Answer:
Rs. 20246
Step-by-step explanation:
According To the Question,
Given, A man borrows Rs. 50000 at 12% per Annum(compounded half-yearly). Thus the Rate of Interest for 6 months would be 6%. Now, He pays back Rs. 18000 at the end of every six months.Thus, the third payment, he has to make to clear the entire loan.
First-Payment = ( 50000 x 1.06 ) - 18000 ⇔ 35000 Rs.
Second-Payment = (35000 x 1.06) - 18000 ⇔ 19100 Rs.
Third-Payment = (19100 x 1.06 ) ⇔ 20246 Rs. the third payment, he has to make to clear the entire loan.
Solve the equation below :
7/8 = q + 1/2
A : q = 3/8
B : q = 1 3/8
C : q = 7/16
D q = 1 3/4
Answer:
q = -3/8
Step-by-step explanation:
Clearing out the fractions first simplifies this problem. The LCD here is 8, so we multiply all three terms of 7/8 = q + 1/2 by 8 and simplify the result:
7 + 8q = 4.
Combining the constants, we get: 8q = 4 - 7, or 8q = -3.
Finally, solve for q:
q = -3/8
Which are the solutions of the quadratic equation?
x² = 7x + 4
Answer:
[tex]x = \frac{7 + \sqrt{65}}{2} \ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = \frac{7 \pm \sqrt{7^2 - (4 \times 1 \times -4)}}{2 \times 1}\\\\x = \frac{7 \pm \sqrt{49 + 16}}{2 }\\\\x = \frac{7 \pm \sqrt{65}}{2 }\\\\x = \frac{7 + \sqrt{65}}{2}\ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
Please solve with explanation
Step-by-step explanation:
total wood= 45½=22.5 units
cut wood= 8⅞= 7 units
wasted wood= 1/16=0.06
now wood left is,
total wood -cut wood-wasted wood
22.5-7-0.06
15.44 units
determine the equation of the circle graphed below.
( help me please )
Answer:
(x+5)²+(y-4)²=17
Step-by-step explanation:
I think it's safe to assume that the (-5,4) coordinate is in the center
To find the x and y coordinate just flip the signs
which means it would look like
(x+5)²+(y-4)²=?
the question mark is equal to the raidus squared
to find the radius use the distance formula
√((-4+5)²+(8-4)²)= 4.123106
square this to get 17
the final answer is then
(x+5)²+(y-4)²=17
A sphere has a diameter of 32 ft. What is its surface area?
The surface area of the sphere is
ft?. (Type an exact answer in terms of t.)
Step-by-step explanation:
the answer is in the above image
======================================================
Explanation:
The diameter 32 cuts in half to 16, which is the radius. So r = 16.
Use this to find the surface area of the sphere in the formula below
SA = 4*pi*r^2
SA = 4*pi*16^2
SA = (4*16^2)*pi
SA = 1024pi
This is the exact surface area in terms of pi.
The area units are in square feet, or ft^2 for short.
Answer plsssss………………
Answer:
The corresponding angles theorem works for cases where we have two parallel lines intersecting another line.
Two lines are parallel if, at any point, the distance between these two lines is always the same.
Now, if we look at the image, we can see that the distance between the two horizontal lines changes (is smaller at the right and larger at the left)
Thus, these lines are not parallel.
Then the corresponding angles theorem can not be used here, and we have that:
∠9 ≠ ∠10
I need the answers and it's due today, please help
Answer:
1. 3
2. 1
3. 2
4. 4
5. 5
Step-by-step explanation:
one dozen mangoes cost $120.00. what is the cost of 8 mangoes??
Answer:
$80.00
Step-by-step explanation:
12m = 120
m = 10
Therefore, 8m must equal 80.
Answer:
The cost of 8 mangos would be $80.00
Step-by-step explanation:
A dozen is equal to 12 so its 10 bucks per mango since there are 12 mangos
the sum of three consecutive even intergers is 30. what are the intergers?
Answer:
8, 10, 12
Step-by-step explanation:
3 consecutive even integers are 8, 10, 12
8 + 10 + 12 = 30.
Answer:
8, 10 ,12
Step-by-step explanation:
Let x be the first integer
x+2 is the second
x+4 is the third
The sum is 30
x+ x+2 + x+4 = 30
Combine like terms
3x+6 = 30
Subtract 6 from each side
3x+6 -6 =30-6
3x = 24
Divide by 6
3x/6 = 24/6
x = 8
x, x+2, x+4 is 8, 8+2, 8+4,
8, 10 ,12
In the given figure alongside,prove that
Triangle ABC is simalar to Triangle SRT
Find the length of AC
Answer:
let's use Pythagoras theorem,
h²=b²+l²
so,
ad²=ac²+dc²
6²=ac²+3²
36-9=ac²=27
√27 can be written as 3√3,
hence ac= 3√3
Find the equation of the line that passes through the point (-5,7) and is perpendicular to the line y=-x+12.
Answer:
y=x+12
Step-by-step explanation:
y=-x+12; is a line with slope m1=-1
to find perpendicular slope of intersecting line take the negative inverse of m1. so -1*(1/(-1))=1=m2
use equation for a line of y=m*x+b and put in the point (-5,7) and solve for b=the y axis intercept
7=1*(-5)+b
7=-5+b
12=b
so
y=x+12
Which of the following is NOT true about mathematical induction?
A.The first possible case is always n = 1.
B.Mathematical induction depends on a recursive process.
C.It can be used to prove that 1 + 2 + 3+...+n =
n(n+2)
2
D. Since Sn is valid for n = 1, it is valid for n = 2. Since it is valid for n = 2, it is valid for n = 3, and so on, indefinitely.
Answer:
A. the first possible case is always n = 1
Step-by-step explanation:
Mathematical induction is a technique used to provide proof for a statement such that the statement holds for all natural numbers which are the non-negative integers
Therefore, given that the natural numbers are 0, 1, 2..., we have that mathematical induction can start from n = 0
Therefore, the statement which is not true is that the first possible case is always n = 1
Which sign makes the statement true?
5.01 x 10-3 ? 0.00105
Answer:
47.1 > .00105
Step-by-step explanation:
Given :
5.01×10-3 ? 0.00105
Now,
5.01×10-3 ? 0.00105
50.1-3?0.00105
47.1?0.00105
From the above equation, we can say that 47.1 is greater than 0.00105
Therefore, 47.1 > .00105
Find the value of x in the triangle shown below
Answer:
x = 48°
Step-by-step explanation:
Two sides of the triangle are equal, both 7, Then the 2 base angles are congruent, both 66°
The sum of the 3 angles in the triangle sum to 180° , so
x = 180° - (66 + 66) = 180° - 132° = 48°
Answer:
[tex]{ \tt{x + 66 + 66 = 180}} \\ x = 48 \degree \\ \\ { \boxed{ \bf{or : }}} \\ { \bf{ from \:lamis \: theorem : }} \\ { \tt{ \frac{5.7}{ \sin(x) } = \frac{7}{ \sin(66 \degree) } }} \\ \\ { \tt{x = { \sin }^{ - 1}( \frac{5.7 \times \sin(66 \degree) }{7} ) }} \\ x = 48 \degree[/tex]
23. About how much would 4 horses weigh? Write the weight two different ways.
An average horse weighs 900-2,000 pounds, depending on size and breed. A lean, racing fit Thoroughbred, for example, has an average weight of 900-1,100 pounds, while the average Clydesdale (think Budweiser) weighs in at 1,800-2,000 pounds
Answer:
If one horse will weigh about 2000 pounds, or 1000kg, then four horses will weigh about 8000 pounds or 4000kg
According to the Rational Root Theorem, -2/5 is a potential rational root of which function? ) = 4x4.72#*#25 O Foxo = 9x47x+10 OF) = 10x - 729 Fox) = 25x4.72
Answer:
Option (4)
Step-by-step explanation:
Option (1)
f(x) = 4x⁴- 7x²+ x + 25
Possible rational roots will be,
[tex]\frac{\pm \text{Factors of constant term '25'}}{{\pm \text{Factors of leading coefficient '4'}}}[/tex]
For the given function,
Possible rational roots = [tex]\frac{\pm 1, 5, 25}{\pm 1,2}[/tex]
= [tex]\pm 1, \pm 5, \pm 25, \pm \frac{1}{2},\pm\frac{5}{2},\pm\frac{25}{2}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.
Option (2)
f(x) = 9x⁴- 7x²+ x + 10
Possible rational roots = [tex]\frac{\pm 1,\pm 2,\pm 5,\pm10}{\pm 1,\pm3,\pm9}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.
Option (3)
f(x) = 10x⁴- 7x²+ x + 9
Possible rational roots = [tex]\frac{\pm1, \pm3, \pm9}{\pm 1,\pm2,\pm5,\pm10}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.
Option (4)
f(x) = 25x⁴- 7x²+ x + 4
Possible rational roots = [tex]\frac{\pm 1,\pm2,\pm5}{\pm1,\pm5,\pm 25}[/tex]
= [tex]\pm1,\pm2,\pm5,\pm\frac{1}{5},\pm\frac{1}{25},\pm\frac{2}{5},\pm\frac{2}{25}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is the possible rational root.
Option (4) will be the answer.
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Unit Pre Test
Submit Test
20
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s)
The equation of a line is 2[v+ 1) = 10x* 3.
The yuntercept of the line is
and the slope of the line is
Answer:gotta go sorry
Step-by-step explanation:
What is the common solution for the equations y = 2x + 1 and y = x + 3?
Write your answer an ordered pair!
Answer:
y^2 = 2x^2+x = x(2x+1) = xy => y^2 = xy => either y=0 or x = y
If y=0 then from y-2x=1, x=-1/2
If X=y then from y-2x = -x = 1 => x=y=-1
Step-by-step explanation:
answer=1
Answer:
(2,5)
Step-by-step explanation:
This is the graph for both equations and the solution is where both lines cross each other.
Hope this helps
f(x)=15x³+22x²-15x+2
Write f(x) as a product of linear factors.
Answer:
[tex](5x - 1)(3x - 1)(x + 2)[/tex]
Step-by-step explanation:
[tex](15 {x}^{3} + 22 {x}^{2} - 15x + 2)[/tex]
Apply Rational Root Theorem, our possible roots will be
plus or minus( 2/15, 2/5,2/3,2, 1/15,1/5,1/3,1).
I
I tried root -2 and it work so
If we apply synthetic dividon, we would be left with
[tex]15 {x}^{2} - 8x + 1[/tex]
We can factor this regularly.
Apply AC method that a number
AC will multiply to 15 but add to -8.
The answer are -5 and -3 so we write this as
[tex]15 {x}^{2} - 5x - 3x + 1[/tex]
Factor by grouping
[tex](15x {}^{2} - 5x) - (3x + 1)[/tex]
[tex]5x(3x - 1) - 1(3x - 1)[/tex]
So our factor are
[tex](5x - 1)(3x - 1)(x + 2)[/tex]
In the circle below, segment AB is a diameter. If the length of are ACB is 6pi what is the length of the radius of the circle?
Answer:
The radius is 6
Step-by-step explanation:
Arc length ACB = 6 pi
The arc length = fraction of a circle times the circumference
6 pi = 180/360 * 2 * pi *r
6 pi = 1/2 * 2 * pi*r
6 pi = pi r
The radius is 6
The quartile deviation and coefficient of quartile deviation of a continuous frequency distribution are 2 and 0.25 respectively. Find lower and upper quartiles.
Answer:
Lower quartile = 6
Uppwr quartile = 10
Step-by-step explanation:
Coefficient of quartile deviation = 0.25
Quartile deviation = 2
Coefficient of quartile deviation = (Q3 - Q1) / (Q3 + Q1)
Quartile deviation = (Q3 - Q1) / 2
Hence;
Quartile deviation = (Q3 - Q1) / 2 = 2
Q3 - Q1 = 2 * 2
Q3 - Q1 = 4 - - - - (1)
Q3 = 4 + Q1 - - - - (2)
(Q3 - Q1) / (Q3 + Q1) = 0.25
Q3 - Q1 = 4
4 = 0.25(Q3 + Q1)
Q3 + Q1 = 4 / 0.25
Q3 + Q1 = 16 - - - - (3)
Put Q3 = 4 + Q1 in (3)
4 + Q1 + Q1 = 16
4 + 2Q1 = 16
2Q1 = 16 - 4
Q1 = 12 / 2
Q1 = 6
Q3 = 4 + Q1
Q3 = 4 + 6
Q3 = 10
Hihi , please help if able.
Answer:
9(9m + 3t) = 81m + 27t
Step-by-step explanation:
With brackets with more than one term inside multiplied by a number;
The rule of thumb to know is that with brackets, everything inside must be multiplied by everything outside;
So, in this case, the number 9 must be multiplied by each term inside the brackets:
9 × 9m = 81m
9 × 3t = 27t
So to expand, opening the brackets, you get:
81m + 27t
Surface area is the sum of the areas of all the surfaces of a three-dimensional object.
(True or false)
Answer: True
Think of a 3D box. It has 6 faces and the surface area is the total of all six individual rectangular faces. This idea applies to any polyhedron.
What is the completely factored form of this polynomial?
x^4- 8x^2 + 16
A. (X+2)^2(x-2)^2
B. (x^2-4)^2
C. (x^2+4)(x+2)(x-2)
D. (x+2)(x-2)
Answer:
A. (x + 2)²(x - 2)²
Step-by-step explanation:
x⁴ - 8x² + 16 =
(x² - 4)(x² - 4) =
(x - 2)(x + 2)(x - 2)(x + 2) =
(x - 2)²(x + 2)²
I need help on this question, URGENT so please help asap
Answer: D is correct since the two angles are vertical angles and can be proven congruent by the vertical angle theorem
Step-by-step explanation:
Help please no links
Answer:
D
Step-by-step explanation:
The question states you need a square. That means whatever you do, must leave a square number like 49 or 64
If you add 6 or 7 to 56 you do not get 64 A and C are both wrong.
If you subtract 7 from 56 you get 49 which is a perfect square and all 4 sides will equal 7.
Which is greater, 2 miles or 1,000 yards? How much greater? Explain. Of 2 miles and 1,000 yards, _____ is greater. Since 2 miles is the same as _____ yards, _____ is __ yards greater than _____ .
Answer:
yards
Step-by-step explanation:
Answer:
Which is greater, 2 miles
1 mile = 1760 yards
2 miles = 2 * 1760
2 miles = 3,520 yards
How much greater?
3,520 - 1000 = 2520 yards
Please help me
The question is write the question for the table given.
The multiple choices are
Y=1/3x
Y=1/2x
Y=3x
Y=2x
Answer:
The answer is Y=3x
when x is 0, y is 0
y=3x
Y= 3 X 0 = 0 (correct)
when x is 1, y is 3
y=3x
y=3 X 1= 3 (correct)
when x is 2 , y is 6
y=3x
y= 3 X 2= 6 (correct)
when x is 3, y is 9
y=3x
y= 3 X 3= 9 (correct)
when x is 4, y is 12
y=3x
y= 3 X 4= 12 ( Correct)
Sora paid $26.46 for 8.4 gallons of gasoline. How much was each gallon of gasoline?
$0.211
$0.315
$2.11
$3.15
Answer:
last one
Step-by-step explanation:
Select the outlier in the data set.
93
82
10
61
99
89
84
95
75
98
If the outlier were removed from the data set, would the mean increase or decrease?
Answer:
10
The mean would increase after the outlier is removed
Step-by-step explanation:
An outlier in a dataset is a number that differs significantly from the other data in the set.
In this question, 10 is the number that differs significantly from the other data in the set. Thus, it is the outlier.
Mean = sum of the numbers / total number
Mean including the outlier =
(93+ 82 + 10 + 61 + 99 + 89 + 84 + 95 + 75 + 98) / 10 = 78.6
Mean without the outlier =
(93+ 82 + 61 + 99 + 89 + 84 + 95 + 75 + 98) / 9 = 86.2
the mean increased after the outlier was removed