A number multiplied by a sum is the same as the sum of the number multiplied by each addend; a(b + c) = ab + ac
Answer:
the distributive property of binary operations generalizes the distributive law from elementary algebra, which asserts that one has always For example, one has One says that multiplication distributes over addition.
the lengths of the sides of a triangle are in as ratio 3:4:5., find the lengths of the sides of this triangle if its perimeter is 96 cm
Answer:
24,32,40
Step-by-step explanation:
side 1: side2: side3: total
3 4 5 3+4+5=12
The total is the perimeter = 96
96/12 = 8
Multiply each term by 8
side 1: side2: side3: total
3*8 4*8 5*8 12*8
24 32 40 96
Let the sides of the triangle ABC be 3x , 4x and 5x.
Where x is a multiple.Perimeter of triangle = 3x + 4x + 5x
[tex] \bf \rightarrow \: 96 \: = \: 12x[/tex]
[tex]\bf \rightarrow \: \frac{96}{12} \: = \: x \\ [/tex]
[tex]\bf \rightarrow \: \cancel\frac{96}{12} \: ^{8} \: = \: x \\ [/tex]
[tex]\bf \rightarrow \: x \: = \: 8[/tex]
Required sides are :[tex] \bf \implies \: 3x \: = \: 3 \: \times \: 8 \: = 24[/tex]
[tex]\bf \implies \: 4x \: = \: 4 \: \times \: 8 \: = 32[/tex]
[tex]\bf \implies \: 5x \: = \: 5 \: \times \: 8 \: = 40[/tex]
Hence , the sides of the triangle are 24 , 32 and 40.
A market vendor sells pawpaws and guavas. In a week the number of pawpaws sold and the number of guavas sold were in the ratio 3:5 respectively. The total number of pawpaws and guavas sold in a week was 328. (a) How many pawpaws were sold in a week? (1 ma (b) How many guavas were sold in a week? (1 ma Yoon Dohored a prize money of $400.00 in
Total awpaws and guavas sold in a week = 328
Let the number of pawpas and guavas be x
ATQ
3x + 5x = 328
8x = 328
x = 328/8
x = 41
Pawapas in a week = 123
Guavas in a week = 205
Must click thanks and mark brainliest
Select the correct answer.
What is V200in simplest form?
OA. 2/10
OB.
1072
O C. 100/2
OD
20/10
Darot
Answer:
It is 10√2
Step-by-step explanation:
[tex] = \sqrt{200} \\ = \sqrt{2 \times 100} \\ = ( \sqrt{2} ) \times ( \sqrt{100} ) \\ = \sqrt{2} \times 10 \\ = 10 \sqrt{2} [/tex]
The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles.
Answer:
Step-by-step explanation:
A right triangle has one right angle and two acute angles.
A and B are the acute angles.
A+B = 90°
One acute angle is 45 less than twice the other acute angle.
A = 2B-45°
(2B-45°) + B = 90°
3B = 135°
B = 45°
A = 45°
Identify the errors made in the finding the inverse of y= x^2 +12x
X= y^2+12x
Y^2= x- 12x
Y^2 = -11x
Y=√11x, for x greater than or equal to 0
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Answer:
y was not substituted for every x
Step-by-step explanation:
To find the inverse of ...
y = f(x)
you need to solve ...
x = f(y)
Here, f(x) = x^2 +12x, so f(y) = y^2 +12y
This is not the expression we see on the right of ...
x = y^2 +12x
Apparently y was not properly substituted into f(x).
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
-3y=3x-9
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
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Answer:
y = -x +3
m = -1
b = 3
Step-by-step explanation:
To solve the given equation for y, divide by the coefficient of y.
(-3y)/(-3) = (3x -9)/(-3)
y = -x +3
__
The slope is the x-coefficient, M = -1.
__
The y-intercept is the added constant, B = 3.
__
Both equations are graphed in the attachment. Texture has been added to the original so you can see the graphs are the same line.
please help me I need help
Answer:
This is so hard for me. I can't understand. I am in grade 9 now.
Giải phương trình vi phân cấp 2
Answer:
bajskalakbskajalabsnsja
Pass The following Journal Entry .
1. Salaries remaining unpaid Rs.15000 and rent due to landlord Rs.2000
Please This is Accountancy questions Don't spaim
good lesson udayy...........
Step-by-step explanation:
1.→ Salaries A/c Dr. 15,000 To O/s Salaries A/c 15,000→ Rent A/c Dr. 2,000To O/s Rent A/c 2,0001st (´-ω-｀)))。。
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. d) She will have a hard time focusing.
Consider the following theorem. Theorem If f is integrable on [a, b], then b a f(x) dx = lim n→[infinity] n i = 1 f(xi)Δx where Δx = b − a n and xi = a + iΔx. Use the given theorem to evaluate the definite integral. 9 (x2 − 4x + 6) dx 1
Split up the interval [1, 9] into n subintervals of equal length (9 - 1)/n = 8/n :
[1, 1 + 8/n], [1 + 8/n, 1 + 16/n], [1 + 16/n, 1 + 24/n], …, [1 + 8 (n - 1)/n, 9]
It should be clear that the left endpoint of each subinterval make up an arithmetic sequence, so that the i-th subinterval has left endpoint
1 + 8/n (i - 1)
Then we approximate the definite integral by the sum of the areas of n rectangles with length 8/n and height [tex]f(x_i)[/tex] :
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx \approx \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right)[/tex]
Take the limit as n approaches infinity and the approximation becomes exact. So we have
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx = \lim_{n\to\infty} \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right) \\\\ = \lim_{n\to\infty} \frac8n \sum_{i=1}^n \left(1+\frac{16}n(i-1)+\frac{64}{n^2}(i-1)^2-4-\frac{32}n(i-1)+6\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=1}^n \left(64(i-1)^2-16n(i-1)+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=0}^{n-1} \left(64i^2-16ni+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(64\sum_{i=0}^{n-1}i^2 - 16n\sum_{i=0}^{n-1}i + 3n^2\sum{i=0}^{n-1}1\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{64(2n-1)n(n-1)}{6} - \frac{16n^2(n-1)}{2} + 3n^3\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{49n^3}3-24n^2+\frac{32n}3\right) \\\\= \lim_{n\to\infty} \frac{8\left(49n^2-72n+32\right)}{3n^2} = \boxed{\frac{392}3}[/tex]
Can anyone please help me with this ?
Answer:
6.7
Step-by-step explanation:
The formula for volume is V=lwh.
320=(6)(8)x
Solve.
320=48x
Divide both sides by 48.
6.6666666=x
Round to the nearest tenth.
x=6.7
I hope this helps!
pls ❤ and give brainliest pls
Answer:
6.7 =x
Step-by-step explanation:
The volume is given by
V = l*w*h
320 = 8*6*x
320 =48x
Divide each side by 48
320/48 = 48x/48
6.6666666 = x
Rounding to the nearest tenth
6.7 =x
Simplify 4^-4.
please help I have 10 minutes
Answer:
1/256
Step-by-step explanation:
[tex]4^{-4}[/tex]
[tex](1/4)^{4}[/tex]
=> 1/256
Simplify: 41a-2b + 3c) + 11a
Step-by-step explanation:
41a+11a-2b+3c
52a-2b+3c
Step-by-step explanation:
(41a-2b+3c) +11a
open the bracket
41a-2b+3c+11a
collect like terms
41a+11a-2b+3c
52a-5bc
so final answer is 52a-5bc
because they are not like terms they are unlike terms
The perimeter of a square is 14 cm. Find the area
Step-by-step explanation:
A = 12.25cm2
P perimeter 14cm
Answer:
A=12.25cm²
P=14
what is equivalent to (160 times243)1/5th
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Answer:
480
Step-by-step explanation:
The expression evaluates to ...
160·243^(1/5) = 160·(3^5)^(1/5) = 160·3 = 480
find the measure of a
Answer:
Hello,
answer D 48°
Step-by-step explanation:
In the right triangle down, a+42°=90° ==> a=90°-42°=48°
what decimal is equivalent to 0.85
Answer: 17/20
Step-by-step explanation:
0.85 = 85/100 = 17/20
The number 0.85 can be written using the fraction 85/100 which is equal to 17/20 when reduced to lowest terms.
Convert the degree measurement to radians. Express answer as multiple of π: - 60°
A. π/3
B. −π/4
C. −π/5
D. −π/3
Answer:
-pi/3
Step-by-step explanation:
To convert from degree to radians, multiply by pi/180
-60 * pi/180 = -60/180 *pi = -pi/3
Answer:
D. -pi/3
Step-by-step explanation:
degree to radians formula: x=degree, x*pi/180
x=-60
-60*pi/180=-pi/3
I am 10% older than my wife,my wife is x% younger than i am find x
You = her*1.1
her = you/1.1 = you*0.9090...
her = you - you*(1 - 0.9090...) = you - you*0.0909...
--> 9.09% younger
x = 9.09
HOPE SO IT HELPS YOU
The required value of x is 0.909.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The husband is 10% older than wife.
And, the wife is x% younger than husband.
Suppose the age of husband is h and of wife be w.
The following equations can be written for the given case,
(h - w)/w × 100 = 10 (1)
And, (h - w)/h × 100 = x (2)
Divide both equations to get,
h/w = 10/x
Equation (1) can be written as,
h/w - 1 = 10
=> 10/x - 1 = 10
=> 10/x = 11
=> x = 10/11
=> x = 0.909
Hence the value of x for the given case is 0.909.
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Enter a value that would not make relation a function (-4,0),(?,8),(9,0),(-5,2)
Answer:
Step-by-step explanation:
? = -4, 9, or -5
The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).
What are zeros of quadratic function?The zero of the function is where the y-value is zero. The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
here, we have,
from the given the information , we get,
If one zero is x= 4, then one factor of the expression would be (x - 4).
Similarly if another zero is x=-9, then another factor of the expression would be (x+9)
We have two answers with these two factors and both are possible. So, the answers are b and c.
Hence, The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).
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complete question:
Which function's graph has a zeros at (4,0) and (-9,0)?
Thomas' dog
had 10 puppies. 2
were yellow, 5. were
mixed and the rest
were black. What
decimal represents black dogs out of the total.
black dogs out of
the total?
Answer
0.3
Step-by-step explanation:
A coffee pot holds 3 1/4 quarts of coffee. How much is this in cups? Write your answer as a whole number or a mixed number in simplest form.
Answer:
13 cup i hope this help
Step-by-step explanation:
Show that the points A(2, 2), B(5,7), C(-5, 13), and D(-8, 8) are the vertices of a rectangle.
A. AB = CD = 18; BC = DA = 4
B. AB = CD = 34: BC = DA = V136
C. AC = BD = 170
D. AB = CD = 34: BC = DA = V136; AC = BD = v170
Please select the best answer from the choices provided
Answer:
Step-by-step explanation:
Using V as a substitute for √ is misleading. Better to write “square root of x”.
AC = BD = √170
Part of the population of 6,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 3 of them are infected. How many elk are likely to be infected?
Answer:
405
Step-by-step explanation:
We can use a ratio to solve
3 infected x infected
------------------ = ----------------
50 sampled 6750 population
Using cross products
3*6750 = 50x
Divide each side by 50
3*6750/50 = x
405
Answer:
Around 405 elk should be infected with the parasite.
Step-by-step explanation:
6,750/50=135
135 * 3 = 405
hope this helps :)
what are the coordinates of A,B and C
Answer:
Please display full question . your question is incomplete ..
Answer:
Step-by-step explanation:
Please display a picture
3x7-12-2=7?
I have no clue please help...
Answer:
X = 28/3, or 9 1/3 or 9.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
PRACTICE ANOTHER A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? m (b) How much wire should be used for the square in order to minimize the total area? m
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 18 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (18 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (18 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(18 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(18 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(18 - x)/3 = 0
2x/4 - (√3/6)(18 - x) = 0
2x / 4 = (√3/6)(18 - x)
√3x = 18 - x
√3x + x = 18
x (√3 + 1) = 18
x = 18 / (1.732 + 1)
x = 18/2.732
x = 6.58
x = 7
Thus,
The length of the square must be 7 m in order to maximize the total area.
Learn more about maxima and minima here:
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(PLEASE HELP ITS THE LAST QUESTION)
Find the measure of angle L.
A) 21.6°
B) 43.8°
C) 33.4°
D) 21.9°
Answer:
A
Step-by-step explanation:
lemme meh knw if it was helpful..
How is the graph of y=4(2)^x-3 translated from the graph of y=4(2)^x
Subtracting 3 at the end of the equation shifts the graph down 3 units
