:
Top boxes are 18 and bottom boxes are 9
Step-by-step explanation:
Left side
Frist answer
2x3 =6, so 6 x3 = 18. 18 Goes into the top box on the left.
2 x [tex]\frac{3}{2}[/tex] = 3, so 6 x[tex]\frac{3}{2}[/tex] = 9 9 goes in the bottom box on the left.
Top right: 6 x 3 = 18. 18 goes in the top right
bottom right 3x3 = 9 9 Goes in the bottom right.