The statement is true for parallelogram is a square is a) All the rhombuses are squares.
What are the 4 properties of a rhombus?In a rhombus, the opposing sides are parallel. In a rhombus, the opposing angles are equal. Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals.
What is the rule of rhombus?Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals. One of the most significant characteristics of rhombus diagonals is this. Two adjacent angles added together equal 180°.
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i-Ready
◄» Mrs. Garcia is making brend using a total of 400 grams of gluten-free flour. The recipe calls
for 70% of the flour to be almond flour. She needs to know how much almond flour to use.
How do you write 70% as a rate
Therefore , Mrs. Garcia needs 280 grams of gluten-free flour.
Which of the several equation types is present?Equations are classified by identity equations or conditional equations. There is an identity for each possible value of the variables. A conditional equation can only have a certain set of variable values. Equation is represented by equals ("="), which divides two expressions.
Here,
Mrs. Garcia needs 70% of the flour to be almond flour
Thus ,
70% of 400 is
=> 70/100*400 = 280
Therefore , Mrs. Garcia needs 280 grams of gluten-free flour.
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Can you please help I will mark BRAINLIEST
Answer:
yeah im sorry i have no idea
Step-by-step explanation:
bro im soooooooo sorry
pls answer I need reassurance im correct
10 x (4 + (-9)) / ((-5) - (-3))
Answer: Answer would be -65
It should be that?
Let V be a finite-dimensional vector space and let \mathcal{B}=\left\{\alpha_{1}, \dots, \alpha_{n}\right\}B={α 1…,α n } be a basis for V. Let (\quad | \quad)(∣) be an inner product on V. If c_{1}, \dots, c_{n}c 1,…,c nare any n scalars, show that there is exactly one vector \alphaα in V such that \left(\boldsymbol{\alpha} | \boldsymbol{\alpha}_{i}\right)=c_{i}, j=1, \ldots, n(α∣α )=c ij=1,…,n.
Let V be a finite-dimensional vector space and let B ={α 1…,α n } be a basis for V . Let ( | ) be the inner product of V. If c 1,...,c n , are n is a scalar, then show that there exist one vector α∈ V such that (α∣αj)=cj, j=1 ,…,n.
We have given that V is a finite dimensional vector space.
Consider α∈ V defined as
α = α₁β₁ + α₂β₂ + -----+ αₙβₙ where,
β₁ = α₁
β₂= α₂ - (α₁ |β₁)/β₁/β₂ |(β₁)
similarly, __
βⱼ = αⱼ - ( ∑ (αⱼ|βⱼ) / βᵢ|(βᵢ) βᵢ ) , j = 2,n bar
As defined aᵢ, i = 1, j bar
α₁ = c₁/ (β₁ )|β₁
___
α₂ = c₁/ (β₁ )|β₁ - a₁ ( α₂|β₂/β₁|β₂)
proceeding like as we get
_______
αⱼ = 1/β₁|(β₁) (cⱼ - ∑ αⱼ ( αⱼ |βⱼ)
then conider
(α|αⱼ )= ( α₁β₁ + α₂β₂ + -- + αₙβₙ |αⱼ )
= α₁β₁ + α₂β₂ + -- + αₙβₙ |βⱼ ) + ∑ α₁β₁+ α₂β₂ +---+αⱼβᵢ /βᵢβᵢ)
______
(α|αⱼ) =αⱼ(βⱼ |βⱼ) + (cⱼ - ∑ αⱼ ( αⱼ |βⱼ) βⱼ |βⱼ
__ ___
= (cⱼ - ∑ αᵢ ( αⱼ |βᵢ) + ∑αⱼ |βᵢ
(α|αⱼ) = cj, j = 1,n
Hence proved.
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find the dimensions (radius r and height h) of the cone of maximum volume that can be inscribed in a sphere of radius 2.
The dimensions of the radius is 4/3[tex]\sqrt{2}[/tex] and that of height is 8/3.
Let r be the radius of the cone, be the radius of the sphere and h be the height of the cone.
Let's put DˆOB=x with limitations 0≤x≤π.
In the right-angled triangle DOB:
r=DB=Rsinx, OD=Rcosx, than
h=CD=OC+OD=R+Rcosx=R(1+cosx).
So the volume of the cone is:
V=1/3πr²h ⇒V=1/3π(Rsinx)²⋅R(1+cosx)
V=1/3πR³sin²x(1+cosx)
V'=1/3πR³⋅[2sinx⋅cosx⋅(1+cosx)+sin2x(−sinx)]
=1/3πR³sinx[2cosx(1+cosx)−sin2x]
=1/3πR³sinx(2cosx+2cos2x−sin2x)
=1/3πR³sinx(2cosx+2cos2x−1+cos2x)
=1/3πR³sinx(3cos2x+2cosx−1)
Now let's find the signum of the derivative, since sinx≥0 for every x in the limitations, then:
V'≥0⇒3cos²x+2cosx−1≥0
⇒Δ/4=(b/2)²−ac =1+3=4
cosx=(−b/2)±√Δ/4 / a
=−1±2/3,
So:
cosx≤−1∨cosx≥1/3
The first one has only the solution:
x=π
the second:
−arccos(1/3)≤x≤arccos(1/3), but for the limitations:
0≤x≤arccos(1/3).
The function gros from zero to arccos(1/3), and then it decreases.
So x=arccos(1/3) is the maximum requested.
Let's find now r and h:
r=Rsinx
=R√1−cos2x
= 2√1−(1/3)²
= 2√1−1/9
=2√9−1/9
=2√8/9
=2⋅2√2/3
=4/3√2
h=R(1+cosx)=2(1+1/3)
=2(3+1/3)
=8/3.
Therefore the radius is 4/3√2 and the height is 8/3.
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Select ALL expressions that are equivalent to -40x+100
4(10x+96)
20(-2x+5)
2
10(4x-10)
10(-4x+10)
Answer:
20(-2x+5)
10(-4x+10)
Step-by-step explanation:
20(-2x+5) = -40x+100
10(-4x+10) = -40x+100
You just need to expand the brackets
For any positive integer x, let x^R be the integer whose binary representation is the reverse of the binary representation of x. (Assume no leading 0s in the binary representation of x.) Define the function R^+: N rightarrow N where R+(x) = x + x^R. a. Let A_2 = { | R^+ (x) = y}. Show A_2 elementof L. b. Let A_3 = { | R^+ (R^+ (x) = y}. Show A_3 elementof L.
Define the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y} language A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y} language A₃ ∈L.
Given that,
For any positive integer x, let [tex]x^{R}[/tex] be the integer with the opposite of x's binary representation in terms of representation. (Assume that x's binary form has no leading 0s.) Specify the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y}. Show A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y}. Show A₃ ∈L.
We know that,
Consider the Turing machine M, which computes the inverse of x for every positive inter. The result will also be x if the computation is done using both the integer x and its inverse.
This is because the result of adding a binary number 1 to 0 is always 1. The criterion is that the binary representation of x must not contain 0. In this case, a positive integer x is converted into binary representation.
Only x values with a binary representation of 1 will be accepted by the Turing machine. Even the Turing machine will accept inverse-of-x values with binary representations of 0.
Therefore, It is proved that language A₃ ∈L.
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What Is a Coordinate Plane? Definition, Examples, Facts
A Coordinate Plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.
What is a Coordinate Plane?
A Coordinate Plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.
Elements of the Coordinate Plane
Quadrants: The two number lines divide the coordinate plane into 4 regions. These regions are called Quadrants. The quadrants are denoted by roman numerals and each of these quadrants have their own properties.
Quadrant I: The upper right Quadrant is the first Quadrant denoted as Quadrant I. In this quadrant, the x-axis and the y-axis both have positive numbers.
Quadrant II: The upper left Quadrant is the second Quadrant denoted as Quadrant II. In this quadrant, the x-axis has its negative numbers and the y-axis has positive numbers.
Quadrant III: The bottom left Quadrant is the third Quadrant denoted as Quadrant III. In this quadrant, both the x-axis and the y-axis have negative numbers.
Quadrant IV: The bottom right Quadrant is the fourth Quadrant denoted as Quadrant IV. In this quadrant, the x-axis has positive numbers and the y-axis has negative numbers.
Fun Facts:1.The coordinate plane was created hundreds of years ago. The system is commonly referred to as the Cartesian coordinate system because French mathematician René Descartes invented it.
2.The points on the x-axis have their y-coordinate 0 so the points on x-axis are represented as (x,0) and similarly the points on y-axis have their x-coordinate 0, so they are represented as (0,y).
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Answer:
Definition - The plane containing the "x" axis and "y" axis.
Examples - (4,9), (24,90), etc
Facts - The coordinate plane is a two-dimension surface formed by two number lines. One number line is horizontal and is called the x-axis. The other number line is vertical number line and is called the y-axis. The two axes meet at a point called the origin.
Step-by-step explanation:
the Celisius and the Fahrenight temperature scales are relased by the equation c=5/6 (F-32) expresses F in terms of C.
Answer:
F = (9/5)C + 32
Step-by-step explanation:
C = 5/9(F-32) **you wrote the fraction wrong in your question, it's 5/9, not 5/6
C = (5F)/9 - 160/9
C + 160/9 = (5F)/9
9C + 160 = 5F
(9C + 160)/5 = F
F = (9/5)C + 32
Answer: F = (6C/5) + 32
To express F in terms of C, rearrange the equation to isolate 'F'.
Inverse OperationsTo rearrange the equation, we want 'F' to be by itself. To move numbers to the other side, we do the other pair of inverse operation to both sides. This cancels out what we don't need while keeping the left and right sides equal.
Pairs of inverse operations
Multiply ⇔ DivideAdd ⇔ SubtractCalculate[tex]\displaystyle { C = \frac{5}{6}*(F-32) }[/tex] Start with the equation in the question.
[tex]\displaystyle { C = \frac{5*(F-32)}{6} }[/tex] Rewrite. This is the same as the question.
[tex]\displaystyle { 6C = \frac{5*(F-32)}{6}*6 }\\[/tex] Multiply both sides by 6.
[tex]\displaystyle { 6C = 5*(F-32) }[/tex] Cancelled out 6 on the right.
[tex]\\\displaystyle { \frac{6C}{5} = \frac{5*(F-32)}{5} }[/tex] Divide both sides by 5.
[tex]\displaystyle { \frac{6C}{5} = (F-32) }[/tex] Cancelled out 5 on the right.
[tex]\displaystyle { \frac{6C}{5} = F-32 }[/tex] We don't need the brackets if 'F - 32' is alone.
[tex]\displaystyle { \frac{6C}{5}+32 = F-32+32 }[/tex] Add 32 to both sides.
[tex]\displaystyle { \frac{6C}{5}+32 = F }[/tex] Cancelled out 32 on the right.
[tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex] Keep lone variables on the left side.
Therefore, the equation to convert Celsius to Fahrenheit is:
[tex]\displaystyle { F = \frac{6C}{5}+32 }[/tex]
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name the additive inverse of 5 + i
The additive inverse of 5 + i is (-5) + (-1)
what is additive Inverse?
To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
Given:
5 + I
As, the additive inverse is the opposite sign of the given number.
For example, if the number is -6 and we have to find its additive inverse.
So, the additive inverse will be 6.
Similarly for 5 + i ;
the additive inverse is (-5) + (-1)
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Doreen Schmidt is a chemist. She needs to prepare 24 ounces of a 10% hydrochloric acid solution. Find the amount of 12 % solution and the amount of 16% solution she should mix to get this solution
Jimena purchased $24 worth of crafting supplies. The tax rate in her city is 6.25%. What is the total cost of the crafting supplies?
The total cost of the crafting supplies is $25.5. This can be find using percentage and rate concepts.
What is tax rate and percentage?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent , half of it is 50 percent , none of something is 0 percent.
Tax is the money that govt collects based on income, sales and other activities.
A tax rate is the percentage at which an individual or corporation is taxed.
In the given que,
Purchased amount = $24.
Tax rate = 6.25%
Tax paid = 24*(6.25/100)
= $1.5
So, total amount paid = $1.5 + $24
= $25.5
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Find the volume of the garden shed
Answer:
47.3 m³
Step-by-step explanation:
The garden shed is made up of a rectangular prism and a pyramid.
Volume of a rectangular prism[tex]\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}[/tex]
Volume of a pyramidFrom inspection of the given diagram, the slant height of the pyramid is 3.5 m.
Calculate the perpendicular height of the pyramid using Pythagoras Theorem:
[tex]\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}[/tex]
Volume of the garden shed[tex]\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}[/tex]
how can you prove that these two triangles are congruent?
Jennifer planted a tree that was 0.17 of a meter tall after 10 years the tree was 100 times as tall as when she planted it what is the height of it now
Answer:
Step-by-step explanation:
.17(100)=17
17 meters
TRUE OR FALSE in html5, it is only possible to check a form for valid inputs (say within a given range) once the data has been submitted to the server.
The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.
HTML5
HTML5 is a markup language used for structuring and presenting content on the World Wide Web. It is the fifth and final major HTML version that is a World Wide Web Consortium recommendation. The current specification is known as the HTML Living Standard.
On-premises servers
On-premises servers refer to the group of servers that are under the control of a private entity. This is not like the traditional cloud computing method where resources can be leased to third-party service providers.
The use of the term, on-premises refers to the local installation of these resources as against the cloud type where the resource is on the vendor's server and a client can reach the software via their internet browsers.
Hypertext Markup Language revision 5 (HTML5) is markup language for the structure and presentation of World Wide Web contents. HTML5 supports the traditional HTML and XHTML-style syntax and other new features in its markup, New APIs, XHTML and error handling.
The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.
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What is the independent variable in a linear function?; How do the independent and dependent values change in linear functions?; Which function has a constant additive rate of change of?; Which must be true of the data set if a linear function can be used to represent the data?
x is the independent variable in the linear equation ax + by + c = 0
and y is the dependent variable in the linear equation.
Given, an independent variable in a linear function,
we have to define the independent and dependent variables.
Let suppose a linear equation be,
ax + by + c = 0
now, in the above linear equation,
by = -ax - c
y = -(ax + c)/b
So, the value of variable x in the above linear equation, is independent and don't depend on any other variable whereas the value of variable y in the above linear equation, is dependent as it depends on the value of the variable x.
Therefore, x is the independent variable in the linear equation and y is the dependent variable in the linear equation.
The value of independent variables can be changed by us whereas the value of dependent variables changes on the basis of the value of independent variables.
Hence, the value of independent variables can be changed by us whereas the value of dependent variables changes on the basis of the value of independent variables.
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21. Which relation is a function?
A. (,0), (0, 1), (2, 2)}
B. {(-2,2), (-1, 1), (-2,4)}
C. {(-1,4), (0, 5), (0,4)}
D. {(2, 1), (4,3), (6,5)}
Answer:
The correct answer is D
Step-by-step explanation:
In order for a relation to be a function, every input for x can only have one output. Therefore, D is the correct answer.
Answer:
D
Step-by-step explanation:
A function is a relation where every input has only 1 output.
Inputs are the x's and outputs are the y's.
Answer a is missing an input. You have (,0) The first number is missing.
B is not a function because the input -2 has to outputs 2 and 4.
C is not a function because the input 0 has two outputs 5 and 4
Evaluate the following expression for x = 8.
2x² +6x+2
Answer:
306
Step-by-step explanation:
Which is the best description for the shape of the distribution below?
Answer: Unimodal and Right Skewed
Explanation:
When almost all the data is falls to the right of the graph's peak is known as a right skewed histogram.
A left skewed histogram would have almost all the data falling to the left of the graph's peak.
A histogram is described as uniform if every value in a dataset occurs roughly the same number of times. There are usually no peaks and the data set looks similar to a rectangle.
A Symmetric histogram would be symmetrical, both side of the peak of the graph are mirrored/completely identical.
I hope this helps to better understand :)
You planted 60 seeds seeds.80% actually grow. how many seeds grew? To word it another way, what is the amount of seeds that grew if 80% of 60% seeds grew?
Answer:
48
Step-by-step explanation:
0.8 * 60 = 48
The population of bears on a nature preserve was 95 last year.This year , the population increased by 20% . what is the new bear population on the preserve
Answer: 19 new bears
Step-by-step explanation: To find the percentage of something, let's recall the formula:
Whole number x part % / 100
So, let's plug in the numbers to the formula:
95 x 20 / 100
95 x 20 = 1900
So, 1900 / 100 = 19; our answer
I hope this helped!
The figure below is dilated by a factor of 4/3 centered at the origin. Plot the resulting image.
The geometric figure above has been dilated by a scale factor of 4/3 centered at the origin and plotted in the graph attached below.
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 4/3 centered at the origin as follows:
Coordinate X (-3, -6) → Coordinate X' (-3 × 4/3, -6 × 4/3) = Coordinate A' (-4, -8).
Coordinate Y (3, 3) → Coordinate Y' (3 × 4/3, 3 × 4/3) = Coordinate A' (4, 4).
Coordinate Z (-3, 6) → Coordinate Z' (-3 × 4/3, 6 × 4/3) = Coordinate A' (-4, 8).
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find the unknown size of the angles.
Answer:
y = 57,5°
z = 57,5°
n = 65°
Step-by-step explanation:
Answer:
Your answer is x = 65° , y = 57.5° , z = 57.5°
Step-by-step explanation:
There is a triangle isoscocles so two angles are the same. There is a parallel line where two lines are the same.
<x = 65° and <y° = <z°
so
<x + <y + <z = 180
Plug in angle x.
65° + <y° + <z° = 180°
Subtract 65 to both sides.
<y° + <z° = 180° - 65°
<y° + <z° = 115°
Since <y° = <z° we substitute one of them
<y° + <z° = 115°
<y° + <y° = 115°
Add the <y° together
2y = 115°
Divide 2 to both sides to get y by itself.
<y° = 57.5°
So <y° = <z° = 57.5°
Suppose the value of b is false and the value of x is 0. What is the value of each of the following expressions? a. b && x = = 0 b. b || x = = 0 c. !b && x = = 0 d. !b || x = = 0 e. b && x != 0
Answer:
a. False
b. True
c. True
d. True
e. False
Step-by-step explanation:
You want to know the truth value of various logical expressions when b = False, and x = 0.
And, OrAn And (&&) expression is true if and only if all parts are true. An OR (||) expression is true if any part is true.
When 'b' is false, b&&__ will be false, and !b||__ will be true. This makes (a) and (e) false, and (d) true.
When x = 0, __||x==0 will be true, so (b) is true.
The And (&&) of expression (c) will only be true when both parts are true. For b = False and x = 0, both parts are true, so (c) is true.
{a, b, c, d, e} = {False, True, True, True, False}
20% of the school are seniors, 30% Juniors, 15% sophomores, and 35% freshman. What is the probability that if I select 10 people, I will get 2 seniors and 8 freshmen?
The probability that if I select 10 people, I will get 2 seniors and 8 freshmen is 0.00000901
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Seniors = 20%Juniors = 30%Sophomores = 15%Freshman = 35%Also from the question, we have
Number of people selected = 10
To get 2 seniors and 8 freshmen, the probability equation is
Probability = (Seniors)² * (Freshman)⁸
Substitute the known values in the above equation, so, we have the following representation
Probability = (20%)² * (35%)⁸
Evaluate
Probability = 0.0000090075
Approximate
Probability = 0.00000901
Hence, the probability is 0.00000901
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hey can anyone help I pay?
Answer:
The Venn diagram below shows information
about the number of items in sets A and B.[asy]
label("A",(0,75));
label("B",(100,75));
label("C",(50,0));
label("D",(0,45));
label("E",(100,45));
draw(Circle((50,60), 40));
draw(Circle((50,30), 40));
draw(Circle((20,60), 20));
draw(Circle((80,60), 20));
[/asy]To find P(A'|B), we can use the formula:P(A'|B) = P(A' and B) / P(B)We can find P(A' and B) by looking at the Venn diagram. It is the number of items in the intersection of sets A' and B, which is represented by the region labeled "D" in the Venn diagram. This region contains 10 items.To find P(B), we can look at the Venn diagram and add up the number of items in both sets B and the intersection of A and B. This is represented by the regions labeled "D" and "E" in the Venn diagram, and contains a total of 20 items.Plugging these values into the formula above, we get:P(A'|B) = (10 items) / (20 items) = 1/2So, the probability that an item chosen at random belongs to A' given that it belongs to B is 1/2. This fraction is already in its simplest form.
Step-by-step explanation:
Resources that are available in limited quantities on the earth are called ___________
Resources that are available in limited quantities on the earth are called Exhaustible resources.
The resources which are present in limited amounts are referred to as exhaustible resources. These resources can be consumed and end someday and are also termed non-renewable resources.
Exhaustible natural resources are available in a limited quantity and cannot be replaced within a reasonable period of time and have the risk of being exhausted by human activities. Such Resources take millions of years to form.
Exhaustible resources are usually not environmentally friendly since they are improperly and inefficiently used and are generally very expensive.
Coal, petroleum, and Forests are examples of exhaustible natural resources.
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the set of numbers that include all the positive and negative whole numbers and zero; there are integers that are not whole numbers.; is 0 a whole number; are all integers natural numbers; are whole numbers rational numbers; there are whole numbers that are not rational numbers.; the set of whole numbers and their opposites are called; classifying numbers
Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. [tex]| - 4| = 4 and | 4| = 4;[/tex]
What are real numbers?Positive and negative integers, fractions, rational numbers, including irrational numbers, and negative integers are all examples of real numbers. fictitious numbers, Real numbers are those that fall between the two extremes,
Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. | - 4| = 4 and | 4| = 4; The collection of positive numbers used to count items is known as the counting numbers, sometimes known as natural numbers. 1, 2, 3, 4, 5, ...; Fractions and decimals are not integers; rather, integers are the set of all whole numbers, along with their opposites (the positive whole numbers, the negative whole numbers, and zero). -3, -2, -1, 0, 1, 2, 3, ...; Irrational Numbers - The collection of all non-terminating, non-repeating decimal numbers; Natural Integers: The collection of positive numbers utilized in object counting (also called counting numbers). 1, 2, 3, 4, 5, ...; Unfavorable Numbers - the range of numbers on the number line that are less than zero and to the left of zero.; Number Line - a horizontal line with points representing different numbers. In a number line with just whole numbers or integers, the dots are uniformly spaced out according to the value of the number they represent.; Opposite - a number that is on the other side of zero and at the same distance from zero as a given integer. For instance, the opposites of 7 and -7 and 9 and 9 are both 7; positive figures - the group of numbers on the number line that are greater than zero and to the right of zero.
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A family has at most $25 to spend on activities at Fun zones. It cost $10 an hour to use the trampolines and $5 an hour to use the pool. The family can stay less than 4 hours.
a. Write an inequity that represents the cost constraints.
b. Can the family spend 1 hour in the trampoline and 3 hours in the pool? Explains your reasoning
c. Can the family spend 2 hrs on trampoline and 1.5 hours in the pool? Explains your reasoning
d. Can the family spend 1 houron the trampoline and 2 hours in the pool? Explain your reasoning
The family can spend 1 hour on the trampoline and 2 hours in the pool and the inequalities are 10t + 5p ≤ 25 and t + p < 4.
How many hours can the family spend within the budget?
a ) Let the time on the trampolines = t
Let the time in the pool = pThe cost constraints is represented with the system of inequalities by :10t + 5p ≤ 25
The time constraints is represented with the system of inequalities by :t + p < 4
b )No, the family cannot spend 1 hour in the trampoline and 3 hours in the pool.
We can infer that this is the case because the family desires to spend less time together than 4 hours, which is what those periods total to.However, as we can plainly see, the point (1, 3)is not a solution because it is located on the dashed line of one graph.(Refer image for graph )c ) No, the family cannot spend 2 hours in the trampoline and 1.5 hours in the pool.
We are aware that these two periods total less than four hours.But we must compute the cost, which comes out to 27.5 and is higher than the budget.10t + 5p ≤ 25
10(2)+ 5(1.5) = 27.5
d ) Yes, the family can spend 1 hour on the trampoline and 2 hours in the pool.
We are aware that these two periods total less than four hours.We must compute the cost, which comes out to 20 and is lesser than the budget of 25 .The point (1,2)is a solution because it is not located on the dashed line but within the shaded region of the graph (Refer image for graph )10t + 5p ≤ 25
10(1)+ 5(2) = 20
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