Answer:
[tex]\sqrt{2}+\sqrt{5}[/tex]
Step-by-step explanation:
Since there are 2 diagonal angles that are 90 degrees, we can figure out the shape is made of 2 right triangles, so we can use the Pythagorean theorem to find out the length of each side.
The problem said that there must be 2 distinct sides with integer lengths, but there are no 2 integers that satisfy [tex]x^2+y^2 = 3^2[/tex] so we can deduce that both right triangles contain 1 integer value side and 1 non-integer value side.
There are only 2 positive integer values that would fit in [tex]x^2+y^2 = 3^2[/tex] for x: 1 and 2. That means the 2 triangles' equation is:
[tex]1^2+\sqrt{8}^2 = 3^2[/tex] and [tex]2^2 + \sqrt{5}^2 = 3^2[/tex].
Now, since these are right triangles, their areas are just going to be their 2 legs multiplied by 1/2.
The first triangle's area is:
[tex]1\cdot\sqrt{8}\cdot1/2 = 1\cdot2\sqrt{2}\cdot1/2 = \sqrt{2}[/tex]
The second triangle's area is:
[tex]2\cdot\sqrt{5}\cdot1/2 = \sqrt{5}[/tex]
The total area of the quadrilateral would be the sum of the 2 triangles, which is just [tex]\sqrt{2}+\sqrt{5}[/tex].
I hope this helped you.
The total area of the quadrilateral ABCD is [tex](\sqrt{2}+ \sqrt{5} )[/tex] and this can be determined by using the formula of the area of the triangle.
Given :
Quadrilateral ABCD has right angles at B and D, and AC=3. ABCD has two sides with distinct integer lengths.The following steps can be used in order to determine the area of ABCD:
Step 1 - Let the length of the segment AD be 'x' and the length of the segment CD be 'y'.
Step 2 - Now, apply the Pythagorean theorem on the triangle ACD.
[tex]x^2+y^2= 3^2[/tex]
Step 3 - According to the given data, ABCD has two sides with distinct integer lengths. So, there are two possibilities:
[tex]1^2+(\sqrt{8} )^2= 3^2[/tex]
[tex](2)^2+(\sqrt{5} )^2=3^2[/tex]
So, the possible sides of the quadrilateral will be [tex]\rm 1, \;2,\; 2\sqrt{2},\;and \;\sqrt{5}[/tex].
Step 4 - So, the area of the triangle ABC is:
[tex]A=\dfrac{1}{2}\times \sqrt{8} \times 1\\A = \sqrt{2}[/tex]
Step 5 - Now, the area of the triangle ACD is:
[tex]A'=\dfrac{1}{2}\times \sqrt{5} \times 2\\A' = \sqrt{5}[/tex]
Step 6 - So, the total area of the quadrilateral ABCD is:
[tex]{\rm Area } = \sqrt{2} + \sqrt{5}[/tex]
The total area of the quadrilateral ABCD is [tex](\sqrt{2}+ \sqrt{5} )[/tex].
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A bottle of hot sauce is 3/4 full. Leigh uses 2/9 of the contents of the hot sauce bottle for lunch. How much of a full bottle of hot sauce did Leigh use for lunch?
Leigh uses [tex]\frac{1}{6}[/tex] of full bottle of hot sauce
What is 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.
Given,
A bottle of hot sauce is 3/4 full.
Leigh uses 2/9 of the contents of the hot sauce bottle for lunch.
Therefore
How much of a full bottle of hot sauce did Leigh use for lunch = [tex](\frac{3}{4}).(\frac{2}{9})[/tex]
= [tex]\frac{1}{6}[/tex]
Hence, Leigh uses [tex]\frac{1}{6}[/tex] of full bottle of hot sauce
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Solve the system of equations
Y = 4x - 11
Y = x + 13
x = ??????
Y = ??????
Please tell me what Y and X are first..
double the sum of x and 5
Answer:
2(x+5) = 2x+10
Step-by-step explanation:
2(x+5)
= 2*x + 2*5
= 2x+10
A line segment (DE) joining the midpoints of two sides of a triangle is
parallel
to the third sid
Answer:
Given = A △ABC in which D and E are the mid-points of side AB and AC respectively. DE is joined .
To Prove : DE || BC and DE = 1 / 2 BC.
Const. : Produce the line segment DE to F , such that DE = EF. Join FC .
Proof : In △s AED and CEF, we have
AE = CE [∵E is the mid point of AC]
∠AED = ∠CEF[vert. opp.∠s]
and DE = EF [by construction]
∴ △AED ≅ △CEF [by SAS congruence axiom]
⇒ AD = CF ---(i)[c.p.c.t.]
and ∠ADE and ∠CEF ---(ii) [c.p.c.t.]
Now, D is the mid point of AB.
⇒ AD = DB ---(iii)
From (i) and (iii), CF = DB ---(iv)
Also, from (ii)
⇒ AD = || FC [if a pair of alt. int. ∠s are equal then lines are parallel]
⇒ DB || BC ---(v)
From (iv) and (v), we find that DBCF is a quadrilateral such that one pair of opposite sides are equal and parallel.
∴ DBCF is a ||gm
⇒ DF || BC and DF = BC [∵opp side of ||gm are equal and parallel]
Also, DE = EF [by construction]
Hence, DE || BC and DE = 1 / 2 BC
I need help with #66 and #68
Step-by-step explanation:
66. Δy = -3.4 Δx
Δy/Δx = -3.4
The slope of the line is -3.4. Slope-intercept equation of the line is:
y = -3.4x + b
Plug in the given point to find b:
2 = -3.4(4) + b
b = 15.6
Therefore, the equation is y = -3.4x + 15.6.
Use the equation to find the y coordinates.
[tex]\left[\begin{array}{cc}x&y\\-4&29.2\\4&2\\6&-4.8\\18&-45.6\end{array}\right][/tex]
68. Repeat the same steps as 66.
Δy = -1.7 Δx
Δy/Δx = -1.7
The slope of the line is -1.7. Slope-intercept equation of the line is:
y = -1.7x + b
Plug in the given point to find b:
3 = -1.7(-7) + b
b = -8.9
Therefore, the equation is y = -1.7x − 8.9.
Use the equation to find the x or y coordinates.
[tex]\left[\begin{array}{cc}x&y\\-19&23.4\\-7&3\\-2.412&-4.8\\3.2&-14.34\\9.1&-24.37\end{array}\right][/tex]
Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!
Answer:(f/g)(x)=(1+2x)/(1-3x) where x<>0
Step-by-step explanation:
f(x)= 1/x+2= (1+2x)/x , x<>0
g(x)=1/x-3=(1-3x)/x , x<>0
=>f(x)/g(x)= (1+2x)/(1-3x) , x<>0
If y varies inversely with x and y=11 when x=3, find the equation that relates x and y.
Answer:
y = [tex]\frac{33}{x}[/tex]
Step-by-step explanation:
Use the inverse relationship equation, y = [tex]\frac{k}{x}[/tex]
Plug in what we know to solve for k:
11 = [tex]\frac{k}{3}[/tex]
33 = k
Plug 33 in as k to find the equation:
The equation will be y = [tex]\frac{33}{x}[/tex]
Please help me ?! ❤️❤️
Answer:
Hey there!
(3,5) is your answer.
Hope this helps :)
Answer:
its (3,5)
hope it helps
The line graph shows the average daily cost, rounded to the nearest 10 cents, that a homeowner paid for electricity each month of a year. In which month(s) was the average daily cost less than $2.00? May, September September only May only March, April, May
Answer:
Only May
1.09 Statistical Graphs 1_Optional Quiz
A graph is a way to represent a lot of data in such a visual format. The month in which the average daily cost is less than $2.00 is may only.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
In order to know the month in which the average daily cost is less than $2.00, we need to find the dot which is below 2.
Now, if we look at the graph as shown below, the point that will be less than 2 is may.
Hence, the month in which the average daily cost is less than $2.00 is may only.
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A wall Of a building is 34 inches wide, 14 inches is concrete, 12 inches is brick, and 8 inches is limestone. what fraction of the wall is brick?
Step-by-step explanation:
It is given that,
A building is 34 inches wide. Its 14 inches is concrete, 12 inches is brick, and 8 inches is limestone. We need to find the fraction of the wall is brick.
A fraction is in the form of x/y. y is total value and x is a part of y.
Here, 12 inches is brick. So, its fraction is :
[tex]F=\dfrac{12}{34}=\dfrac{6}{17}[/tex]
So, fraction of [tex]\dfrac{6}{17}[/tex] is the wall which is brick.
19. If the polynomial P(x) = 27x^3 + 9x^2 – 3x – 10 is divided by 3x – 2, the remainder will be
options:
A) 1
B) 2
C) 3
D) 0
Answer:
D) 0
Step-by-step explanation:
Remainder is zero as 10 is fully divisible by 2.
Proof:
27x^3 + 9x^2 – 3x – 10 = (3x -2) (9x^ 2 +9x+5)Correct choice is D) 0
M is the midpoint of LN. What is the measure of LM= 3x and LN= 2x + 2, find LM.
Answer:
LM = 1.5
LN = 3
Step-by-step explanation:
From the question given:
M is the midpoint of LN
LM = 3x
LN= 2x + 2
LM =.?
Next, we shall determine the value of x. This is illustrated below:
Since M is the midpoint of LN, it means that when we divide LN by 2 the result will be LM i.e
LN /2 = LM
With the above formula, we can obtain the value of x as follow:
LN= 2x + 2
LM = 3x
x =..?
LN /2 = LM
2x + 2/ 2 = 3x
Cross multiply
2 × 3x = 2x + 2
6x = 2x + 2
Collect like terms
6x - 2x = 2
4x = 2
Divide both side by 4
x = 2/4
x = 0.5
Finally, we can obtain LM and LN as follow:
LM = 3x
x = 0.5
LM = 3 × 0.5
LM = 1.5
LN= 2x + 2
x = 0.5
LN = 2(0.5) + 2
LN = 1 + 2
LN = 3
Three white balls and three black balls are distributed in two urns in such a way that each contain three balls. We say that the system is in state i, i=0,1,2,3, if the first urn contains i white balls. At each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn denote the state of the system after the nth step. Explain why {Xn, n=0 ,1, 2} is a Markov chain and calculate its transition probability matrix.
Answer:
Following are the answer to this question:
Step-by-step explanation:
In-state 0, it has urns of the 100% chance of shifting towards state 1 because a colored ball must be substituted.
In the [tex]state 1: \frac{1 \ white}{2 \ black} \ \ \ and \ \ \frac{2 \ white}{1 \ black}[/tex]
The probability to select White from both the probability to select Black from both are 2/9, therefore there are 4/9 possibilities to remain in State 1.
It is probable which white from both the beginning is selected and black from the second, so that 1/9 probability of 0.
The probability is 4/9 that the first black and the second white will be chosen and 4/9 possibility will be made to state 2.
In the [tex]state 2: \frac{2 \ white}{1 \ black} \ \ \ and \ \ \frac{1 \ white}{2 \ black}[/tex]
This is essentially a state 1 mirror image because identical claims are used for reverse colors.
In-State 3, the urns are 100% likely to revert to State 2.
It is the representation of matrix M is, therefore:
[tex]( ..0. ..1. ..0. ..0. )\\\\( \frac{1}{9} \frac{4}{9} \frac{4}{9}.. 0. )\\\\( ..0. \ \frac{4}{9} \ \frac{4}{9} \ \frac{1}{9})\\\\( ..0. ..0. ..1. ..0. )\\\\So, \\ X_n = M \times X_{n}-1 \\\\Or\\X_n = M^n \times X_0[/tex]
I need help where do I plot the point help asap please
Answer:
Plot the point at the minimum of the graph.
Step-by-step explanation:
If you keep moving the graph down, pick the point with the lowest y value that is still on the blue.
arrange the following fraction in ascending order 2/3 1/6 3/5
Answer:
2/3 3/5 1/6
Step-by-step explanation:
look at the denominators and arrange from least to greater
Solve the following:
2x – 7 > 9
a
3> 8
b
x > 1
C
3 < 8
d
x>-1
Answer: x > 8
2x - 7 > 9
2x > 9+7
2x > 16
2x / 2 > 16 / 2
x > 8
Arnold deposited $732.19 in a savings account that earns 2.7% simple interest. What is Arnold's account balance after seven years?
Answer:
Step-by-step explanation:
$870.57
use equation total = Principal(1 + rate*time)
3-7, please help BRAINLEST
Answer:
s =2
Step-by-step explanation:
__3s__ = __6__
3 3
s = 2
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------
Answer: s = 2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]6 = 3s[/tex]
Divide both sides by 3.
[tex]\frac{6}{3} = s[/tex]
Divide 6 by 3 to get 2.
[tex]2 = s[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]s = 2[/tex]
Numbers 2-4 Will choose brainliest
Answer:
2. 9, 8+9
3. 17-8=9, 17, 8, 9
4. 13-7=6
Step-by-step explanation:
Solve -4r + 18= 6 I need this equation
Answer:
r = 3Step-by-step explanation:
[tex]-4r + 18= 6\\\\\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}\\\\-4r+18-18=6-18\\\\\mathrm{Simplify}\\\\-4r=-12\\\\\mathrm{Divide\:both\:sides\:by\:}-4\\\\\frac{-4r}{-4}=\frac{-12}{-4}\\\\\mathrm{Simplify}\\\\r=3[/tex]
Simplify the expression: 42 + 8 ÷ 2.
its 46.
42+8/2
42+4
=46
PLEASE HELP!!!! what is the value of 6n - 2 when n = 3?
A: 7
B: 6
C: 16
D: 12
Answer: C, 16
Step-by-step explanation:
6n - 2 when n = 3
Replace n with 3
1. 6(3) -2
2. 6(3) =18
3.18-2 = 16
Answer is 16.
Answer: C: 16
Step-by-step explanation: 6*3 =18. 18-2=16
Calculate the total surface area of a rectangular box 10cm long, 8cm wide and 6cm tall.
Answer:
The answer is
376 cm²Step-by-step explanation:
Since the rectangular box is a cuboid,
Total surface area of a cuboid is given by
2( lw + wh + lh)Where
l is the length
w is the width
h is the height
From the question
l = 10 cm
w = 8cm
h = 6cm
Substitute the values into the above formula
That's
Total surface area of the rectangular box is
2 [ (10)(8) + (8)(6) + (10)(6) ]
2 [ 80 + 48 + 60 ]
2( 188)
We have the final answer as
Total surface area = 376 cm²Hope this helps you
round 24.927 in two decimal places.
Answer:
24.93
Step-by-step explanation:
Rounding to two decimal places is the same as rounding to the nearest hundredth.
Locate the hundredth:
24.927
Check the number to the right of it:
24.927
If the number is greater than or equal to 5, then we round up. If the number is less than or equal to 4, we round down.
7 is greater than 5. So, we round up.
24.927 ≈ 24.93
2.94 is the answer.
What are the places in a decimal?The first digit after the decimal represents the tenth place. the subsequent digit after the decimal represents the hundredth area. The closing digits retain to fill within the vicinity values till there are no digits left.
What does preserving 2 decimal places suggest?Rounding a decimal quantity to two decimal locations is the same as rounding it to the hundredth place, that's the second area to the right of the decimal factor. as an instance, 2.83620364 may be spherical to two decimal locations as 2.94, and 0.7035 can be spherical to 2 decimal places as zero.70.
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-13+(-4)÷2-3[-{(-3)×(-7)-(3+5)}]
How many time is 0.02 contained in 807 or 80
Answer:
0.02 appears 40,350 times in 807 & 4000 times in 80
Step-by-step explanation:
807/0.02=40,350
80/0.02=4000
What are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of −10? an = 5(−2)n − 1; all integers where n ≥ 1 an = 5(−2)n − 1; all integers where n ≥ 0 an = 5(−15)n − 1; all integers where n ≥ 1 an = 5(−15)n − 1; all integers where n ≥ 0
Answer:
A
Step-by-step explanation:
The standard form of an explicit formula for a geometric sequence is given by:
[tex]x_n=a(r)^{n-1}[/tex]
Where n is the nth term, a is the initial term, and r is the common ratio.
We are given that the first term is 5. Hence, a = 5.
Also, we are given that the second term is -10. Therefore, the common ratio r is -2, because we multiply the first term by -2 to acquire -10.
Substituting yields:
[tex]x_n=5(-2)^{n-1}, n\geq 1, n\in\mathbb{Z}[/tex]
(Note: Z means the set of all integers. This is required because the term number can only be positive starting from one. For instance, we can't have the 0th term or the 1.5th term.)
In conclusion, the answer is A.
rounds the capacity of a 1.85 liter jug to the tenth
Answer:
1.9 liters.
Step-by-step explanation:
The hundredths digit is 5 so we add 1 to the tenths digit.
Answer: 1.9 liter
Step-by-step explanation: the tenth is the first digit after the decimal point. Anything greater than it equal to 5 will be rounded up. So 1.85 is rounded up to 1.9
pls help im dumb so yeahhhhh
Answer: they use 2 cups of pineapple juice for every cup of orange juice
Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)
Answer:
2x^3-11x^2+9x+18
Step-by-step explanation:
By multiplying both the binomial and the trinomial given, we obtain a polynomial which contains both as factors. We notice as well that the given trinomial doesn't have 3 as a root (so there is no multiple root x = 3 in the product we obtain:
[tex](-x+3)\,(-2x^2+5x+6)=2\,x^3-5x^2-6x-6x^2+15x+18=2x^3-11x^2+9x+18[/tex]
Then, this new polynomial
[tex]2x^3-11x^2+9x+18[/tex]
has both given polynomials as factors.