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
13 x 24 =
pleze go very fast or i mite fale
Answers
Answer:
312
Step-by-step explanation:
what is the slope of the line 5x +2y = -15
Answers
Answer:
-5/2
Step-by-step explanation:
5x +2y = -15
-5x -5x
2y = -5x - 15
y = -5/2x - 7.5
y = mx + b
Slope (m) = -5/2
down 5, right 2
y = Mx + b
5x + 15 = - 2y
-5/2x -15/2 = y
Which equation represents a proportional relationship?
a y = 7x – 3
b y = 150x
c y = 21x
d y = 2x + 1
Answers
I am not certain but I think c? if its wrong sorry
Every 2.5 hours, a machine produces 150 baskets.
What is the unit rate of this proportional relationship? (Hint: You are trying to find how many baskets in one hour.)
60 baskets per hour
60 baskets per hour
2.5 baskets per hour
2.5 baskets per hour
25 baskets per hour
25 baskets per hour
16.6 baskets per hour
Answers
Answer:
60
Step-by-step explanation:
We use unit rate function,
Let h be hours
Let b be baskets
2.5h = 150b
We divide both sides by 2.5
2.5h/2.5 = 150b/2.5
Which will give us
h = 60
plz help me with this plz
Answers
Answer:
Slope: [tex]-\frac{3}{4}[/tex]
Y intercept: 7
Equation: [tex]y=-\frac{3}{4}x+7[/tex]
Step-by-step explanation:
The slope is found by doing the equation [tex]\frac{rise}{run}[/tex]. When looking at the first two points, it's shown that the rise (difference between the two y values) is -3 (since it decreased by 3) and the run (difference between the two x values) is 4 (since it increased by 4).
This gives us a slope of [tex]-\frac{3}{4}[/tex].
The y intercept is found by looking at the y value when x = 0. In this picture, it is clear that it is 7.
The equation you want to use is y = mx + b , where b is the y intercept and m is the slope. Just plug in the numbers and you got your equation!
Forty of the staff of 85 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, what would be the expected mean, variance and standard deviation?
Answers
Answer and Step-by-step explanation:
The computation is shown below;
Here we use the binomial distribution
p = 40 ÷ 85 = 0.47
q = 1 -0.47 = 0.53
n = 180
Now
mean [tex]\mu[/tex]
= np
= 180 × 0.47
= 84.6
The Variance is
= npq
= 180 × 0.47 × 0.53
= 44.84
And, Standard deviation
= √npq
= √44.84
= 6.69
We simply applied the above formula so that the correct value could come
And, the same is to be considered
Constant of proportionality characteristics what are some?
Answers
Answer: The constant of proportionality is the ratio between two directly proportional quantities.
Two quantities are directly proportional when they increase and decrease at the same rate.
Step-by-step explanation:
Which describes the effect of the transformations on the graph of ƒ(x) = x2 when changed to ƒ(x) = x^2+2
Answers
-10 + 4
plz heeeeeelp
Answers
Answer:
-6
Step-by-step explanation:
Answer:
- 6
Step-by-step explanation:
The graph shows the membership of a student group: x represents the number of years since the group was formed and y represents the number of members.
The equation is y = 14x + 10.
Which is true regarding the slope?
Membership grows by 14 each year.
The group was formed with 14 members.
Membership is recorded every 14 years.
Answers
Answer:
we conclude that Membership grows by 14 each year.
Step-by-step explanation:
Given the equation
[tex]y=14x+10[/tex]
Comparing the equation with the slope-intercept form
[tex]y=mx+b[/tex]
Here, m is the slope and b is the y-intercept.
From the equation, we can determine the slope
[tex]y=14x+10[/tex]
[tex]m=14[/tex] ∵ [tex]y=mx+b[/tex]
Hence, the slope is m=16.
We know that the slope is referred to as the 'rate of change'.
For example, if you have a part-time job at a store. You save for her tour at a rate of $20 every week. It means, your rate of change will be $20 per week.
So given the equation
[tex]y=14x+10[/tex]
m = rate of change = slope = 24
The slope is basically a vertical change divided by the horizontal change.
Therefore, we conclude that Membership grows by 14 each year.
what is the value of x?
Answers
Answer:
I honestly have no clue.
Step-by-step explanation:
I honestly have no clue.
I WILL MARK BRAINIEST
Answers
Answer:parallel
Step-by-step explanation:
Please help me out :)
Answers
A line has a slope of 3/2 and has a x-intercept of 2 . What is the y-intercept of the line?
Answers
Answer:
- 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute the x- intercept (2, 0 ) into the partial equation
0 = 3 + c ⇒ c = 0 - 3 = - 3 ← y- intercept
PLEASE HELP! 80 POINTS AND BRAINLIEST TO FIRST ANSWER!
A rectangular pen is constructed with 300m of fencing against a barn wall. What dimensions give the maximum area?
Answers
since it’s against a barn wall, then there would be three sides left. But I could be wrong. ¯\_(ツ)_/¯
what is f(x) = 0,5 (x-3)( x-5) in general form??
Answers
Answer:
[tex]f(x)=0.5x^2-4x+7.5[/tex]
Step-by-step explanation:
The general form of a quadratic function is:
[tex]y=ax^2+bx+c[/tex]
We'll find the general form of the function:
[tex]f(x)=0.5(x-3)(x-5)[/tex]
Multiplying the expressions in parentheses:
[tex]f(x)=0.5(x^2-5x-3x+15)[/tex]
Simplifying:
[tex]f(x)=0.5(x^2-8x+15)[/tex]
Operating:
[tex]\mathbf{f(x)=0.5x^2-4x+7.5}[/tex]
What is the slope of the line through (0,5) and (-2,-1)?
Answers
Answer:
c
Step-by-step explanation:
the slope is 3
Rise over run. You rise 3 points to get to the other, and run over one. Hope this helps.
Given p(x)=2x^3-3x-5 what is the value of p (-2)
Answers
Answer:
The value of p(x) at -2 is:
[tex]p(-2) = -15[/tex]
Step-by-step explanation:
Given polynomials is:
[tex]p(x) = 2x^3-3x-5[/tex]
We have to find p(-2)
This means that we have to find the value of the polynomial at -2. Finding value of a polynomial at a certain number is done by putting the number in the polynomial in place of variable. So putting x = -2
[tex]p(-2) = 2(-2)^3-3(-2)-5\\= 2(-8)+6-5\\= -16+1\\=-15[/tex]
Hence,
The value of p(x) at -2 is:
[tex]p(-2) = -15[/tex]
Which equation best describes a relationship between x and y in the table below?
Answers
Answer:
y = [tex]\frac{1}{3}[/tex] x + 5
Step-by-step explanation:
Slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y = mx + b , "b" is y-intercept with coordinates (0, b)
(0, 5)
(6, 7)
m = [tex]\frac{7-5}{6-0}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + 5
Explain the difference between a Polynomial and a Monomial, and how do you add/subtract and multiply and factoring them?
Answers
Answer:
HEY PLS DON'T JOIN THE ZOOM CALL OF A PERSON WHO'S ID IS 825 338 1513 (I'M NOT SAYING THE PASSWORD) HE IS A CHILD PREDATOR AND A PERV. HE HAS LOTS OF ACCOUNTS ON BRAINLY BUT HIS ZOOM NAME IS MYSTERIOUS MEN.. HE ASKS FOR GIRLS TO SHOW THEIR BODIES AND -------- PLEASE REPORT HIM IF YOU SEE A QUESTION LIKE THAT. WE NEED TO TAKE HIM DOWN!!! PLS COPY AND PASTE THIS TO OTHER COMMENT SECTIONS!!
Step-by-step explanation:
HEY PLS DON'T JOIN THE ZOOM CALL OF A PERSON WHO'S ID IS 825 338 1513 (I'M NOT SAYING THE PASSWORD) HE IS A CHILD PREDATOR AND A PERV. HE HAS LOTS OF ACCOUNTS ON BRAINLY BUT HIS ZOOM NAME IS MYSTERIOUS MEN.. HE ASKS FOR GIRLS TO SHOW THEIR BODIES AND -------- PLEASE REPORT HIM IF YOU SEE A QUESTION LIKE THAT. WE NEED TO TAKE HIM DOWN!!! PLS COPY AND PASTE THIS TO OTHER COMMENT SECTIONS!!
Determine if the expression 9y5 – 10y3 is a polynomial or not. If it is a polynomial,
state the type and degree of the polynomial.
Answers
I am going to assume that the equation was supposed to be [tex]9y^{5}[/tex][tex]-10y^{3}[/tex]
Answer:
It is a polynomial. It is a binomial and it has a degree of 5.
Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables so [tex]9y^{5}[/tex][tex]-10y^{3}[/tex] will be considered a polynomial.
A binomial is a polynomial with 2 terms.
The degree of a polynomial is the highest exponent in it which in this equation is 5.
select the correct equation of the graph...
Answers
Answer:
d
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The slope is -1/2 and the y-int is 2.
PLZ HELP ASAP 20 POINTS!! wrote an equation in slope-intercept (y=mx+b) form for each line.
Answers
Answer: I’m sorry I cannot explain this any other way because I can not see the answers but —> If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line. ✨
Step-by-step explanation: hope it help you later on!
Answer:
Y= -4x + 3
Step-by-step explanation: because the x value goes with mx, and the y value goes with b. :)
A line contains points (3,5) and (5,8). What is the slope
Answers
Answer:
3/2x
Step-by-step explanation:
Plug in to this formula
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{8-5}{5-3} \\\\\frac{3}{2}[/tex]
Your slope is 3/2x
If you want to find the y-intercept just plug in one of the points into this..
( ) = 3/2( ) + b
Hope this helps ya!!
I'll mark you brainiest if you give me the correct answer.
Answers
Answer:
42b -7.5
I think that's the answer since you are getting a discount which means you are subtracting
PLEASE HELP:(........thank you
Answers
Answer:
the answer is C
Step-by-step explanation:
ms.kirklan is baking muffins.each batch of muffins use 3/4 of a pound of flour. How many batches of muffins can she bake with 5 pounds of flour
Answers
Divide 5 by 3/4 (or .75 for a calculator)
You get 6.667
Round down
6
Good luck!
The number of batches of muffins Ms.Kirklan can bake with 5 pounds of flour is 7.
Given that, Ms.Kirklan is baking muffins. Each batch of muffins use 3/4 of a pound of flour.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
We need to find the number of muffins she can bake with 5 pounds of flour
Now, 5 ÷ 3/4
= 5 ÷ 0.75
= 6.6
≈ 7
Hence, the number of batches of muffins Ms.Kirklan can bake with 5 pounds of flour is 7.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ2
someone help please
Answers
Answer:
Type: polynomial
degree: 3
leading coefficient: 8
Step-by-step explanation:
The given equation is: f(x) = -7x^2 + 8x^3 + 6 - 4x
To find the type, degree, and leading coefficient of the equation, the first thing we should do is rewrite the terms in decreasing order:
f(x) = 8x^3 - 7x^2 - 4x + 6
The term with the highest value is 8x^3. We can use this to determine the degree and the leading coefficient.
8 is the leading coefficient. The degree is 3.
To find the type of equation this is, we have to count how many terms there are. We can see that there are 4 terms in this equation, making this a polynomial.
Which statement regarding the diagram is true?
m∠MKL + m∠MLK = m∠JKM
m∠KML + m∠MLK = m∠JKM
m∠MKL + m∠MLK = 180°
m∠JKM + m∠MLK = 180°
Answers
Answer:
b. m∠KML + m∠MLK = m∠JKM
Step-by-step explanation:
right on edge
The statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have a triangle shown in the picture:
As we know, triangle is a polygon with three sides and three interior angles.
From the definition of the triangle, The triangle's interior angles add up to 180°
m∠MKL + m∠MLK + m∠KML = 180
Also, the sum of the two interior angles is equal to the exterior angle.
m∠KML + m∠MLK = m∠JKM
Thus, the statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.
Learn more about the triangle here:
brainly.com/question/25813512
#SPJ5
whats 1/2 + 8 9/14 please help ASAP
Answers
Answer: 9 /17 as fraction 9.143 Simplify
Step-by-step explanation:
Answer:
9 1/7
The explanain of this is that 1/2 + 8 + 9 1/4 so... 1/2+9/14=?
7 1/4 + 9/14=16/14 and so... 16/14=8/7 then.. 8/7=1 1/7 then last thing 8 + 1 + 1/7= 9 1/7