Answer:
120/100
Step-by-step explanation:
120÷20= 6
100÷20=5
6/5 = 1⅕
Is (8, –2) a solution to the equation y = 2?
Answer:
No
Step-by-step explanation:
Any point that aligns on the line of y = 2 is a solution. But (8, -2) falls below that line since the point's y-coordinate is equal to -2, not 2. Hope this helps!
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
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
helppppppppppppppppppppppppppppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
Answer:
-9
math websites helpp:)
You can work only 13 hours this week. The following week you can work 6 hours. How much additional time will it take the third week if the job will take 27 total hours?
Answer:
8 more hours
Step-by-step explanation:
13 hrs + 6 hrs = 19
27hrs total - 19hrs
27-19+=8 more hours. TADA!!!!
Answer:
8
Step-by-step explanation:
total hours you can work 3 week : 27 hours
total hour you can work in first and second week: 13+6= 19 hours
=>the third week will take: 27 - 19=8 hours
simplify the expression
(1.5 × 10^-6) × (4 × 10^9)
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]
Help me with this question!
Answer:
...
Step-by-step explanation:
how do you classify 2x^3-9x
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.
-3(2m+1)+7=-5
What does m equal?
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
Need help explaining why this happens
please help! this is due my today and i don't understand it
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
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
Answer:
600
almost got confused with hundredth lol decimals
Answer:
600
Step-by-step explanation:
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
Answer:
y = 4x
k = 4
Step-by-step explanation:
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system is shown represents this equation. x + y = 24 3x + 5y = 100
X=10
Y=14
Step-by-step explanation:
Solve simultaneously using substitution method as shown in the image
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
Answer:
This is an incomplete question.
Step-by-step explanation:
Can you please repeat the question properly.
evaluate it..........
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
YOU WILL GET 50 OR 100 POINTS TO THE FIRST PERSON TO ANWSER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!What number makes this statement true? (12×3)×6=12×( □×6)
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!
Plz help answer this question
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.
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
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
what is 0.714285 repeating as a fraction
Answer:
5/7 i believe thats the answer to your question
-8=x+ll/-2 solve for x step by step and answer
Answer:
x=(-5)/2
Step-by-step explanation:
-8×(-2)=-2x+11
16-11=(-2x)
x=(-5)/2
F(x) = Х
Need to transform it into a vertical stretch by a factor of 2 followed by translation 1 unit up
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
Answer:
92% of Income is Rs 18400
Step-by-step explanation:
I = 18400/.92 = Rs 20000
anyone this help ,,,,,
=======================================================
Explanation:
We start with set M = {m,a,t,h,s}
Then we cross off any letter we find in set N
So we'll cross off the 'm' and 'a' since they are both in N. We're kicking these letters out of the set.
We go from {m,a,t,h,s} to {t,h,s}
We leave t,h and s alone as those letters aren't in set N. So we don't kick them out.
Answer: {t,h,s} choice A
What is the value of x in the equation 3x - 4 (2x - 5) = 15
Hey there! I'm happy to help!
Here is our equation
3x - 4 (2x - 5) = 15
First, we will sue the distributive property to remove the parentheses. The term outside the parentheses is -4, so that is what we multiply the insides by.
3x-8x+20=15
We combine our like terms (our x-values).
-5x+20=15
We subtract 20 from both sides.
-5x=-5
We divide both sides by -5.
x=1
Have a wonderful day and keep on learning! :D
Answer: x = 1
Step-by-step explanation:
Given
3x - 4 (2x - 5) = 15
Expand parentheses and apply the distributive property
3x - 4 · 2x - 4 · (-5) = 15
3x - 8x + 20 = 15
Combine like terms
(3x - 8x) + 20 = 15
-5x + 20 = 15
Subtract 20 on both sides
-5x + 20 - 20 = 15 - 20
-5x = -5
Divide -5 on both sides
-5x / -5 = -5 / -5
[tex]\boxed{x=1}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Given f(3) = -x + 2, find f(6).
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]
Line RS bisects segment PQ at R. If RQ = x + 9 and RP = 2x, find PQ.
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.
Which equation has the solution x=-4? a 2(x-4)=16 b 3x+6-2x=-2 c 1/4x+4=3 d(x+6)3=-6 need help plz
Answer:
C: 1/4x + 4 = 3
Step-by-step explanation:
1/4x + 4 = 3
1/4x = 3 - 4
x = - 4
Thus, option c gives out the solution x = - 4.
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
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
11) Dan worked 7 3/4 hours on Saturday and 6 2/3 hours on Sunday. He earns
$15 3/4 per hour. How much did he make that weekend?
Answer:
[tex]227 \frac{1}{16} [/tex]
Step-by-step explanation:
[tex]15 \frac{3}{4} \times (7 \frac{3}{4} + 6 \frac{2}{3} ) [/tex]
[tex] = \frac{63}{4} \times ( \frac{31}{4} + \frac{20}{3} )[/tex]
[tex] = \frac{63}{4} \times ( \frac{93}{12} + \frac{80}{12} )[/tex]
[tex] = \frac{63}{4} \times \frac{173}{12} [/tex]
[tex] = 227\frac{1}{16} [/tex]