Answers
Answer:
Step-by-step explanation:
E ⊂ F ⊂ G
Related Questions
Help me with this question!
Answers
Answer:
...
Step-by-step explanation:
Practice
1. Hyatt Home Improvement uses H-shaped tile Design 1 Design 2
Design 3
designs on their buildings, advertisements, and
vehicles. The designs they use follow a specific
pattern. The first three designs are shown.
a. Describe the pattern in the designs.
b. Write two different expressions to represent
the number of tiles used in Design n. Use
algebraic properties to prove the two expressions are equivalent.
c. Explain how you could use technology to prove the two expressions in part (b)
are equivalent.
d. Create a table that displays the number of tiles used in each of the first 6 designs.
e. Create a graph of the data points in your table on the coordinate plane shown. Draw a smooth
curve to connect the points.
f. Do all of the points on the smooth curve make sense in terms of the problem situation? Explain
your reasoning.
g. Describe the pattern as linear, exponential, quadratic, or none of these. Explain your reasoning.
h. The owner of Hyatt Home Improvement wants to put one of their designs on an empty
rectangular sign in front of their headquarters. The empty sign is 10 feet tall and 12 feet wide. If he
Answers
Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:
The pattern is that the number of tiles increases as the design number increasesThe expressions for the number of tiles are [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]The expression can be proved to be equivalent using graph technology The points on the curve make sense in this scenario because all values are positiveThe pattern is quadratic.The largest design number that can enter an empty 10 by 12 ft sign is design number 8The pattern
The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)
The expressions for the number of tiles
The design number and the number of tiles is represented as follows
[tex]1 \to 7[/tex]
[tex]2 \to 12[/tex]
[tex]3 \to 19[/tex]
From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.
Design 1 has 1 tile at the center and 6 tiles at either sides.
So, we have:
[tex]1 \to 1 + 6[/tex]
[tex]2 \to 4 + 8[/tex]
[tex]3 \to 9 + 10[/tex]
Expand
[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]
[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]
[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]
Notice the pattern,
The number of tiles in design n will be:
[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]
Open bracket
[tex]Tiles = n^2 + 2n + 4[/tex]
Hence, the expressions for number of tiles in design n are:
[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]
Technology to prove that both expressions are equivalent
To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared
The table and graph for the first 6 designs
The table entry for the first 6 designs is calculated as follows:
[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]
[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]
[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]
[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]
[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]
[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]
So, we have:
[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]
See attachment for the graph of the above table
All the points on the curve make sense in this scenario because all values are positive.
The pattern type
We have:
[tex]Tiles = n^2 + 2n + 4[/tex]
When an equation has a degree of 2, the equation is quadratic.
Hence, the pattern is quadratic.
The largest design that an empty sign of 10ft by 12ft can contain.
From the first three designs:
The number of tiles on a complete row and column are always the same.
Design 1 has 3 tiles in its complete row and column
Design 2 has 4 tiles in its complete row and column
Design 3 has 5 tiles in its complete row and column
The relationship between the design number (d) and the number of complete tiles (t) is:
[tex]d = t - 2[/tex]
For the 10ft by 12ft empty sign
[tex]t = 10[/tex] because [tex]10 < 12[/tex]
So, we have:
[tex]d = t - 2[/tex]
[tex]d = 10 - 2[/tex]
[tex]d = 8[/tex]
Hence, the largest design number is design 8
Read more about patterns at:
https://brainly.com/question/13382968
what is 0.714285 repeating as a fraction
Answers
Answer:
5/7 i believe thats the answer to your question
Given f(3) = -x + 2, find f(6).
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f(6) = -4
Step-by-step explanation:given:
[tex]f(x) = -x+2[/tex]
find:
[tex]f(6) [/tex]
~~~~~~~~~~~~
➡️ [tex] f(6) = -(6) + 2[/tex]
➡️ [tex] f(6) = -(6 -2) [/tex]
➡️ [tex] f(6) = -4 [/tex]
evaluate it..........
Answers
Answer:
the answer is [tex]\frac{1}{41} (23x-2ln(5sinx+4cosx))[/tex]
Step-by-step explanation:
[tex]\int {\frac{3sinx+2cosx}{5sinx+4cosx} } \, dx[/tex]
here,
a=3, b=2, c=5, d=4
[tex]M=\frac{ac+bd}{c^2+d^2 }=\frac{3*5+2*4}{5^2+4^2}=\frac{23}{41}[/tex]
[tex]N=\frac{bc-ad}{c^2+d^2 }=\frac{2*5-3*4}{5^2+4^2}=\frac{-2}{41}[/tex]
[tex]\int {\frac{3sinx+2cosx}{5sinx+4cosx} } \, dx=\int{\frac{\frac{23}{41}(5sinx+4cosx)-\frac{2}{41}(5cosx-4sinx) }{5sinx+4cosx} }\,dx[/tex]
[tex]=\frac{23}{41}\int\, dx -\frac{2}{41} \int{\frac{5cosx-4sinx}{5sinx+4cosx} }\, dx[/tex]
[tex]=\frac{1}{41} (23x-2ln(5sinx+4cosx))[/tex]
pls mark it as the brainliest
how do you classify 2x^3-9x
Answers
Answer:
it is a cubic bi-nominal
Step-by-step explanation:
Answer:
Step-by-step explanation:
before it is factored, it is a binomial. I think that is the way I would answer the question. If you take out an x, you get one monomial and something that does not factor giving rational results for the numerical coefficients.
x (2x^2 - 9) This can't be factored giving rational coefficients.
Peter has a bag of marbles. In the bag are 4 white marbles, 2 blue marbles, and 6 green marbles. Peter randomly draws one marble, sets it aside, and then randomly draws another marble. What is the approximate probability of Peter drawing out two green marbles
Answers
Answer:
0.2272727
Step-by-step explanation:
The total number of marbles to begin with is 4 + 2 + 6 = 12
He draws 1 marble, which makes the total 11
He draws another marble, which makes the new total 10
6/12 * 5 / 11 = 30 / 132 = 1/2 * 5 / 11 = 5/22
I take it that the approximate probability is a decimal.
30/132 = 0.22727 ...
5/22 = 0.2272727 ....
The answers to the two fractions are the same and approximately the right answer of 5/22
This is line segments.
Answers
Step-by-step explanation:
[tex]here \: b \: is \: the \: mid \: point \\ so \: ab = bc \\ 10x - 17 = 6x + 11 \\ x \: terms \: togather \\ 10x - 6x = 11 + 17 \\ 4x = 28 \\ x = \frac{28}{4} \\ x = 7 \\ thank \: you[/tex]
We are given that line AB is 10x-17, with x as the unknown variable. Line BC is 6x+11. Line AB is equal to Line BC. Now we need to use that information to find x, so we’ll set up the equation.
Line AB=Line BC
10x-17=6x+11
Minus 6x to both sides (like terms)
4x-17=11
Add 17 to both sides (like terms)
4x=28
Divide both sides by 4
x=7
The answer is B. 7
YOU WILL GET 50 OR 100 POINTS TO THE FIRST PERSON TO ANWSER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!What number makes this statement true? (12×3)×6=12×( □×6)
Answers
Answer:
3
Step-by-step explanation:
12 times 3 = 36
36 times 6 = 216
12(x times 6)
(12)6x
72x
216 = 72x
216/72 = 3
Answer:
The number 3 makes this statement true.
[tex]x=3[/tex]
Step-by-step explanation:
Given the equation:
[tex](12*3)*6=12*(x*6)[/tex]
Using the order of operations, we can evaluate the terms in the parentheses through the process of multiplication:
[tex]36*6=12*6x[/tex]
Multiply the terms on both sides of the equation:
[tex]216=72x[/tex]
Finally, divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]72[/tex]:
[tex]3=x[/tex]
[tex]x=3[/tex]
-
Let's check our work by substituting the solved [tex]x[/tex] value for
[tex](12*3)*6=12*(3*6)[/tex]
[tex]36*6=12*18[/tex]
[tex]216=216[/tex]
Since both sides of the equation are equal to each other, our solution is correct!
Convert .18 into a fraction. Simplify
Answers
Explanation:
6 3/8
= 6 + 3/8
= 6 + 0.375
= 6.375
Plz help answer this question
Answers
Answer:
Option I
Step-by-step explanation:
Let
[tex]f(x)=x^2+3x-28[/tex]
We know by subsitution,
[tex]f(-9)=(-9)^2+3(-9)-28=26>0[/tex]
[tex]f(0)=0^2+3(0)-28=-28<0[/tex]
[tex]f(5)=5^2+3(5)-28=12>0[/tex]
Since a quadratic equation only have 1 turning point, we know for some values a in (-9, 5) such that f(a)<0. And the option of the range of a must lie with in (-9, 5).
Therefore, only Option I is correct.
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $77. A season ski pass costs $450. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Answers
Answer:
5
Step-by-step explanation:
Given:
Daily pass = $77Season ski pass = $450Skis = 2077 + 20 = 97
450 + 20 = 470
Keep multiplying 97 with random numbers until it passes 470.
97 × 4 = 388
97 × 5 = 485
So, the skier will have to pay daily passes 5 times to be more expensive than the season pass.
Hope this helped.
Line RS bisects segment PQ at R. If RQ = x + 9 and RP = 2x, find PQ.
Answers
Answer:
PQ measures 36 units.
Step-by-step explanation:
Line RS bisects segment PQ at R. By the definition of a bisector:
[tex]\displaystyle PR = RQ[/tex]
Hence:
We are given that RQ = x + 9 and RP = 2x, and we want to determine PQ.
Solve for x. Substitute:
[tex]\displaystyle (2x) = (x+9)[/tex]
Hence:
[tex]\displaystyle x = 9[/tex]
PQ is given by:
[tex]\displaystyle PQ = PR + RQ[/tex]
Since PR = RQ:
[tex]\displaystyle PQ =2PR[/tex]
Substitute and evaluate:
[tex]\displaystyle \begin{aligned} PQ &= 2PR \\ &= 2(2x) \\ &= 4x \\ &= 4(9) \\ &= 36 \end{aligned}[/tex]
Hence, PQ measures 36 units.
-8=x+ll/-2 solve for x step by step and answer
Answers
Answer:
x=(-5)/2
Step-by-step explanation:
-8×(-2)=-2x+11
16-11=(-2x)
x=(-5)/2
kristen is paid $5.60 per hour. she works 6 hours on saturday, 3 hours on sunday, and 5 hours on monday. on saturday her hourly rate in 1,1/2 times her
Answers
Answer:
This is an incomplete question.
Step-by-step explanation:
Can you please repeat the question properly.
5. After paying a tax of 8 palsa per rupee a man saves Rs. 18,400 per month Then his monthly income is 2 Points) 20,000
Answers
Answer:
92% of Income is Rs 18400
Step-by-step explanation:
I = 18400/.92 = Rs 20000
PLEASE HELP ME!!
algebraic terminology
Answers
Answer:
Step-by-step explanation:
Which one of the following pairs of sets has no members in common?
{all composite numbers} , {all odd numbers}
{all multiples of three} , {all multiples of four}
{all odd numbers} , {all even numbers}
{all prime numbers} , {all even numbers}
none of these
Answers
Answer:
{all multiples of three} , {all multiples of four}
Step-by-step explanation:
hope it helps u
pls mark me as branliest
Answer:
option d!!!!!!
12, and 18
Solve the following simultaneous equations:
5x + 3y = 21
2x + y = 3
2x+3y=12
5x+4y=23
Answers
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
(-6) + (-8) + (-3)² + (-13)
işleminin sonucu kaçtır?
A-3
B) -6
C) -8
D) -24
Answers
Answer: -6 is the answer
Chcek the file step by step calculation
Please like my answer if it helps you.
The choose B) –6
Ans; (-6)+(-8)+(-3)²+(-1³) = -6 -8 +9-1= –6
I hope I helped you^_^
Find the GCF from the two numbers, and rewrite the sum using the distributive property. 24 + 36
Do not put any spaces in your answer
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Answer:
i dont really know to be honest
Need help explaining why this happens
Answers
Evaluate the equation 2L+6=6L-10
Answers
Answer:
2
Step-by-step explanation:
2L + 6 = 6L - 10 Add 10 to both sides
2L + 6 + 10 = 6L Combine the left.
2L + 16 = 6L Subtract 2L from both sides
16 = 6L + 2L Combine the right
16 = 8L Divide by 8
8L = 16
8L/8 = 16/8
L = 2
determine whether y varies directly with x. if so, find the constant k and write the equation x =6,18,54,162 y= 24,72,216,648
Answers
Answer:
y = 4x
k = 4
Step-by-step explanation:
please help! this is due my today and i don't understand it
Answers
-3(2m+1)+7=-5
What does m equal?
Answers
Answer:
m = 3/2
Step-by-step explanation:
-3(2m+1)+7=-5
Distribute
-6m -3 +7 = -5
Combine like terms
-6m +4 = -5
Subtract 4 from each side
-6m+4-4 = -5-4
-6m =-9
Divide each side by -6
-6m/-6 = -9/-6
m = 3/2
simplify the expression
(1.5 × 10^-6) × (4 × 10^9)
Answers
Answer:
[tex]6 \times {10}^{3} = 6000[/tex]
Step-by-step explanation:
[tex](1.5 \times {10}^{ - 6} ) \times (4 \times {10}^{9} )[/tex]
[tex] = (1.5 \times 4) \times ( {10}^{ - 6} \times {10}^{9} )[/tex]
[tex] = 6 \times ( {10}^{ - 6} \times {10}^{9}) [/tex]
[tex] = 6 \times {10}^{ - 6 + 9} [/tex]
[tex] = 6 \times {10}^{3} [/tex]
[tex] = 6000[/tex]
helppppppppppppppppppppppppppppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
Answers
Answer:
-9
math websites helpp:)
1-37.
Write an expression for the area of each rectangle below.
a.
b.
11
0 0 C
11
cm
3x
3 cm
Please give me an equation for each a and b PLEASEE I’ll give you Brainly lol
Answers
Answer:
a. 33 sq.m
b.33x sq.m
Step-by-step explanation:
In a) formula of area of rectangle is:
Area= length * width
where 3m is width and 11m is length
Now area = 3 *11
area= 33 sq.m
In b) formula is same as above
area= 3x * 11
area= 33x sq.m
Round 557 to the nearest hundred.
550
560
500
600
Answers
Answer:
600
almost got confused with hundredth lol decimals
Answer:
600
Step-by-step explanation: