The right angle triangle is the name of the 3, 4, and 5 triangles.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.
The formula states that in a right triangle:
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
(Hypotenuse)² = (Base)² + (Altitude)²
c²=a²+b²
The three numbers which satisfy the above formula are the Pythagorean triplets
Properties of right angle:
The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.
The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.
consider c=5 a=3, b=4 substitute in above formula:
5²=3²+4²
⇒25=9+16
⇒25=25
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I need help with this question, its confusing.
Simplify the expression. Explain each step. 7(9w) 7(9w) = 11 Associative Property of Multiplication Multiply 7 and 9.
Answer:
Step-by-step explanation:
7(9w)7(9w) = 11
(7 ×7)(9×9)(w×w) = 11
49 ×81 w² = 11
3969w² = 11
[tex]\frac{3969w^{2} }{3969}[/tex] = [tex]\frac{11}{3969}[/tex]
w² = [tex]\frac{11}{3969}[/tex]
[tex]\sqrt{w^{2} }[/tex] = [tex]\sqrt{11/3969}[/tex]
w = ± [tex]\frac{\sqrt{11} }{63}[/tex]
Because the solution contains a square root the answer contains both a negative and a positive solution.
Classify each variable as qualitative or quantitative.
1. Marital status of nurses in a hospital.
2. Time it takes to run a marathon.
3. Weights of lobsters in a tank in a restaurant.
4. Colors of automobiles in a shopping center parking lot.
5. Ounces of ice cream in a large milkshake.
6. Capacity of the NFL football stadiums.
7. Ages of people living in a personal care home.
Quantitative variable are - 2,3,5,7 and Qualitative are 1, 4 ,6
1. Marital status of nurses in a hospital-qualitative
2. Time it takes to run a marathon-quantitative
3. Weights of lobsters in a tank in a restaurant- quantitative
4. Colors of automobiles in a shopping center parking lot- qualitative
5. Ounces of ice cream in a large milkshake- quantitative
6. Capacity of the NFL football stadiums -qualitative
7. Ages of people living in a personal care home- quantitative
Qualitative variables are categorized or labelled to belong to a certain category or group.
There are two types of qualitative variables, Categorical and ordinal.
Categorical variable are those variables that are labelled in non-numeric or numeric form, where the numbers have no value. The order also does not matters. For example, the number on the jerseys of football players. It is not necessary that the player number 1 is actually the best player.
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Three consecutive odd integers have a sum of -75 what are the three numbers
Simon builds this podium on a platform.
What is the combined volume of the podium and the platform?
Enter your answer in the box
The combined volume of the podium and the platform is 64 cubic feet.
This sort of figure offers several choices. We really only need to consider how to divide the front face into appropriate rectangles, since the depth of the figure is 2 feet everywhere.
The volume is the area of the front face times that depth.
1) A 2 ft × 4 ft upright atop a 12 ft × 2 ft horizontal base. The frontal area is
(2 ft)(4 ft) +(12 ft)(2 ft) = 8 ft² +24 ft² = 32 ft
so, the total volume is:
V = frontal area × depth
V= (32 ft²)(2 ft)
V=64 ft³
2) A vertical post of 2 ft × 6 ft at the left side with a horizontal protrusion of 10 ft × 2 ft from its bottom.
The frontal area calculated this way is:
(2 ft)(6 ft) +(10 ft)(2 ft) = 12 ft² +20 ft² = 32 ft²
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
3) A 6 ft × 12 ft rectangle with a 4 ft × 10 ft cutout from the upper right corner. The area calculated this way is
(6 ft)(12 ft) -(4 ft)(10 ft) = 72 ft² -40 ft² = 32 ft² . . . . . same as above
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
V=64 ft³.
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the american veterinary association claims.. what is the probabilty that your anual cost will ve within 5 of the mean
The probability that the annual cost will be 5 of the mean is 0.0912.
How does probability analysis work?A method used by risk managers to predict upcoming events, like accidental and commercial losses. In order to determine a probability distribution that can be applied to forecast future losses, this procedure involves reviewing historical loss data.
X = Annual cost of medical care for dogs.
X~ Normal (μ = 200, σ = 60)
Sample size n = 16
We know that the sample mean Xbar has a normal distribution with mean = μ and sd = σ/√n
Xbar ~ Normal (μ’ = 200, σ’ = 60/√16 = 15)
Required probability -
P[Average cost of medical care for 16 sampled dogs is > 220]
= P[Xbar > 220]
= P[(Xbar-μ’)/σ’ > (220-200)/15]
= P[Z > 1.3333], Z is a standard normal variable.
= 1 - P[Z < 1.3333]
= 1 - 0.9087, from standard normal table.
= 0.0912
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The complete question is:
A veterinary association claims that the annual cost of medical care for dogs averages $200 with a standard deviation of $60, and for cats averages $240 with a standard deviation of $70. Assume the costs follow a normal distribution. What is the probability the average annual cost of medical care for 16 randomly chosen dogs is greater than $220.
A small box can hold 94.24 g of candy. If each candy has a mass of 1.52 g, how many candies can fit into each box?
Answer:
62 candies can fit into each box
Step-by-step explanation:
We know
A small box can hold 94.24 g of candy
Each candy has a mass of 1.52 g
How many candies can fit into each box?
To find it we take
94.24 divided 1.52 = 62 candies
So, 62 candies can fit into each box
An operator works a basic fortnight at a basic
rate of $8. 95 and earns $671. 25. Determine the
basic fortnight for the operator.
just the answer pls
To determine the basic fortnight for the operator, we need to divide the operator's earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
The basic fortnight for an operator is the number of fortnights the operator has worked at their basic rate of pay. In this case, the operator has earned $671.25 at a basic rate of $8.95 per fortnight. To determine the basic fortnight, we need to divide the operator's total earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
So, the operator has worked 75.05 basic fortnights. It means he has been working for 75.05*14=1053 days. This is the number of days the operator has worked at their basic rate of pay. It is important to note that this calculation assumes that the operator has not earned any overtime pay or other bonuses.
$671.25 ÷ $8.95 = 75.05
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Mario wait table at a retaurant where he make money by earning tip. One night, two of hi regular cutomer dined at the retaurant. Cutomer A had a total bill of $430. 50 and tipped 20% of the bill. Cutomer B had a total bill of $184. 00 and tipped 25% of the bill. How much did Mario make from the tip of hi two regular cutomer
Mario make total $132.1 from the tip of his two customers.
The amount of tip obtained = total bill × percentage of the bill
Put the respective values in equation depending on the customer A or B
Tip from customer A
Tip = 430.50 × 20%
Now find percentage by multiplication and division on Right Hand Side of the equation
Tip = $86.1
Tip from customer B
Tip = 184 × 25%
Again perform multiplication and division on Right Hand Side of the equation
Tip = $46
Total tip earned = 86.1 + 46
Simply add the two numbers on Right Hand Side of the equation to find the total tip earned
Total tip earned = $132.1
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What is the difference between log 10 and log e?
The difference between log with base 10 and log with base e is that the log with base 10 is called a common logarithmic function and the log with base e is called a Natural Logarithmic Function .
What is Logarithmic Function ?
The logarithm is defined as a power to which a number must be raised in order to get some other values. Log is the most convenient way to express the large numbers.
The Logarithm with base 10 is defined as a power to which the number must be raised to get some other number. It can also be called as the logarithm of base 10, or common logarithm.
The general form of Common logarithm is written as: [tex]log_{10} (x)[/tex] ;
The Logarithm with base e is called as Natural Log , where e is an irrational number .
The general form to represent a Natural Log is : [tex]log_{e} (x)[/tex] or [tex]ln(x)[/tex] .
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HI!!
can someone help with ts
Function Notation: another way of representing the relation between two variables, y is denoted as f(x) and x remains.
x is the input and f(x) is the output
This question is essentially asking what is the output of the function when the input is equal to 5.
[tex]f(5) = (5)^2-2(5)[/tex]
[tex]f(5) = 25-10[/tex]
[tex]f(5) = 15[/tex]
Which relationships describe the angle pair x° and 157º? Select each correct answer. Complementary angles vertical angles supplementary angles adjacent angles Two lines intersecting in a V shape with the left angle of one hundred fifty seven degrees and a bottom angle of X degrees
Angles x° and 157° are neighboring because they share a shared vertex and side, preventing them from overlapping, the sum of any two angles on a straight line equals 180°.
what is angle ?Two lines converge at a common point to form an angle. They are expressed by the sign ° and are measured in degrees. Acute, right, obtuse, and reflex angles are four crucial types. There are 360° in a circle. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms. The vertex of an angle is the point at which all points meet .
given
If two angles' sums are same, they are said to be supplementary.
If two angles' sums are same, they are said to be complimentary.
Each set of opposite angles generated by crossing lines are referred to as vertical angles. The term "adjacent angles" refers to two angles that share a common vertex and side but do not overlap.
Angles x° and 157° are neighboring because they share a shared vertex and side, preventing them from overlapping, and they are supplementary angles because the sum of any two angles on a straight line equals 180°.
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A pair of shoes is on sale for 20% off they now cost 50$
The original price of the pair of shoes is $62.5.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Original price = 100%
Offer price = $50
Offer = 20%
Now,
80% = 50
Multiply 100/80 on both sides.
100% = 100/80 x 50
100% = $62.5
Thus,
The original price is $62.5.
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The price of a particular stock is represented by the linear equation y = negative 0.91 x + 103.47, where x represents the number of weeks the stock has been owned and y represents the price of the stock, in dollars. If this relationship continues, what is the price of the stock after it has been owned for 12 weeks?
Answer:
Step-by-step explanation:
We have, C(x) = 0.005x3 – 0.02x2 + 30x + 5000
Clearly, the marginal cost, MC (x) = \(\frac{d}{d x}\)C(x)
= \(\frac{d}{d x}\)(0.005x3 – 0.02x2 + 30x + 500)
= 0.005 × 3x2 – 0.02 × 2x + 30 + 0
= 0.015x2 – 0.04x + 30
Now, marginal cost when 3 units arei produced
MC(3)= 0.015(9) – 0.04(3) + 30
= 0135 – 0.12 + 30= 30.015
What would the answer be?
Answer:
[tex]w^{2}[/tex]
Step-by-step explanation:
using factorization middle school way ☹️
On solving the provided question, we can say that - by the prime factors we have x^2 + 1 +2x = X= -1, -1
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
here we have the equation,
[tex]x^2 + 1 + 2x\\[/tex]
(x+1)(x+1)
x = -1, -1
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In ΔEFG, g = 8.4 inches, mm∠G=79° and mm∠E=25°. Find the length of f, to the nearest 10th of an inch.
The 8.4 inches length of g and the 79° and 25° measures of the angles ∠G and ∠E, using the law of sines, indicates that the length of the side EG = f is about 8,3 inches.
What is the law of sines?The law of sines states that the ratio of the sine of an interior angle of a triangle to the length of the opposite side to the angle is the same for the three sides and angles in a triangle.
Mathematically, the law of sines can be presented as follows;
[tex]\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}[/tex]
Where;
a, b, and c are the length of each of the sides of the triangle, and ∠A, ∠B, and ∠C are the measure of each of the interior angles of the triangle.
The details of the triangle ΔEFG, specifying the side g as the side opposite the angle ∠G, and the side f as the side opposite the ∠F we get;
The length of EF = g = 8.4 inches
Length of EG = f
The angle sum property of a triangle indicates that we get;
∠E + ∠F + ∠G = 180°
∠F = 180° - (∠E + ∠G)
∠F = 180° - (25° + 79°) = 76°
According to the law of sines, we get;
8.4/(sin(79°) = f/(sin(76°))
f = (sin(76°)) × 8.4/(sin(79°) ≈ 8.3
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30PTS 30PTS don’t explain just answer (it’s not 90)
Answer:
20
Step-by-step explanation:
110 -70 = 40 40/2= 20
Answer:
[tex] \sf \: x = {20}^{o} [/tex]
Step-by-step explanation:
Let's take the value of y as,
→ y = 90°
(Because, it is a right angle)
Forming the equation,
→ x + y + 70° = 180°
Now the value of x will be,
→ x + y + 70° = 180°
→ x + 90° + 70° = 180°
→ x + 160° = 180°
→ x = 180° - 160°
→ [ x = 20° ]
Hence, the value of x is 20°.
Does 4 8 12 make triangles?
No, a triangle with side length 4 units, 8 units , and 12 units does not exist.
As given in the question,
Let us consider the triangle be ABC,
Side length of the triangle are given as follow:
AB = 4units
BC = 8units
CA = 12units
Triangle inequality for the given triangle ABC is given by:
AB + BC > CA
AB + CA > BC
CA + BC > AB
To check whether the given side length forms a triangle apply triangle inequality we get,
AB + BC
= ( 4 + 8 )units
= 12 units
= CA
Here triangle fails.
Therefore, the given side length does not forms a triangle.
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How do you get from 4 to 4/3?
4 times what gives us 4/3?
m = the unknown value
4m = four times that unknown value
4m = 4/3
m = (4/3)*(1/4)
m = 4/12
m = 1/3
Therefore, we multiply 4 with 1/3 to end up with 4/3.
The figure below is a scale drawing of a playhouse. In the drawing, the side of each house represents two and a half feet. Find the actual length of each segment.
5. The width of the house. = 30 feet
6. The height of the house. = 22.5 feet
7. The height of the first floor. = 12.5 feet
8. The height of the roof. = 10 feet
9. The width of the door. = 5 feet
10. The height of the door. = 7.5 feet
How to find the actual length of each segmentThe actual length of each segment is calculated by counting the units in the scale drawing and multiplying by the scale factor
In the problem, the scale factor is two and a half feet = 2.5 feet
5. The width of the house
number of units from the drawing = 12 units
actual length = number of units from the drawing * scale factor
actual length = 12 * 2.5 = 30 feet
6. The height of the house
number of units from the drawing = 9 units
actual length = 9 * 2.5 = 22.5 feet
7. The height of the first floor
number of units from the drawing = 5 units
actual length = 5 * 2.5 = 12.5 feet
8. The height of the roof
number of units from the drawing = 4 units
actual length = 4 * 2.5 = 10 feet
9. The width of the door.
number of units from the drawing = 2 units
actual length = 2 * 2.5 = 5 feet
10. The height of the door.
number of units from the drawing = 3 units
actual length = 3 * 2.5 = 7.5 feet
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A triangle has side lengths of 3x, 24, and 5x. The side with 5x is the longest side. What value of x would make a right triangle?
Answer:
To form a right triangle, one of the sides of the triangle must be the hypotenuse and the other two sides must be the legs. The hypotenuse is the longest side of a right triangle and the side opposite the right angle. In this case, the side with length 5x is the hypotenuse. Therefore, the sides with lengths 3x and 24 must be the legs.
We can use the Pythagorean Theorem to determine the value of x that will make this a right triangle. The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:
5x^2 = 3x^2 + 24^2
Solving for x, we get:
x = sqrt(24^2/(5^2 - 3^2)) = sqrt(576/16) = 6
Therefore, a value of x = 6 will make this a right triangle.
Step-by-step explanation:
How do you tell if a graph is linear quadratic or exponential?
A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.
To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.
For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:
y = mx + b
3 = m*2 + b
7 = m*5 + b
Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.
A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.
For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:
y = ax^2 + bx + c
6 = a*1^2 + b*1 + c
13 = a*2^2 + b*2 + c
24 = a*3^2 + b*3 + c
Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.
An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.
For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:
y = a*b^x
16 = a*b^2
24 = a*b^3
Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.
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Finding the slope ?identify the slope
the slope of the given straight line will be -3
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
Slope is = y2-y1/x2-x1
=9-0/0-3
=-3
Hence the slope of the given straight line will be -3
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The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys.
Company A: 1/5=5 25/5=5 50/10=5 75/15=5.
These ratios are all equivalent
This relationship is proportional.
company B: 5/1=5 20/5=4 40/10=4 69/15=4.
These ratios are not all equivalent.
This relationship is not proportional.
Is the ratio constant or varying for company B? Explain
When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.
Find the equivalent ratio by what method?Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. Finding equivalent fractions follows the same procedure.
A ratio formula is what?The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
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PLS HELP QUICK
give two different first steps you could use to solve this equation
-3(2x+6)=12
There are two steps of solving the equation -3(2x+6)=12.
The steps are given below.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given equation:
-3(2x+6)=12
The first step:
Solving the parenthesis first,
-6x -18 = 12
Adding 18 to both sides,
-6x = 30
Divide by -6,
x = -5
The alternate step:
-3(2x+6)=12
Divide by -3,
2x + 6 = -4
2x = -10
x = -5
Therefore, x = -5 is the solution of the equation.
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A basking shark measures 25 feet long. A giant squid measures
33 feet long. How many inches longer is the basking shark than
the giant squid?
ounds and
Answer: 8 feet
Step-by-step explanation:
you take 33-25 to get the sum of 8. so the squid is 8 feet longer than the shark.
What are the domain and range of the function fix) = x* - 2x2 - 4?
Answer: domain(-oo,oo). range= f(x) >-5
Step-by-step explanation:
A radioactive compound with mass 320 grams decays at a rate of 27% per hour. Which equation represents how many grams of the compound will remain after 7 hours?
Answer:
320 grams ÷ 27% = 8.3 grams
Step-by-step explanation:
mark brainliest plss
It is a problem about the systems of equations that do not arise.
It is desired to distribute 420 € among three people, so that the first has €40 more than the second, and the third has half of what they have between the first two.
a) It proposes a system of linear equations to calculate what corresponds to each one. b) It solves, using the Gauss method
The solution to the equations is
The value of first x = € 160
The value of second y = € 120
The value of third z = € 140
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first , second and third be represented as x , y , and z
The total amount to be distributed = € 420
So , x + y + z = € 420 be equation (1)
Now , first has €40 more than the second
So , x = y + 40 be equation (2)
And , third has half of what they have between the first two
So , z = ( 1/2 ) ( x + y ) be equation (3)
Substituting the value of x in the equation (3) , we get
z = ( 1/2 ) ( 2y + 40 )
z = y + 20 be equation (4)
Substituting the value of z and x in equation (1) , we get
( y + 40 ) + y + ( y + 20 ) = 420
On simplifying the equation , we get
3y + 60 = 420
Subtracting 60 on both sides of the equation , we get
3y = 360
Divide by 3 on both sides of the equation , we get
y = € 120
Therefore , the value of x = € 160
The value of z = € 140
Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420
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