Given, that the sides of a triangle are [tex]$5 \mathrm{~cm}, 12 \mathrm{~cm}$[/tex] and [tex]$13 \mathrm{~cm}$[/tex] semi-perimeter [tex]$=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$[/tex]
[tex]$$\begin{aligned}&\mathrm{s}=\frac{(5+12+13)}{2} \\&\mathrm{~s}=\frac{30}{2} \\&\mathrm{~s}=15 \mathrm{~cm}\end{aligned}$$[/tex]
Area of the triangle (according to Heron's Formula)
[tex]$$\begin{aligned}&=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \\&=\sqrt{15(15-5)(15-12)(15-13)} \\&=\sqrt{15(10)(3)(2)} \\&=\sqrt{900} \\&=30 \mathrm{~cm}^{2}\end{aligned}$$[/tex]
What is Heron's Formula?
Heron's formula was first given by Heron of Alexandria. It is used to calculate the area of various triangles such as equilateral, isosceles, and scalene triangles or quadrilaterals. When we know the sides of a triangle, we can use Heron's formula to find its area. Using Heron's formula, we find the area of a triangle by taking its semi-perimeter and side lengths.Heron's formula is used to calculate the area of triangles given the lengths of all their sides, as well as the area of quadrilaterals. It's also known as Hero's formula. This formula for calculating the area does not rely on the angles of a triangle. It is solely determined by the lengths of all triangle sides. It contains the term "s," which stands for semi-perimeter, which is obtained by halving a triangle's perimeter. Similarly, the concept of determining the area is extended to determine the area of quadrilaterals.To learn more about Hero's formula visit:
https://brainly.com/question/20934807
#SPJ1
The family minivan can hold 14 gallons of gas. During a trip to the Seattle Zoo, the van uses 8.4 gallons of gas. What percent of the total gas was used?
Answer: To find the percent of gas used, we need to divide the amount of gas used by the total amount of gas the van can hold and multiply by 100.
Percent of gas used = (Gas used / Total gas) * 100
Given that the van uses 8.4 gallons of gas and can hold 14 gallons of gas, we can substitute these values into the formula:
Percent of gas used = (8.4 / 14) * 100
By performing this calculation we can get that the percent of gas used was: 8.4/14 = 0.6 = 60%
So, 60% of the total gas was used during the trip to the Seattle Zoo.
Step-by-step explanation:
Answer:
60%
Step-by-step explanation:
8.4 divided by 14 = 0.6. Let 1 be the 100%. Since 0.6 is the same as 0.60, we remove the decimal and make it 60.
What is the area of the triangle??? Don’t pay attention to the stuff on the bottom of the screen lol
The area of the triangle is equal to 36 square units.
How to determine the area of a triangle
In this question we find a triangle whose base (b), in units, is parallel to x-axis and whose height (h), in units, is parallel to y-axis. The area formula for the triangle is shown below:
A = 0.5 · b · h
Where A is the area of th triangle, in square units.
If we know that b = 9 and h = 8, then the area of the triangle shown in the image is:
A = 0.5 · 9 · 8
A = 36
The triangle has an area of 36 square units. (Correct choice: B)
To learn more on areas of triangles: https://brainly.com/question/27683633
#SPJ1
At pizza Pi, 30 percent of the pizza made last week had extra cheese. If 150 pizzas were made, how many pizza had extra cheese
As 30% of the pizza were made, we will have 500 pizzas that as extra cheese.
How do we calculate the number of pizza that has extra cheese?At Pizza Pi, the number of Pizzas that had extra cheese last week = 150
The percentage of Pizzas that had extra cheese last week = 30%
Now, let us assume that number of Pizzas made last week = X. Then, we will write the equation as:
30X/100 = 150
30X = (150 * 100)
30X = 15000
X = 15000/30
X = 500. Therefore, it can be deducted that 500 pizzas were made last week .
Read more about Fraction
brainly.com/question/17220365
#SPJ1
help me fast as you can, please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Divide by 2
Step-by-step explanation:
48 divided by 2 is 24 and 24 divided by 2 is 12.
What is the name of the triangle whose all sides are of different measures?
The name of the triangle whose all sides are of different measures is Scalene triangle
What is a Scalene Triangle ?A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.
One of the three kinds of triangles that are categorized according to their sides is the scalene triangle. The isosceles triangle and the equilateral triangle are the other triangles depending on their sides. A triangle with scalene sides is one with distinct lengths on each side.
The following are a few of the scalene triangle's key characteristics:
It does not have equal sides.No equivalent angles exist.It lacks a symmetry line.No point symmetry exists.This triangle can have acute, obtuse, or right angles inside of it.The circumscribing circle's center will be within a triangle if all of the triangle's angles are less than 90 degrees (acute).The circumcenter will be outside the triangle in a scalene obtuse triangle.Obtuse, acute, or right triangles are all examples of scalene triangles.To learn more about triangles refer to :
brainly.com/question/2293045
#SPJ4
The name of the triangle whose all sides are of different measures is Scalene triangle
What is a Scalene Triangle ?A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.
One of the three kinds of triangles that are categorized according to their sides is the scalene triangle. The isosceles triangle and the equilateral triangle are the other triangles depending on their sides. A triangle with scalene sides is one with distinct lengths on each side.
The following are a few of the scalene triangle's key characteristics:
It does not have equal sides.No equivalent angles exist.It lacks a symmetry line.No point symmetry exists.This triangle can have acute, obtuse, or right angles inside of it.The circumscribing circle's center will be within a triangle if all of the triangle's angles are less than 90 degrees (acute).The circumcenter will be outside the triangle in a scalene obtuse triangle.Obtuse, acute, or right triangles are all examples of scalene triangles.
To learn more about triangles refer to :
brainly.com/question/2293045
#SPJ4
Aviv and Marco were trying to decribe part of the expreion
5
a
2
a
3
2a3
5a
tart fraction, 5, a, divided by, 2, a, plu, 3, end fraction. Aviv aid, "The entire expreion i the quotient of
5
a
5a5, a and
2
a
3
2a32, a, plu, 3. "
Marco aid, "On it own,
2
a
3
2a32, a, plu, 3 i a um with
2
22 term. "
Who i correct?
Both aviv and marco were correct about the expression
given that
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Many authors distinguish an expression from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects
Aviv and Marco were trying to describe the parts of the expression 5a/2a+3.
Aviv said, "The entire expression is the quotient of 5a and 2a+3"
Marco said, "On it's own, 2a+3 is a sum with 2 terms."
now , we need to find who is correct
according to aviv The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).
according to marco the expression 2a+3 is sum of two terms
Therefore both aviv and marco are correct
To learn more about quotient:
https://brainly.com/question/16134410
#SPJ4
In a bag of Christmas treats,there are 3 red candy canes for every 5 gingerbread men. If there are a total of 40 treats, how many are candy canes?
Answer:
Candy canes are a classic Christmas treat, traditionally white with red stripes and flavored with peppermint. They have been popular since the 1600s and are thought to have originated in Germany. Today, 90 percent of all candy canes are sold between Thanksgiving and Christmas.
In a bag of Christmas treats, there are 3 red candy canes for every 5 gingerbread men. If there total is 40 treats, then the number of candy canes will be 24. This can be calculated by taking 40 divided by 8 (5+3) which equals 5, and then multiplying this by 3 which equals 15. Therefore, 24 candy canes are included in the bag of 40 Christmas treats.
Step-by-step explanation:
- 44 + 3.4
what does the question equal?
Answer:
-40.6
Step-by-step explanation:
What should be added to the product of X and 2 to get X Class 8?
X should be subtracted from the product of X and 2 to obtain X, this can be represented as 2X - X = X, This operation is the inverse of addition, therefore it undoes the addition of X to 2X, resulting in the original number X.
To obtain the equation X from the product of X and 2, you would need to subtract X from the product. In other words, you would need to subtract the factor X from the product.
X × 2 - X = X
This can be simplified as
2X - X = X
So, X should be subtracted from the product of X and 2 to get X.
It is important to note that this is only true when X is not equal to zero, because if X is zero, any number multiplied by zero will give zero, and subtracting zero from zero will not give zero.
It can be seen that the operation of subtraction is the inverse of addition, therefore if you subtract X from 2X, you are essentially undoing the addition of X to 2X, which gives the original number X.
To learn more about the algebraic expression at
https://brainly.com/question/30191360?referrer=searchResults
#SPJ4
How do latitudes and longitudes help in locating a point Class 6?
Latitudes and longitudes help in locating a point by providing a reference system for navigation.
They are used to pinpoint a specific location on the earth’s surface by providing coordinates. These coordinates are measured in degrees and minutes and are written in the form of a pair of numbers. Latitudes are measured in degrees north or south of the equator and are referred to as the lines of latitude. Longitudes are measured in degrees east or west of the prime meridian and are referred to as the lines of longitude. By using the coordinates of a point, the location can be accurately determined. This is especially useful for navigation, as it enables people to determine their position and travel to a specific destination.
Learn more about Latitudes and longitudes here:
https://brainly.com/question/3070484
#SPJ4
To paint a house, a company charges a flat rate of $500 for supplies, plus $50 for each hour of labour. How much would the painting company charge paint a house that needs 20 hours of labour? A house that requires 50 hours? 20 hours: $ Question B1 of 2 type your answer... 50 hours: $ Question Blank 2 of 2
Answer:
$1500
$3000
Step-by-step explanation:
let x = # of hours
$500 + ($50/hr)(20 hr) = $1500
$500 + ($50/hr)($50 hr) = $3000
Compute C7,5. (Enter an exact number.)
The permutation and combination C(n ,r) of
C(7,5) = 21.
Permutation
Permutation is the arrangement of objects, some or all of which are acquired at the same time, in a particular order. Consider ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number of different 4-digit PINs that can be formed from these 10 digits is 5040. P(10, 4) = 5040. This is a simple example of permutation. The permutation of 4 numbers out of 10 is equal to the factorial of 10 divided by the factorial of the difference between 10 and 4.
Combinations
Combinations are about grouping. Combinations can be used to calculate how many different groups can be formed from existing ones. Let's try to understand this with a simple example. Five students (William, James, Noah, Logan and Oliver) form teams of two.
According to the question:
C (n, r) = C( 7,5)
⇒ 7!/ 5! × 2!
⇒ 7 × 6 ×5!/ 5! × 2 ×1
⇒ 21.
Therefore, C(n ,r) = 21
Learn more about Permutation:
https://brainly.com/question/1216161
#SPJ4
Find the missing side length. Round to the nearest tenth if needed.
Answer:
b = 10.24 units.
Step-by-step explanation:
Pythagorean Theorem The Pythagorean Theorem explains the connection between a right triangle's three sides. The area of the square produced on the hypotenuse of any right triangle is equal to the sum of the areas of the squares formed on its legs: a2 + b2 = c2.a, is the shortest leg of the triangle or the opposite.b, is the adjacent leg of the triangle. This leg typically forms the right angle of the triangle.c, is the hypotenuse. This is the longest leg of the triangle. Applying the theorem[tex]a^{2} + b^{2} = c^{2}[/tex][tex]4^{2} + b^{2} = 11^{2}[/tex][tex]16 + b^{2} = 121[/tex][tex]b^{2} = 121-16[/tex][tex]b^{2} = 105[/tex][tex]\sqrt{b^{2}} = \sqrt{105}[/tex][tex]b = 10.24[/tex]The adjacent is 10.24 units long.
Please let me know if this helped!!!
PLEASE HELP ASAP!!!!!
Therefore ,ecklaces cost $15.67, and the equation for the inequality in the statement is $7.62, therefore 7.62x + 15.67y ≥ 450.
What is inequality, exactly?In mathematics, an inequality is a link between two phrases or values that isn't equal. As a result, inequality results from imbalance. In mathematics, an inequality establishes a connection between two non-equal numbers. Egality is different from inequality. Use the or equal sign most frequently to indicate that two values really aren't equal (). Values of any size can be contrasted using various inequalities. By changing the two sides till it variables are all that is left, many straightforward inequalities can be resolved. But a lot of factors support inequality: On either side, negative values are split or added. Exchange lefts
Here,
Let X equal the quantity of bracelets.
give Y the quantity of necklaces.
Equation of inequality: 450 = 7.62x + 15.67y
Inequality in the sentence's equation Because bracelets cost $7.62 and necklaces cost $15.67,
her revenue needs to be at least $450 (7.62x + 15.67y ≥ 450).
To know more about inequality visit :-
brainly.com/question/29914203
#SPJ1
edin has £300 in his savings account.
his bank offers him a fixed 5% simple interest rate per annum,
for a peirodof 3 years.
how much interest will he earn in 3 years?
The simple interest earned by Edin after 3 years is $45.
Define the term simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest does not really compound, therefore a creditor will indeed charge interest upon that principal sum, and a borrower will never be required to pay further interest on the interest which has already accrued.The formula for the simple interest is-
SI = PRT/100
Amount P = £300Rate of Interest r = 5%Period n = 3 yearsThe interest which would be earned in 3 years:
SI = 300*5*3 / 100
SI = 45
Thus, the interest earned by Edin after 3 years is $45.
To know more about the simple interest, here
https://brainly.com/question/25793394
#SPJ1
X^2 - x=2
Solve for x
Answer:
To solve for x, you can start by moving the constant 2 to the other side of the equation by adding x to both sides:
x^2 - x = 2
x^2 - x + (1/4) = 2 + (1/4)
(x - 1/2)^2 = 9/4
x - 1/2 = +- (3/2)
x = -1/2 or x = 2
So the solutions for x are -1/2 and 2.
Only one more question to my assignment! Please tell me what to write in part A and B, Thank you
Answer:
A) See below
B) Yes
Step-by-step explanation:
A)
Substitute 0 for x
3(x + 2) + 2x - 1
3(0 + 2) + 2(0) -1
3(2) + 0 - 1
6 + 0 - 1
5
5x + 5
5(0) + 5
0 + 5
5
B
Yes, I got the same answer 5.
We can also simplify the first expression and we can see that the expressions are equal.
3(x + 2) + 2x -1 Distribute the 3
3x + 6 + 2x -1 Combine like terms
5x + 5
This equals the second expression.
A wood stove burns 4 same-sized logs in 2 hours. How many log does the stove burn in 8
hours?
Answer:
16 logs
because if 4 logs are burned in 2 hours then in 8 hours it would be 16 because 2hrs times 4 is 8 hours
you do the same to the logs which is 4 x 4
then u get 16
hope this helps!
so if you divide 30 by 775 how would get the remainder
The remainder of 30 divided by 775, is 0.0387.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
The number 30 is called the numerator or dividend, and the number 775 is called the denominator or divisor.
The quotient of 30 and 775,
30 divided by 775,
that means,
30/775
= 0.0387, this is the remainder.
Therefore, 0.0387 is the remainder.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ1
reflection of (−5.25, −5.25) across the y-axis?
Answer:
(5.25, - 5.25 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(- 5.25, - 5.25 ) → (-(- 5.25), - 5.25 ) → (5.25, - 5.25 )
Which equation is equivalent to ? x + 9 = x + 10 x + 9 = x2 + 20x + 100 x2 + 81 = x2 + 100 x2 + 81 = x2 + 20x + 100.
The equation (√x^2+81 = x+10 ) is equivalent to D: ( x^2 + 81 = x^2 + 20x + 100).
To prove that ( √x^2+81 = x+10 )is equivalent to ( x^2 + 81 = x^2 + 20x + 100 ), we will show that one equation is a consequence of the other.
First, we begin by squaring both sides of the equation ( √x^2+81 = x+10 ). This gives us ( x^2+81 = x^2+20x+100 ).
We can see that if ( √x^2+81 = x+10 ) is true, then (x^2 + 81 = x^2 + 20x + 100) must also be true because the left side of the equation is the square of the right side.
The other way around, if ( x^2 + 81 = x^2 + 20x + 100 ) is true, then we can take the square root of both sides and get (√x^2+81 = x+10 ).
So, the equation ( √x^2+81 = x+10 ) is equivalent to ( x^2 + 81 = x^2 + 20x + 100).
You can learn more about equivalent equation at
https://brainly.com/question/2972832
#SPJ4
What is the sin ratio of angle ~0 ? Start by finding the lengths of the sides of the triangle.
Answer:
sinΘ = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
given the point (3, 4 )
the x- coordinate indicates the horizontal length of the triangle, that is 3
the y- coordinate indicates the vertical length of the triangle, that is 4
the triangle is right and is a 3- 4- 5 , hypotenuse is 5
then
sinΘ = [tex]\frac{vertical}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]
Shen and Kaitlin each opened a savings account today. Shen opened his account with a starting amount of $770, and he is going to take out $30 per month.
Kaitlin opened her account with a starting amount of $935, and she is going to take out $45 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in the account after x months.
Amount of money in Shen's account (in dollars) =
Amount of money in Kaitlin's account (in dollars) =
(b) Write an equation to show when the two accounts would have the
same amount of money.
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by SAS
Mark the sides BC and DF as congruent.
What are triangle?
A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.
The vertex is the intersection of two straight lines. The triangle therefore has three vertices.
According to our question-
We are given a side and an adjacent angle, and we must figure out which side or angle is needed in order for SAS to provide proof.
SAS stands for side-angle-side and calls for the congruency of two sides and the included angle on both triangles.
The side of the designated angle B and D that is missing is as follows:
side DF or BC.
learn more about triangles click here:
brainly.com/question/1058720
#SPJ1
Jee ha aved $51 if we have aved five time a much money a Jee how much money ha Lee aved
Lee has saved $255. This can be found by multiplying Jee's aved amount of $51 by 5. Therefore, Lee has aved $255.
First, we need to calculate how much money Jee has aved. We know Jee has aved $51, so we multiply that by 5 to find out how much money Lee has aved.
51 x 5 = 255
Therefore, Lee has aved $255. Jee has aved $51, and if we multiply that amount by 5, we can calculate how much money Lee has aved. To find the answer, we first need to multiply 51 by 5. When we do this, we get the amount of money that Lee has aved, which is $255. This means that Lee has aved five times as much money as Jee has aved, which is $255. This can be found by multiplying Jee's aved amount of $51 by 5. Therefore, Lee has aved $255.
Learn more about amount here
https://brainly.com/question/8082054
#SPJ4
Can someone pls help me. The test is time so please help quickly. The picture should be linked.
Answer:(f+g) is 2668, (f-g) is -2800
Step-by-step explanation:
An inventory study determines that, on average, demands for a particular item at a warehouse are made 5 times per day. What is the probability that on a given day this item is requested (a) more than 5 times? (b) not at all?.
(a) To find the probability that the item is requested more than 5 times on a given day, we would need to know the distribution of the demand for the item. Without that information, it is not possible to calculate this probability.
(b) To find the probability that the item is not requested at all on a given day, we would need to know the probability distribution of the demand for the item. Without that information, it is not possible to calculate this probability.
Item Demand Probabilities(a) To find the probability that the item is requested more than 5 times on a given day, we would need to know the distribution of the demand for the item. Without that information, it is not possible to calculate this probability. This is because the average demand of 5 times per day does not provide enough information to determine the likelihood of the demand exceeding 5 times. We would need to know more information such as the standard deviation, skewness, kurtosis and the underlying distribution of the data, in order to calculate this probability.
(b) To find the probability that the item is not requested at all on a given day, we would also need to know the distribution of the demand for the item. Without that information, it is not possible to calculate this probability. The average demand of 5 times per day does not provide enough information to determine the likelihood of the demand being zero. We would need to know more information such as the standard deviation, skewness, kurtosis and the underlying distribution of the data, in order to calculate this probability.
It's important to note that if the demand follows a Poisson distribution, you can use the expected value (λ = 5) to calculate the probability of the demand being zero (P(X = 0) = e^(-λ)).
Learn more about Demand Probability here:
https://brainly.com/question/15412371
#SPJ4
Percy Verence breeds long-eared whistle mice. He has four in his incubator named Amin, Brenda, Carthik
and Dorothy. Amin weighs twice as much as Carthik, Brenda weighs 100g less than Carthik, Dorothy is 152g
grams. The mean weight of the mice is 238g.
How much does Carthik weigh?
Carthik weighs 225 grams, and the mean weight of the mice is 238g.
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Given that Dorothy weighs 152 g. Let x represent the weight of Amin, y represent that of Brenda and z represent Carthik.
Amin weighs twice as much as Carthik, hence:
x = 2z
x - 2z = 0 (1)
Brenda weighs 100g less than Carthik, hence:
y = z - 100
y - z = -100 (2)
The mean weight of the mice is 238g. hence:
(x + y + z + 152)/4 = 238
x + y + z = 800 (3)
Solving the 3 equations by elimination gives:
x = 450, y = 125 and z = 225
Carthik weighs 225 grams
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Which statement describes data that is normally distributed? A. The majority of the data is to the left of the mean. B. The majority of the data is to the right of the mean. C. The majority of the data is in the center with the mean. D. The majority of the data is split to the right and left of the mean.
The majority of the data is split to the right and left of the mean.
What is normal distribution?The data is mostly divided to the right and left of the mean. The normal distribution is symmetric and continuous. Positively skewed data will have a higher mean than the median. If the data distribution is tilted to the left, the mean is less than the median, which is frequently less than the mode. A probability function that defines how the values of a variable are distributed is known as the normal distribution. The mean, median, and mode values in a normal distribution are all equal. So, in the context of a normal distribution curve, point (ii) is valid.
Here,
The data is mostly divided to the right and left of the mean. The normal distribution is symmetric and continuous. Positively skewed data will have a higher mean than the median.
The data is mostly divided to the right and left of the mean.
To know about normal distribution,
https://brainly.com/question/11822836
#SPJ1
what is the answer to this question?