Answers
We are given with information that , we have to find two consecutive positive integers , sum of whose squares is 365 .
[tex]{\pmb{\bf Assumption \: :-}}[/tex] Let's assume that the first number is x , and as the other no. is it's consecutive so , the second no. is (x+1)
Now , According to the question ;
x² + (x+1)² = 365[tex]{: \implies \quad \sf x^{2}+x^{2}+1^{2}+ 2\cdot x \cdot 1 = 365\quad \{\because (a+b)^{2}=a^{2}+b^{2}+2ab\}}[/tex]
Can be further written as ;
[tex]{: \implies \quad \sf 2{x^{2}}+2x -364=0}[/tex]
[tex]{: \implies \quad \sf 2(x^{2}+x-182)=0}[/tex]
As , [tex]\sf 2 \neq 0[/tex] . So ;
[tex]{: \implies \quad \sf x^{2}+x-182=0}[/tex]
Using splitting the middle term ;
[tex]{: \implies \quad \sf x^{2} +14x-13x-182=0}[/tex]
[tex]{: \implies \quad \sf x(x+14)-13(x+14)=0}[/tex]
[tex]{: \implies \quad \sf (x+14)(x-13)=0}[/tex]
Case I :-When (x+14) = 0 , then x = - 14 , which is rejected as it's not +ve
Case II :-When (x-13) = 0 , then x = 13 , which is +ve
Now ,
First no. = x = 13 Second no. = (x+1) = (13+1) = 14Hence , The required numbers are 13 and 14 respectively .
Related Questions
A regular pentagon with sides each measuring 6 inches is dilated by a scale factor of 3.1. What is the length of each side of the dilated pentagon?
Answers
Answer:
18.6inches
Step-by-step explanation:
Given the length of a side of a pentagon to be 6 inches.
If this length is dilated by a factor of 3.1, the new length will be;
New length = Old length * dilation factor
New length = 6 * 3.1
New length = 18.6inches
Hence the length of each side of the dilated pentagon is 18.6inches
Can anybody please help me with question 1 please...I would really appreciate it so much
Answers
Answer:
The total time the water balloon is in the air is 8 seconds. The balloon reaches the maximum height of 25 fee after 3 seconds. The water balloon has a height of 24 feet at 2 seconds and a half.
Step-by-step explanation:
Answer:
I was saying the same thing
Step-by-step explanation:
At the store, Jan bought 1.25 pounds of roast beef, 2 pounds of ham, and 0.8 pounds of
turkey. How many pounds of deli meat did Jan buy in all?
Answers
Answer:
4.05
Step-by-step explanation:
1.25+2+0.8
3.25+0.8
4.05
Answer:
4.05
Step-by-step explanation:
did the math
HELP ME PLS!!!
Thank you!
Answers
In a department store a $40 dress is marked save 25%.You also pay a 7% sales tax. What is the sale price of the dress?
Answers
Answer:
$32.1
Step-by-step explanation:
First find out what 25% of 40 is:
$40 x .25 = $10
Take the answer and subtract that from the original price:
$40 - $10 = $30
Next, take the sales tax (7% or 0.07) and multiply that by the new price:
$30 x 0.07 = $2.1
Lastly, take the answer and add that to the new price:
$30 + $2.1 = $32.1
Then you would get your answer:
$32.1
What is the gcf of 18 and 9?
Answers
Answer:
The GCF is 9
Step-by-step explanation:
9=1,3,9
18=1,2,3,6,9,18
How do find the area of this figure? Answer ASAP Tysm
Answers
Answer:
26
Step-by-step explanation:
6+10+10=26
Answer:
80m²
Step-by-step explanation:
area of rectangle-&10m×6m=60m²
10m-6m=4m
10m×4m=40m²
area of triangle->40m²÷2=20m²
area->60m²+20m²=80m²
PLEASE HELP!!!! The class was given this problem and asked to solve for "x". Craig says that x = 11/cos(37). Laura disagrees and says that x = 11/sin(53). Who (if anyone) is correct?
Answers
Answer:
both
Step-by-step explanation:
they are both correct. sin and cosine are complements (90-x) of each other ( that's where cosine gets its name).
Please help me with this one
Answers
Answer:
70
Step-by-step explanation:
since you are solving for the middle angle, you solve for the average for both angles on the side
(112+28)/2=70
x=70
Hope that helps :)
The milligrams of a asprin in a persons body is given by the equation a=500 (3/4)^t where the t is the numbers of hours since the patient took the medicine. How much asprin will be in the patients body after two hours
Answers
Answer: 281.25 milligram
Step-by-step explanation:
Given
Milligrams of aspirin left after t hours is given by
[tex]\Rightarrow a=500(\frac{3}{4})^t[/tex]
for [tex]t=2\ hr[/tex]
[tex]\Rightarrow a=500(\frac{3}{4})^2\\\Rightarrow a=500\times (0.75)^2=281.25\ \text{milligram}[/tex]
What is the y-intercept of the line that is perpendicular to y = −3x − 5 and passes through the point (−3, 7)?
NEED BEFORE 11:59 ASAP
Answers
Answer:
b=8
Step-by-step explanation:
Perpendicular lines are negative and reciprocal; when you multiply the slopes together, the result is -1.
we are given the line y=-3x-5
we need to find the slope of the new line. To do that, we can use this equation:
-3m=-1
divide by -3 on both sides
m=1/3
so the slope of the perpendicular line is 1/3
We can write our line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept, which is what we need
so far our equation is:
y=1/3x+b
we need to find b
we can substitute the point (-3,7) into the equation, since the line will pass through it to solve for b
so:
7=1/3(-3)+b
7=-1+b
8=b
so the y intercept of the line is 8; as a point it's (0,8)
hope this helps!
Please help me!
I am confused
Answers
Answer:
Step-by-step explanation:
A line is expressed as y=mx+b where m=slope and b=y intercept. As long as we have two points we can solve the equation of that line.
y=mx+b
For the top line I found two points (5,200) and (30,325)
m=(y2-y1)/(x2-x1)=(325-200)/(30-5)=125/25=5
y=5x+b, using point (5,200) we can solve for b
200=5(5)+b, b=200-25=175 so the line is
y=5x+175
For the bottom line we have points (5,50) and 10,100)
m=(100-50)/(10-5)=50/5=10
y=10x+b, using point (5,50) we have
50=10(5)+b, b=50-50=0 so
y=10x
Find the value of: I need help)
Answers
What is 500 time 200 i konw it do you
Answers
Answer:
100,000
Step-by-step explanation:
Hope this helped
On his death, a wealthy businessman left R132 000 to charity. He declared that the money should be given to the following charities: 'The Reach for a Dream Foundation', NSPCA and Smile, in the following ratio 3 : 4 : 5.
Determine the amount each foundation received.
Answers
Answer:
The Reach for a Dream Foundation received R33000, NSPCA received R44000, and Smile received R55000.
Step-by-step explanation:
Total money for charity = R132,000
Ratio:
3 : 4 : 5
Charities:
The Reach for a Dream Foundation : NSPCA : Smile
x : y : z
3x + 4y + 5z = R132000
Charity 1 = Charity 2 = Charity 3
x = y = z
3x + 4x + 5x = R132000
x = 11000
The Reach for a Dream Foundation:
3(11000) = R33000
NSPCA:
4(11000) = R44000
Smile:
5(11000) = R55000
Double Check:
R33000 + R44000 + R55000 = R132000
Dustin computed his family's road trip as
4.43 x 103 miles. How many miles did
Dustin's family travel on the road trip?
Answers
Answer:
456.29 miles
Step-by-step explanation:
Hope this helps!
PLEASE HELP !!!
Jim rolls a fair dice 54 times.
How many times would Jim expect to roll an even number?
Answers
please delete my answer it was wrong I don't want to get a point for the wrong answer. I want other people that have the right answer to get the points. (my answer: 1/54)
Answer: 27
Step-by-step explanation:
It’s soooo correct
who ever knows what 12×75 is I'll give brainliest
Answers
Answer:
900
Step-by-step explanation:
Answer:
Answer: 12×75
= 900
Step-by-step explanation:
Hope this helps
Quadrilateral HIJK is similar to quadrilateral LMNO. Find the measure of side OL.
Round your answer to the nearest tenth if necessary.
K
19
J
58
O
N
42
H
Answers
Answer:
OL = 128.2
Step-by-step explanation:
If the two quadrilaterals are similar, the ratio of their corresponding sides are equal;
Thus;
KJ/KH = NO/OL
19/42 = 58/OL
OL = (42 * 58)/19
OL = 128.2
plz help
A line passes through the point (2,1) and has a slope of 7/2 Find
the equation of the line.
Answers
Answer:
1/7 and 2/2
Step-by-step explanation:
Solve for x. Round to the nearest hundredth.
Answers
tan32 = x/26
26tan32 = x
x = 16.25
Help me please with this question
Answers
Answer:
P=152
A=79
Step-by-step explanation:
add all the sides
Please help me it would help a lot
Answers
Bec 4x-5
Answer:
x=11°
<Bec = 33°
<Ced = 39°
Step-by-step explanation:
That's a right angle so it would be 90 degrees angle.
18+3x+4x-5=90
Lets simplify it to make it easier to work out by collecting like terms.
First all the variable 3x+4x=7x
Then the numbers 18+-5=13
13(-13)+7x = 90(-13)take away 13 from both sides
(Opposite operators EG, Add becomes subtract)
7x = 77 then divide 7 from both sides
x=11
Then work out
3x11=33 degrees
4x11=44-5=39 degrees
To double check 39+33+18=90 degrees
Melanie invested $3,800 in an account paying an interest rate of 2% compounded
quarterly. Sebastian invested $3,800 in an account paying an interest rate of 2%
compounded monthly. After 6 years, how much more money would Sebastian have in
his account than Melanie, to the nearest dollar?
Answers
Answer:
101
Step-by-step explanation:
Answer:101
Step-by-step explanation:
plz help..... A car travels 205 km on 20 liters of petrol. how many liters of petrol is needed for a journey of 820 km?
Answers
Answer:80 liters of petrol
Find the area of the figure.
Answers
Equation= 1/2 (b)(h)
Can someone help me please?
Answers
Answer:
So the answer is 2^-3
Step-by-step explanation:
The principle is the same no matter what the base.
Log_2 (7) + Log_2(3/28) - Log_2(6)
+ means multiply
- means divide
Log_2(7 * 3/28 /6)
Log_2(7/6 * 3/28)
Log_2(1/2 * 1/4) 3 divides into 6 twice. 7 divides into 28 four times
log_2 (1/8)
This is equivalent to 2^(-3)
solve for slope / y intercept and equation
Answers
Answer:
slope = 5/2
y-intercept = 3
equation: y = 5/2x + 3
Step-by-step explanation:
i used the points (-2,-2) and (0,3) to find slope
can someone help me with this question.
Answers
Answer:
C.
Step-by-step explanation:
F(n) = 2.4 N-1
PLEASE HELP 76 POINTS! Please answer both questions, giving brainliest to correct answer.
Answers
Answer:
2 5/6 ft
Step-by-step explanation:
Paul perimeter = 4 1/2+6+3 1/3+3 1/3+6 = 23 1/6 ft
Ian perimeter = 2(8+5) = 26 ft
26-23 1/6 = 2 5/6 ft
Answer:
It’s c. B)))))
Step-by-step explanation: