The Rs. 10,000 Regan lent to Sandip and Saline and the Rs.2160 more interest Saline paid than Sandip after 3 years at an 18% simple interest rate, indicates by expressing the amounts using equations, that the amount Regan gives to Sandip and Saline is Rs. 3,000 and Rs. 7,000 respectively.
What is an equation?An equation is the presentation of a statement of the equivalence between quantities, or expressions, by joining the expressions with a '=' sign.
The amount Regan has = Rs. 10,000
Let x represent the amount Regan lent to Sandip, we get;
The amount Regan lent to Saline = 10,000 - x
The interest rate of the loan Regan lent to Sandip and Saline = 18% simple interest
The interest Saline paid to Regan after 3 years, using simple interest = Rs. 2160 + The interest Saline paid to Regan
The simple interest formula is; I = P·R·T/100
Where;
P = The principal amount loaned
R = The interest rate = 18%
T = The time or duration of the loan = 3 years
Therefore;
(10000- x) × 18/100 × 3 = 2160 + x × 18/100 × 3
5400 - 0.54·x = 2160 + 0.54·x
5400 - 2160 = 0.54·x + 0.54·x = 1.08·x
3240 = 1.08·x
x = 3240 ÷ 1.08 = 3000
The amount Regan lent to Sandip, x = Rs. 3000
The amount Regan lent to Saline = 10,000 - x
x = 3000
10,000 - x = 10,000 - 3000 = 7,000 (substitution property)
The amount Regan lent to Saline = Rs. 7,000
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In the triangle below, with right angle R, suppose that m is Angle Q=(5x-13) and m is Angle S=(4x-5) Find the degree measure of each angle in the triangle.
Answer:
Degree measure of each angle is 90⁰, 47⁰ and 43⁰
Step-by-step explanation:
since the triangle is right angled, we assume that Q and S are the other angles of this triangle R
Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰
5x - 13 + 4x - 5 = 90⁰
9x = 108
x = 12
We now replace x in Q and S to get the angles
Q = 5(12) -13
= 47⁰
S = 4(12) - 5
= 43⁰
What is the length of leg y of the right triangle? (1 point)
A right triangle with hypotenuse 85 and legs 84 and y
1
9
13
26
The value of the other leg of the right triangle will be 13 units. Then the correct option is C.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A right triangle with hypotenuse 85 and legs 84 and y. Then by the Pythagoras theorem, the value of the variable 'y' is calculated as,
85² = y² + 84²
Simplify the equation, then we have
85² = y² + 84²
7225 = y² + 2056
y² = 7225 - 2056
y² = 169
y = 13
The value of the other leg of the right triangle will be 13 units. Then the correct option is C.
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a circular fish pond has a diameter of 14 m the pond is surrrounding by a concrete path 1.75 meters wide. Find the ponds area. take pi as 22/7
Area of the pond is 86.625 m²
What is the area formula to a circle?The following formulae can be used to determine a circle's area: Area is equal to r2, where r stands for radius. Area is equal to (/4) d2, where d stands for diameter.The region encircled by a circle of radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.Pi () is a unique mathematical constant that expresses the relationship between a circle's circumference and diameter.Given data :
Diameter of the pond = 14m
Radius of the inner circle (pond), r = 7 m
Width of the concrete path = 1.75m
Radius of outer circle (Including pond + Path), R = 7 + 1.75 = 8.75 m
Area of the path = Area of the outer circle − Area of the inner circle.
= πR² - πr²
= 22 / 7 x ( 8.75 + 7) ( 8.75 − 7 )
= 86.625 m²
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What is a opposite of 7?
-7 is the opposite of 7.
Simply adding a negative sign yields the negative number 7, which is the opposite of the positive number 7. 7 and 7 are the opposites of one another since they are both seven units apart from 0 on the number line.
The inverse of a number is the number on the other side of the 0 number line and at the same distance from 0. Oppositely positioned numbers on the number line. The opposite of an integer is its additive inverse. As a result, on a number line, the opposite of a number is the number that is located in the other direction from 0 but at the same distance from it.
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Here are two points: (-3, 4), (1, 7). What is the slope of the line between them?
A.4/3
B.3/4
C.1/6
D.2/3
Answer:
B. 3/4
Step-by-step explanation:
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P = P ( -3 , 4 )
Let the second point be Q = Q ( 1 , 7 )
Now , the slope of the line between the two points is given by the formula ,
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 7 - 4 ) / ( 1 - ( -3 ) )
On simplifying the equation , we get
Slope m = 3 / 4
Question 12
In the figure shown, if J, P, and L are the midpoints of KH, HM, and MK, respectively, find the values of x, y, and z.
Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility test for three.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
add all number
9+9+0 = 18
and 18/3 = 6
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On solving the provided question, we can say that in this triangle 2x-6 = 3 => 2x = 9 => x = 9/2 and 2z = 4 => z = 2
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
in this triangle
2x-6 = 3
2x = 9
x = 9/2
2z = 4
z = 2
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Can u please help ………….
Answer:
x = 17
Step-by-step explanation:
the midsegment of a triangle is half the length of the third side, that is
DE = [tex]\frac{1}{2}[/tex] × BC = [tex]\frac{1}{2}[/tex] × 34 = 17
so x = 17
Anyone pls help :) I'll give brainliest
Answer:
B. -5/2
Step-by-step explanation:
(0, -7) and (-4, 3)
m = 3+7/-4-0
m = 10/-4
m = -10/4
m = -5/2
Answer:
b
Step-by-step explanation:
What is the vector equivalent to the directed line segment from the point?
The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.
The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.
The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.
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6 divided by 791 (long division with remainders) Grade 4 division worksheet
Therefore , the solution of the given problem of long division is Quotient is 131 and the Remainder is 5
How does long synthetic division take place?Synthetic division is another way to divide a polynomial but by binary x - c, while c is a constant. The divisor frequently assumes the form of (x a). In synthetic division, you are just interested in the coefficients of the polynomials, unlike long division.
Here,
The given Divisor = 6 and Dividend = 791
Step 1: Take the first digit of the dividend from the left. ...
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division.
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One year ago, Farid spent $16,600 on a new pizza oven for his restaurant, The Dough Zone.
He checked the value of his oven online and discovered it is worth $15,770 today. The
website also predicts that the oven's value will continue to decrease each year.
Write an exponential equation in the form y = a(b)* that can model the value of the pizza
oven, y, x years after purchase.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Exponential equation in the form y = a(b)* that can model the value of the pizza oven, y, x years after purchase is y = 16000(0.985625)ˣ.
The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The exponential equation is y = a(b)ˣ
The value of y = 15770, a = 16000 and x = 1
b = 0.985625
y = 16000(0.985625)ˣ
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The ruthless queen has asked the royal pharmacist to create a concoction which will straighten her curly hair. If the pharmacist combines a mixture containing 10% milkweed with another mixture containing 50% milkweed to create a 5 ounce mixture containing 30% milkweed, how many ounces of the 10% mixture will the pharmacist use?
The pharmacist utilized a 10% percentage mixture, according to the solution, in a quantity of 2 ounces.
The formula for calculating percentages?To calculate the percentage, we must first determine the value's ratio to the sum of its parts. We must then multiply the result by 100.
Since when do we utilize percentages?Comparing two quantities while rebasing the second quantity to 100 is the most fundamental use of percentages. If the proportion of employed women who are women is of relevance to us, let's say.
According to the given information:We are aware that m = CV, where
V = volume and c = concentration
Let
M is equal to 6.5%, m' is equal to 7.9%, and m = 3.7%.
It is known that m + m' = M.
where cv + c'v' = CV
Since cv + c'v' = CV, the formula is:
c = 3.7% concentration = 0.037;
v = volume of 3.7% = 1 ounce;
c = 7.9% concentration = 0.079;
v' = volume of 7.9%;
C = 6.5% concentration = 0.065;
and V = volume of 6.5% = v + v'
We obtain by altering the values of the variables in the equation
3.7% × 1/3.7% + 7.9 %v' = 6.5%(v + v')
3.7% + 7.9 %v' = 6.5%(1 + v')
3.7% + 7.9 %v' = 6.5% + 6.5%v'
7.9%v' - 6.5%v' = 6.5% - 3.7%
1.4%v' = 2.8%
v' = 2.8%/1.4%
2 ounces are v'.
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Which of the following is correctly written in Standard Form?
Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.
An equation's definitionAn equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.
Here,
Given : 4x-3y = 6
-4x + 2y =8
=> y = 4/5x + 4
=> 4/5x + 2y = 6
Thus ,
From the above following equations we get ,
4x-3y = 6
as a standard equation in all the above options.
Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.
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Find m/R.
P
(3x + 5)°
2
(8.x-12)
S
8x-12+3x+5=180(sum of straight angles)
8x+3x-12+5=180
11x-19=180
11x=180-19
11x=161
x=161÷11
Step-by-step explanation:
sum of straight angles are 180
1. You may get up to 35 gallons of gas at a time at the gas station. What inequality is that?
The inequality is x ≤ 35, where x represents the amount of gas in gallons.
This question means by the statement that we have been given that the number of gallons cannot exceed 35 so it actually means that they are either 35 or less than 35. so will use < = sign to come up with this equation.
You can have up to 35 gallons of gas at a time at the gas station. The inequality x ≤ 35 represents the fact that x (the amount of gas in gallons) is less than or equal to 35.
This means that the equation will be x≤35
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BROO PLS SOMEONE HELP IM SO CONFUSED
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
The 30th term of the arithmetic sequence is 265
What is an arithmetic sequence in math?
Arithmetic sequences are those in which each term is increased by the addition or subtraction of a constant k. In contrast to a geometric sequence, where each term rises by being multiplied by or divided by a constant k,A series of numbers is considered to be an arithmetic progression or sequence if there is a constant difference between the terms. Consider the mathematical progression with a common difference of 2 in the numbers 5, 7, 9, 11, 13, and so on.An is equal to a1 + d(n - 1), where d is the common difference across terms in the series, and a1 is the first term in the sequence.This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words, [tex]a_{n}[/tex]= [tex]a_{1}[/tex]+ d ( n - 1 )
Arithmetic Sequence: d = 9
This is the formula of an arithmetic sequence.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
Substitute in the values of [tex]a_{1}[/tex] = 4 and d = 9
[tex]a_{n}[/tex]= 4 + 9 ( n - 1 )
[tex]a_{n}[/tex]= 4 + 9n - 9
[tex]a_{n}[/tex] = 9n - 5
.30th term = [tex]a_{n}[/tex] = [tex]a_{1}[/tex]+ d ( n - 1 )
= [tex]a_{30}[/tex]= 4 + 9 ( 30 -1 )
[tex]a_{30}[/tex]= 4 + 9 x 29
[tex]a_{30}[/tex]= 265
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Please help with us math work
Following are the mathematical operations for the numerics.
Mathematical operations -An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. Image: The basic mathematical operation symbols. A set of numbers and operations make up a mathematical expression.
24 × 3/4 = 1824 ÷ -3/4 = -3212 - 15 = -312 - 15 = 27-18 ÷ -3/4 = 24To learn more about Mathematical operations from given link
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which values from the set (2,4,6,8,10) make the inequality n + 5 > 10 true ?
Answer: Values; 6,8,10
Step-by-step explanation:
❌ 2 + 5 > 10
❌ 4 + 5 > 10
✔️ 6 + 5 > 10
✔️ 8 + 5 > 10
✔️ 10 + 5 > 10
Seacausus stadium has a seating capacity for 25,000 spectators. The stadium has 25 exits and can be vacated in 20 minutes. The time taken to exit the stadium varies directly with the number of spectators and inversely with the number of exits. Determine the time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional.
The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes
How to determine the time taken for 21,000 spectators to vacate the stadium?
A variation is a relation between a set of values of one variable and a set of values of other variables
Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively
We can write the variation as:
T α N/E
T = kN/E (where k is constant of proportionality)
when N = 25,000, E = 25, T = 20:
T = kN/E
k = TE/N
k = (20×25)/25000 = 0.02
when N = 21,000 and E = 15:
T = kN/E
T = (0.02×21,000)/15 = 28 minutes
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Can u please help............
Answer:
-2 in the first box
2 in the second box
In other words, the circumcenter is located at (-2, 2). Do not type in the parenthesis.
======================================================
Explanation:
Points A and C are (2,-3) and (-6,-3) in that order.
Use the midpoint formula to find that M = (-2,-3) is the midpoint of segment AC. It is halfway between these endpoints.
The perpendicular bisector to segment AC is x = -2
The perpendicular bisector goes through the midpoint, and it is perpendicular to segment AC.
-----------------------
Points A and B are (2,-3) and (2,7) respectively.
The midpoint is at N = (2,2)
The perpendicular bisector of segment AB is the equation y = 2.
------------------------
We found the following:
The perpendicular bisector to segment AC is x = -2The perpendicular bisector to segment AB is y = 2Therefore, the circumcenter is located at (-2, 2) as the circumcenter is located at the intersection of the perpendicular bisectors.
The diagram is shown below. As the diagram shows, the circumcenter marked in red is the center of the circle that goes through points A, B, and C.
Side note: The circumcenter is located on the midpoint of the hypotenuse of any right triangle. See Thales theorem.
The point Q has coordinates (2,3) The point R has coordinates (a,b) A line perpendicular to QR is given by the equation 5x+2y=9 Find an expression for b in terms of a
B = (2a + 11)/5 is an expression for b when expressed in terms of a.
What exactly are slopes and lines?
We are aware that lines might have several kinds of equations; the typical form is
The equation of a line in slope-intercept form is Ax + By + c = 0, and
y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept, or (0,b), is the point where the line crosses the y-axis when x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.
Given:
Coordinates of point Q = (2,3)
Coordinates of point R = (a,b)
The equation of the line is 5x + 2y = 9 ⇒ 2y = - 5x + 9
Therefore, y = (-5/2)x + 9/2.
We know slope m = (y2 - y1) / (x2 - x1)
∴ m = (b - 3)/(a - 2).
∴ (2/5) = (b - 3).(a - 2).
2(a - 2) = 5(b - 3).
2a - 4 = 5b - 15.
2a + 11 = 5b.
b = (2a + 11)/5.
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Im a little stuck on this one yall
The pairs of alternate interior angles are <5<4 and <6<3
What is alternate interior angles ? Alternate interior angles are the pair of angles that are formed on the inner side of the two parallel lines but on the opposite side of the transversal.When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equalAlternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.To learn more about alternate interior angles refers to:
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12x+105=55x+0 solve for x
12y=155 sovle for y
Answer:
Step-by-step explanation:
12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12
Aiden is a spice trader.
The price he charges for an order of cumin (in dollars) as a function of the size of the order (in kilograms) is graphed.
What is the approximate average rate at which the total cost increases, as the order size increases from 100 to 600 kilograms?
Approximately $2.40 per kilogramme is the average rate that the total cost rises as the order size does, from 100 to 600 kg.
How much is the average rate?The average rate of change is the average change rate of one thing in respect to another. Simply explained, a computation that divides the amount of change in one thing by the comparable amount of change in another is known as an average rate of change function.
How are average rates calculated?Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average temperature, finding that average rate of change is especially helpful.
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ORIGINAL ANSWERS PLEASE
If the line of best fit is y = 1.18x + 5.4, what is the residual value for the coordinate (2, 8)?
0.24
−0.24
0.46
−0.46
The residual value of coordinate is 0.24.
what is residual?A residual is the discrepancy between a data point's actual value and the value predicted by a regression or trend line.
Trend lines provide the approximate shape of the data and display the general shape the data takes. The most precise trend lines are those that best suit the data.
Given equation y = 1.18x + 5.4
and coordinates (2, 8)
y at x = 2
y = 1.18x + 5.4
y = 1.18(2) + 5.4
y = 7.76
residual value = actual y axis value - predicted y axis value
residual value = 8 - 7.76 = 0.24
Hence the residual value is 0.24.
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The total number of laps anitia swims, d, is proportional to the total timethat she swims, t, at constant pace, r. Which of the following equations best represents this situation.?
Will Give Brainliest!!! 1. For the circle with equation , answer each question.
(a) What are the coordinates of the center?
(b) What is the radius of the circle?
(c) What is the diameter of the circle?
a) The coordinates of the center is (2 ,-3)
b) The radius of the circle is 3
c) The diameter of the circle is twice the radius = 2(3) = 6
Now, According to the question:
a) The equation of a circle is given by
[tex](x-h)^2 + (y-k)^2 =r^2[/tex]
where (h, k) is the center and r is the radius
(x - 2)² + (y+3)² = 9
(x - 2)² + (y- -3)² = 3^2
The coordinates of the center is (2 ,-3)
b) The radius of the circle is 3
c) The diameter of the circle is twice the radius = 2(3) = 6
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The complete question is this:
For the circle with equation (x - 2)² + (y+3)² = 9 , answer each question.
(a) What are the coordinates of the center?
(b) What are the radius of the circle?
(c) What is the diameter of the circle?
PLEASE HELP NOW IM BEGGING AND PLEADING PLEASE AND THANK YOU
Linear sequences & graphs 206 - Straight line graphs 1 Quiz 1 2 3 4 5 6 7 8 6 of 8 Use the table to work out the values of a , b , c , and d . x y = 5 − 3 x − 3 a − 2 11 − 1 b 0 5 1 c 2 d a = b = c = d =
The values of a, b, c and d are -5, -1, 3 and 5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y=2x+1
Substitute (-3, a) in y=2x+1, we get
a=2(-3)+1
a=-6+1
a=-5
Substitute (-1, b) in y=2x+1, we get
b=2(-1)+1
b=-1
Substitute (1, c) in y=2x+1, we get
c=2(1)+1
c=3
Substitute (2, d) in y=2x+1, we get
d=2(2)+1
d=5
Therefore, the values of a, b, c and d are -5, -1, 3 and 5.
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"Your question is incomplete, probably the complete question/missing part is:"
Use the table to work out the values a, b, c and d.
x y=2x+1
-3 a
-2 -3
-1 b
0 1
1 c
2 d
△BOK∼POS. Identify the coordinates of K and the scale factor.
O = 0, 0
B = 5, 0
P = 8, 0
S = 0, -12
The coordinates of K = (0, -7.5) and the scale factor is 8/5.
Consider the following figure of triangles.
△BOK and ΔPOS.
Since △BOK∼ ΔPOS, the sides of △BOK and ΔPOS must be in proportion. (from definition of triangle similarity)
i.e., OP / OB = OS / OK = PS/BK
Consider an equation,
OP / OB = OS / OK
From the diagram:
OP = 8, OB = 5, OS = 12
Substitute these values in above equation.
8/5 = 12/OK
OK = 60/8
OK = 7.5
We can observe that OK is the distance of point K from origin 'O'
So, the coordinates of K would be (0, -7.5)
And the scale factor is 8/5.
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a new health drink has 150% of the recommended daily allowance. there is a certain vitamin this vitamin is 40 mg. How many milligrams of the vitamin are in a drink?
The numbers of milligrams of the vitamin that are in a drink is 60 milligrams.
What is the vitamin about?The recommended daily allowance (RDA) for the vitamin is 40 mg. A new health drink has 150% of the RDA.
To find out how many milligrams of the vitamin are in a drink, you can use the following formula:
(RDA) x (percentage/100) = milligrams in a drink
So,
(40mg) x (150/100)
= 60mg
Therefore, there are 60 milligrams of the vitamin in a drink.
Note that the RDA of vitamins can vary depending on age, gender, and other factors, so always consult a doctor or nutritionist before starting to consume any new supplement.
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