Answer:
Step-by-step explanation:
If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.
First the area of the inner square. Here we go:
Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.
The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.
Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":
[tex]?^2=b^2+(a-b)^2[/tex] and
[tex]?^2=b^2+a^2-2ab+b^2[/tex] and
[tex]?^2=a^2-2ab+2b^2[/tex] so
?, the length of the hypotenuse, is
[tex]?=\sqrt{a^2-2ab+2b^2}[/tex] and now we can use that to find the area of the inner square. The formula for a square's area is
[tex]A=s^2[/tex] so
[tex]A=(\sqrt{a^_2}-2ab+2b^2})^2[/tex] which gives us finally:
[tex]A=a^2-2ab+2b^2[/tex] **
Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is
A = a²
The ratio of the area of the inner to the outer is:
[tex]\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}[/tex] and that does not reduce.
Answer:
A
Step-by-step explanation:
Edmentum
Hi friends,
Please assist with my question below.
In a right angle triangle, an angle of 30 degrees has an adjacent side which measures 17 cm. what is the length of its hypotenuse?
Answer : 19.6cm
I hope this helps you! Have a good day!
Please find this answer!! :)
Answer:
Amanda's box is in this case, the bigger one. Then subtract the Amanda's by Mary's. The Larger box is 70cm^3 larger then the smaller box.
Step-by-step explanation:
Amanda's box: 13.5*10*10= 1350cm^3
Mary's box: 20*8*8= 1280cm^3
1350-1280=70
The larger box is 70cm^3 larger then the smaller box.
If you have any questions regarding my answer tell me in the comments, i will come answer them. Have a good day.
Write an inequality, in slope-intercept form, for the graph below. If necessary,
use *<=' for sor">=' for .
(0,4)
(2.0)
Answer:
y<=(-2x+4)
Step-by-step explanation:
The equation of line is y=-2x+4. For the region left of it, y<=(-2x+4)
0.3,1/5,1/2,0.706,7/8,57.1%
Place following in ascending order
Answer:
the answer is 0.31/ 5.1/8.57.1% /207067
Step-by-step explanation:
ascending order from the smallest to the largest
Express -6 as the sum of a negative integer and a whole number
ASAP PLSSSSSSSS TYYYYYY
Answer:
20% of students prefer to go to the aquarium
50% of teachers prefer to go to the aquarium
Step-by-step explanation:
1.
8 students prefer the aquarium out of 40 students.
Set up an equation:
Variable x = percentage of students
8/40 = x/100
Cross multiply:
8 × 100 = 40 × x
800 = 40x
20 = x
Divide:
20%
Check your work:
40 students × 20%
Convert percentage into decimal:
40 × 0.20
8
8 students prefered the aquarium so this is correct!
2.
5 teachers prefer the aquarium out of 10 teachers.
Set up an equation:
Variable x = percentage of teachers
5/10 = x/100
5 × 100 = 10 × x
500 = 10x
50 = x
50%
Check your work:
10 × 0.50
5
Correct!
Quan điểm quản lý của trường phái đưc trị
.・。.・゜✭・Srry but which language is this!?
A)15.8 inches
B) 17.8 inches
C)16.2 inches
D)14.8 inches
Answer:
B
Step-by-step explanation:
Use pythagorean theorem
4^2+5^2=AC^2, AC= 6.4
7^2+9^2=CB^2, CB=11.4
If I toss a fair coin five times and the outcomes are TTTTT, then the probability that tails appears on the next toss is
1) 0.5
2) greater than 0.5
3) 1
4) less than 0.5
5) 0
Answer:
1. 0.5
Step-by-step explanation:
The probability of flipping a coin and landing on heads or tails is 100%. So 3)1 would be incorrect. In probability, we learned that just because something was picked more than once, it does not lower the chances of the thing being picked again. So 5)0 would be incorrect. The chances of getting tails are 50% also 0.5 and the chances of getting heads are 50% also 0.5. So 1 is correct.
There is a 0.5 percent chance that the following coin will land on its side.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
The sample space, which is typically represented using set notation, contains a list of all the potential ordered outcomes as elements. A sample space with all possible outcomes exists for a series of five fair coin tosses. The example of a fair coin toss is 2*2*2H,T.
{HHHHH,HHHHT,HHHTH,HHTHH,HTHHH........TTTTT} The likelihood that the next coin will land on its side is always equal to It doesn't matter if previous results were TTTTT, HHHHH, or TTHT. The probability that the next number will be a tails is therefore still 0.5 in each of these cases as well as all others.
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Jeanne has a coupon for 1.95 off a jug of name brand laundry detergent that normally costs 14.99 . The store brand laundry detergent costs 11.53 How much will Jeanne save if she buys the store brand detergent instead of using her coupon and buying the name brand
Step-by-step explanation:
14.99 - 11.53= 3.46+1.95 =4.41
I NEED HELP PLEASE!!!!
9514 1404 393
Answer:
A. 1/2
Step-by-step explanation:
The points on a unit circle are (cos(θ), sin(θ)), where θ is the angle from the +x axis to to the ray from the origin through that point.
If the point is (√3/2, 1/2), then sin(θ) = 1/2.
A line has a slope of 11 and passes through the point (5,7). Which of these is an equation for the line? O A. y-7 = -11(x - 5) B. y + 7 = 11(x + 5) O C. y-5 = -11(x - 7) O D. y - 7 = 11(x - 5) SUBMIT
Answer:
D. y - 7 = 11(x - 5)
Step-by-step explanation:
Use point slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plug in the given slope and point:
y - y1 = m(x - x1)
y - 7 = 11(x - 5)
So, the correct answer is D. y - 7 = 11(x - 5)
Which equation represents a slope of −4 and y-intercept of (0,2)?
y = −4x + 2
y = −2x
y = −2x − 4
y = 4x + 2
Answer:
y=-4x+2
Step-by-step explanation:
Hi there!
We want to find out which equation represents a line with a slope of -4 and a y intercept of (0,2)
The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
We have everything we need to plug into the equation, let's just label the values to avoid confusion
m=-4
b=2 (when you substitute the y intercept as b, b is the value of y in the point)
Now substitute into the equation
y=-4x+2
Hope this helps!
The 3rd and 7th terms of an arithmetic progression are 6and 30 respectively determine the common difference, first term,10th term.
Answer:
d = 6 , a₁ = - 6 and a₁₀ = 48
Step-by-step explanation:
The nth term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 6 and a₇ = 30 , then
a₁ + 2d = 6 → (1)
a₁ + 6d = 30 → (2)
Subtract (2) from (1) term by term to eliminate a₁
4d = 24 ( divide both sides by 4 )
d = 6
Substitute d = 6 into (1)
a₁ + 2(6) = 6
a₁ + 12 = 6 ( subtract 12 from both sides )
a₁ = - 6
Then
a₁₀ = - 6 + (9 × 6) = - 6 + 54 = 48
----------------------------------------------------
Answer:
d=6
a=-6
Step-by-step explanation:
use the formula for the nth term which is
Tn=a+(n-1)d..you will have to create two equations then solve them as a simultaneous equation
T3=6 and T7=30
T3=a+(3-1)d
6=a+2d........... first equation
T7=a+(7-1)d
30=a+6d.......... second equation
then solve them as a simultaneous equation
a+2d=6
a+6d=30
-4d/-4=-24/-4
d=6
a+2d=6
a+2(6)=6
a=6-12
a=-6
I hope this helps
The table above shows the percent of the area of a town
devoted to three uses. If the area devoted to business use
is 7,200 acres less than the area devoted to residential
use, what is the area, in acres, devoted to government
use?
A) 1,400
B) 1,800
C) 5,200
D) 44,000
=========================================================
Explanation:
Let
r = area devoted to residential use
This variable is some positive real number, and it represents the area in acres.
Your teacher says that " the area devoted to business use is 7,200 acres less than the area devoted to residential use"
This means the expression r-7200 represents the area for business use
Note the jump from 25% to 65% is 65/25 = 2.6, meaning that we multiply by 2.6 when going from the business area to the residential area.
So we'll multiply by 2.6 to go from r-7200 to r
We'll have this equation
2.6(r-7200) = r
because it's effectively saying
2.6*(business area) = residential area
--------------------------
Let's isolate r
2.6(r-7200) = r
2.6r-2.6*7200 = r
2.6r - 18720 = r
2.6r - r = 18720
1.6r = 18720
r = 18720/(1.6)
r = 11700
We'll use 11700 acres for the residential portion.
And also r-7200 = 11700-7200 = 4500 acres are set aside for the business district.
--------------------------
The largest region (residential) uses 11700 acres of land.
Note the jump from 10% to 65% involves a multiplier of 6.5 because 65/10 = 6.5
So if g is the amount of government land used, then,
6.5g = r
6.5g = 11700
g = 11700/(6.5)
g = 1800
1800 acres of land are for government use
This is why the answer is choice B.
The area, in acres, devoted to government use is 1800.
Option (B) is correct.
To find the area.
What is percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given that:
Let
r = area devoted to residential use
This variable is some positive real number, and it represents the area in acres.
This means the expression r-7200 represents the area for business use
Note the jump from 25% to 65% is 65/25 = 2.6, meaning that we multiply by 2.6 when going from the business area to the residential area.
To multiply by 2.6 to go from r-7200 to r
The equation is
2.6(r-7200) = r
because it's effectively saying
2.6*(business area) = residential area
--------------------------
Let's isolate r
2.6(r-7200) = r
2.6r-2.6*7200 = r
2.6r - 18720 = r
2.6r - r = 18720
1.6r = 18720
r = 18720/(1.6)
r = 11700
We'll use 11700 acres for the residential portion.
And also r-7200 = 11700-7200 = 4500 acres are set aside for the business district.
The largest region (residential) uses 11700 acres of land.
Note the jump from 10% to 65% involves a multiplier of 6.5 because 65/10 = 6.5
So if g is the amount of government land used, then,
6.5g = r
6.5g = 11700
g = 11700/(6.5)
g = 1800
So, the area, in acres, devoted to government use is 1800.
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144 is the same as 379 less than c
How can this be wrote in a equation
Answer:
144 = c - 379
Step-by-step explanation:
"144 is the same as 379 less than c"
144 = c - 379
Answer and Step-by-step explanation:
This can be written in an equation like this:
144 = c - 379
The question is saying that 144 is the same answer as the result of 379 less than c (or c minus 379). This is why we equal 144 to the result of c minus 379.
#teamtrees #PAW (Plant And Water)
The point (7, 8) is the solution of which of the following systems of equations?
1. 8x - y = 48
9x + 10y = 142
2. 9x - y = 55
8x + 10y = 140
3. x-6y=-41
8x + 9y = 127
4. x-7y=-49
10x + 9y = 142
Option 4
Verification:-
[tex]\\ \sf\longmapsto x-7y=-49[/tex]
[tex]\\ \sf\longmapsto 7-7(8)=-49[/tex]
[tex]\\ \sf\longmapsto 7-56=-49[/tex]
[tex]\\ \sf\longmapsto -49=-49[/tex]
And
[tex]\\ \sf\longmapsto 10x+9y=142[/tex]
[tex]\\ \sf\longmapsto 10(7)+9(8)=142[/tex]
[tex]\\ \sf\longmapsto 70+72=142[/tex]
[tex]\\ \sf\longmapsto 142+142[/tex]
Hence verified
Answer:
4.
Step-by-step explanation:
1. 8x - y = 48
9x + 10y = 142
8(7) - 8 = 48
9(7) + 10(8) = 143
No
2. 9x - y = 55
8x + 10y = 140
9(7) - 8 = 55
9(7) - 10(7) = -24
No
3. x-6y=-41
8x + 9y = 127
7 - 6(8) = -41
8(7) + 9(8) = 128
No
4. x-7y=-49
10x + 9y = 142
7 - 7(8) = 49
10(7) + 9(8) = 142
Yes
If using the method of completing the square to solve the quadratic equation x 2 − 9 x − 8 = 0 x 2 −9x−8=0, which number would have to be added to "complete the square"?
Answer:
Add 81/4 to both sides.
Step-by-step explanation:
x^2 − 9x − 8 = 0
x^2 - 9x = 8
Take the coefficient of the x term: -9
Divide by 2: -9/2
Square it: 81/4
Add 81/4 to both sides.
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. THIS IS NOT A TEST OR AN ASSESSMENT!! Please help me with these math problems. Chapter 12 part 2 PLEASE SHOW WORK!!!
4a. a_n = 2(1/3 + a_n-1), a_1 = 4
4b. a_n= n/(a_n-1), a_1 = 6
4c. 1/6, 2/3, 8/3, . . .
Problem 4a
The instructions are incomplete. You set up the recursive formula, but didn't ask any question about said formula.
I'll assume that your teacher wants you to list out a few terms. I'll list out the first five terms.
The notation a_1 = 4 is the same as writing [tex]a_1 = 4[/tex] where the '1' is a subscript. It tells us that the first term is 4.
The nth term a_n or [tex]a_n[/tex] is defined as such
[tex]a_n = 2*(1/3 + a_{n-1})\\\\[/tex]
Notice how if we replaced n with 2, then we get
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_2 = 2*(1/3 + a_{2-1})\\\\a_2 = 2*(1/3 + a_1)\\\\[/tex]
So the second term is directly tied to the first term, or it is dependent on it.
We'll replace a_1 with 4 to get the following
[tex]a_2 = 2*(1/3 + a_1)\\\\a_2 = 2*(1/3 + 4)\\\\a_2 = 2*(1/3 + 12/3)\\\\a_2 = 2*(13/3)\\\\a_2 = 26/3\\\\[/tex]
So the second term is 26/3.
As you can guess, the third term is going to be found in a similar fashion
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_3 = 2*(1/3 + a_{3-1})\\\\a_3 = 2*(1/3 + a_2)\\\\a_3 = 2*(1/3 + 26/3)\\\\a_3 = 2*(27/3)\\\\a_3 = 2*(9)\\\\a_3 = 18\\\\[/tex]
So 18 is the third term.
We'll repeat for n = 4 to get the fourth term.
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_4 = 2*(1/3 + a_{4-1})\\\\a_4 = 2*(1/3 + a_3)\\\\a_4 = 2*(1/3 + 18)\\\\a_4 = 2*(1/3 + 54/3)\\\\a_4 = 2*(55/3)\\\\a_4 = 110/3\\\\[/tex]
The fourth term is 110/3.
Lastly, we'll plug in n = 5
[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_5 = 2*(1/3 + a_{5-1})\\\\a_5 = 2*(1/3 + a_4)\\\\a_5 = 2*(1/3 + 110/3)\\\\a_5 = 2*(111/3)\\\\a_5 = 2*(37)\\\\a_5 = 74\\\\[/tex]
The fifth term is 74.
Answer: The first five terms are 4, 26/3, 18, 110/3, 74==============================================================
Problem 4b
Again, the instructions are missing. I'll assume the same thing as problem 4a.
[tex]a_1 = 6[/tex] is the first term
Plug n = 2 into the first equation to get
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_2 = \frac{2}{a_{2-1}}\\\\a_2 = \frac{2}{a_{1}}\\\\a_2 = \frac{2}{6}\\\\a_2 = \frac{1}{3}\\\\[/tex]
The second term is 1/3.
Repeat for n = 3
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_3 = \frac{3}{a_{3-1}}\\\\a_3 = \frac{3}{a_{2}}\\\\a_3 = \frac{3}{1/3}\\\\a_3 = 3\div\frac{1}{3}\\\\a_3 = 3\times\frac{3}{1}\\\\a_3 = 9\\\\[/tex]
The third term is 9
Repeat for n = 4.
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_4 = \frac{4}{a_{4-1}}\\\\a_4 = \frac{4}{a_{3}}\\\\a_4 = \frac{4}{9}\\\\[/tex]
The fourth term is 4/9
Repeat for n = 5
[tex]a_n = \frac{n}{a_{n-1}}\\\\a_5 = \frac{5}{a_{5-1}}\\\\a_5 = \frac{5}{a_{4}}\\\\a_5 = 5 \div a_{4}\\\\a_5 = 5 \div \frac{4}{9}\\\\a_5 = 5 \times \frac{9}{4}\\\\a_5 = \frac{5}{1} \times \frac{9}{4}\\\\a_5 = \frac{5*9}{1*4}\\\\a_5 = \frac{45}{4}\\\\[/tex]
Answer: The first five terms are 6, 1/3, 9, 4/9, 45/4==============================================================
Problem 4c
I'm not much help here for this problem. Not only are the instructions missing, but it's not clear how this sequence is set up. If I had to guess, it's somehow recursively defined. How exactly, I'm not sure. I would ask your teacher for any clarification.
Plz this is due today help me explain the answer
Answer:
177.3 feet
This is a classic find the vertex of a parabola question.
if this was a calculus class the solution would be to take the derivative and set it equal to zero... -32t+ 105 = 0
BUT i assume that you are not in a calculus class..
so we try plan "B" the highest (or lowest) point of parabola is it's vertex
the vertex formula is [-b/2a,f(-b/2a)]
in your problem a = -16, b=105, c= 5
so the "X" (TIME) is located at -(105)/(2*-16) = 3.28
plug in 3.28 into -16(3.28)^2 + 105(3.28) + 5 = 177.27
and you will get
Step-by-step explanation:
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Find the 5th term for the following recursive formulas/sequences. SHOW YOUR WORK!!
c. 1/6, 2/3, 8/3, . . .
Answer:
128/3
Step-by-step explanation:
The sequence follow the rule (1/6)*(4)^(n-1). The 5th term will be (1/6)*(4)^4=128/3
Answer:
128/3
Step-by-step explanation:
1/6, 2/3, 8/3, . . .
1/6, 4/6, 16/6
We are multiplying by 4 each time
1/6 *4 = 4/6
4/6 * 4 = 16/6
This is a geometric sequence with the common ratio of 4
an = a1 (r)^(n-1)
an = 1/6 (4) ^(n-1)
Let n = 5
a5 = 1/6 (4)^(5-1)
a5 = 1/6 (4)^4
a5 = 1/6 * 256
a5 =128/3
6x/x+6
Find all real numbers for which the rational expression is undefined.
Answer:
x=-6
Step-by-step explanation:
For the rational expression, 6x/(x+6) to be undefined, the denominator need to be 0, so x=-6 is the point at which the function is undefined.
The rational expression 6x / (x + 6) is undefined when x equals -6, and it is defined for all other real numbers.
To find the real numbers for which the rational expression 6x / (x + 6) is undefined, we need to identify the values of x that would make the denominator equal to zero. When the denominator is zero, the expression becomes undefined.
In this case, the denominator is (x + 6). Setting the denominator equal to zero, we have:
x + 6 = 0
Solving for x, we subtract 6 from both sides:
x = -6
Therefore, the rational expression 6x / (x + 6) is undefined when x = -6.
When x is equal to -6, the denominator becomes zero, which causes division by zero. Division by zero is undefined in mathematics. Hence, for x = -6, the rational expression is not defined.
For any other real numbers other than x = -6, the expression is defined and can be simplified or evaluated.
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What is the phase of y= -3cos (3x-pi) +5
Answer:
[tex]- \frac{\pi}{3}[/tex]
Step-by-step explanation:
Given
[tex]y = -3\cos(3x - \pi) + 5[/tex]
Required
The phase
We have:
[tex]y = -3\cos(3x - \pi) + 5[/tex]
Rewrite as:
[tex]y = -3\cos(3(x - \frac{\pi}{3})) + 5[/tex]
A cosine function is represented as:
[tex]y = A\cos(B(x + C)) + D[/tex]
Where:
[tex]C \to[/tex] Phase
By comparison:
[tex]C = - \frac{\pi}{3}[/tex]
Hence, the phase is: [tex]- \frac{\pi}{3}[/tex]
prove it using mathematical induction
Answer:
Mathematical induction can be used to prove that an identity is valid for all integers n≥1. Here is a typical example of such an identity: 1+2+3+⋯+n=n(n+1)2. More generally, we can use mathematical induction to prove that a propositional function P(n) is true for all integers n≥1.
Step-by-step explanation:
I'd really appreciate a brainleast please:)
find three numbers in dip, such that their sum is 60 and the last one is three times the first
30,20 and 10
30 + 20 + 1/3×30 = 60
50 + 10 = 60
60 = 60
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a person who take 40 paces to cover 20m finds that a square field has a side that is 520 paces long .calculate the length of the side and the area of the field
The area of the square field is 67600 m² and the side is 260 m long.
What is square?A quadrilateral with all sides equal and all angles are right angles.
Given that, a person takes 40 paces to cover 20 m of a square field according to him the field has a side that is 520 paces long, we need to find the measure of the side and the area,
Since,
40 paces = 20 m
1 pace = 1/2 m
Therefore,
520 paces = 0.5 x 520 m
= 260 m
Therefore, the square field is 260 m long,
Area of the square field = side² = 260²
= 67600 m²
Hence, the area of the square field is 67600 m² and the side is 260 m long.
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Given ADEF: ARST, find the scale factor
Answer:
the scale factor is 3/4
x = 16×3/4 = 12
Step-by-step explanation:
the only side length we have for both triangles is the short left side.
we see that we get ED from SR and need to transform 4 into 3. how do we do that ?
well,
4×f = 3
f = 3/4
that is the scaling factor, as all side lengths in EDF are created by multiplying the corresponding side in SRT by the same scaling factor (3/4).
therefore,
x = EF = ST×f = 16×3/4 = 4×3 = 12
Answer:
The scale factor is 4/3 and x is 12
Step-by-step explanation:
→ Divide RS by DE
4 ÷ 3 = 4/3
→ Divide the answer by 16
16 ÷ 4/3 = 12
What ordered pairs are the solutions of the system of equations shown in the graph below?
The solutions are where the two lines cross over each other.
(0,3) and (4,-5)
Aku has less than 3 times as many mangoes as Alaba and half as many mangoes as Amina if alaba has x mangoes the interns of x then how many mangoes do aku alaba and Amina have in combined
Answer:
I have no clue my bad bro.
Solve the following equation for
b
b. Be sure to take into account whether a letter is capitalized or not.
Answer:
b = h*D +hg^3
Step-by-step explanation:
b/h = D +g^3
Multiply each side by h
h* b/h = h*D +hg^3
b = h*D +hg^3
