Thus, the cost would be $60 + $56 = $116 for a group of two persons and $60 + $52 + $52 = $164 for a party of three for number n.
The pricing structure for the tour company is based on a base price of $60 per person, which is then discounted by $4 for each additional person up to a maximum of 8 people. This means that for a group of 2 people, the price would be $60 + $56 = $116, while for a group of 3 people, the price would be $60 + $52 + $52 = $164.
The pricing structure incentivizes larger groups to go on the tour, as they can benefit from the discounted price per person. However, the discount stops at 8 people, which means that larger groups do not receive any further discounts. This is likely because the tour company may have a limit on the number of people they can accommodate on a single tour.
It is important for customers to be aware of the pricing structure when considering booking a tour with the company. They should also consider the benefits and drawbacks of going with a larger group versus a smaller one, such as the potential for a more personalized experience with a smaller group versus a more social experience with a larger group. Overall, the pricing structure is designed to be fair and encourage group bookings, while also accommodating the needs of the tour company.
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Write the recursive formula for 5, 15, 30, 50...........
A recursive sequence is a sequence in which terms are defined using one or more previous terms that are given.
If you know the term n of an arithmetic sequence and you know the common difference, d, you can find the term [tex](n + 1)[/tex] by tossing the recursive formula to [tex]n + 1 = a \ n + d[/tex]
We have then:
[tex]5, 15, 30, 50[/tex]
[tex]an = (\dfrac{5}{2} ) \times (n) \times (n + 1)[/tex]
Answer:
the recursive formula for 5, 15, 30, 50, is:
an = (5/2) x (n) x (n + 1)
a joint probability is the . a. sum of the probabilities of two events b. probability of the intersection of two events c. sum of the probabilities of two independent events d. probability of the union of two events
Option B. It defines the joint probability as the probability of the intersection of two events.
A joint probability refers to the probability of two or more events occurring simultaneously. In other words, it is the probability that two or more events will occur together.
The joint probability of two events A and B is denoted as P(A ∩ B), which represents the probability of the intersection of events A and B. This is the probability that both A and B occur at the same time.
For example, if we toss a coin and roll a dice, the probability of getting heads on the coin and a 4 on the dice would be the joint probability of these two events occurring together. This joint probability can be calculated by multiplying the probability of getting heads (1/2) and the probability of rolling a 4 (1/6), giving a joint probability of 1/12.
Therefore, option (b) is the correct answer, as it defines the joint probability as the probability of the intersection of two events.
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Write an exspression for ''h less than 13''
Answer:h<13
Because h has to be less than 13, so h<13 is the correct answer
Step-by-step explanation:
Answer:
it could either be h<13 or 13-h depending on what you're studying
Avery puts up a radio antenna tower in his
yard. Ella tells him that their city has a law
limiting towers to 50 ft in height. How can
Avery use the lengths of his shadow and the
shadow of the tower to show that his tower is
within the limit without directly measuring it.
Step-by-step explanation:
Using similar triangles:
6ft height is to 5 feet shadow as tower height is to 40 ft tower shadow
6/5 = h / 40 <====solve for 'h'
40 * 6/5 = h = tower height = 48 feet tower height
Q.
A metal block of dimensions 3x3x4 cm are to be cut from a metal cube 1x1x1 m. Calculate the complete number of blocks and volume and surface area of the remaining cube.
Answer: The volume of the metal cube 1x1x1 m is:
V_cube = l × w × h = 1 m × 1 m × 1 m = 1 m^3
The volume of the metal block that is to be cut from the cube is:
V_block = l × w × h = 3 cm × 3 cm × 4 cm = 36 cm^3
We need to convert the volume of the block to cubic meters, as the volume of the cube is given in cubic meters. We can use the conversion factor 1 m = 100 cm to convert cubic centimeters to cubic meters.
V_block = 36 cm^3 ÷ (100 cm/m)^3 = 0.000036 m^3
The number of blocks that can be cut from the cube is:
N_blocks = V_cube ÷ V_block = 1 m^3 ÷ 0.000036 m^3 = 27,777.78
Since we can only have a whole number of blocks, the maximum number of blocks that can be cut from the cube is 27,777.
The remaining volume of the cube after cutting the metal block is:
V_remain = V_cube - V_block × N_blocks = 1 m^3 - 0.000036 m^3 × 27,777 = 0.999 m^3
The surface area of the remaining cube can be calculated as follows:
S_remain = 6 × (l × w) = 6 × (h^2) = 6 × (0.999 m)^2 = 5.994 m^2
Therefore, the complete number of blocks that can be cut from the metal cube is 27,777. The volume of each block is 36 cm^3 or 0.000036 m^3. The remaining cube has a volume of 0.999 m^3 and a surface area of 5.994 m^2.
Step-by-step explanation:
Which shape is a parallelogram with 4 right angle? 50 points
Answer: Square
Step-by-step explanation:
A square has 4 parallel sides and has 4 90 degree angles
What is the radius of a hemisphere with a volume of 939 ft cubed?
Answer:
7.654 ft
Step-by-step explanation:
The volume of a hemisphere is [tex]V=\frac{2}{3}\pi r^3[/tex]. Rearranging this equation gives [tex]r=\sqrt[3]{\frac{3V}{2\pi} }[/tex]. Plug in V=939 to find the value of r.
a pencil costs as much as two erasers, and three erasers cost as much as 2 lollipops. which is more expensive, two pencils or three lollipops?
Three lollipops are more expensive than two pencils.
Given that three erasers cost as much as 2 lollipops.
Let e denote the cost of an eraser and l denote the cost of a lollipop.
A pencil costs as much as two erasers, which implies that the cost of a pencil is two times the cost of an eraser. Therefore, the cost of a pencil is 2e.
Likewise, three erasers cost as much as 2 lollipops, which implies that the cost of an eraser is (2/3) l.
Therefore, the cost of a pencil is 4/3 times the cost of a lollipop.
Thus, the cost of two pencils is 4/3 * 2l = 8/3 l.
The cost of three lollipops is 3l.
Now, we must determine whether 8/3 l is greater than 3l or vice versa.
8/3 l = 2.67 l
Since 2.67 l < 3 l, the conclusion is that three lollipops are more expensive than two pencils.
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What is the probability of drawing a lettered card from a deck of shuffled 52 cards
The probability of drawing a lettered card from a deck of shuffled 52 cards is 50%.
Calcuating the probability of drawing a lettered cardThere are 52 cards in a deck, and 26 of them are lettered cards (A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2) while the other 26 cards are suited cards (clubs, spades, hearts, diamonds).
If the deck is well shuffled, each card is equally likely to be drawn.
Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is simply the number of lettered cards divided by the total number of cards:
P(Drawing a lettered card) = Number of lettered cards / Total number of cards
= 26 / 52
= 1/2
= 0.5
Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is 0.5 or 50%.
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HELP ME PLEASE
is y=4x^2-6x+10 a linear function
Answer:
NO
Step-by-step explanation:
It is a parabola, you can tell cuz of the x^2
:)
HELP!
The faces of a fair 6-sided cube are numbered 1 through 6. Based on the theoretical probability, if a number cube is rolled 120 times, how many should times should a 3 be rolled?
Responses
40
15
3
20
Based οn the theοretical prοbability, we shοuld expect tο rοll a number 3 20 times οut οf 120 rοlls.
Theοretical prοbability:Theοretical prοbability is a type οf prοbability that is based οn mathematical reasοning and analysis. It is the prοbability οf an event οccurring based οn the assumptiοn that all οutcοmes are equally likely.
Fοr example, if yοu rοll a fair six-sided dice, each οutcοme (1, 2, 3, 4, 5, οr 6) is equally likely tο οccur.
Therefοre, the theοretical prοbability οf rοlling a 1 is 1/6, the theοretical prοbability οf rοlling a 2 is 1/6, and sο οn.
Here we have
The faces οf a fair 6-sided cube are numbered 1 thrοugh 6.
The cube is rοlled 120 times,
Since the cube is fair, each οf the six faces has an equal prοbability οf appearing οn any given rοll.
Hence, the theοretical prοbability οf rοlling a 3 οn a single rοll is 1/6.
Here we can use the fοrmula fοr expected value tο find the number οf times we shοuld expect tο rοll a 3:
Expected value = (number οf trials) x (prοbability οf success)
Expected value = 120 x (1/6) = 20
Therefοre,
Based οn the theοretical prοbability, we shοuld expect tο rοll a number 3 20 times οut οf 120 rοlls.
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The size of the largest angle in a triangle is double the size of the smallest angle. the other angle is 20° greater than the smallest angle.
work out the size of each angle in the triangle
Answer:
40, 60 and 80.
Step-by-step explanation:
Let x = t he size of the smallest angle
x + 2x + x + 20 = 180 The sum of the interior angles of a triangle is 180
4x + 20 = 180 Subtract 20 from both sides
4x = 160 Divide both sides by 4
x = 40
The smallest angle is 40. The largest angle is 80. The other angle is 60. The total is 180
Helping in the name of Jesus.
In a jar , there are 4 blue marbles, 3 green marbles, 7 red marbles and 2 white marbles. Find p(g)
The probability of selecting a green marble from a jar containing 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles is 0.1875 or 18.75%.
To find p(g), we need to first determine the total number of marbles in the jar, and then determine the number of green marbles in the jar.
Total number of marbles = 4 blue marbles + 3 green marbles + 7 red marbles + 2 white marbles = 16 marbles.
Number of green marbles = 3.
So p(g) = number of green marbles / total number of marbles = 3 / 16.
Therefore, p(g) = 0.1875 or 18.75%.
Therefore, Choosing a green marble from a container holding 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles has a probability of 0.1875 or 18.75%.
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what is the f-1(x) ?
Answer:
(9x)/(2-2x)
Step-by-step explanation:
let f-1(x) = y
then, f(y) = x
so, (2y)/(9+2y) = x
***remember the thing inside the () in f(x) can change! y can go in x's place, any number or any other variable can go in x's place! BUT, nothing else can be changed in the function***
now just solve for y!
multiply both sides by (9+2y): 2y = 9x + 2xy
bring the y's together (subtract both sides): 2y-2xy =9x
hey! we can factor the left side (where the y's are): 2y(1-x) = 9x
get all the x's together (divide both sides) : 2y = (9x)/(1-x)
get y alone (divide both sides by 2): (9x)/(1-x) * (1/2)
*finally* distribute/simplify: (9x)/(2-2x)
you can double-check the answer on desmos!
~ lmk if u got Qs :>
Fill in the blanks and find the x.
For the right-angled triangle, the value for x is obtained as √2/4.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right angle triangle is given.
It has angles 90°, 45° and 45°.
The hypotenuse measures 4√2.
The perpendicular measures x.
In a 45°-45°-90° right triangle, the legs are congruent and the hypotenuse is √2 times the length of a leg.
Therefore, in this triangle, each of the legs has length -
(4√2)/√2 = 4
So x is equal to one of the legs, which is 4.
To fill in the blanks -
x : 4√2 = 1 : 4
4x = 4√2
x = (√2)/4
Therefore, the value for x is obtained as √2/4.
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21
There are 80 students in a class.
Each student walks to school or cycles to school or gets the bus to school.
There are 44 girls in the class.
17 of the girls walk to school.
14 of the boys cycle to school.
12 of the 20 students who get the bus to school are boys.
Find the number of these students who walk to school.
There are 27 students in the class who walk to school.
How many students in the class walk to school?Word problem refers to problem expressed entirely in words typically used as an educational tool.
Given that:
Total number of students in the class: 80
Number of girls in the class: 44
Number of girls who walk to school: 17
Number of boys who cycle to school: 14
Number of boys who take the bus to school: 12
We have to subtract the students who take the bus or cycle from the total number of students first. The number of boys who walk to school will be:
= Total number of boys - Boys who cycle - Boys who take the bus
= (Total number of boys) - 14 - 12
= (80 - 44) - 14 - 12
= 36 - 14 - 12
= 10
To get total number of students who walk to school, we compute as follow. The number of students who walk to school:
= Number of girls who walk to school + Number of boys who walk to school
= 17 + 10
= 27.
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Find the inverse function in slope intercept form f(x)=-x+3
So, the inverse function of f(x) = -x + 3 is g(x) = 3 - x, and it is in slope-intercept form. The slope of g(x) is -1 and the y-intercept is 3.
What's inverse function?An inverse function is a function that reverses the operation of another function. More specifically, if f is a function that maps inputs from a set A to labors in a set B, also an inverse function g is a function that maps labors from B back to inputs in A, similar that for any input x in A, applying f and also g (or g and also f) results in the same value. In other words, if f(a) = b, also g(b) = a
by the question.
To find the inverse function of f(x) = -x + 3 in slope-intercept form, we need to solve for x in terms of y.
Start by replacing f(x) with y:
[tex]y=-x+3[/tex]
Now, isolate x on one side of the equation. To do this, we can add x to both sides:
[tex]y+x=3[/tex]
Finally, solve for x by subtracting y from both sides:
[tex]x=3-x[/tex]
So, the inverse function of f(x) = -x + 3 is given by:
[tex]f^{-1}(x)=3-x[/tex]
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The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
58.2 $112
64.2 $135
64.3 $138
66.8 $146
68.4 $166
71.6 $180
72.7 $188
76.2 $199
77.8 $220
82.8 $280
What is the slope of the line of best fit, where x represents the average daily temperature and y represents the total ice cream sales? (Round your answer to one decimal place.)
4.2
6.5
8.1
9.1
Using a calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:
y = 6.5x - 279.1.
To find the equation, we need to insert the points (x,y) in the calculator. The same is true for any regression equation such as quadratic or exponential. However, as the problem states, a line of best fit is calculated in this problem.
From the table presented in the problem, the points are given as follows:
(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).
Inserting these points into the calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:
y = 6.5x - 279.1.
Here
x is the daily temperature, in F.
y is the sales, in dollars.
The complete question is-
The table compares the average daily temperature and ice cream sales each day
Temperature ("F) Ice Cream Sales
$112
$135
$138
$146
$166
$180
$188
$199
$220
$280
58.2
642-
64.3
66.8
684
71.6
72.7
76.2
77.8
82.8
Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth
09=38x-1092
09=-38xx-1092
Oý=65x-279.1
O ý= -65x-279.1
and also attached an image of the question.
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joy has thin rods, one each of every integer length from through . she places the rods with lengths , , and on a table. she then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. how many of the remaining rods can she choose as the fourth rod?
Number of remaining rods can she choose as the fourth rod is 10
For the rods to form a quadrilateral with positive area, the fourth rod must satisfy the triangle inequality. That is, the sum of the lengths of any two sides of the quadrilateral must be greater than the length of the remaining side.
Let's start by looking at the rod with length 3 cm. The only other rod that can be paired with it to form a triangle is the rod with length 7 cm, since all the other rods are either shorter or longer than 4 cm. Similarly, the only other rod that can be paired with the rod with length 15 cm is the rod with length 7 cm.
Therefore, to form a quadrilateral with positive area, Joy must choose a rod that is longer than 7 cm but shorter than 18 cm (since the sum of 7 cm and 15 cm is 22 cm). There are 10 rods that satisfy this condition: 8 cm, 9 cm, 10 cm, 11 cm, 12 cm, 13 cm, 14 cm, 16 cm, 17 cm, and 18 cm.
So Joy can choose 10 rods as the fourth rod to form a quadrilateral with positive area.
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The given question is incomplete, the complete question is:
Joy has 30 thin rods, one each of every integer length from 1 cm through 30 cm. She places the rods with lengths 3 cm, 7 cm, and 15 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
I need the area and perimeter!
In the trapezoid , C) Area = 22.5 [tex]mi^2[/tex] , Perimeter = 22.5 mi.
What is area and perimeter?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape.
Here Base a = 3.5 mi , Base b = 5.5 mi and Height h = 5 mi.
Then Area of the Trapezoid = [tex]\frac{1}{2}[/tex] ( a + b ) h square unit
=> A = [tex]\frac{1}{2}(5.5+3.5)\times5[/tex]
=> A = [tex]\frac{1}{2}\times9\times5[/tex]
=> A = 22.5 [tex]mi^2[/tex]
Now perimeter is sum of all sides of the trapezoid. Then,
=> 3.5+5.5+7.5+6
=> 22.5 mi
Hence the area is 22.5 [tex]mi^2[/tex] and perimeter is 22.5 mi.
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ell whether the angles are complementary or supplementary. Then find the value of x
Answer:
These angles are complementary and congruent, so x = 15.
Step-by-step explanation:
[tex]3x + 45 = 90[/tex]
[tex]3x = 45[/tex]
[tex]x = 15[/tex]
What is the length of the rectangular plot of land shown? Use pencil and paper. How are the lengths of the legs of a right triangle related to the lengths of the sides of a rectangle?
Length of rectangular plot is 144ft
Define rectangleA rectangle is a geometric shape that is characterized by having four straight sides and four right angles. It is a type of quadrilateral, which means that it has four sides. The opposite sides of a rectangle are parallel and of equal length, which makes it a type of parallelogram.
Given;
From the image attached below;
Diagonal length, AB=306 ft
Base length, BC=270ft
As triangluar plot is right angled triangle.
According to pythagoras' theorem
AB²=BC²+CA²
Putting the values, we get
Length side of rectangle, BC=√306²-270²
BC=√20736
BC=144ft
Hence, Length of rectangular plot is 144ft
The right angle is inscribed in rectangular plot. The base and height of right angle is one base and height of the rectangular plot. Hence, the lengths of the legs of a right triangle related to the lengths of the sides of a rectangle.
Image is attached below
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Suppose in a quadratic-linear system of equations the vertex of the parabola intersects the line. Which of the following would represent the solution to the system of equations? A. the x-value of the vertex B. the y-value of the vertex C. the x- and y-values of the vertex D. cannot be determined
Answer:
C.
Step-by-step explanation:
The vertex and the point of intersection is just one point identifiied by its x and y vlaues
Find the shaded area.
Hint: Break the figure into simpler shapes, find the area of each shape, and then add all together.
Total area of the composite figure = ____ mm2
According to the given figure, the area of the shaded region in the shape is 49.5mm2.
Explain area?The total area of every one of the shapes which cover an object's surface is known as its surface area. The length and width of this type of rectangle are multiplied to determine its area.
To solve the following question we first need to separate the single shape into two according to the shapes given
Therefore we have two shapes with us, i.e., rectangle and triangle.
First of all, we need to calculate the area of both the shares separately:
Firstly, area of the rectangle, formula is:
Area = length x width
By entering the length and width values,
Area of rectangle= 7 x6
Area of rectangle= 42 mm2
Now, we need to calculate the area of the second shape, that is, triangle,
Triangle area is equal to height x base / 2.
Now, by putting values in the formula:
Area of triangle=3 x 5 / 2
Area of triangle= 15/2
Area of triangle= 7.5 mm2
Therefore, the area of the shaded region:
Area = (rectangular area + triangular area)
Area = 42 + 7.5
Area = 49.5 mm2
Therefore, the area of the shaded region of the shape given is 49.5 mm2.
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Find the probability of rolling a 6-sided dice and getting a number that is a divisor of 20.
Answer: The divisors of 20 are 1, 2, 4, 5, 10, and 20. Out of these, only the numbers 1, 2, 4, and 5 are possible outcomes when rolling a standard 6-sided dice.
The probability of rolling any of these four numbers is the total number of favorable outcomes (4) divided by the total number of possible outcomes (6), which gives:
Probability = Favorable outcomes / Total outcomes = 4/6 = 2/3
Therefore, the probability of rolling a 6-sided dice and getting a number that is a divisor of 20 is 2/3 or approximately 0.667.
Step-by-step explanation:
The probability of rolling a six-sided die and getting a result that divides by 20 is 2/6, or around one-third of the time.
There is a 1/3 chance that you will roll a number that divides by 20 when using a six-sided die. There are 6 possible outcomes when a 6-sided die is rolled, however only the numbers 4 and 5 may divide by 20. There are hence 2 positive events and a total of 6 occurrences that could take place. When the number of successful outcomes is divided by the total number of possible outcomes, the probability is 2/6, or 1/3
Because just one-third of results are likely to meet the criteria, the likelihood of rolling a number on a 6-sided die that is a divisor of Twenty is minimal.
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which pair of parent functions are inverses of each other on the domain x > 0?
A. linear and quardratic
B. cubic and linier C. cubic and square root
D. quadratic and square root
A Linear and Quadratic pair of parent functions are inverses of each other on the domain x > 0.
In mathematics, a parent function is a basic representation of a function type without manipulations such as translation and dilation. For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simply shifting and stretching parallel to the axes. Function is defined as the set of all input values have at least one output value.
According to the question,
a. A pair of linear functions :
let the function be y = x.
Domain : (-∞ , ∞) set of all real numbers
Range : (-∞ , ∞) set of all real numbers
Inverse of linear function is linear domain and range set of all real numbers.
Option A is the correct answer.
b. A cubic function and a cube root function :
Let y = x³
Domain: (-∞ , ∞) set of all real numbers
Range : (-∞ , ∞) set of all real numbers
Inverse function , x = ∛y ,
Domain: (-∞ , ∞) set of all real numbers
Range : (-∞ , ∞) set of all real numbers
Option B is not a correct answer.
c. a quadratic function and a square root function :
Domain of square root function: y = √x is [ 0, ∞)
Range of square root function: y = √x is [ 0, ∞)
Domain of quadratic function is (-∞ , ∞) set of all real numbers.
Range : all possible values of y.
Option C is not a correct answer.
D. A logarithmic function and an exponential function :
Domain : ( 0, ∞)
Range : set of all real numbers
Exponential function:
Domain : set of all real numbers
Range : ( 0, ∞)
Option D is not a correct answer.
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Find the length of the missing side. If necessary, round to the nearest tenth. 16 14 b
Pythagorean Theorem can be used to find the missing side that is equal to 21.3.
What is the distance formula?Distance formula states that the distance between two points is equal to the square root of the sum of the squares of the differences of the coordinates.
The missing side can be found by using the Pythagorean Theorem, which states that the square of the length of the hypotenuse (longest side of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.
Therefore, the missing side is equal to the square root of the sum of the squares of the sides we already have:
b² = (16)² + (14)²
= 256 + 196
= 452
b = √452
= 21.3
We can also use the distance formula here.
The distance between (16, 14) and (0, 0) =
√(16² + 14²)
= √(256 + 196)
= √452
= 21.3.
This confirms that the missing side is equal to 21.3.
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Question:
Find the length of the missing side. If necessary, round to the nearest tenth.
21.3
30
15
7.7
(it is a triangle and it has a right angle and you are looking for b and the numbers on the triangle are 16 [this is the longest side and slanted] and 14 [this is straight with no slant)
HELPPPPPP PLEASEEEEEEEE ASAPPPPP
Tamara has a box of fruit. There are 2 strawberries for every 3 cherries in the box. If there are 12 cherries in the box, how many strawberries are there?
Identify the slope and y-intercept of the following equation:
y = x - 2
Answer:
The given equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Comparing this with the given equation:
y = x - 2
We can see that the slope (m) is 1 and the y-intercept (b) is -2.
Therefore, the slope is 1 and the y-intercept is -2.