Select all the expressions that are equivalent to 3^2 · 3 ^(-6)
Answer:
[tex] {3}^{2} \times {3}^{ - 6} \\ = {3}^{2 + ( - 6)} \\ = {3}^{2 - 6} \\ = {3}^{ - 4} [/tex]
a triangle has a width of 4 cm and perimeter of 26 cm. find the length
Answer:
9 ufh fcnbscbhbvxdfhbbhukkkocd
(1/2)^x=2^-x could anyone tell me why
Answer:
Anything to a negative power is always the reciprocal. An example might be 2⁻² can be written as 1/4
Step-by-step explanation:
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
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
I needddddd heelllpppp pleaseeee
Answer:
3/2
Step-by-step explanation:
Csc(theta) = 1/Sin(theta)
So we have to find the side opposite theta.
a = 3*sqrt(5)
b = ?
c = 9
a^2 + b^2 = c^2
(3sqrt(5)) ^2 + b^2 = 9^2
9*5 + b^2 = 81
b^2 = 81 = 45
b^2 = 36
sqrt(b^2) = sqrt(36)
b = 6
Sin(theta) = 6/9
Csc(theta) = 1 / sin(theta) = 9/6
Csc(theta = 3/2
Problem 3
Answer: 3/2=====================================================
Explanation:
Use the pythagorean theorem to find the length of the missing side.
[tex]a^2 + b^2 = c^2\\\\a^2 + (3\sqrt{5})^2 = 9^2\\\\a^2+3^2*(\sqrt{5})^2 = 9^2\\\\a^2 + 9(5) = 81\\\\a^2 + 45 = 81\\\\a^2 = 81-45\\\\a^2 = 36\\\\a = \sqrt{36}\\\\a = 6\\\\[/tex]
This is the length of the missing vertical side. This side is opposite the angle theta.
[tex]\csc = \text{cosecant}\\\\\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{9}{6}\\\\\csc(\theta) = \frac{3*3}{3*2}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]
Alternatively, you can compute it like this
[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{6}{9}\\\\\sin(\theta) = \frac{2}{3}\\\\\csc(\theta) = \frac{1}{\sin(\theta)}\\\\\csc(\theta) = 1 \div \sin(\theta)\\\\\csc(\theta) = 1 \div \frac{2}{3}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]
hewo um what is 1804 divided by 12 and has anyone seen my hacker friend.
Answer:
150.333
Step-by-step explanation:
The three is repeated
30, 32, and 34 Please! I WILL GIVE BRAINLIEST
Answer:
see explanation
Step-by-step explanation:
Since AL bisects ∠ KAT then ∠ 1 = ∠ 2
(30)
7x + 3 = 6x + 7 ( subtract 6x from both sides )
x + 3 = 7 ( subtract 3 from both sides )
x = 4
(32)
SAT is a straight line , then
∠ 1 + ∠ 2 + ∠ 3 = 180° , then
x + x + 4x = 180
6x = 180 ( divide both sides by 6 )
x = 30
(34)
Similar to (32)
x + 12 + x + 12 + 6x - 20 = 180 , that is
8x + 4 = 180 ( subtract 4 from both sides )
8x = 176 ( divide both sides by 8 )
x = 22
Answer:
30) x= 4
32) x=30
33) x=22
Step-by-step explanation:
All step by step explainations are in pic below
−1 4/5−(−2 7/8)
4 3/4−(−1 1/12)
−1 4/5−(−2 7/8)
3 1/3-5
−1/3−(−1/2
Answer:
1) 43/40
2) 35/6
3) 43/40
4) -5/3
5) 1/6
Step-by-step explanation:
1) -1 4/5 = -(1*5 +4)/ 5= -9/5
or 1= 5/5 so -1 4/5= -( 5/5+ 4/5)=-9/5
-2 7/8= -(2*8+7)/8=-23/8
=> -9/5 - ( -23/8)= -9/5 + 23/8 = (( -9*8)+(23*5))/40= (-72+ 115)/40
= 43/40
2) 4 3/4= (4*4+3)/4= 19/4
-1 1/12= -(1*12+1)/12= -13/12
=> 19/4 - (-13/12)= 19/4 + 13/12 = ((19*3)+13)/12= (57+13)/12= 35/6
3) same like 1)
4) 3 1/3 = (3*3+1)/3= 10/3
=> 10/3 -5= (10- 3*5)/3= (10-15)/3= -5/3
5) -1/3 + 1/2= ((-1*2)+(1*3))/6 = (-2+3)/6= 1/6
9. El radio de una pelota de básquetbol es aproximadamente 3.6 veces mayor
que el radio de una pelota de tenis. ¿Cuántas veces mayor es el volumen
de una pelota de básquetbol que el volumen de una pelota de tenis?
4
Nota: El volumen de una esfera es V = -tr
Answer:
so the volume of the basketball is 46.656 times greater than the volume of the tennis ball.
Step-by-step explanation:
Martha has a French cookie recipe that calls for baking the cookies for 14 to 18 minutes at 180∘C. Her oven measures temperature in Fahrenheit only. At what temperature in degrees Fahrenheit should she set her oven to make the cookies per the recipe?
Answer:
180° Celsius is equal to approximately 356° Fahrenheit
Step-by-step explanation:
I hope this helps.
The value of 180 degree Celcius in Fahrenheit is 356.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Martha has a French cookie recipe that calls for baking the cookies for 14 to 18 minutes at 180∘C.
The temperature in Fahrenheit will be calculated as,
F = 1.8C + 32
F = ( 1.8 x 180 ) +32
F = 356
Therefore, the value of 180 degree Celcius in Fahrenheit is 356.
To know more about unit conversion follow
https://brainly.com/question/26141817
#SPJ2
Solve for x: 4x + 1/2 (2x + 4) > 12
( 9th grade Algebra 1)
Answer:
x > 2
Step-by-step explanation:
Distribute and cross-simplify 1/2 with parenthesis
4x + x + 2 > 12
Solve left side
5x + 2 > 12
Subtract 2 from both sides
5x > 10
Divide both sides by 5
x > 2
PLZZZZ help it will mean a lot :)
3x = 18
Divide both sides by 3 and simplify
x=6
Answer:
Step-by-step explanation:
assuming that you need to find the value of x
3x = 18
-divide both sides by 3
3x/3 = 18/3
-use the facts that 3/3 =1 and 18/3 = 3*6/3 = 6
x = 6
Donna cut a wire into 7 equal pieces. The wire was originally 9.52 meters long. How long is each piece?
Answer:
1.36
Step-by-step explanation:
9.52/7
1.36 is the length of one of the 7 equal pieces
4z - 15 = 4z + 11
How would this one work?
Please help! Please don't answer if you don't know!
Answer:
[-0.25 1.25]
[ ]
[-0.75 2.75]
If not satisfied than..
You can write it in other way as show in step by step
Step-by-step explanation:
Step 1:
First of all find the determinate.
Cross multiply the number 11 ✖ -1
detA = 11 × -1= -11 ---eq1
And now cross multiply the number 3 ✖ - 5
detA = 3 × -5= -15 ---eq2
Now we use eq 1 and 2
detA = (-11)-(-15)
Minus cancels minus
So it becomes
detA = -11 + 15
= 4
Step 2:
We find adjacent of the given.
[11 -5]
adjA= [ ]
[3 -1 ]
We change the places. The number 11 goes to in place of -1. -1 goes in place of 11.
And we change the signs of -5 and 3. -5 becomes 5 and 3 becomes -3.
We get
[-1 5]
adjA = [ ]
[-3 11]
Step 3:
Now we use the following formula
1
A^-1 = -------- adjA
detA
1 [-1 5]
A^-1 = ------- [ ]
4 [-3 11]
And now multiply
1
---- with each number of adjA.
4
And than subtract..
And you will get the inverse matrix
If the answer comes same than that's the answer for inverse matrix
Thank you.
Johhny Badoingas collects $0.12 from a 1000 people, how much does he have altogether. Now he has to share that total product with 100 people, how much does each person get?
Find total collected by multiplying the amount per person by number of people:
1000 x 0.12 = $120.00
Total collected = $120.00
Divide total collected by number of people:
120.00 / 109 = $1.20
Each person gets $1.20
Someone answer this
Answer:
1st box is "a 90°clockwise rotation about the origin
2nd box is "a 180° rotation about the origin
3rd box is "a 90° counterclockwise rotation about the origin
Find the coordinates of the point 7/10 of the way from A to B.
Answer:
The coordinates are (6.5, 1.7).
Step-by-step explanation:
The difference between A and B's x-coordinate is 15. 7/10 of this is 10.5, which added to -4 gives us an x-coordinate of 6.5.
The difference between A and B's y-coordinate is 11. 7/10 of this is 7.7, which added to -6 gives us a y-coordinate of 1.7.
Therefore, the coordinates are (6.5, 1.7).
What’s the answer???
Answer:
Step-by-step explanation:
Simplify the answer has to be a positive exponent Please help!
5^4 /5
Use the exponent rule x^a/x^b = x^a-b
5^4/5 = 5^4-1 = 5^3
Answer as a positive exponent is 5^3
Please help ASAP 17x - 4(4x - 3)
Step-by-step explanation:
17x-4(4x-4)
17x-16x+8
X+8
Answer:
x + 12
Step-by-step explanation:
17x - 4(4x - 3)
17x - 16x + 12
x + 12
true or false? in a two-column proof, the left column states your reasiong
PLSSS HELPPPPP- Evaluate the expression. 1 1 4 25 3 Write your answer as a fraction or as a whole or mixed number.
Answer:
Mixed number form 4 4/5 exact form 24/5
Step-by-step explanation:
hope this helps
Answer:
Step-by-step explanation:
8/15
PLEASE HELP!!!!!! Im being timed
Answer:
9,6 hope this helps
Ray has gone 3/5 of a kilometre. How many metres has he gone?
Step-by-step explanation:
3/5 of a kilometre
=3/5×1000 meters
=3000/5 meters
=600 meters
Answer:
600 metres
Step-by-step explanation:
1 kilometre equals 1,000 metres.
[tex]\frac{3}{5}[/tex](1000) = 600 metres
If you need more clarification, ask me in the comments. Thanks!
[tex]\frac{7}{8} + \frac{3}{4}[/tex]
Answer:
Step-by-step explanation:
7/8 + 3/4
7/8 + 6/8
13/8 = 1 5/8
1. Your school's Key Club decided to sell fruit baskets to raise
money for a local charity. The club sold a total of 80 fruit
baskets. There were three different types of fruit baskets.
Small fruit baskets sold for $15.75 each, medium fruit baskets
sold for $25 each, and large fruit baskets sold for $32.50
each. The Key Club took in a total of 52086.25. and they sold
twice as many large baskets as small baskets.
a. Formulate a system of three linear equations in three
variables to represent this problem situation. Be sure to
define your variables.
b. Solve the system of three linear equations using
technology with matrices. Write your answer in terms of
the problem situation.
c. Describe the solution in terms of the problem situation.
2. Is it always easier to solve a system of linear equations using
matrices? Explain your reasoning.
Let the small , medium and large baskets be denoted by s,m & l
Formulating the equations
s+m+l= 80--------- equation1
$15.75s+ $25 m + $32.5l = $2086.25------equation2
2s=l---------equation 3
Using the technology s=15, m=35 and l= 30
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
2(15)=(30)---------equation 3
Yes because multiple variables can be easily calculated through matrices using technology
In Matrix form
[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex] = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]
Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]
B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Z= A⁻¹ B
A⁻¹= A mod/ det A
det A= -1
Using the technology s=15, m=35 and l= 30
15 small baskets,
35 medium baskets
30 large baskets were sold.
Part C:
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
236.25+ 875+ 975=$2086.25
$2086.25=$2086.25
2(15)=(30)---------equation 3
Answer 2:
Yes because multiple variables can be easily calculated using technology.
N.B There is a typing error in question its $2086.25 not 52086.25
Anyone know the answers 11 through 14?Please help me.I’m tired
Answer:
11. [tex]x^{5}[/tex]
12. 5*[tex]x^{2}[/tex]
13. x+21
14. 2x-8
Step-by-step explanation:
factors of 15,17 ,26 & 80
Answer:
Factors of 15: 1, 3, 5 and 15.
Factors of 17: 1 and 17.
Factors of 26: 1, 2, 13 and 26
Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.
Actually you can find all the answers in the Internet.
