Answers
Triangle 1's x value is 8 and LN's length is 14 units. Triangle 2's x value is 8 and IH's length is 11 units. Triangle 3's x value is 9 and CB's length is 23 units. Triangle 4's x value is 11 and its IH length is 11 units.
What is similar triangle?If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.
Here,
Since these are similar triangle,
ME=EN
MN=ME+EN
MN=2ME
this will be same for all the triangles,
1. 2x-9/2x-2=1/2
2(2x-9)=2x-2
4x-18=2x-2
2x=16
x=8
LN=2x-2
LN=14 units
2. 2x-5/x+14=1/2
2(2x-5)=x+14
4x-10=x+14
3x=24
x=8
IH=2x-5
=11 units
3. (x+14)/(x+19)=1/2
2(x+14)=x+19
2x+28=x+19
x=9
CB=x+14
CB=23 units
4. 2x-11/x+11=1/2
2(2x-11)=x+11
4x-22=x+11
3x=33
x=11
IH=2x-11
IH=11 units
In triangle 1, The value of x is 8 and length of LN is 14 units. In triangle 2, The value of x is 8 and length of IH is 11 units. In triangle 3, The value of x is 9 and length of CB is 23 units. In triangle 4, The value of x is 11 and length of IH is 11 units.
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Related Questions
The mean mass of 5 boys is 62kg.When the mass of a boy is excluded,the mean mass of the remaining 4 boys becomes 64kg.Find the mass of the boy that has been excluded
Answers
The mass of the boy removed is 54.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
let's take the weight of five boys is x
so,
x/5 = 62
x = 310
and let's take the weight of four boys is y.
so,
y/4 = 64
y = 256
let's take the weight of a boy which is removed from them is z
so,
x - z = y
x - y = z
310 - 256 = z
z = 54
Hence, the mass of the boy removed is 54.
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There are a certain number of hens and rabbits in a room. The number of feet of the hens exceeds the number of feet of the rabbits by 12, while the number of heads of the hens exceeds the number of the heads of the rabbits by 28. Then the number of hens and rabbits, respectively, in the room are:
Answers
Answer:
22 rabbits and 50 hens
Step-by-step explanation:
Let H and R stand for the numbers of Hens and Rabbits. Each hen has two feet and each rabbit has four feet. Each only has 1 head.
We can set the quantities of feet and heads:
Hens: 2H feet and 1H heads
Rabbits: 4R feet and 1R heads
We are told that:
1.) "The number of feet of the hens exceeds the number of feet of the rabbits by 12" Rewrite this as an expression:
2H - 4R = 12 [feet]
2) "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28" This is written as:
1H = 1R + 28 [heads]
Since each critter only has one head, this last expression will tell us, quickly, how many more Hens there are, which is 28. But by substituting the first expression (the feet) into the second, we can detrermine the exact number of each animal.
Rearrange 2H - 4R = 12 to isolate one of the variables. I'll choose H:
2H - 4R = 12
2H = 12 + 4R
H = (12 + 4R)/2
H = 6+2R
Now use this definition of H in the second equation:
1H = 1R + 28
1(6+2R) = 1R + 28
6 + 2R = 1R + 28
R = 22 There are 22 rabbits
Use this in the second equation to find the number of hens:
1H = 1R + 28
1H = 22 + 28
H = 50 There are 50 hens.
=================
Check:
1.) "The number of feet of the hens exceeds the number of feet of the rabbits by 12."
Hens have 100 feet total. Rabbits have 88 feet. The hens have 12 more total feet: This checks
2.) "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28"
There are 50 heans and 22 rabbits. The number of hen heads exceed the number of rabbit heads by 28. This also checks.
Pat and Sandy took a break for lunch.
They spent of an hour resting and
of an hour eating. What fraction
of an hour was their break?
Answers
Answer:
50%
Step-by-step explanation:
I’m so smart fr
express x² - 8x + 5 in the form {x-a]²-b where a and b are the integers
Answers
x² - 8x + 5 can be expressed as (x - 4)² - 11 in the form (x - a)² - b, where a = 4 and b = 11.
Let y = x² - 8x + 5 ..................( 1 )
Expanding (x - a)² - b we get,
x² - 2ax + a² - b ......................( 2 )
Equating ( 1 ) and (2), we get
x² - 8x + 5 = x² - 2ax + a² - b
Comparing the coefficient of x,
- 8 = - 2a
a = 4
Comparing constants,
a² - b = 5
since we know a = 4
4² - b = 5
16 - b = 5
b = 11
Hence x² - 8x + 5 = (x - 4)² - 11
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Landon is building new bookshelves for his bookstore's new mystery section. Each shelf can hold 35 books. There are 1,190 mystery books. How many shelves will he need to build?
How many shelves will he need to build?
Answers
Single bookcase units with two sides, top and bottom should be no wider than 36 inches without a center support.
How wide should shelves be?For most shelves made from 3/4 inch stock, a practical span is 30 to 36 inches. Shelf depth is determined by the size of the items to be stored, generally within the range of 6 to 24 inches. Shelf depth for a general purpose bookshelf is usually 10 to 12 inches. Landon is building new bookshelves for his book store.Plywood for shelves should be 3/4 inch thick or thicker. Standard sheets of plywood come in 1/4-inch, 3/8-inch, 1/2-inch, 5/8-inch, and 3/4-inch thicknesses. Plywood panels over 3/4 inch in thickness are usually special order products.I cut 1 1/2″ strips of plywood and secured three strips to each shelf, including the top and bottom of the bookshelf. The plywood strips are attached on edge, or on their sides, providing the most rigidity.Plywood is the go-to material used for pantry shelves. It's versatile, available in virtually any species of hardwood, and can easily be cut using any table saw. Plywood is ideal for pantry shelves because its edges can be finished with wood trim or iron-on veneer bandingEach shelf can hold 33 books
There are 1221 mystery books
Therefore the number of shelves he will need to build can be calculated as follows
= 1221/33
= 37
Hence Landon will need to build 37 shelves,
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Each of the 6 people in Mandy' family order 2 taco. Each taco cot $3. What
i the total cot of the taco?
Answers
Answer:
Step-by-step explanation:
12 x 3 = 36
answer is 36
Answer:
12 x 3 = 36
Step-by-step explanation:
Which equation represents the transformation formed by vertically stretching the graph of f(x)=√ by a factor of 6 and then
vertically shifting the graph 7 units up?
O g(x) = √6x + 7
O g(x)=6√x+7
○ g(x)=√x+7
O g(x)=√√√x+7
Answers
Answer:
(b) g(x) = 6√x +7
Step-by-step explanation:
You want the equation of the square root function after it has been vertically stretched by a factor of 6 and translated up 7 units.
StretchA vertical stretch is accomplished by multiplying the function value by 'a', where 'a' is the vertical stretch factor. That means the stretched square root function will be ...
f(x) = √x . . . . original square root function
h(x) = 6·f(x) = 6√x . . . . . vertically stretched by a factor of 6
TranslationA translation upward is accomplished by adding the translation amount to the function value. The translated function will be ...
h(x) . . . . . original function
g(x) = h(x) +7 . . . . . translation upward by 7 units
Our stretched and translated function is ...
g(x) = 6√x +7
What is the 10th term of the geometric sequence 9, -18, 36,
Answers
Answer:
Step-by-step explanation:
Answer: -4608
========================================================
Explanation:
a = 9 = first term
r = -2 = common ratio
We multiply each term by -2 to generate the next term
The nth term for this geometric sequence is a*(r)^(n-1) which becomes 9(-2)^(n-1)
If you tried plugging in say n = 2, you should find that,
9(-2)^(n-1)
9(-2)^(2-1)
9(-2)^1
9(-2)
-18
So that confirms the second term. I'll let you try the other values of n to confirm it further.
----------------------
From here, you plug in n = 10 to find the tenth term
9(-2)^(n-1)
9(-2)^(10-1)
9(-2)^9
9(-512)
-4608
(4x² - 6x + 1) (5x² + 8x+6)
Answers
Step-by-step explanation:
here is your answer to your question
Answer: 20x^4 + 2x³ - 19x² - 28x + 6
Step-by-step explanation:
20. A gym membership
is offered in January
for $29.00 per month. If you pay upfront for
the year, you are given a 20% discount on the
monthly cost. How much money do you save
after a year by paying upfront rather than
monthly?
Answers
Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.75. Each refill is $1.50. She also decided to get a bagel for $3.15. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$11.40
$10.65
$9.90
$9.40
Answers
Answer: ($9.40) or (d)
Step-by-step explanation:
An ice cream shop sells a small bowl of ice cream for $2.25 and a large bowl for $3. One day, the shop sold 63 bowls of ice cream and made $159. How many of each size bowl did the shop sell?
Answers
The number of small size and large size bowls of ice cream sold in the shop is 40 and 22 respectively.
How to determine the number of each bowl size sold?let
Number of small bowl = x
Number of large bowl = y
x + y = 63
2.25x + 3y = 159
From (1)
x = 63 - y
Substitute into (2)
2.25x + 3y = 159
2.25(63 - y) + 3y = 159
141.75 - 2.25y + 3y = 159
- 2.25y + 3y = 159 - 141.75
0.75y = 17.25
divide both sides by 0.75
y = 17.25 / 0.75
y = 23
Substitute y = 23 into (1)
x + y = 63
x + 23 = 63
subtract 23 from both sides
x = 63 - 23
x = 40
In conclusion, The ice cream shop sold 40 small size bowls and 23 large size bowls
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is -10,-7,-4, 1, an arithmetic sequence
Answers
What is the image point of (2,-7)(2,−7) after a translation right 4 units and up 3 units?
Answers
Answer: (6, -4)
Step-by-step explanation:
Because it translate right 4 units, so the x increase by 4, so x=6
It up 3, so y increase by 3, so y= -4
HELP please last question for sparx due at midnight :)) i’ll give brainiest
Answers
Check the picture below.
so let's check the middle of the picture, inscribed angle "b" is intercepting the purple arc, wait a second!!! angle 22° is intercepting the same arc! ahaaa!.
now let's check the right of the picture, inscribed angle "a" is intercepting that brown arc, wait a second!!! angle 45° is intercepting the same arc!! ahaa!!.
well, you can see what's "c" and "d".
If the area of the smaller circle is half the area of the larger, the ratio of the radius of the smaller circle to that of the larger circle is?
Answers
The ratio of the radii of smaller circle to that of larger circle is 1/√2.
Let the Radius of smaller circle is "r".
So the area of the smaller circle will be π(radius)²=πr²
Let the Radius of the larger circle is "R".
So the area of the larger circle will be π(radius)²=πR².
In question it is given that, the area of the smaller circle is half of the area of larger circle.
That means,
area of smaller circle=1/2 area of larger circle
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2r/R=1/√2
Ratio of smaller circle to that of larger circle is 1/√2 .
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2. Given f(x) = |x|-4, determine the range of f.
(yl y> 0) or (0, 0)
b. {yl y < 0) or (-∞, 0)
c. (yl y2-4] or [-4, ∞)
d. (yl y s-4) or (-∞. -4]
Answers
Your answer will be letter C [-4, ∞)
Solve the following system of equations by elimination. What is the value of y?
2x5y = 1
-3x+2y=-18
y = 3
y = -3
y = 1.5
y=-1.5
Answers
The value of the variable 'y' will be 3. Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the linear equation is given below.
2x - 5y = 1 ...1
-3x + 2y = - 18 ...2
Multiply equation 1 by 2 and equation 2 by 5, then we have
4x - 10y = 2
-15x + 10y = - 90
Add both equations, then we have
4x - 15x = 2 - 90
11x = 88
x = 8
Then the value of the variable 'y' is calculated as,
-3 (8) + 2y = - 18
- 24 + 2y = - 18
2y = 24 - 18
2y = 6
y = 3
The worth of the variable 'y' will be 3. Then the right choice is A.
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Donna bought 3 bags of dog treats for $6.03. What is the cost per bag of dog treats?
Answers
3x=6.03
3x being all 3 bags times the amount of money for each, and 6.03 being the total amount for each bag.
To undo multiplication, we need to divide. In this case; we need to divide each side by three.
That leaves us with;
x=$2.01
So, wa he bag costs $2.01
(If you have questions, feel free to ask them in the comments!)
How do you solve the following:
−3+ |n-2 | >5
Please help!!!!
Answers
Step-by-step explanation: To solve this inequality, we can first isolate the absolute value term on one side of the inequality by subtracting |n-2| from both sides of the inequality. This gives us the inequality -3 + |n-2| > 2. Then, we need to consider two cases: when |n-2| is positive and when |n-2| is negative.
If |n-2| is positive, then we can drop the absolute value bars and rewrite the inequality as -3 + (n-2) > 2. Solving this inequality, we find that n > 7.
If |n-2| is negative, then we must reverse the direction of the inequality because subtracting a negative number is the same as adding a positive number. This gives us the inequality -3 - (n-2) > 2. Solving this inequality, we find that n < -1.
Therefore, the solution to the inequality is the set of all numbers that are greater than 7 or less than -1, which is the interval (-1, 7).
Seven line segments are shown on the coordinate plane. Which of these segments could be the image of segment AB after a sequence of reflections, rotations, and/or translations?
Select each correct answer.
A. Line segment GH
B. Line segment EF
C. Line segment LM
D. Line segment NP
E. Line segment JK
F. Line segment CD
Please hurry
Answers
The segments that could be the image of segment AB after a sequence of reflections, rotations, and/or translations include:
A. Line segment GH
D. Line segment NP
F. Line segment CD
What are the segment?From the information, the coordinates of the point A is (1, 2), the coordinates of the point B is (5, 2)
Therefore, the length of the line AB = 5 - 1 = 4 units
In this case, the transformations are, reflections, rotations, and/or translations which are rigid transformations, such that the length of the image of AB will be the same as the length of AB
Therefore, the possible images of AB are;
PN with coordinates P(5, -2) and N(9, -2) and length 9 - 5 = 4 units
HG with coordinates H(-4, -4) and G(-4, -8) and length -4 - (-8) = -4 + 8 = 4 units
CD with coordinates C(-4, 6) and D(-4, 2) and length 6 - 2 = 4 units
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the ratio of the four sides of a trapezoid is 2:1:1:1 the area of the trapezoid is 27sqrt(3) find the length of the median of the trapezoid
Answers
Answer:
9
Step-by-step explanation:
;)
Solve each equation by using the graph of the related function.
9th grade algebra
Answers
Answer:
Q14 x = 3
Q15 No unique solution
Step-by-step explanation:
Q14
The value of x where the line crosses the x axis is the solution for x
Here we see the line crosses the x axis at x = 3 so solution is x =3
Mathematically,
2x - 3 = 3
2x = 3 + 3 adding 3 to both sides
2x = 6
x = 6/2 = 3
Q15
This is a horizontal line which crosses the y-axis at y = 1
Since this does not cross the x axis but is parallel to it, there is no unique solution for x
Mathematically,
-4x + 2 = -4x + 1
Adding 4x to both sides we get the absurdity that 2 = 1 and that indicates no unique solution for x. Alternatively we can say that x has an infinite number of solutions
PLEASEEEEHELP OMG
I NEED THE ANSWER ASAPAPPAPP
Answers
Answer:
A- negative
B-positive
C- zero
Step-by-step explanation:
Going up= positive
Going down= negative
Horizontal line= zero
vertical line= undefined
A=NEGATIVE
B=POSITIVE
C=ZERO
what is the digital index of 23475
Answers
answer:the answer for digital index of 23475 is 3
answer: 3
explanation: the digital index is 3 because 23475 is divisible by 3
Find the equation of the line through point (4,−7) and parallel to y=−23x+32. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
(check the image)
Answers
The equation of the required line is given as y = -23x - 92.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The given problem can be solved as follows,
The equation of the line is y = −23x + 32.
Then, its slope is given by -23.
Since the parallel lines have the same slope, the slope of the line parallel to y = −23x + 32 is -23.
Now, the equation of the line passing through (4, -7) and parallel to the given line can be written as,
(y + 7)/(x - 4) = -23
=> y + 7 = -23x - 92
=> y = -23x + -99
=> y = -23x - 92
Hence, the equation of the line passing through (4, -7) and parallel to y = −23x + 32 is y = -23x - 92.
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The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 5 : 4. What are the 2 numbers?
Answers
Answer:
10 and 8
Step-by-step explanation:
must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.
Is Side-Side-Side a postulate or a theorem? Explain
Answers
Answer: Postulate
Step-by-step explanation:
Side-Side-Side (SSS) Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the two are congruent.
Morgan ha 98 baeball card in hi collection, which i twelve le than the product of 5 and the number of card Tyler ha
Answers
Answer:
98-5 = 93
Step-by-step explanation:
Solve the ytem of equation by the addition method.
−4x = −4y − 12
−16x 6y = 12
Answers
For the above system of equations, 4x-4y=12 and 16x-6y=-12, the values of x and y are 4.5 and -10 respectively.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
4x-4y=12
16x-6y=-12
multiply equation 1 by 4,
16x-16y=48
-16x+6y=12
-10y=60
y=-10
-16x-60=12
-16x=72
x=72/16
x=4.5
The value of x is 4.5 and y is -10 for the given system of equation as 4x-4y=12 and 16x-6y=-12.
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