The fact that the sum of the interior angles of a triangle add up to 180 is equivalent to the parallel postulate. Therefore, the sum of the interior angles of a triangle in this type of geometry be different from those of triangle in Euclidean geometry.
How to illustrate the information?There is only one parallel to the given line in Riemannian geometry. A straight line of finite length that can be continued endlessly is the second postulate of Euclid.
One of the non-Euclidean geometries that entirely rejects the validity of Euclid's fifth postulate and alters his second postulate is Riemannian geometry, commonly known as elliptic geometry. The fifth postulate of Euclid states that there is only one line that passes through a point that is not on a particular line and is parallel to that line.
In this case, the angles won't change as it's always equal
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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]
Find the value of x when 6-2x=5x-9x+12 .
Answer:
x=3
Step-by-step explanation:
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:
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.
identify the type of angle formed between the hands of each clock
Answer:
5) acute
6)acute
7)reflex
8)reflex
Step-by-step explanation:
No 6&5 are acute because they are each less than 90 degrees while no7&8 are reflex because they exceed 180 degrees.
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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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
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! :)
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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Can that be simplified???
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
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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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]
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"
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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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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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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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
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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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.
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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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.
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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What is the answer to this problem?
Answer: 3
Step-by-step explanation:
A/B
30/10 = 3
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:
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
Can Someone help me?
Step-by-step explanation:
first- b
swcond- a
third- c
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
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 -∞ .
. 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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