Answers
Step-by-step explanation:
2 similar triangles (the angles are the same, and the lengths of the corresponding sides have the same multiplication factor from one triangle to the other) :
1. support post (14ft), post to back (b), the long roof line
2. front to post (f), support post (14ft), dotted line
so, because the multiplication factor is the same for the sides, the ratio
"support post" / f
must be the same as
b / "support post"
14 / f = b / 14
b = 14²/f = 196/f
and then we know that
f + b = 53
by putting the first into the second equation we get
f + 196/f = 53
f² + 196 = 53f
f² - 53f + 196 = 0
the solution of such a quadratic equation in general is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = f
a = 1
b = -53
c = 196
f = (53 ± sqrt(53² - 4×1×196))/(2×1) =
= (53 ± sqrt(2809 - 784))/2 = (53 ± sqrt(2025))/2 =
= (53 ± 45)/2
f1 = (53 + 45)/2 = 98/2 = 49
f2 = (53 - 45)/2 = 8/2 = 4
as the distance "front to post" is shorter than "back to post", f2 = 4 must be or solution.
therefore, the support post is positioned 4ft from the front of the house.
Related Questions
I need help asap!!
Triangle 1 is composed of line segments AB, BC, and CA.
Triangle 2 is composed of line segments DE, EF, and FD.
The triangles are similar with a scale of 5:2.
Select the true statement about the proportions of the sides.
Answers
Similar triangles that have a scale ratio other than 1 are not congruent triangles.
The true statement about the proportions of the sides is [tex]\frac{AC}{DF} = \frac 52[/tex]
The scale ratio is given as: 5 : 2
And the corresponding sides are given as:
AB and DE.BC and EF.CA and FD.The above highlights mean that,
[tex]\frac{AC}{DF} = \frac{BC}{EF} = \frac{AB}{DE} = \frac 52[/tex]
Hence, the true statement is [tex]\frac{AC}{DF} = \frac 52[/tex]
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Simplify
8(x+3)²/2(x + 3)
Answers
Answer:
4x+12
Step-by-step explanation:
4(x+3)²/x+3=4x+12
Whats the answer to these questions?
Answers
Answer:
answer is attached
What are the factors of the trinomial 3x^2 + 16x + 5? Show your work analytically
Answers
Answer:
3x+1 and x+5 are the factors
Step-by-step explanation:
Here's the slide-and-divide method to find the factors:
[tex]3x^2+16x+5[/tex]
[tex]\frac{3x^2}{3}+16x+5(3)[/tex]
[tex]x^2+16x+15[/tex]
[tex](x+1)(x+15)[/tex]
[tex](3*x+1)(x+\frac{15}{3})[/tex]
[tex](3x+1)(x+5)[/tex]
4(2x-5) = 5x + 4
What is the answer? Please include step by step method.
Answers
Answer:
x=8
Step-by-step explanation:
4(2x-5) = 5x + 4
First, use distributive property for the first part of the equation:
8x - 20 = 5x + 4
Then, move everything to the left of the equation:
Remember, when you move something over an equals sign, the sign in front of the number changes.
8x - 20 - 5x - 4 = 0
Then, combine the like terms:
3x - 24 = 0
Move the -24 to the other side of the equation:
3x = 24
Finally, divide both sides by 3 to isolate the x.
3x/3 = 24/3
3 cancels out on the first half.
x = 24/3
x = 8
Hope this helps! Have a great day!
Answer:
x=8
Step-by-step explanation:
Step 1.
4(2x-5)=5x+4
8x-20=5x+4
Step 2.
Add 20 to both sides
8x-20=5x+4
8x-20+20=5x+4+20
Step 3.
Simplify add the numbers
8x=5x+24
Step 4.
Subtract 5x from both sides of the equation
8x=5x+24
8x-5x=5x+24-5x
Step 5
Simplify
combine like terms
3x=24
Step 6
Divide both sides of the equation by the same term
3x=24 3x/3=24/3
Step 7
Simplify
Cancel terms that are in both the numerator and denominator
divide the numbers
x=8
Geometry - Isosceles & Equilateral Tirangles
Solve for x *
Answers
Answer:
x = 11
Step-by-step explanation:
Here, the two angles given are equal to each other. So, it is an isosceles triangle.Therefore, the sides opposite to the two angles are equal.Therefore,(x + 13) ft = 24 ft
or, x ft = 24 ft - 13 ft
or, x ft = 11 ft
or, x = 11
Hope it helps.
Don't forget to click the Brainliest button if you like my answer and if you have any query, feel free to ask in the comment section.
Answer:
x = 11ftStep-by-step explanation:
Isosceles Triangle: A triangle with two equal sides. The angles opposite the equal sides are also equal.
so
(x + 13) = 24
x + 13 = 24
x = 24 - 13
x = 11
--------------------
check
11 + 13 = 24
24 = 24
the answer is good
Use the zero product property to find the solutions to the equation x2 â€"" 15x â€"" 100 = 0. X = â€""20 or x = 5 x = â€""20 or x = â€""5 x = â€""5 or x = 20 x = 5 or x = 20.
Answers
The values for [tex]x[/tex] are -5 and 20
Given to us:
[tex]x^2-15x-100=0[/tex]
In order to use the zero product property, we need to find out a 2 numbers whose product is -100 and sum is -15.
for that you can take the LCM of 100 and check all factors of 100.
for example,
factors of 100 are 100, 50, 25, 20, 10, 5, 4, 2, 1.
from this -20 and +5 are the numbers whose sum will give -15 and product will be -100. therefore,
[tex]x^2-15x-100=0\\x^2-20x+5x-100=0[/tex]
taking out common terms, we get
[tex](x^2-20x)+(5x-100)=0\\x(x-20)+5(x-20)=0\\(x+5)(x-20)=0\\[/tex]
to find out the value of [tex]x[/tex] equating both the factors with 0, we get
[tex](x+5)=0\\x=-5\\(x-20)=0\\x=20[/tex]
Hence, the values for [tex]x[/tex] are -5 and 20
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Answer:
C or x=-5 or x=20
Step-by-step explanation:
Are the given lines parallel? How do you know?
Y=0, x=1
And
X=-2, x=5
Answers
Answer:
those aren't limes, they're points.
Step-by-step explanation:
yeah-ya.......... right?
Evaluate the expression if r = 2 and y = 3 3r2 + 2y
Answers
Step-by-step explanation:
please mark me as brainlest
Rewrite 4/8 : 1/4 as a unit rate pls help
Answers
the denominator has to be one so you multiply 1/4 by 4, and 4/8 by 4 also
2:1
the smallest number that is divisible by each one of 9,12 and 15 is
(a) 60. (b) 90. (c) 120 (d) 180
Answers
The easiest way to solve the question mathematically is to find the LCM of all the numbers.
And I personally will only just start from their 10th multiple
9 - 90, 99, 108 e.t.c
12 - 120, 132, 144 e.t.c
15 - 150, 165, 180 e.t.c
The end
Simplify the expression
x - (-2x + 4)
Answers
14x-21y
factorise this equation
Answers
Answer:
7(2x - 3y)
Step-by-step explanation:
Take out what they both have, put it on the outside.
Put the rest on the inside.
Answer:
7 (2 x - 3y)
Step-by-step explanation:
What is the greatest common factor for 36 and 60
Answers
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
k12 test
Fawzia has two summer jobs. During the week she works in the grocery store, and on the weekend she works at a nursery. She gets paid $19 per hour to work at the grocery store and $21 per hour to work at the nursery. How many total hours does she work if she does 15 hours at the grocery store and 6 hours at the nursery? How many total hours does she work if she does g hours at the grocery store and n hours at the nursery?
Answers
Answer:
In total she works 21 hours and for the equation its gn=g+n
Step-by-step explanation:
got the equation i just put gn but that can be replaced with 21 since g and n both represent the number of hours fawzia works
MEDIUM) Ana gave Bill and Clare as much money as each had. Then Bill gave Ana and Clare as much money as each had. Then Clare gave Ana and Bill as much money as each had. Then each of the three people had $24. How much money did each have to begin with
Answers
Answer:
At the very end, the amounts of money are:
A -- 24
B -- 24
C -- 24
If A and B received as much as they had just prior to the last transaction, they must each have received 12 and they must have received it from C, so at the end of the previous step, the situation must have been:
A -- 12 (24 minus 12)
B -- 12 (24 minus 12)
C -- 48 (24 plus 12 plus 12)
Before that, A and C got half of what they had above from B, so:
A -- 6 (12 minus 6)
B -- 42 (12 plus 6 plus 24)
C -- 24 (48 minus 24)
And initially, B and C got half of what they had above from A, so:
A -- 39 (6 plus 21 plus 12)
B -- 21 (42 minus 21)
C -- 12 (24 minus 12)
Step-by-step explanation:
Solve 2(x - 5) + 11 = 17
Show how you got your answer(s).
Are either of your answer extraneous yes or no. Justify your response
Answers
Answer:
x=8 and is not extraneous
Step-by-step explanation:
2(x-5)+11=17
2x-10+11=17
2x+1=17
2x=17-1
2x=16
x=8
extraneous means it is a solution, but it is not possible in the equation, to determine if it is extraneous, plug it in to the original equation
2(8-5)+11=17
2(3)+11=17
6+11=17
17=17
since it works in the orignial equation it is not extraneous
The solution to the equation 2(x - 5) + 11 = 17 is x = 8
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
2(x - 5) + 11 = 17
When the like terms are evaluated, we have
2(x - 5) = 6
Divide through the equation by 2
x - 5 = 3
So, we have
x = 3 + 5
Evaluate
x = 8
Hence, the solution to the equation is x = 8
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Which set of equations has (3, 1)as its solution?
O A and B
O And D
O Band D
O A and D
Answers
Answer:
A and D is representing the solution.
Step-by-step explanation:
We can see that the lines (A and D) are both intersecting at 3, 1. Remember, if the lines are intersecting at a point, that point is the solution of the equation. Therefore, Option B is correct.
Hoped this helped.
[tex]GeniusUser[/tex]
Which linear inequality is represented by the graph?
6-
-5
y s 2x + 4
oys 2x + 3
O y2+x+3
-3
O yz 2x + 3
Please help!!
Answers
Answer: y ≤ (1/2)x + 3
Step-by-step explanation:
The slope is 1/2 and the y-intercept is 3.
The linear inequality represented by the graph is [tex]y \le \frac 12x + 3[/tex]
From the graph, we have the following highlights:
The inequality has a closed line, and the bottom part is shadedThe slope of the line is 1/2The y-intercept is 3The first highlight implies that the inequality sign to use is ≤
The slope (m) is calculated as:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{3 -4}{0-2}[/tex]
[tex]m = \frac{-1}{-2}[/tex]
[tex]m = \frac{1}{2}[/tex]
The y-intercept (b) is where the line crosses the y-axis:
b = 3
The linear inequality is represented as:
[tex]y \le mx + b[/tex]
So, we have:
[tex]y \le \frac 12x + 3[/tex]
Hence, the linear inequality is [tex]y \le \frac 12x + 3[/tex]
Read more about linear inequality at:
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Allison buys some cloud storage for her files. On average, she adds files that take up 2 megabytes each day. After 64 days, she has 96 megabytes of memory remaining in the cloud.
Determine the equation, in slope-intercept form, of the line that represents the amount of memory remaining after xecks days.
Answers
Answer:
the answer is 224, if it is asking for the amount of megabytes she bought
Step-by-step explanation:
If she adds 2 megabytes each day, and after 64 days she only has 96 megabytes then
64 times 2 = 128
128 + 96 = 224
so 224 = the amount of megabytes she bought
What is the unit rate of scoops of high-protein food to scoops of high-fiber food if the food is made up of 80% high-fiber chimp food to 20% high-
protein food?
(answer in fraction)
Answers
Answer:
10. 31.14
10/31+14
Step-by-step explanation:
What is the product?
Answers
it tells you the answer..
The product of matries [tex]\left[\begin{array}{cc}5&-2\\-6&2\end{array}\right][/tex] and [tex]\left[\begin{array}{c}-1\\-1\end{array}\right][/tex]is option c. [tex]\left[\begin{array}{c}-3\\4\end{array}\right].[/tex] By perform matrix multiplication of 2x2 matrix with 2x1 matrix.
Given the matrices:
[tex]A = \left[\begin{array}{cc}5&-2\\-6&5\end{array}\right][/tex]
[tex]B = \left[\begin{array}{c}-1\\-1\end{array}\right][/tex]
To find the product, perform matrix multiplication.
Using the given matrices, the multiplication can be done as follows:
[tex]\left[\begin{array}{cc}5&-2\\-6&2\end{array}\right] \times \left[\begin{array}{c}-1\\-1\end{array}\right][/tex]
Multiply each element in the corresponding row of the first matrix by the corresponding column of the second matrix and summing the products.
[tex]=\left[\begin{array}{cc}(5\times-1)+(-2\times-1)\\(-6\times-1)+(2\times-1)\end{array}\right][/tex]
On multiplying the term in brackets gives:
[tex]=\left[\begin{array}{cc}-5+2\\6-2\end{array}\right][/tex]
On performing the algebraic sum gives:
[tex]=\left[\begin{array}{cc}-3\\4\end{array}\right][/tex]
Therefore, the product of the matrices is [tex]\left[\begin{array}{cc}-3\\4\end{array}\right].[/tex]
Matrix multiplication is an important operation in linear algebra and has applications in various fields, including physics, computer science, and engineering.
It allows us to perform transformations, solve systems of equations, and represent linear relationships between variables.
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In the figure below, m∠1 = x and m∠2 = x - 4. Which statement could be used to prove that x = 47?
A) m∠1 = m∠2
B) m∠2 = 47
C) m∠1 + m∠2 = 90
D) m∠1 + m∠2 = 180
Answers
The answer is C) m∠1 + m∠2 = 90
Explanation: So ∠1 is x and ∠2 is x-4
Basically you know than ∠3 is 90° ... And a straight line is 180° .. So technically we can just find out 180-90 is 90(the other angle 1 + 2).
To get 90° we'll add ∠1 and ∠2 in other ways, like technical thinking-
So you already know adding ∠1 and ∠2 is 90°. So ∠1 + ∠2 = 90°
In other words you can say m∠1 + m∠2 = 90
HELPPP EASY MATH IM IN 5 GRADE
Answers
Answer:
What's the question of the problem
The 13th arithmetic sequence of whose common difference is d=7 and first term is A1=3
Answers
Answer:
Step-by-step explanation:
a1 = 2
d = 7
n = 13
I take it you want the 13th term.
t_13 = a1 + (n - 1) * d
t_13 = 3 + (13 - 1) * 7
t_13 = 3 + 12*7
t_13 = 3 + 84
t_13 = 87
the quotient of a number and 4 is at most 5.
Answers
Answer:
The equation would be x ÷ 4 ≤ 5
Jeremiah is taking two of his friends out for pancakes. If he spends $17.55 on their meals and has $26 to spend in total, Jeremiah’s pancakes must cost no more than what amount?
Inequality Question
Answers
Answer:
$8.45
Step-by-step explanation:
if he has $26 to start and spends 17.55 on his friends, he has 8.45 leftover to spend on himself, but since he bought his friends pancakes for 17.55 their pancakes would have cost 8.775 each which suggests that Jeremiah likely cannot afford his own pancakes
what is it and why? having a good explanation would really help me. thx <3
Answers
Answer:
B. (-4-2)
Step-by-step explanation:
since the numerator is one you can divide -8 by the denominator of each fraction. -8/2 = -4, -8/4 = -2
(-4-2)
You have to make sure you distribute the -8 to all parts inside the parenthesis for it to be right.
i hope this helps :)
If 3 cans of beans cost 90¢, how many can you buy for $2.70?
If you can buy 10 juice packs for $3.00, how much will you spend to buy 4 juice packs?
please answer asap
Answers
Answer:
Step-by-step explanation:
1. 3 cans cost 90 cents
3=0.90 & x=2.7
by ratio:
3/0.9 = x/2.7
0.9x=8.1
x= 9
So you can buy 9 cans for 2.7 dollars
2. 10 Juice cost 3 dollars
by ratio:
10/3 = 4/x
10x=12
x=1.2
so you will spend 1.2 dollars to buy 4 juice packs
How do I write two time the quotient of a number and two
Answers
Answer:
2(quotient of x) + 2..............