Answer:
A = 50 square units
Step-by-step explanation:
Right Triangles
A right triangle is identified because it has one internal angle of 90°.
The longest side is called hypotenuse and the other two sides are called legs. Being c the hypotenuse and a and b the legs, the Pythagora's theorem relates the with the equation:
[tex]c^2=a^2+b^2[/tex]
If the triangle is also isosceles, then both legs have the same measure or a=b:
[tex]c^2=a^2+a^2=2a^2[/tex]
Since we know the hypotenuse has a measure of 10\sqrt{2}:
[tex](10\sqrt{2})^2=2a^2[/tex]
Operating:
[tex]100*2=2a^2[/tex]
Dividing by 2:
[tex]a^2=100~~\Rightarrow a=\sqrt{100}[/tex]
a = 10 units
The area of the triangle is:
[tex]\displaystyle A=\frac{a.b}{2}[/tex]
[tex]\displaystyle A=\frac{10*10}{2}[/tex]
A = 50 square units
A person begins with $1500 in her savings account. She deposits $40 per month. Let N represent the number of months she has the account. Let A represent the amount in dollars in the account
Answer:
1500+40N=A
Step-by-step explanation:
40 per month (N) plus the initial amount = $ in account (A)
Do you guys know this
Answer && Step-by-step explanation:
Simple plug and chug
we know a+b == 6 so replace the set as 6 so:
2(6)+6/6+(6)^2-2
12+1+36-2
49-2
==47
Can someone please do this?
whats the y-intercept of y= 1/3 x-1y
Answer:
(0, 0)
Reasoning:
Y-intercept means set x to 0 and solve, therefore;
[tex]y=1/3(0) -1y[/tex]
[tex]y=0-1y[/tex]
[tex]2y=0[/tex]
[tex]y=0/2=0[/tex]
Thus, the y-intercept is (0,0)
I hope this helps you and good luck!
$120 less than half of d dollars
Answer:
[tex]\frac{d}{2} - 120[/tex]
Step-by-step explanation:
You work backwards:
Half of d dollars is d/2. Then you take 120 less than that, which means you are subtracting.
Answer:
1/2d-120
Step-by-step explanation:
Alright.
d=amount of money
1/2d=half of the amount of money
1/2d-120=half of the money minus 120
Write an equation of a line that passes through (-3, 5) and (-7, 5).
Answer:
y=5
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 5-5)/( -7 - -3)
= ( 5-5) / ( -7+3)
= 0/-4
The slope is 0
This means it is a horizontal line
Horizontal lines are in the form
y =
The y coordinate is 5
y=5
29.9.2+ n+ 8.4 = 20.8
Please help
Answer:
n=6.42
Step-by-step explanation:
Following the steps for this equation.
Answer:
29.9.2+
Step-by-step explanation:
That should be right
An investor invested a total of $2,100 in two mutual funds. One fund earned a 5% profit while the other earned a 3% profit. If the investor’s total profit was $83, how much was invested in each mutual fund?
The amount invested in the mutual fund that earned 5% was $___.
The amount invested in the mutual fund that earned 3% was $___.
Answer:
The amount invested in the mutual fund that earned 5% was $1000.
The amount invested in the mutual fund that earned 3% was $1100.
Step-by-step explanation:
Let the amount invested in the mutual fund that was earned 5% be x and the amount invested in the mutual fund that earned 3% be y.
Statement 1: [tex]\frac{5}{100}[/tex]X+[tex]\frac{3}{100}[/tex]y = 83
Statement 2: x+y = 2100
I'll use the elimination method:
Statement 1 × 20: x+[tex]\frac{60}{100}[/tex]y = 1660
Minus Statement 1 × 20 from Statement 2: x+y-x-[tex]\frac{60}{100}[/tex]y = 2100-1660
[tex]\frac{40}{100}[/tex]y = 440
y = [tex]\frac{100}{40}[/tex]×440
= 1100
x = 2100-1100
= 1000
Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.Area: 49 square feet ft (smaller value) ft (larger value)
Answer:
Length = 7 ft
Breadth = 7 ft
Step-by-step explanation:
Let lenght of rectangle be x
and breadth be y
Area = [tex]49\ \text{ft}^2[/tex]
[tex]xy=49\\\Rightarrow x=\dfrac{49}{y}[/tex]
Permiter of a rectangle is given by
[tex]P=2(x+y)\\\Rightarrow P=2x+2y\\\Rightarrow P=2\times\dfrac{49}{y}+2y\\\Rightarrow P=\dfrac{98}{y}+2y[/tex]
Differentiating with respect to y we get
[tex]\dfrac{dP}{dy}=-\dfrac{98}{y^2}+2[/tex]
Equating with zero
[tex]0=-\dfrac{98}{y^2}+2\\\Rightarrow -2=-\dfrac{98}{y^2}\\\Rightarrow y^2=\dfrac{98}{2}\\\Rightarrow y^2=49\\\Rightarrow y=7[/tex]
Double derivative of the equation
[tex]\dfrac{d^2P}{dy^2}=2\dfrac{98}{y^3}\\\Rightarrow \dfrac{d^2P}{dy^2}=\dfrac{196}{y^3}>0[/tex]
So the value of y is minimum at 7.
[tex]x=\dfrac{49}{y}=\dfrac{49}{7}\\\Rightarrow x=7[/tex]
Hence, [tex]x=7,y=7[/tex]
The mimimum length and breadth of the rectangle is both 7 ft.
How many elements are in this equation:Mg2N3?
Answer:
there are 2 Magnesium and Nitrogen
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP
Answer:
some dumb mod deleted my answer because i didnt show work. Who cares about the work everyone just wants the answers.
55.) A.9 B. 29
57.) SAS
Step-by-step explanation:
in a study of 300 students under 25 years old, 21have not yet learned to drive. What percentage can drive?
Answer:
93%
Step-by-step explanation:
From the question given above, the following data were obtained:
Total number of student = 300
Number of student that can not drive = 21
Percentage of student that can drive =.?
Next, we shall determine the number of student that can drive. This can be obtained as follow:
Total number of student = 300
Number of student that can not drive = 21
Number of student that can drive =?
Number of student that can drive = (Total number of student) – (Number of student that can not drive)
Number of student that can drive = 300 – 21
Number of student that can drive = 279
Finally, we shall determine the percentage of student that can drive as illustrated below:
Total number of student = 300
Number of student that can drive = 279
Percentage of student that can drive =?
Percentage of student that can drive =
279/300 × 100
= 93%
Thus, 93% of the student can drive.
The selling price of a watch is rs 220. If 10% profit has been included in the marked price of the watch, what is the marked price??
Answer:
22 is 10 of 220
Step-by-step explanation:
hope it help
10 .find the partial sum S10 of the arithmetic series with a1 = 4, d = 5.
Answer:
S10 = 320
Step-by-step explanation:
The formula for calculating the sum of the nth term of an AP is expressed as
Sn = n/2(2a+(n-1)d))
Given
a = 4
d = 5
n = 10
S10 =10/2{2(5)+(10-1)5}
S10 =5{10+9(6)}
S10 =5{10+54}
S10 = 5(64)
S10 = 320
Hence the sum of the first ten terms of the sequence is 320
Among all pairs of numbers with a sum of 105 , find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.
Answer: Hence Pair( x, y) = [ 105/2, 105/2]
Step-by-step explanation:
Given that;
Among all pairs of numbers with a sum of 105;
the pair whose product is maximum = ?
so let pairs of numbers with a sum of 105 be x and y respectively
x + y = 105
let y = 105 - x
now
product = xy = x( 105 - x ) = 105x - x²
now
p(x) = 105x - x²
for maximum value of p
dp/dx =0
⇒ dp/dx = 105 - 2x = 0
2x = 105
x = 105/2
y + x = 105
y = 105 - x
y = 105 - 105/2 = 105/2
Hence Pair( x, y) = [ 105/2, 105/2]
find the value of x if log3 (x+6) =2
Answer:
3(x+6) =2
3x+18 =2
3x=2-18
3x=16
x=16/3
x=5.33333333
y= p2 + qr write p in terms of y, q and r
Step-by-step explanation:
y=p²+qr
y-qr=p²
p=√y-qr
now, is it fine..
Solve the inequality 2 (x - 2) +8.6 < 14.
Answer:
x<4.7
Step-by-step explanation:
2(x-2)+8.6<14
2x-4+8.6<14
2x=4.6<14
2x<14-4.6
2x<9.4
_____
x<4.7
mom said its my turn to be brainliest answer ;0
also, help me on my math hw maybe ?
Answer: x < 4.7
Step-by-step explanation:
1. Suppose y varies directly with and y= 14 when x = -4. What is the value ofy when x= -6? (1 point)
0-21
O 10
O 18
O21
y=kx
14=k×-4
k=14÷-4
k=-3.5
y=-3.5×-6
y=21.
Solve for e
7 = 15 - 2e
e equals....
Answer:
e=4
Step-by-step explanation:
Help please
Will mark as brainliest!!!
Answer:
c
Step-by-step explanation:
If you can answer this it would help me out so much!
A certain quadratic function has the factors (x + 3) and (2x - 1). What are the solutions of the function?
A- (0,3) and (0, -1)
B- (-1,0) and (3,0)
C- (6,0) and (-3,0)
D- (0,1/2) and (0, -3)
Answer:
Thx for my points back that you stole
Step-by-step explanation:
4) On a 75-question multiple choice test, Niran answered 64 questions correctly. What was his percentage score?
will someone plz do this question
Answer:
the answer is a your welcome
The sum of the ages of David and Morgan is 78 years. 7 years ago, David's age was 3 times Morgan's age. How old is David now?
Answer:
David is 55 years old
Morgan is 23 years old
__________________________________________________________
Step-by-step explanation:
Let the age of David = x years
Let the age of Morgan = y years
We are Given:
The sum of David and Morgan's age is 78
7 years ago, David's age was 3 times Morgan's age
__________________________________________________________
Making the equations:
from the first statement, the sum of their ages is 78
So, we can write it as:
x + y = 78
from the second statement,7 years ago, David's age was 3 times Morgan's age
David's age 7 years ago = (x - 7)
Morgan's age 7 years ago = (y-7)
So, we can write the equation as:
(x - 7) = 3(y - 7)
which can be simplified to:
x = 3y - 14
__________________________________________________________
Solving the equations:
We have the 2 equations:
x + y = 78x = 3y - 14from the first equation, we can say that:
x = 78 - y
Using this value in the second equation:
x = 3y - 14
78 - y= 3y - 14 [since x = 78 - y]
78 + 14 = 4y
4y = 92
y = 23
Using this value in the first equation:
x + y = 78
x + 23 = 78 [since y = 23]
x = 55
__________________________________________________________
The Age of David and Morgan:
Since we assigned x to the age of David:
David is 55 years old
We assigned y to the age of Morgan. So,
Morgan is 23 years old
84 y is directly proportional to x. Given that y = 144 and x = 12. Find the value of y when x = 7.
The hypotenuse is always the __________ side of a right triangle.
Answer:
the answer is opposite
Heidi has $4.55. She needs to buy bolts at the hardware store. Bolts cost $0.13 each.
What division equation and related multiplication equation could Heidi use to find how many bolts she can buy?
Answer
35
Step-by-step explanation:
4.55/.13=35. Also, Heidi could do 35x13. I hope this helps!
What partial products can be used to find the product 3x219
Answer:
You can do (3x200)+(3x10)+(3x9) Hope it helps!
The product is 657 if you need it!
Step-by-step explanation:
find the factor 12n-18
Answer:
Hope this helps!!!
Step-by-step explanation:
6(2−3)
Answer:
6(2n - 3)
Step-by-step explanation: