As a result, the total area of these four triangular regions, a2 - b2, represents the disparity between the two squares' surface areas.
what is triangle ?A triangle is a two-dimensional geometric shape with three straight edges and three angles. It is one of the fundamental geometric forms and can be categorised in various ways based on the sides and angles it has. Triangles are typically categorised according to their edges as follows: Equilateral triangles have three identical sides and three equal angles, each measuring 60 degrees. A triangle with an isosceles triangle has two edges that are equal and two angles that are equal.
A triangle called a scalene triangle lacks equal edges and angles.
given
The four triangular areas outside the smaller square but inside the bigger square are the regions that stand for a2 and b2.
Consider the size of the large rectangle, which is a2, to understand why this is the case. Consider the smaller square's size, which is b2.
These two areas vary by (a2) - (b2), which we can also write as:
(a + b)(a - b) (a - b)
According to this formula, the difference between the two squares' areas is equivalent to the product of their side lengths' sum and differences.
We can write the sum and difference of their side lengths as (a + b) and (a - b), respectively, because the big square's side length is a and the smaller square's side length is b.
The area of the four triangular areas outside the smaller square but inside the larger square is represented by the product (a + b)(a - b).
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1. margie's parents have invested $900 into a puppy so that she could still have him when she's older. If the money grows at a simple interest rate of 3% for the next 10 years how much will the original investment have grown
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 900[1+(0.03)(10)] \implies A = 1170~\hfill \stackrel{ \textit{it grew by} }{\text{\LARGE 270}}[/tex]
Lamar claims that the weight, w, of her cat is almost 11 pounds. Which inequality
represents her claim?
A w ≤ 11
B w < 11
C w > 11
D w ≥ 11
Answer:
Lamar claims that the weight of her cat is "almost 11 pounds".
Since Lamar is using the word "almost", we can assume that she means the weight of her cat is very close to 11 pounds, but not exactly 11 pounds.
Therefore, we can represent Lamar's claim with the inequality:
B) w < 11
This is because if the weight of Lamar's cat is almost 11 pounds, but not exactly 11 pounds, then the weight must be less than 11 pounds.
Write an equation for the relationship between time and distance for each horse.
The equations of the relationship are
A: y = 1/4x
B: y = 2/5x
How to determine the equations of the relationshipFrom the question, we have the following parameters that can be used in our computation:
The graph
We can see that the lines pass through the origin
This means that the equations can be represented as
y = mx
Where
m = slope
From the graph. we have
A = (8, 2)
B = (5, 2)
When these points are substituted, we have
A: 8m = 2
B: 5m = 2
When solved, we have
A: m = 1/4
B: m = 2/5
So, the equations are
A: y = 1/4x
B: y = 2/5x
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Answer: The number that makes this number sentence true is ______. Fill in the blank. Look at the picture.
Answer:25
Step-by-step explanation:39+26=65,
65-40=25,
39+26=25+40
Answer:
Step-by-step explanation:
65-40=25,
39+26=25+40
1/2 divided by 7 . Help asap .
To solve this division problem, we can use the rule "division is the same as multiplication by the reciprocal".
So, 1/2 ÷ 7 is the same as 1/2 x 1/7.
Multiplying the numerators and denominators, we get:
1/2 x 1/7 = 1/14
Therefore, 1/2 divided by 7 is equal to 1/14.
Answer: 1/14
Step-by-step explanation:
To solve 1/2 divided by 7, you would first make 7 a fraction as well, which is 7/1. Then you do the inverse operation and fraction which is multiplying. So now, the question is 1/2 multiplied by 1/7. That equals 1/14
Determine whether the relation is a function.
((-3, -8), (3, 6), (5, -5), (7,-6), (10, 6)}
Select one:
A. Not a function
B. Function
The relation given is a function since each of the input value only maps to a single output value.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given are set of coordinate values of a relation.
We have to determine whether the relation is function or not.
The points are,
{(-3, -8), (3, 6), (5, -5), (7,-6), (10, 6)}
Domain of the relation are {-3, 3, 5, 7, 10}
Range of the relation are {-8, 6, -5, -6, 6}
We can see that each of the input value only maps to a single output value.
So the relation is a function.
Hence the relation is a function.
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What is X-5>10 ??!!!!!
The inequality expression x - 5 > 10 has its solution to be x > 15
How to evaluate the inequality expressionFrom the question, we have the following parameters that can be used in our computation:
x - 5 > 10
The above is an inequality; this is so because an inequality is a mathematical statement that compares two values or expressions, typically using symbols such as < , >, ≤, or ≥
Add 5 to both sides of the inequality expression
So, we have the following representation
x - 5 + 5 > 10 + 5
Evaluate the like terms
So, we have the following representation
x > 15
The above expression cannot be further simplified
Hence, the solution to the expression is x > 15
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I WILL GIVE BRAINLESS PLSSSSSSSSSSSSSSSSSSSSSSSSSS
The equation that represents Anthony's reading ⁵/₆ hours each day for 2 days is B. 2 × ⁵/₆ = 10 × ¹/₆.
What is an equation?An equation is an algebraic statement that two or more mathematical expressions share equality or equivalence.
Unlike mathematical expressions which combine variables with the mathematical operands, equations are depicted using the equal symbol (=) to show that the expressions are equal or equivalent.
2 × ⁵/₆ = 10 × ¹/₆
= 10/6 hours or 100 minutes (10/6 × 60)
or 1 hour 40 minutes.
Thus, the correct equation of Anthony's reading time for 2 days is Option B.
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Equation B. 2 × ⁵/₆ = 10 × ¹/₆ is the option that represents Anthony's reading ⁵/₆ hours each day for 2 days.
Helppp! The tree diagram below shows all of the outcomes for flipping 3 coins. Which outcome is represented x? Picture below.
Answer:
Option 1 is the correct choice
Step-by-step explanation:
All possible outcomes are represented with the exception of {HHT}
This would correspond to x
Option 1 is the correct choice
3. A gallon of paint covers about 500 square feet. How many square feet will 1 4/5 gallons
of paint cover?
A 650 ft²
C 800 ft²
B 750 ft2
D 900 ft²
Answer:
To solve the problem, we simply need to multiply 1 4/5 (or 9/5) by 500:
1 4/5 gallons x 500 ft²/gallon = 9/5 gallons x 500 ft²/gallon = 4500/5 ft² = 900 ft²
Therefore, 1 4/5 gallons of paint will cover 900 square feet. The answer is D.
Seven subtracted from c is most 22
What is the sum of I+k
260
140
320
220
Answer:
320 degrees
Step-by-step explanation:
For the whole circle of angles there it is 360 degrees. We already have 40 degrees on the interior angle, and we know K has to be 180 degrees. 360-40 is 320.
in
f
4
5.NBT.I
5) Which is 19,502 in expanded
form.
x 9000 + 10x 50 + 2 x 1
2
9006 + 500
b) 1 x 1000 + 9 x 1000 + 5 x 100 +
2X1
c) 1 x 10000+ 9 x 1000 + 5 x 100 +
2 x 1
5.NF.I
6) TC
Swis
Ame
mor
pur
che
The expanded form of 19,502 is 1 x 10,000 + 9 x 100 + 5 x 10 + 0 x 1 + 2 x 1
How to determine the expanded formFrom the question, we have the following parameters that can be used in our computation:
19,502
The number 19,502 in expanded form is:
1 ten thousand + 9 hundreds + 5 tens + 0 ones + 2 units
So, in expanded form, 19,502 is written as:
Represent the words with numbers
So, we have the following representation
10,000 + 9 x 100 + 5 x 10 + 0 x 1 + 2 x 1
Hence, the expanded form is 1 x 10,000 + 9 x 100 + 5 x 10 + 0 x 1 + 2 x 1
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Complete question
5) Which is 19,502 in expanded form.
(a) 1 x 9000 + 10x 50 + 2 x 1
(b) 1 x 1000 + 9 x 1000 + 5 x 100 + 2 x 1
(c) 1 x 10000+ 9 x 1000 + 5 x 100 + 2 x 1
EXCERSIZE 2 Eastern Cape Sept V2 2013 Anver, who recently lost his job, decided to start his own rental car (taxi) business. Anver was paid a round sum of money of R400 000 from his previous employer. He used some of this money to pay a 15% deposit on a vehicle to the car dealer. After doing some research, he decided to buy a Toyota Quantum 2.5D-4D 14-seater passenger van. 1.1 r PH M'S Price: R392 900 Interest rate: Prime rate + 1% Term: 72 months
The answer of the question based on monthly installment is Anver's monthly installment is R6 253.27.
What is Formula?
In mathematics, formula is set of symbols or expressions representing mathematical relationship or the rule. Formulas are often used to describe and solve the problems in mathematics, science, engineering, and other fields.
To determine the amount of the loan, we can calculate 85% of the price of the van, which is the amount that Anver would have to borrow after paying the 15% deposit:
Amount of loan = 85% of R392 900
= 0.85 x R392 900
= R333 965
To determine the monthly installment, we need to use the formula for the present value of an annuity:
PV = PMT x (1 - (1 + r/n)^(-nt)) / (r/n)
We can calculate the annual interest rate by adding 1% to the prime rate. According to the South African Reserve Bank, the prime rate in September 2013 was 9%.
Annual interest rate = prime rate + 1%
= 9% + 1%
= 10%
Therefore, we can substitute the given values into the formula:
PV = R333 965
r = 10% / 12 = 0.8333%
n = 12
t = 72 / 12 = 6
Rearranging the formula to solve for PMT, we get:
PMT = PV x (r/n) / (1 - (1 + r/n)^(-nt))
Substituting the values, we get:
PMT = R6 253.27 (rounded to two decimal places)
Therefore, Anver's monthly installment is R6 253.27.
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Raju went to a shop and bought 4 books at the rate of Rs 222.75 each, and 2 books are sold at Rs. 14 each.
Answer:
Raju spent a total of Rs 919.50. He bought 4 books at Rs 222.75 each, which cost Rs 891, and 2 books at Rs 14 each, costing Rs 28.50
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let's first calculate the total cost of the 4 books that Raju bought:
Cost of 1 book = Rs 222.75
Cost of 4 books = 4 x Rs 222.75 = Rs 891
Now, let's calculate the amount of money Raju received by selling 2 books at Rs 14 each:
Amount received by selling 1 book = Rs 14
Amount received by selling 2 books = 2 x Rs 14 = Rs 28
Therefore, the total cost of 4 books is Rs 891 and the total amount received by selling 2 books is Rs 28. To find Raju's overall expenditure, we need to subtract the amount received from the total cost of 4 books:
Raju's overall expenditure = Total cost of 4 books - Amount received by selling 2 books
= Rs 891 - Rs 28
= Rs 863
Therefore, Raju's overall expenditure is Rs 863.
José wants to join a swim club with a membership fee of $25 plus a charge of$1.25 each time he uses the pool. How many times can he swim before he has spent the $100 his grandparents gave him for his birthday? Identify the variable. Write an equation to represent the problem and solve it.
Answer:60
Step-by-step explanation:
100- 25= 75
75/1.25=60
2.1 Determine the number of faces the container has.(2)
If the container is closed rectangular it has six faces - a top, a bottom, and four rectangular sides. If the container has an opening, it has five faces - a top, a bottom, and four rectangular sides.
What is the number of faces of any geometry?The number of faces of any geometry can vary depending on its specific shape and design. In geometry, a face is a flat surface that forms part of the boundary of a solid object.
For example, a cube has six faces, a rectangular prism has six faces, and a sphere has no faces (because it is a curved surface with no edges or corners).
The number of faces in a container can vary depending on its shape and whether it has any openings. Here are some common types of containers and the number of faces they have:
Rectangular container: If the container is completely closed, it has six faces - a top, a bottom, and four rectangular sides. If the container has an opening, it has five faces - a top, a bottom, and four rectangular sides.
Circular container: If the container is completely closed, it has two faces - a top and a bottom. If the container has an opening, it has three faces - a top, a bottom, and a curved side.
Cylindrical container: If the container is completely closed, it has three faces - a top, a bottom, and a curved side. If the container has an opening, it has four faces - a top, a bottom, a curved side, and an additional flat side where the opening is located.
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Answer:
Step-by-step explanation:
I need helpppppp.....?!
Answer:
You need a rizz god????
Step-by-step explanation:
In a certain weather forecast, the chances of a thunderstorm are stated as "5 in 23." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Therefore, the likelihood of a thunderstorm is roughly 0.2174, or a 21.74% chance that one will occur.
What is probability?The study of random events or phenomena falls under the category of probability, which is a branch of mathematics. It is a way to quantify the possibility or likelihood of an event happening. A number between 0 and 1, where 0 denotes an improbable occurrence and 1 denotes a certain event, is used to express probability. By dividing the number of favorable outcomes by the total number of possible outcomes, one can determine the probability of an occurrence. In many disciplines, including statistics, economics, engineering, and science, probability is used to make predictions and well-informed choices in uncertain situations.
given
We must divide the amount of beneficial outcomes (chances of a thunderstorm) by the total number of possible outcomes in order to express the suggested degree of likelihood as a probability value between 0 and 1 inclusive.
When the likelihood of a thunderstorm is stated as "5 in 23," it indicates that out of a possible 23, 5 outcomes are likely to be favorable.
Therefore, the likelihood of a rainstorm is:
P (thunderstorm) is the ratio of the number of successful outcomes to all other possible outcomes.
Thunderstorm P(thunder) = 5 / 23
As a result, the probability value for the indicated degree of likelihood can be expressed as:
P(thunderstorm)= 5/230.2174
Therefore, the likelihood of a thunderstorm is roughly 0.2174, or a 21.74% chance that one will occur.
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Assume that the variable represents a positive real number.
The variable represents a positive real number, it can be simplified as follows [tex]u^{19/2}[/tex].
What are exponents?The amount that indicates how many times to multiply the base is known as an exponent. The base is the larger number at the bottom, while the exponent is the smaller number on top.
The reverse of an exponent is a root, which involves determining the base given an exponent. Thus, if the square root of 64 has to be obtained, find the number that has been multiplied by itself twice.
The given expression is:
√u¹⁹
Using the exponents rule we have:
[tex]u^{19/2}[/tex]
Hence, the variable represents a positive real number, it can be simplified as follows [tex]u^{19/2}[/tex].
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Kaylee has a points card for a movie theater.
She receives 80 rewards points just for signing up.
She earns 11.5 points for each visit to the movie theater.
She needs at least 210 points for a free movie ticket.
Which inequality can be used to determine v, the minimum number of visits Kaylee needs to earn her first free movie ticket?
The correct option is (b) i.e. the given inequality best describes the situation.
What is an inequality?
inequality, a declaration of the relation of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions. Theorems are statements of fact that express an inequality. Inequalities can also be expressed as questions that are solved using methods similar to those used to solve equations.
Given : She receives 80 rewards points just for signing up
She earns 11.5 points for each visit to the movie theater
the min. number of visits she needs to visit = v
and, She needs at least 210 points for a free movie ticket.
So, The inequality can be written as :
reward points + 11.5 points per visit ≥ 210
80 + 11.5 v ≥ 210
or, 210 ≤ 80 + 11.5 v
So, The correct option is (b).
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Consider the given system of equations. How many (x,y) solutions does this system have ? 2x+4y=15
2x+4y=13
Answer:It has no solution
Step-by-step explanation:
Suppose you want to have $600,000 for retirement in 25 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
$
b) How much interest will you earn?
$
According to given conditions, I will earn $913,441.60.
What is interest ?
Interest is the cost of borrowing money, usually expressed as a percentage of the amount borrowed. It is also the amount earned on an investment, usually expressed as a percentage of the amount invested. The rate of interest is determined by factors such as the level of risk involved, the term of the loan or investment, and prevailing market conditions.
To calculate the monthly deposit required, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/n)[tex]^{(n*t)}[/tex]- 1) / (r/n))
where FV is the future value, P is the monthly deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we want to solve for P, so we can rearrange the formula:
P = FV * (r/n) / (((1 + r/n)[tex]^{(n*t)}[/tex]- 1))
Substituting the given values, we get:
P = 600000 * 0.04/12 / (((1 + 0.04/12)[tex]^{(12*25)}[/tex]- 1))
Simplifying and solving for P, we get:
P ≈ $1,518.14 per month
To calculate the interest earned, we can use the formula:
I = FV - P * t
where I is the interest earned, FV is the future value, P is the monthly deposit, and t is the number of years.
Substituting the given values, we get:
I = 600000 - 1518.14 * 12 * 25
Simplifying, we get:
I ≈ $913,441.60
Therefore, according to given conditions, I will earn $913,441.60.
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Please help I don’t understand
Answer:
7863
Step-by-step explanation:
i donk know soeet
Tommy goes to the video store and rents 2 video games for $3.99 each. He also rents the latest Sonic The Hedgehog movie for $3.50. He gives the clerk a twenty-dollar bill. How much change should Tommy receive?
Answer:
Step-by-step explanation:
he recives 8.52
Answer: $8.52
Step-by-step explanation:
First, you have to calculate how much Tommy spent, which is shown below:
2 x 3.99 = 7.98
7.98 + 3.5 = 11.48
Now that we know Tommy spent 11.48, we just subtract that from 20
$20.00 - $11.48 = $8.52
What is the value of x in the figure?
63°
56°
(x-3)
The value of x in the figure and given in the task content is; x = 64.
What is the value of variable x in the given figure?As evident in the task content; the figure is a triangle with angle measures; 63°, 56° and (x - 3)°.
Since the sum of interior angles of a triangle is; 180°.
Therefore, we have;
63° + 56° + (x - 3 )= 180°
open parenthesis
63 + 56 + x - 3 = 180°
x = 180 + 3 - 63 - 56
x = 64°.
Ultimately, the value of variable, x from the triangle is; 64°.
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is the square root of 2,809.
Answer:53
Step-by-step explanation:
) Kamal's Burgers cooks its burgers either well done or medium. The restaurant served
100 burgers last night, 15% of which were well done. How many well-done burgers did the
restaurant serve?
Answer: 15
Step-by-step explanation: to find a percent of a number you use the formula : ( % x N )/100 where N is the number you are trying to find the percent of. So here 15x100= 1500 and this divided by 100 is 15
Answer:
15
Step-by-step explanation:
of means "x"
15% of which were well done
who is the which they refer here?
15% of 100 burgers were well done
15% x 100 burgers
15/100 x 100 burgers = ans
In AABC, G is the centroid and DC = 36.
Find DG and GC. Help me please!
Answer:
DG = 12 , GC = 24
Step-by-step explanation:
DC is a median of Δ ABC
on each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, that is
GC = 2 DG , then
DG + GC = DC , that is
DG + 2 DG = 36
3 DG = 36 ( divide both sides by 3 )
DG = 12
thus
DG = 12 and GC = 2 × 12 = 24
You go into a car dealership and tell them that you have a budget of $300/month. You are interested in getting a Chevy Cruze that is on sale for $16,000. Due to your excellent credit score, you qualify for a 5-year loan at 4% APR with No Down Payment. What is your monthly payment? Are you within budget?
how much will the car cost you after the loan has been paid in full?
Answer: $17,788.20
Step-by-step explanation:
To calculate the monthly payment, we can use the loan formula:
P = (r * A) / (1 - (1 + r)^(-n))
where:
P is the monthly payment
A is the loan amount, which is the sale price of the car ($16,000) in this case
r is the monthly interest rate, which is the annual percentage rate (APR) divided by 12 (4% / 12 = 0.003333...)
n is the total number of payments, which is the number of years of the loan multiplied by 12 (5 years * 12 = 60)
Substituting these values into the formula, we get:
P = (0.003333... * $16,000) / (1 - (1 + 0.003333...)^(-60))
P ≈ $296.47
Therefore, the monthly payment is approximately $296.47, which is within the budget of $300/month.
To calculate the total cost of the car after the loan has been paid in full, we can multiply the monthly payment by the total number of payments (60) and add the original sale price of the car:
Total cost = P * n + A
Total cost = $296.47 * 60 + $16,000
Total cost = $17,788.20
Therefore, the total cost of the car after the loan has been paid in full is approximately $17,788.20.