The length of the rectangle is x cm. The length of a diagonal of the rectangle is 8 crn. The perimeter of the rectangle is 20 cm. Show that ia + 91 +b=0 where a and b are integers to be found.
Answers
Answer:
[tex]x^2-10x+18=0[/tex]
a = -10 and b = 18.
Step-by-step explanation:
Let w represent the width of the rectangle.
We are given that the perimeter of the rectangle is 20 cm, this means that:
[tex]20=2(x + w)[/tex]
Let's put w in terms of x. Divide both sides by two:
[tex]10=x+w[/tex]
And solve for w:
[tex]w=10-x[/tex]
So, the rectangle measures x by (10 - x) cm.
According to the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
a and b are the legs and c is the hypotenuse.
Substitute x for a, w for b, and 8 for c:
[tex]x^2+w^2=8^2[/tex]
Simplify and substitute:
[tex]x^2+(10-x)^2=64[/tex]
Square:
[tex]x^2+(100-20x+x^2)=64[/tex]
Isolate the equation. So:
[tex]2x^2-20x+36=0[/tex]
Since the leading coefficient is one, divide both sides by two:
[tex]x^2-10x+18=0[/tex]
Therefore, a = -10 and b = 18.
Related Questions
The third term in a sequence is 25. The fifth term is 225. What are the possible values of the 4th term of the sequence if it is arithmetic? If it is geometric?
Answers
Answer:
if it is arithmetic, ach item us increase linearly. The general term is - 175+100(n-1)
where n is the number of term.
the 4th term is 125
if it is geometic, each item us increased exponetially. T he general term is 25/9 x 3^(n-1)
where n is the number of term
the 4th term is 75
A square has the same perimeter as a triangle. The triangle's area is 16 root 3. What is the hypotenuse of the square?
Answers
Answer:
12\sqrt{2}
Step-by-step explanation:
To get the hypotenuse, first we need to get the side length of the square
Area of the square = L²
16\sqrt{3} = L²
L = 4×3
L = 12
Using pythagiras theorem to get the hypotenuse
Hyp² = 12²+12²
Hyp² = 144+144
Hyp² = 288
Hyp = \sqrt {288}
Hyp = 12\sqrt{2}
Hence the hypotenuse of the square is 12\sqrt{2}
Please Answer, giving Brainliest and 50 points to the best answer!
40 is the LCM of which two numbers?
20 and 60
40 and 80
10 and 40
5 and 20
Answers
Answer:
10 and 40
Step-by-step explanation:
Find the prime factorization of 10
10 = 2 × 5
Find the prime factorization of 40
40 = 2 × 2 × 2 × 5
Multiply each factor the greater number of times it occurs to find the LCM:
LCM = 2 × 2 × 2 × 5
LCM=40
20% of j is 12 what is j
Answers
Answer:
60
Step-by-step explanation:
20/100 * j = 12
j = 12 * 100/20
j = 60
Please help me I put 100 points for anyone who helps me
Answers
Answer:
a)
The discount id 40%, so the function is:
d = 0.4pb)
p = 100 ⇒ d = 40p = 200 ⇒ d = 80p = 300 ⇒ d = 120p = 400 ⇒ d = 160p = 500 ⇒ d = 200The graph is attached
c)
p = $85 ⇒ d = 0.4*$85 = $34Sale price is:
CP = p - d = $85 - $34 = $51Answer:
please give me some thanks please good morning
Which of the following shows the correct order of the given numbers?
1, 1, 1.6
Answers
https://imgur.com/a/GMyk3iX
Answers
Answer:What’s the link about ?
153 = 17x
That means x = 9
Instructions: Find the equation of the line through point (3, 4) and perpendicular to y = –2x – 4
Answers
Answer:
y=1/2x+5/2
Step-by-step explanation:
y=ax+b
vuông góc với y = –2x - 4 ⇒a.(-2) =-1⇒a=1/2
phương trình của đường thẳng đi qua điểm (3, 4) ⇒4=3.1/2+b⇒b=5/2
⇒y=1/2x+5/2
PLEASE PLEASE HELP ME
Answers
Answer:
Step-by-step explanation:
I actually don't know tttttttttttþyyyyyyyyyttyyytrreeeee
(-6)(4) preform indicated operation
Answers
Answer:
-24
Step-by-step explanation:
(-6)(4)
The indicated operation is multiplication
-24
Answer:
-24
Step-by-step explanation:
Multiply -6 and 4
An artist made a 54-inch-tall statue of a former president. If the president was 6 feet tall, what scale did the artist use?
Answers
Answer:
[tex]1\text{ inch}=\frac{1}{9}\text{ foot}[/tex]
Step-by-step explanation:
To get a scale of inches to feet, divide both 54 and 6 by 54:
[tex]54\:\text{inches}=6\:\text{feet},\\\implies 1\:\text{inch}=\frac{6}{54}\:\text{ft}\implies \boxed{1\:\text{inch}=\frac{1}{9}\:\text{foot}}[/tex]
A computer store bought a program at a cost of $10 and sold it at a selling price of $13. Find the percent markup.
Answers
Step-by-step explanation:
Cost = $10
Selling price = $13
Markup = selling price - cost price
= $13 - $10
= $3
percent markup = markup/cost
= $3/$10
= 0.3 = 30%
Percentage markup is 30
You basically look at the bar graph on the right and see which statement is true. Brainliest and thank you!
Answers
Answer:
d. if graphed, the ordered pairs would form a straight line.
Question 19 of 25 The graph of F(x) shown below resembles the graph of G(X) = x4, but it has been vertically stretched. Which of the following could be the equation of F(x) ? 5 5 ÜL O A F(x) = -1x*
Answers
Please help asap. Thank you! :)
Answers
When he cubed ,
Result is x³
On further squaring x³, he got = (x³)²
[tex] {x}^{6} [/tex]
Therefore, k = 6
Wendy has $17 to buy seed for her birdfeeders. Each bag of seed costs $2. How many bags of seed can she buy?
Answers
Answer:
It depends if there is tax or not, if there isn't she can buy 8 of them.
Step-by-step explanation:
$17 is the total so we need to see how many $2 fit in $17.
8×2=16, and 16 is the closest number we can get to.
Solve the given portion 4/x=3/6 x=?
Answers
Answer:
8
Step-by-step explanation:
4/x=3/6
4=3/6x
4*6=3x
24/3=x
8=x
Please mark me as brainliest
Solve x2+x-1=0 using the quadratic formula.
Answers
Answer:
x = [tex]\frac{-1 ±\sqrt{5} }{2}[/tex]
Step-by-step explanation:
Ignore the A that doesn't belong in the answer
60 points and brainiest!!!!!! Pls help me
Answers
Answers:
1.) x - 3, x < -3
2.) x - 3, x>3
3.) x - 3, -3 <_ x > 3
4.) 2/5, 3/6
5.) 8, 10
There are 5 trees in Melinda's front yard. 2 of them are maple and 3 are oak. What percent
of the trees in Melinda's front yard are maples?
Answers
Explanation:
2 divided by 5= 0.4
Move the decimal to the right twice is 40%
2 = ?
2x100\5= 40%
Please help me with this geometry question and show work
Answers
(3) 8
Step-by-step explanation:
Note that ∆ADE is similar to ∆ABC. As such, the ratios of their legs are equal. Also note that AD = AB + BD.
BC/AB = DE/AD
BC/10 = 12/(10 + 5) = 12/15 = 4/5
or
BC = 10(4/5) = 8
Part A
Whose scatter plot matches the data, and what is wrong with the incorrect scatter plot?
Answers
Answer: hello your question has some missing data attached below is the missing data
answer:
The second scatter plot
Step-by-step explanation:
The scatter plot that matched the data is the second scatter plot while the first scatter plot wrongly represents the data because values of the Iron not present in the data is also represented in the scatter plot and also some values present in the data table is also missing in the First scatter plot
Answer:
Hello, I am currently doing the same assignment and the brothers scatter plot would be wrong.
Step-by-step explanation:
If you do not believe me then check and see how the table says the iron used were 2, 3, 4, 5, 6, 7, 8, and 9 but in the brothers scatter plot it is shown to have the irons down as 1, 2, 3, 4, 5, 6, 7, and 8.
(in other words the other person who answered is correct)
Kalon has $175 and needs to save atleast $700 for a computer.if he can save $35 per week, what is the minimum number for of weeks kalon will need to reach his goal
Answers
Answer:
15 weeks
Step-by-step explanation:
First, calculate the total that is needing to be saved not including the money she already has.
So 700 minus 175 is 525.
Next, to find the number of weeks, divide 525 by 35 which gives you 15 even.
So if Kalon continues to save $35 a week, it will take him 15 weeks to reach his goal of $700.
What is the y-intercept of 4(0.6)^x
Answers
Answer:
4
Step-by-step explanation:
The y-intercept is where x = 0
y = 4(0.6)^0
y = 4(1)
y = 4
The mass, m grams, of a ball is 415g, correct to the nearest 5 grams. Complete the statement about the value of m
Answers
this is g mail ok dont do enything messed up ok :)
Describe the relationship between ∠2 and ∠8
Answers
Answer:
Alternate Interior Angles
Step-by-step explanation:
Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.
Answer:
They are alternate interior angles
Step-by-step explanation:
<2 and <8 are inside the parallel lines and on opposite sides of the transversal
They are alternate interior angles
The half-life of a radioactive kind of iodine is 12 hours. How much will be left after 24 hours,
if you start with 96 grams of it?
Answers
Answer:
Step-by-step explanation:
Half life means the period after which the material will have only 50% of it left, as if by magic.
Half life is given as 12 hours, so 24 hours is twice half-life.
If we start with 96 grams, after 12 hours, there will be 48 grams left.
After another 12 hours, (total of 24 hours), only half is left, namely 24 grams.
Mia records the distance traveled in x minutes in the table below, while Alexa uses a graph to record her distance traveled over the same time period.
Alexa’s Graph
A graph has time (minutes) on the x-axis and Distance traveled (miles) on the y-axis. A line goes through points (4, 3) and (8, 6).
Mia’s Table
A 2-column table with 4 rows. Column 1 is labeled Time (minutes) with entries 10, 18, 20, 26. Column 2 is labeled Distance Traveled (miles) with entries 5, 9, 10, 13.
Answers
Answer:
A
Step-by-step explanation:
i got it right
Answer:
A
Step-by-step explanation:
Find the product of (2x-3)(x-1)
Answers
Answer:
Step-by-step explanation:
[tex](2x -3)(x-1) = 2x(x-1) -3(x-1)[/tex]
[tex]=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3[/tex]
combine the radicals 9✔x -3✔x
Answers
Answer:
6√x
Step-by-step explanation:
Given :-
9√x - 3√x .For combining , take √x as common ,
=> √x ( 9 - 3 )
=> √x * 6
=> 6√x
