Answer:
1.) -12
2.) 28
3.) 40
Step-by-step explanation:
The elevation of an object is the height or depth of the object relative to the sea level. If the object is above sea level, its elevation will be positive. However, if the object is below sea level, its elevation will be negative. Therefore, we can conclude that the elevation of the fish is -12 m because it is below sea level.
Translate the sentence into an equation.
Seven more than the quotient of a number and 5 is equal to 3.
Use the variable B for the unknown number
Answer: 7 + [tex]\frac{B}{5}[/tex] = 3
Step-by-step explanation:
Its pretty simple, just do as the words say. :) the only issue could be "of a number and 5", so you go in order, letting B be the number, it's B/5
which of the following statements is true? a.) to imply causation, the correlation must be -1. b.) a high correlation can indicate a relationship but cannot prove causation. c.) a high correlation indicates that explanatory variable is a direct cause of the response variable. d.) having a low correlation is sufficient enough to imply causation.
The statement that is true is:
b.) A high correlation can indicate a relationship but cannot prove causation.
Correlation measures the strength and direction of the relationship between two variables, but it does not necessarily imply causation. A high correlation means that there is a strong linear relationship between the two variables, but it does not indicate whether one variable causes the other. There can be other factors that influence the relationship. Therefore, it is important to use other methods, such as experiments or observational studies, to determine causation. Correlation is useful for identifying associations between variables, but it cannot be used as evidence of a causal relationship.
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Find the coordinates of the orthocenter for ▲ABC. A(5,5), B(5,-4), C(-1,-1).
The orthocenter of ▲ABC is the point (27/4, 17/4)
What is Orthocenter in coordinate geometry?
Any triangle's three altitudes are contemporaneous line segments (they intersect in a single point), and this point is known as the triangle's orthocenter.
To find the orthocenter of ▲ABC, we need to first find the altitude lines of the triangle, which are the perpendicular lines from each vertex to the opposite side. The point where these three lines intersect is the orthocenter.
The slope of this line is:
BC = (-1 - (-4)) / (-1 - 5)
BC = 3/2
Using point-slope form, the equation of the line BC is:
[tex]y -y_{b} = m_{BC} (x - x_{b} )[/tex]
y - (-4) = (3/2)(x - 5)
y = (3/2)x - 17/2
To find the altitude from vertex A to BC, we need to find the equation of the line passing through A and perpendicular to BC. The slope of this line is the negative reciprocal of the slope of BC:
[tex]m\ altitude_A = -2/3[/tex]
The point-slope form of the equation of the altitude from A is:
[tex]y -y_{A} = m_{BC} (x - x_{A} )[/tex]
y - 5 = (-2/3)(x - 5)
y = (-2/3)x + 25/3
Similarly, we can find the equations of the altitudes from vertices B and C to the opposite sides AC and AB, respectively:
Altitude from B to AC:
[tex]m_{AC} = \frac{(y_{C} -y_{A})}{(x_{C} -x_{A})} \\\\m_{AC} = \frac{-3}{2}[/tex]
AC = 2/3
y - (-4) = (2/3)(x - 5)
y = (2/3)x - 2/3
Altitude from C to AB:
[tex]m_{AB} =\frac{(y_{B}- y_{A})}{(x_{B}- x_{A})} \\[/tex]
= (-4 - 5) / (5 - 5)
= undefined
x = -1
Now, we need to find the point of intersection of these three altitudes, which is the orthocenter. To do this, we can solve the system of equations formed by the three altitude lines:
y = (3/2)x - 17/2
y = (-2/3)x + 25/3
y = (2/3)x - 2/3
Substituting the third equation into the first two equations, we get:
(2/3)x - 2/3 = (-2/3)x + 25/3
(4/3)x = 9
x = 27/4
Substituting x = 27/4 into any of the three equations, we get:
y = (2/3)(27/4) - 2/3 = 17/4
Therefore, the orthocenter of ▲ABC is the point (27/4, 17/4).
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Principal: $250
Annual Rate: 5%
Time (years): 10
Find the simple interest
Using the value of principal, annual rate and time, the simple interest is $375
What is simple interestSimple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.
The formula for simple interest is:
I = P * r * t
where:
I is the interest amount
P is the principal amount
r is the interest rate (expressed as a decimal)
t is the time period (in years)
In the given problem, we can calculate the simple interest by substituting the values into the formula
A = P(1 + rt)
A = 250(1 + 0.05(10))
A = 375
The simple interest is $375
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ANSWER ASAP
Three points of a parallelogram are (4, 3), (-4 3), and (2, -3).
What are the coordinates of the 4th point that would complete the parallelogram?
Given parallelogram points are (4,3),(-4 3), and (2, -3).
Let's say A= (4,3) , B=(-4 3) ,C=(2, -3) and D=(x, y)
Parallelogram defined as opposite sides are equal and parallel to each other.
From the properties of parallelogram :
We can say diagonals bisect each other.
From this we can easily find 4th point of parallelogram by using mid point concept.
Mid point formula
(X,Y)=[tex](\frac{x_{1} +x_{2}}{2},\frac{y_{1} +y_{2}}{2})[/tex]
Find mid point between AC line
midpoint (X,Y)= [tex](\frac{4 +2}{2},\frac{3-3}{2})[/tex]
(X,Y)=[tex](\frac{6}{2},\frac{0}{2})[/tex]
(X,Y)=(3,0)
Find mid point between BD Line
Mid point (X,Y)= [tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]
Mid point of AC and BD are equal to each other
(3,0)=[tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]
Equate x-coordinate and y-coordinate.
[tex]3=(\frac{-4 +x}{2})[/tex] and [tex]0=(\frac{3+y}{2})[/tex]
6=-4+x and 0=3+y
x=10 and y=-3
Therefore ,the coordinates of the 4th point is D(x, y)=(10,-3)
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The coordinates of the fourth point that would complete the parallelogram are (10, -3).
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
We know A, B, and C, where A = (4, 3), B = (-4, 3), and C = (2, -3).
To determine the fourth point, which represents D.
First, we need to find the vector representing side AB.
Subtracting the coordinates of point B from the coordinates of point A. So:
AB = A - B = (4, 3) - (-4, 3) = (8, 0)
Next, we need to find a point that is on the line that is parallel to AB and passes through point C.
The vector CD (where D is the point) is equal to AB. So:
CD = AB = (8, 0)
We know that C = (2, -3),
We can start by adding CD to C to get D:
D = C + CD = (2, -3) + (8, 0) = (10, -3)
Therefore, the coordinates of the fourth point are (10, -3).
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Plot a point on the coordinate plane to represent each of the ratio values in the table.
Answer: X=2
Step-by-step explanation:
X times 2
1 x 2 = 2
3 x 2 = 6
6 x 2 =12
9 x 2 = 18
what is - 3x > 15 equal to
Answer:
x < -5
Step-by-step explanation:
- 3x > 15 is equal to x < -5
What is the length of the other diagonal, df? 5 cm 16 cm 21 cm 32 cm
Referring to the given kite, the length of the other diagonal. DF, is 21 cm.
A kite is a quadrilateral shape, meaning it has four sides. The two pairs of adjacent sides are of equal length, while the opposite sides are not.
The shape of a kite is typically described as having two pairs of congruent adjacent sides that are connected by two diagonal lines that intersect at a right angle. The diagonal lines of a kite are perpendicular to each other, and the shorter diagonal bisects the longer diagonal.
Let's denote the point of intersection of the two diagonals as O.
Since the two diagonal intersect at a right angle, diagonal DF is perpendicular to diagonal EG.
DG = 13 cm
FG = 20 cm
OG = 1/2 EG = 1/2 x 24 = 12 cm
Using the Pythagorean Theorem:
OD = √(DG² - OG²)
= √(13² - 12²) = 5 cm
OF = √(FG² - OG²)
= √(20² - 12²) = 16 cm
DF = OD + OF
= 5 + 16 = 21 cm
The picture in your question is missing, most likely it was like on the attached picture.
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Answer: c
Step-by-step explanation: I got it right
can someone explain as well so i can understand......A savings account with simple annual interest rate of 3.92% and an initial deposit of $5,460.75 yields a final account balance of $6,370.51 after 51 months. Part A: Using the rate and term as the simple interest account, calculate the final account balance if the initial deposit is invested for the same number of months, with interest compounded semiannually. Show all work. (3 points) Part B: Compare that simple interest final account balance with the compound interest final account balance. (2 point)
Answer:
Step-by-step explanation:
To calculate the final account balance for a savings account with an initial deposit of $5,460.75, compounded semiannually with an interest rate of 3.92%, for 51 months, we need to use the formula:
A = P * (1 + r/n)^(nt)
where A is the final account balance, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times the interest is compounded in a year, t is the number of years, and nt is the number of compounding periods.
In this case, n = 2 (since the interest is compounded semiannually), r = 3.92%/100 = 0.0392, t = 51 months / 12 months/year = 4.25 years, and nt = 2 * 4.25 = 8.5.
Substituting the values into the formula, we get:
A = $5,460.75 * (1 + 0.0392/2) ^ (8.5)
A = $5,460.75 * 1.0196^8.5
A = $5,460.75 * 1.2408
A = $6790.32
So, the final account balance if the initial deposit is invested with interest compounded semiannually is $6790.32.
B) Comparing the final account balance of the simple interest account and the compound interest account, we can see that the compound interest account yields a higher balance ($6790.32) than the simple interest account ($6370.51). This is because compounding interest allows for the interest earned in one period to be reinvested, so the interest earns interest in future periods, which increases the overall amount of interest earned over time. In contrast, simple interest is calculated only on the initial deposit, so the amount of interest earned remains constant over time.
j–18≥1 Need help pls
Answer:
j≥19
hope this helpss :))
3) we have 2 engineers and 10 computer scientists. we need to create a committee of 10 people with at least one engineer represented there. how many different ways are there to create such a committee? show at least 2 different ways to solve this problem.
Answer:
Step-by-step explanation:
Method 1: Counting the number of committees with exactly one engineer:
There are 2 ways to choose the engineer, and 10 ways to choose the remaining 9 computer scientists. Hence, there are 2 * 10 = 20 different committees with exactly one engineer.
Method 2: Using the combinations formula:
There are 12 people in total, and we need to choose 10 of them for the committee. We can use the combinations formula to calculate the number of different ways to choose 10 people from 12: C(12, 10) = (12!) / (10! * (12-10)!) = (12!) / (10! * 2!) = 66.
So, there are 66 different ways to create a committee of 10 people with at least one engineer represented.
Sketch and graph please
The graph of the linear inequality [tex]y\geq -3x+4[/tex] is given below.
What is linear inequality?
The expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. A linear inequality, which is an inequality including at least one linear algebraic expression, is when a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1. There are numerous ways to depict various kinds of linear inequalities.
Given linear inequality is [tex]y\geq -3x+4[/tex] for which y region will be in the positive range.
Hence, the graph of the given linear inequality is given below.
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Find the common factor of all the terms of the polynomial 16x² - 14x.
Answer:
The common factor of all the terms of the polynomial 16x² - 14x is:
2x
Step-by-step explanation:
We are given a polynomial:
16x²-14x
We have to find the common factor of all terms.
First we factorize each term separately and then see the common factor.
16x²=2×2×2×2×x×x
14x=2×7×x
We observe that the common factor is:
2x
Hence, the common factor of all the terms of the polynomial 16x² - 14x is:
2x
Answer:
2x
Step-by-step explanation:
16 = 2^4
14 = 2 × 7
Common factor of 16 and 14 is 2.
x² = x × x
x = x
Common factor of x² and x is x
The common factor of the two terms is 2x.
Now look at the exponential expression you found to be equivalent to 100,000 • 1/100,000 can you use addition or multiplication on the powers of this exponential expression to simplify it if not which operation works and which one doesn’t
The expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1.
The exponential expression that is equivalent to 100,000 • 1/100,000 is:
[tex](10^5) * (10^-5)[/tex]
To simplify this expression using addition or multiplication on the powers, we can use the property of exponents that states:
[tex]a^m *a^n = a^{(m+n)[/tex]
This means that when we multiply two numbers with the same base, we can add their exponents to simplify the expression. However, this property does not work for division, as we need to subtract the exponents instead.
Using this property, we can simplify the expression as follows:
[tex](10^5) * (10^-5) = 10^{(5-5)} = 10^0 = 1[/tex]
Therefore, the expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1. We can see that in this case, addition and multiplication do not help us simplify the expression, but we can use the exponent property to do so.
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two paintings in an art display have shapes that are similar figures. the similarity ratio is 9:7. the perimeter of the smaller painting is 6 meters. which is the perimeter of the larger painting to the nearest tenth?
Two paintings in an art display have shapes that are similar figures. the similarity ratio is 9:7 and the perimeter of the smaller painting is 6 meters therefore the perimeter of the larger painting to the nearest tenth is 7.7 meters.
What is Perimeter?This is referred to as the total distance around a two-dimensional shape.
Perimeter of the smaller painting is 6 meters and similarity ratio is 9:7
9 = x
7 = 6
7x = 54
x = 54/7 = 7.7 meters.
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Find the Measure of Angle D.
Round to one decimal place if necessary. If your answer
is correct you will see an image appear on your screen.
The measure of angle D is 90 degrees
How to determine the valueThe sum of the interior angle of a parallelogram is equivalent to 360 degrees
From the information given, the measure of the angles are;
17x + 5, 13x + 7 + 118 and 80
Equate the angles to the sum of interior angles
17x + 5 + 13x + 7 + 118 + 80 = 360
collect the like terms, we get;
30x = 360 - 210
substract the like terms
30x = 150
Make x the subject
x = 5
Hence, the angle is 90 degrees
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The measure for the angle m∠D of the quadrilateral CDEF is equal to 90°
How to evaluate for angle m∠D of the quadrilateralFor any quadrilateral, the sum of its four interior angles is equal to 360°, hence we shall calculate for the angle m∠D by first finding the value of x as follows:
17x + 5 + 13x + 7 + 118° + 80° = 360°
30x + 210° = 360°
30x = 360° - 210° {subtract 210° from both sides}
30x = 150°
x = 150°/30
x = 5
m∠D = 17(5) + 5 = 90°
Therefore, the measure for the angle m∠D of the quadrilateral CDEF is equal to 90°.
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scores turned in by an amateur golfer at the bonita fairways golf course in bonita springs, florida, during and are as follows: 2018 season: 73 77 78 76 74 72 74 76 2019 season: 70 69 74 76 84 79 70 78 a. use the mean (to the nearest whole number) and standard deviation (to decimals) to evaluate the golfer's performance over the two-year period. mean standard deviation mean standard deviation b. what is the primary difference in performance between and ? - select your answer - what improvement, if any, can be seen in the scores? - select your answer -
A) The mean of 2018 scores: μ₂₀₁₈ = 75
The mean of 2019 scores: μ₂₀₁₉ = 75
The standard deviation of 2018 scores: s₂₀₁₈ = 2.07
The standard deviation of 2019 scores: s₂₀₁₉ = 5.26
B) The primary difference is that variation is higher in the 2018 season than the 2019 season.
A)
We know that the mean is nothing but the sum of all scores divided by the number of scores.
Thus the mean for 2018 scores is:
μ₂₀₁₈ = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8
μ₂₀₁₈ = 75
Similarly the mean for 2019 scores is:
μ₂₀₁₉ = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8
μ₂₀₁₉ = 75
We know that the formula for the standard deviation is:
[tex]s=\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1} }[/tex]
where s sample standard deviation
n the size of the sample
[tex]x_i[/tex] each value from the sample
[tex]\bar{x}[/tex] the sample mean
Using this formula, the standard deviation for 2018 scores is:
s₂₀₁₈ = [tex]\frac{\sqrt{ (73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 +(74-75)^2 + (76-75)^2} }{7}[/tex]
s₂₀₁₈ = 2.07
And the standard deviation for 2019 scores is:
s₂₀₁₉ = [tex]\frac{\sqrt{ (70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 +(70-75)^2 + (78-75)^2} }{7}[/tex]
s₂₀₁₉ = 5.26
B)
We cwn observe that both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.
Thus, the variation in scores was higher in 2019.
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Find the complete question below.
(5 pts) interpolation is used to determine values beyond a given set of data points. a) true b) false
The statement "interpolation is used to determine values beyond a given set of data points" is true
The given statement is " interpolation is used to determine values beyond a given set of data points"
The interpolation is a method in statistics that used to determine or estimate the unknown values in the given set of values. So it is usually used to estimate the price and the potential yield of security
In the interpolation, we use the values from the given set of the data point and estimate the unknown values or values beyond the given set of data points
Therefore, the given statement is true
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Reynold can make 4 baked zitis in 8 hours. With Donald’s help, they can bake the same amount of food in 4 hours. How long will it take Donald to make 4 baked zitis without help?
Donald and Reynold work at the same rate, the it also takes 8 hours for Donald to make 4 baked zitis.
How long will it take Donald to make 4 baked zitis without help?We know that Reynold can make 4 baked zitis in 8 hours, then his rate of work is:
R = (4 zitis)/(8 hours) = 0.5 zitis per hour.
Whit Donald's help they can make 4 zitis in 4 hours, if we define D as Donald's rate we can write:
(R + D)*4 hours = 4 zitis.
Replacing R we get:
(0.5 zitis/hour + D)*4 hours = 4 zitis
(0.5 zitis/hour + D) = (4 zitis)/(4 hours)
(0.5 zitis/hour + D) = 1 ziti/hour
D = 1 ziti/hour - 0.5 zitis/hour = 0.5 zitis/hour
So Donald works at the same rate than Reynold, then it will take 8 hours for Donald to make 4 baked zitis.
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Which graph shows the function y = 3x - 5 ?
The solution is, Option A. Line X
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
We have to identify the line which represents the function f(x) = 3x - 5
The given equation is y = 3x -5, in which slope of the line should be 3 and y- intercept is -5.
In these lines line x is having y-intercept as -5.
Line x passes through (1, 2) and (0, -5)
So slope of the given line will be = y2 - y1/ x2 - x1
= -5-2/ 0-1
= 3
Therefore, option A : Line X is the answer.
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pour le carnaval un fleuriste dispose de 283 roses et 397 tulipes. il décide de décorer de façon identique le plus grand nombre de chars pour accompagner les carnavalier. après avoir décorer le chars il lui reste 3 roses et 2 tulipes.
combien a t-il décorer de chars et quelle est la composition de chaque décor?
Answer:
I don't understand French
Step-by-step explanation:
What is the area of ∆AOB?
The Area of Rhombus is 97.5 cm².
What is area of Rhombus?The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.
Given:
As, diagonals of rhombus bisect perpendicularly.
so, In triangle OAD using Pythagoras theorem
AD² = OD² + OA²
10² = 7.8² + OD²
OD= 6.25 cm
So, length of BD = 2 x 6.25 = 12.5 cm
Now, area of Rhombus = 1/2 x a x b
= 1/2 x 15.6 x 12.5
= 97.5 cm².
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The table represents a function.
A 2-column table with 4 rows. The first column is labeled x with entries negative 4, negative 1, 3, 5. The second column is labeled f of x with entries negative 2, 5, 4, negative 8.
What is f(5)?
–8
–1
1
8The table represents a function.
A 2-column table with 4 rows. The first column is labeled x with entries negative 4, negative 1, 3, 5. The second column is labeled f of x with entries negative 2, 5, 4, negative 8.
What is f(5)?
–8
–1
1
8
The value of function f(5) is 8.
What do you mean by function?A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
The general representation of a function is y = f(x).
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective Function or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials
Inverse function: The function which can invert another function.
Given:
x with entries -4, -1, 3 and 5.
f(-4) = 2
f(-1) = 5
f(3) = 4
f(5) = 8
The value of f(5) is 8.
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Answer: f(5) is -8
Step-by-step explanation:
took the quiz
Michael runs a distance of 5 1/4 miles in 45 3/4 minutes during a race. Which statements correctly represent
Michael's race? Select ALL the correct answers.
A. Michael's unit rate of minutes per mile was about 8.7.
B. Michael's average pace was about 0.11 miles per minute.
C.
Michael's unit rate of minutes per mile was about 6.9.
D. Michael's average speed during the race was about 6.9 miles per hour.
E.
Michael ran about 8.7 miles in 1 minute.
eria wall
Answer:
A. Correct
B. Correct
C. Not correct
D. Correct
E. Not correct
Step-by-step explanation:
We are told that Michael's race numbers are:
5.25 miles
45.75 minutes
Divide the miles by the minutes to get mIchael's running rate:
0.114754098 mi/min
This result matches option B. " Michael's average pace was about 0.11 miles per minute."
======
Check all the answer options:
A. Michael's unit rate of minutes per mile was about 8.7.
Take 0.11475409 mi/min and invert it to find min/mile:
1/(0.11475409 mi/min) = 8.71 min/mile
This is a correct statement.
B. Michael's average pace was about 0.11 miles per minute.
From above: This is a correct statement.
C. Michael's unit rate of minutes per mile was about 6.9.
Take the given numbers: (45.75 minutes)/(5.25 miles) = 8.71 min/mile
This is not a correct statement.
D. Michael's average speed during the race was about 6.9 miles per hour.
Take the calculated rate of 0.11475409 mi/min and covert it to miles/hour:
Use the conversion factor (60 min/1 hr)
(0.11475409 mi/min)*((60 min/1 hr)) = 6.89 miles/hr
This is a correct statement.
E. Michael ran about 8.7 miles in 1 minute.
We know from above that he runs at 6.89 miles per hour. Running 8.7 miles in 1 minute would mean he is running at (8.7)*(60) = 413 miles/hour.
Perhaps he had some good energy bars, but the data do not support this conclusion.
This is not a correct statement.
Use the following data sets to answer the question.
Set {12, 9, 30, 1, 15, 10,
A:
12}
Set
B:
9, 30, 12, 3, 16, 11,
18}
Which statement about the shape of the data is true?
Both sets have the same median, but Set A has a larger mean.
O Both sets have the same median, but Set B has a larger mean.
O Set B has a larger mean and median than Set A.
O Set A has a lower median but a higher mean than Set B.
Answer:
Both have the same median but set A has a larger mean.
Step-by-step explanation:
You're welcome.
Please solve the radical equation.
Please show work
Answer:
Step-by-step explanation:
Find common denominator.
1/x + x-1/9x = 1 => 9/9x + x-1/9x = 1 (The common denominator is 9x.)
Combine like terms.
9 + x - 1 / 9x = 1 => x + 8/ 9x = 1
Cancel out 9x from denominator. What you do to one side, you do to the other.
(9x)(x + 8/9x) = 1(9x) => x + 8 = 9x
Solve for x.
8 = 8x => x = 1 (subtract x from both sides at the beginning and then simplify.)
At MeDonald's four cheeseburgers and three medium fries have a total of 2290 calories.Six cheeseburgers and two medium fries have 2560 calories. How many calories does each
Item contain?
Answer:
350 calories
Step-by-step explanation:
see the attachment.
Calories in one cheeseburgers = 135
And, Calories in one medium fries = 583
We have to given that,
At McDonald's four cheeseburgers and three medium fries have a total of 2290 calories.
And, Six cheeseburgers and two medium fries have 2560 calories.
Let us assume that,
Calories in one cheeseburgers = x
And, Calories in one medium fries = y
Hence, We get;
4x + 3y = 2290 . (i)
6x + 3y = 2560 .. (ii)
From (i);
3y = 2290 - 4x
Substitute above value in (ii);
6x + (2290 - 4x) = 2560
6x - 4x + 2290 = 2560
2x = 2560 - 2290
2x = 270
x = 270 / 2
x = 135
From (ii);
6 x 135 + 3y = 2560
810 + 3y = 2560
3y = 2560 - 810
3y = 1750
y = 1750/3
y = 583
Therefore, Calories in one cheeseburgers = 135
And, Calories in one medium fries = 583
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If a cuboid weighs 100N has sides 5cm by 10cm. Find the area of the cuboid
If a cuboid weighs 100N and has sides 5cm by 10cm, then the area of cuboid is 0.005m².
Weight of the cuboid = 100N
Sides of the cuboid = 5cm by 10cm
A solid structure or a three-dimensional shape in geometry is called a cuboid. It is similar to a cube in that a cuboid can become a cube by changing the angles between faces or the lengths of the edges. A convex polyhedron with the same polyhedral graph as a cube is referred to as a cuboid in mathematics.
Calculating the area of the Cuboid -
= 5cm × 10cm
= 50cm²
Converting -
Area of Cuboid
= 50/10000 m²
= 0.005 m²
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HELLPP IM CONFUSED :(
Answer:
(b) area = 29 units²
Step-by-step explanation:
You want the area of the irregular shape shown in the figure.
AreaThe area of a rectangular shape is the product of its length and width:
A = LW
The given shape can be considered to be a 6 unit square with some pieces removed. The area of the remaining shape is the area of that square less the areas of the removed pieces.
Upper LeftThe piece removed from the upper left corner is a 2-unit square. Its area is ...
A = (2 units)(2 units) = 4 units²
Lower RightThe piece removed from the lower right side is 3 units by 1 unit, so its area is ...
A = (3 units)(1 units) = 3 units²
OverallThe area of the square before those pieces were removed was ...
A = (6 units)(6 units) = 36 units²
Remaining shapeThen the area of the remaining shape after the pieces are removed is ...
Area = 36 units² -4 units² -3 units² = (36 -7) units² = 29 units²
The area of the figure is 29 units².
__
Additional comment
Quite often, the area of an irregular shape is more easily found by subtracting missing areas than by dividing up the existing shape into pieces whose area formulas you know.
The second attachment shows division of the area into smaller rectangles. Working clockwise from upper left, their areas are 1×2, 3×4, 3×1, 3×4, for a total of 2+12+3+12 = 29 square units.
PLS EXPLAIN THIS TO ME I DONT UNDERSTAND
The statement must be true are A, B and D.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
We are Given that Triangle DKL is congruent to Triangle PVX
We know that when two triangles are congruent then Acc. to CPCT [ Corresponding Parts of Congruent Triangle]
the corresponding parts are also congruent keeping in mind the vertices and the segments are in same comparison as given in the congruent triangles.
(a) Triangle LKD is congruent to Triangle XVP.
(b) Triangle VPX is congruent to Triangle KDL.
(c) Triangle VPX is not congruent to Triangle DLK as according to CPCT, V vertex is not congruent to D, P vertex is not congruent to L and X vertex is not congruent to K.
(d) Angle D is congruent to angle P.
(e) Thus Segment DL is not congruent to Segment PV ( as according to CPCT, Segment DL is congruent to PX and not PV.)
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