Answers
Answer:
B
Step-by-step explanation:
Substitute x = 5 into the expression
[tex]\frac{4(5+5)(5+1)}{(5+3)(5-3)}[/tex]
= [tex]\frac{4(10)(6)}{8(2)}[/tex]
= [tex]\frac{240}{16}[/tex]
= 15 → B
Answer:
15
Step-by-step explanation:
Numerator ; 4(X+5)(X+1)
substitute : X=5
The first expression becomes : 4(5+5)(5+1)
= 4(10)(6)
=4×10×6
=240
Denominator : (X+3)(x-3)
substitute: X=5
=(5+3)(5-3)
=(8)(2)
=16
Now, Dividing the numerator by the denominator we have 240÷16=15
Related Questions
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
if b = 5, what is b³
Answers
Answer:
125
Step-by-step explanation:
5³= 5 × 5 × 5 = 125
Answer:
125 is your answer.
Step-by-step explanation:
b = 5
=5 X 5 X 5
=125
Equation : -2 (4g - 3) = 30
Answers
Answer:
g = -3
Step-by-step explanation:
-2 (4g - 3) = 30
-8g + 6 = 30
-8g = 24
g = -3
Answer:
[tex] \boxed{g = -3} [/tex]
Step-by-step explanation:
[First, distribute the factored term on the left side of the equation (distribution property of equality)]
-2 ( 4g – 3 ) = 30 →
-2 ( 4g ) – -2 ( 3 ) = 30 →
-8g + 6 = 30 →
[Next, subtract 6 from both sides (subtraction property of equality)]
-8g + 6 – 6 = 30 – 6 →
-8g = 24 →
[Finally, divide both sides by -8 to cancel out the coefficient of -8 in -8g and reduce it to solve for g (division property of equality)]
-8g / -8 = 24 / -8 →
g = -3
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]
David makes 17 dollars in an hour and works 25 hours a week.linda makes 25 dollars a hour abd works 7 hours each week. How much do they both make together
Answers
Step-by-step explanation:
David makes 17(25)
and
Linda maked 25(7)
so it would make the equation 17(25)+25(7)
425+175 together they would be making
600 dollars a week
is 1/3 and -1/3 parallel?
Answers
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.
Circle the statement or statements that are not equal to 1.
5/9 X 9/5
17/12-5/12
3/4 + 2/8
12/4 - 11/9
10 X 1/10
Answers
Simplify 5/8+3/4+2/5
Answers
5 1/2
score
Help plz
Answers
someone pls explain how to get the answer pls..
Answers
What’s the value of the 6 in 558672? It’s 600.
What’s the value of the 3 in 74139? It’s 30.
What do you get when you multiply 600*30? 18,000
Answer: 18,000
Answer:
B
Step-by-step explanation:
For example, if i gave u 28
The digit two stands for 20, and the digit 8 stands for 8, therefore u call it 28
Each spot has it own name
For example if i gave u the number 12345
5 is in the first spot, therefore 5 x 1 =5
4 is in the tenth spot, therefor 4 x 10 = 40
3 is in the hundred spot, therefore 3 x 100 =300
2 is in the thousand spot, therefore 2 x 1000=2000
1 is in the ten thousand spot, therefore 1 x 10000
=100000
So if u add all these numbers together u will get
12345
OK, so for your question, the 6 in 558672, is in the hundred spot, so 6 x 100 =600
The 3 in 74139 is in the ten spot, so 3 x 10=30
So the product is to multiply them together
600 x 30 =18000
What is the value of x in the equation 3x - 4 (2x - 5) = 15
Answers
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
8 + 9x + 4(11 -- 2x)
-41-2x – 7) + 6x - 7
9 - 31–4 + 3x) + 12x
Answers
Answer:
240766 - 52731x + 840x^2 + 144x^3
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
Answers
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.
F(x) = Х
Need to transform it into a vertical stretch by a factor of 2 followed by translation 1 unit up
Answers
Divide 48 into the ratio of 2:6
Answers
Answer:
12:36
Step-by-step explanation:
2 + 6 = 8
48/8 = 6
6 * 2 = 12
6 * 6 = 36
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
1.Can someone explain to me about decimal place? take this as example. please help me.
2. and also, please help me with significant figures, i don't understand it.
Answers
Example: In the number 258.16, the decimal point separates the whole number 258 from the fractional part 16, which is 16 hundredths.
And for significant figures if there is a zero between two non-zero digits then it is a significant figure.
For example; 4.5006 have five significant figures.
Zeroes at the end or on the right side of the number are also significant.
For example; 0.500 has three significant figures.
 This has to be 20 letters long, but !!!!!Im overthinking this
Answers
Answer:
2559458#763677_6$7387353637648383636
Answer:
For part5 every single one will be 'move 2 units right and 7 units down.'
Step-by-step explanation:
Because on part2 it told to translate the figure 2 units right and 7 units down, so every point will move 2 units right and 7 units down. I hope this helps.
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?
Answers
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]
ABCD is rotated counterclockwise about the origin. By how many degrees
was ABCD rotated?
O A. 360°
• B. 180°
• C. 270°
O D. 90°
Answers
Answer:
B. 180 degrees
Step-by-step explanation:
They are exactly across from one another. Here, this will make more sense.
0 (starting point)
|
270-- -- 90
|
180 (where you ended up)
Now till the screen towards the right. The zero and the 180 should be pointing in the same direction as the squares.
Degrees was ABCD rotated or transformed to form A'B'C'D' is 180 degrees about the origin .
What is rotation in graph?In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. A rotation is an example of a transformation where a figure is rotated about a specific point (called the center of rotation), a certain number of degrees.
According to the question
ABCD is rotated counterclockwise about the origin.
Degrees was ABCD transformed to form A'B'C'D' is
180 degrees about the origin
As when we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.
So, as per figure ABCD which is in first quadrant were x and y both are positive and figure A'B'C'D' third quadrant were x and y both are negative.
Hence, Degrees was ABCD rotated or transformed to form A'B'C'D' is 180 degrees about the origin .
To know more about rotation in graph here:
https://brainly.com/question/12091224
#SPJ2
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
Answers
X=10
Y=14
Step-by-step explanation:
Solve simultaneously using substitution method as shown in the image
helppppppppppppppppppppppppppppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
Answers
Answer:
-9
math websites helpp:)
anyone this help ,,,,,
Answers
=======================================================
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
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
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP
Answers
Answer:
please help me my friend
PLEASE HELP 25 points and brainliest!
Answers
Answer: 8.1 × 10¹⁰
Concept:
When multiplying exponents, add the exponents together.
When dividing exponents, subtract the exponents.
Solve:
Given expression
(3 × 10⁶) × (2.7 × 10⁴)
Put like terms together
=3 × 2.7 × 10⁶ × 10⁴
Combine like terms
=8.1 × 10⁶⁺⁴
=[tex]\boxed{8.1*10^{10}}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
8.1 x 10^10
Step-by-step explanation:
When you do this type of problem you want to combine the like terms together, in this case is this.
3 × 2.7 × 10⁶ × 10⁴. So you will get.
8.1 x 10⁶⁺⁴
Which is 8.1 x 10^10 simplified
4. Andrea's savings change by -$9 each time she
goes bowling. In all, it changed by $99 during the
summer. How many times did she go bowling in the
Summer?
I need help.
Answers
She went bowling 11 times.
Explanation:
Divide 99 by 9 to find out how many times she went bowling. The answer comes out to be 11.
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?
Answers
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
Is (8, –2) a solution to the equation y = 2?
Answers
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!
PLEASE HELP ASAP -- WITH THE WORKK
50 points
Answers
Part-A:-
(f×g)=[tex]\\ \sf\longmapsto x^2+3x-70(4x-12)[/tex]
[tex]\\ \sf\longmapsto 4x^2+12x-280-12x^2+36x+840[/tex]
[tex]\\ \sf\longmapsto -8x^2+48x+560[/tex]
Now
[tex]\\ \sf\longmapsto (f.g)(3)[/tex]
[tex]\\ \sf\longmapsto -8(3)^2+48(3)+560[/tex]
[tex]\\ \sf\longmapsto -72+144+560[/tex]
[tex]\\ \sf\longmapsto 72+560[/tex]
[tex]\\ \sf\longmapsto 632[/tex]
Part-B:-
[tex]\\ \sf\longmapsto f(3)[/tex]
[tex]\\ \sf\longmapsto (3)^2+3(3)-70[/tex]
[tex]\\ \sf\longmapsto 9+9-70[/tex]
[tex]\\ \sf\longmapsto 18-70[/tex]
[tex]\\ \sf\longmapsto -52[/tex]
Now
[tex]\\ \sf\longmapsto g(f(3))[/tex]
[tex]\\ \sf\longmapsto g(-52)[/tex]
[tex]\\ \sf\longmapsto 4(-52-3)[/tex]
[tex]\\ \sf\longmapsto 4(-55)[/tex]
[tex]\\ \sf\longmapsto -220[/tex]
Part:-C
[tex]\\ \sf\longmapsto g(-2)[/tex]
[tex]\\ \sf\longmapsto 4(-2-3)[/tex]
[tex]\\ \sf\longmapsto 4(-5)[/tex]
[tex]\\ \sf\longmapsto -20[/tex]
Now
[tex]\\ \sf\longmapsto f(g(-2))[/tex]
[tex]\\ \sf\longmapsto f(-20)[/tex]
[tex]\\ \sf\longmapsto (-20)^2+3(-20)-70[/tex]
[tex]\\ \sf\longmapsto 400-60-70[/tex]
[tex]\\ \sf\longmapsto 400-130[/tex]
[tex]\\ \sf\longmapsto 270[/tex]
Part-D:-
g×f=f×g[tex]\\ \sf\longmapsto (g.f)(-2)[/tex]
[tex]\\ \sf\longmapsto -8(-2)^2+48(-2)+560[/tex]
[tex]\\ \sf\longmapsto 32-96+560[/tex]
[tex]\\ \sf\longmapsto -64+560[/tex]
[tex]\\ \sf\longmapsto 496[/tex]