A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as shown.If the ratios $9:\text{S}$ and $\text{S}:\text{T}$ are both equal to 3 and $\text{S}$ and $\text{T}$ are the side lengths of the shaded squares, what is the total shaded area?
Answers
Answer:
[tex]3\sqrt{3} + 72[/tex]
Step-by-step explanation:
I attached an image to aid the understanding of the question.
Looking at the image, we see that the 8 shaded parts are congruent, as affirmed in the question as well. And we are told that T = 3, this implies that the area of the square with T as it's side is 9ft². Since all the 8 squares are congruenrt, it means each square has its area to be 9. Therefore, the total area of the 8 shaded squares will be:
[tex]9 \times 8 = 72ft^{2}[/tex]
It remains the area of the shaded square with side S.
From the question, we have the following ratio:
[tex]\frac{9}{S} = \frac{S}{T}[\tex]
But
[tex]\frac{9}{S} = \frac{S}{3}[\tex]
Multiplying through by 3S we have
27 = S² and this gives:
[tex]S = \sqrt{27} = 3\sqrt{3}[/tex]
I did not add ± because length is always positive, so the case of negative is eliminated.
Now the areas of S is [tex]3\sqrt{3}[/tex]
Therefore, the total area of the shaded squares is
[tex]3\sqrt{3} + 72[/tex]
Answer:
17
Step-by-step explanation:
We are given that [tex]$\frac{9}{\text{S}}=\frac{\text{S}}{\text{T}}=3.$\[\frac{9}{\text{S}}=3\][/tex]gives us S=3, so[tex]\[\frac{\text{S}}{\text{T}}=3\][/tex]gives us T=1. There are 8 shaded squares with side length [tex]$\text{T}$[/tex] and there is 1 shaded square with side length [tex]$\text{S},$[/tex] so the total shaded area is [tex]$8\cdot(1\cdot1)+1\cdot(3\cdot3)=8+9=\boxed{17}.$[/tex]
Related Questions
What is the slope of this line?
Answers
Answer:
[tex]m=\frac{2}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-2, -1)
Point (4, 3)
Step 2: Find slope m
Substitute: [tex]m=\frac{3+1}{4+2}[/tex]Add: [tex]m=\frac{4}{6}[/tex]Simplify: [tex]m=\frac{2}{3}[/tex]A chili recipe includes 2 tablespoons of salt and 5 tablespoons of red pepper. Choose ALL statements that are true about this
relationship
A)
There is
tablespoon of salt for each tablespoon of red pepper
B)
There is
IN
tablespoon of red pepper for each tablespoon of salt.
There is tablespoon of salt for each tablespoon of red pepper,
D)
The recipe has a ratio of 5 tablespoons of red pepper to 5 tablespoons of
salt
The recipe has a ratio of 5 tablespoons of red pepper to 2 tablespoons of
salt.
Answers
Answer:
Step-by-step explanation:
D
Solve for b. ab + c = d
b = (d-c)/a
b = a + c/d
b = a/(c-d)
Answers
Answer:
1st Option
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
ab + c = d
Step 2: Solve for b
Subtract c on both sides: ab = d - cDivide both sides by a: b = (d - c)/aAnswer:
B = (d-c)/a
Step-by-step explanation:
NEED HELP ASAP!
In this geometric sequence, what is the common ratio?
104, -52, 26, -13, ...
1/2
2
-1/2
-2
Answers
Answer:
the third one: -1/2
Step-by-step explanation:
if you multiply 104 by -1/2 you get -52, and so on the pattern will continue
Answer:
C. -1/2.
Step-by-step explanation:
Common ratio = -52/104 = 28/-52 = -13/26 = -1/2.
Claire is painting some doors that are all the same size. She used 2 liters of paint to cobe 1 3/5 doors. How many liters of paint are needed for 1 door.?
Answers
Answer:
[tex]1 \dfrac{1}{4} \ liters[/tex]
Step-by-step explanation:
Given that:
Claire uses 2 liters of paint to cover 1 3/5 doors
Then in order for her to paint 1 door, She will need:
2 L = 1 3/5 door
x L = 1 door
[tex]x (L) = \dfrac{2 L \times 1 door }{ 1 \dfrac{3}{5} \ door}[/tex]
[tex]x (L) = \dfrac{2 L }{ 1 \dfrac{3}{5} }[/tex]
[tex]x (L) = \dfrac{2 L }{ \dfrac{8}{5} }[/tex]
[tex]x (L) = \dfrac{2 L\times 5 }{ 8 }[/tex]
[tex]x (L) = \dfrac{10 \ L }{ 8 }[/tex]
[tex]x(L) =1 \dfrac{1}{4} \ L[/tex]
(Puzzle 2 - Scientific Notation Directions: Using the digits 1 to 9 to fill in the boxes only once, write the largest and smallest absolute value. Then find the decimal equivalent. EX|3.1 X 104- 6.5 X 102| =|31000-650|=|30, 350| is this the largest or smallest? Once you find the largest, start again with new digits and find the smallest. _x10^blank - _ x 10^_
Answers
Answer:
8x(10)^9 - 2 x (10)^1
1x(10)^3 - 9 x (10)^2
Step-by-step explanation:
3.1 X (10)^4- 6.5 X (10)^2
= 31000- 650
= 30,350
For greater number
_x10^blank - _ x 10^_
8x(10)^9 - 2 x (10)^1 ( we use 9 as the power because greater number used as power gives the bigger number and the next smaller number 8 as base. Similarly we use smaller number for power to get a smaller for the greatest difference)
= 8,000,000,000 -20
= 7,999,999,980
For smaller number
_x10^blank - _ x 10^_
1x(10)^3 - 9 x (10)^2 ( we use 3 as the power because smaller number used as power gives the smaller number and the next smallest number 1 as base. Similarly we use next smaller number for power to get the next smaller for the smallest difference)
= 1000- 900
= 100
We fill in the blanks keeping in mind that we do not have to repeat the numbers from 1-9 and also the numbers should have such an arrangement that they show the smallest and largest possible differences.
What are the vertical asymptotes of 10/X-1
Answers
Answer:
Enter a problem...
Algebra Examples
Popular Problems Algebra Find the Asymptotes f(x)=10/(x^2-1)
f
(
x
)
=
10
x
2
−
1
Find where the expression
10
x
2
−
1
is undefined.
x
=
−
1
,
x
=
1
Since
10
x
2
−
1
→
∞
as
x
→
−
1
from the left and
10
x
2
−
1
→
−
∞
as
x
→
−
1
from the right, then
x
=
−
1
is a vertical asymptote.
x
=
−
1
Since
10
x
2
−
1
→
−
∞
as
x
→
1
from the left and
10
x
2
−
1
→
∞
as
x
→
1
from the right, then
x
=
1
is a vertical asymptote.
x
=
1
List all of the vertical asymptotes:
x
=
−
1
,
1
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
where
n
is the degree of the numerator and
m
is the degree of the denominator.
1. If
n
<
m
, then the x-axis,
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
.
3. If
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
and
m
.
n
=
0
m
=
2
Since
n
<
m
, the x-axis,
y
=
0
, is the horizontal asymptote.
y
=
0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
1
,
1
Horizontal Asymptotes:
y
=
0
No Oblique Asymptotes
image of graph
The vertical asymptotes of the given function are x = 1 and x = -1,
We have given the rational function is 10/(x²-1).
We need to find the vertical asymptotes of this function.
Since Vertical asymptotes occur when the denominator of the function becomes zero and the numerator is not zero.
To determine the vertical asymptotes of the function, we need to solve the denominator for x²-1=0.
x²-1=0
x²=1
x=±√1
x=±1
Therefore, the vertical asymptotes of the given function are x = 1 and x = -1, since the denominator becomes zero at x=1 and x=-1.
To learn more about vertical asymptotes visit:
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A card is drawn from a standard deck of 52 cards. What is the probability this card will be a king or an ace?
A. about 3.9%
B. about 7.7%
C. about 15.4%
D. about 50%
Answers
Answer:
C. about 15.4%
Step-by-step explanation:
There are 52 cards in a deck
There are 4 kings and 4 aces
so, 8/52 is the chance of getting either of those two.
8/52 is about 0.1538 or 15.38%
15.38% rounded would be 15.4%
11.6.21 You randomly select one card from 52-card deck Find the probability of selecting the jack of diamonds or the ace of clubs. The probabilitiy is . An integer a fractionSimplify your answer.)
Answers
Answer: 1/26
Step-by-step explanation:
Out of the 52 card deck there is a single Jack of diamonds and a single ace of clubs. Their individual probabilities are therefore both 1/52.
For the probability that you can pick either of those card you have to add up their probabilities;
= 1/52 + 1/52
= 2/52
= 1/26
Find the sum of the digits 10^15−1.
Answers
Answer:
149
Step-by-step explanation:
Answer:
135
Step-by-step explanation:
10^15 = 1 000 000 000 000 000
10^15 - 1 = 999 999 999 999 999
There are 15 nines
15*9 = 135
45/8 =
When you get the answer convert it to fraction form
I need it please
Answers
Answer:
Exact Form:
45/8
Decimal Form:
5.625
Mixed Number Form:
5 5/8
Answer:
5 and 5/8
Step-by-step explanation:
The price of a necklace was increased by 20% to £186.
What was the price before the increase?
Answers
Answer:
£223.20
Step-by-step explanation:
20%=37.2
186+37.2=223.2
£223.2
need help plzz
20 points
Answers
Answer:
42 cm
Step-by-step explanation:
Area of rectangle (shaded area):
length × breadth
length: 7 cm
breadth: 7 - 2(0.5) = 6 cm
7 × 6 = 42 cm
Answer:
42 cm is the correct answer of this one
PLS ANSWER
An employee's time at work increased from 32 hours per week to 40 hours per week. By what percentage did the
time at work per week increase?
Answers
If you add 25% to 32 your answer will be 40
Answer:
You have to take the ratio so you divide the new value on the old value and compare It with 100 so you write
(40)/(32)=(x)/(100)
And this means that x = 125
So the ratio of the increase of the new time is 125%
But the real increase is 125 - 100 = 25%
Please answer for me. Will make you brainiest
Answers
Answer:
.
Step-by-step explanation:
I tried to solve this but I don't get it maybe use another app for it bc it looks hard lolz
please help i will give brainliest
Answers
How do I distribute 9 - (8r +5)
The - part confuses me
Answers
Answer:
you distribute the - not the 9
Step-by-step explanation:
so your problem would be
9-8r-5
( act as if there is a one in front of the negative sign)
hope this helps :)
g(x) = 5x - 12. What is g(8)?
Your answer
Answers
Answer:
28
Step-by-step explanation:
Replace x for 8 in the equation and solve it normally
Each fall, a horse ranch gives wagon rides. Tickets for adults are $10 each, and tickets for children are $6 each. No more than 25 people can fit on the wagon, and the ranch owners have a goal earning a minimum of $200 on each ride.
The system of inequalities that represents this situation is graphed below, where x represents the number of adults and y represents the number of children on the wagon ride.
X+y<_ 25
20x+ 6y_> 200
A. (19,6)
B. (17.5,5)
C. (10,15)
D. (30,-10)
Answers
Answer:
the equations are off
Step-by-step explanation:
x represents adults cost 10 not 20
y childen at g
x+y less than 25 people
10(x) + 6(y) greater than 200 dollars
Answer:
19,6
Step-by-step explanation:
Elvira used 4 cups of grape juice, 15 cups of cranberry juice, and 2 1 / 2 cup of pineapple juice to make punch. One liter is approximately equal to 4.23 cups. Which measurement is closest to the number of liters of punch Elvira made
A: 1:42 L
B: 10.23 L
C: 25.38
D: 1.77 L
Answers
Answer:
C
Step-by-step explanation:
6.4 ÷ 0.043
Round your answer to the nearest whole number.
Answers
Answer:
149
Step-by-step explanation:
6.4 ÷ 0.043
= 148.837209302
= 149 (rounded to the nearest whole number)
Hope this helped!
Answer:
6.4 ÷ 0.043=148.83...so the nearest whole number it is 149
Step-by-step explanation:
since 5-9 are rounded up
A car’s wheels spin at 1000 revolutions per minute. The diameter of the wheels is 23 inches. You want to know how fast the car is travelling.
A:Circumference
B:Area
Answers
Answer:
Speed = 72,285 in/min
Step-by-step explanation:
Given:
Total revolution per min = 1,000
Diameter = 23 in
Radius = 23/2 in
Time = 1 min
Find:
Speed
Computation:
Total distance = 2πr(1000)
Speed = Distance / time
Speed = 2πr(1000) / 1
Speed = 2π(23/2)(1000) / 1
Speed = 72,285 in/min
Consider the parent function f(x)=e^x and transformed function g(x)=-f(x)-4. Which features of function F function G are different
Y intercept
End behavior
Domain
Range
Horizontal asymptote
(More than one answer)
Answers
Answer:
y-intercept,
end behavior,
range,
and horizontal asymptote
Step-by-step explanation:
I just finished the PLATO test and these are the answers
The answers are y-intercept, end behaviour, range and horizontal asymptote.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a parent function:
f(x) = eˣ
The transformed function:
g(x) = -f(x) - 4 = -eˣ - 4
g(0) = -5
f(0) = 1
From the graph, we can say the y-intercept, end behaviour, range and horizontal asymptote are different from the parent function.
Thus, the answers are y-intercept, end behaviour, range and horizontal asymptote.
Learn more about the function here:
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Eddie found a store that sells cell phone cases for $18.50 plus $0.15 per letter engraved on the case. A second store sells cases for $18.00 plus $0.25 per letter engraved on the case. How many letters would Eddie have to engrave on his case for it to cost the same at either store?
Answers
Answer:
5 letters
Step-by-step explanation:
Let x = the number of letters engraved.
For the first store, the cost can be written as (18.50 + 0.15x).
For the second store, the cost can be written as (18 + 0.25x).
For the cost and value of x to be the same, let them equal eachother and evaluate x:
18.5 + 0.15x = 18 + 0.25
0.1x = 0.5
∴x=5
2.4 *10^2
5.25*10^2
2.53*10^1
1.8*10^3
Order from least to greatest
Answers
2.53*10* (1)
5.25*10^1 (3)
1.8*10^3 (4)
Gina is using a grid to plan where to dig her garden. She has drawn this figure.
10
9
8
7
3
2
1
0 1 2
8 9 10
Gina decides to reflect her drawing so that Point G is at (1, 1). Which of the
following points will be a corner of her garden?
r
A (6,6)
B. (5, 1)
C. (0,0)
D. (5,7)
Answers
This is collection of data made by comparing objects in standard units. In science, the units are metric.
Answers
Answer:
You didn't even write a question.
An employee at an electronics store makes $12 per hour plus commission of 4.5% of her sales. This week she has sold 36 television averaging $620 each.What is her commission this week?
Answers
Answer: $1004.4
Step-by-step explanation:
Simple math
The total commission of the employee will be $1004.4 for the given sale.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
4.5% of commission on sales.
Total selling = 36 x 620 = $22320
4.5% of $22320 = (4.5/100)22320 = $1004.4
Hence "The total commission of the employee will be $1004.4 for the given sale".
For more about the percentage,
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ax + bx = 0
Solve equation for x
Answers
Answer:
you cant have two variables
Step-by-step explanation:
The axis of symmetry of the graph of h is x = - 3. which ordered pair represents the additional point on the graph of h?
Answers
Answer: (1,-5)
Step-by-step explanation:it’s the answer