A right triangle is a triangle with one right angle (90 degrees). The hypotenuse of a right triangle is the side opposite the right angle and is usually the longest side of the triangle.
To find the area of the triangle, you will need to use the base and the height of the triangle. In this case, the base of the triangle is 48cm and the height is the length of the side opposite to the right angle.
To find the length of the side opposite to the right angle, you can use the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as:
c^2 = a^2 + b^2
where c is the hypotenuse, and a and b are the other two sides.
So, substituting the values we have:
50^2 = a^2 + 48^2
2500 = a^2 + 2304
a^2 = 2500 - 2304
a^2 = 196
a = 14
Area of the triangle = (1/2) * base * height
= (1/2) * 48 * 14
= 336 cm^2
So, the area of the triangle is 336 cm^2
The area of the triangle is 336 cm²
The area of a triangle can be found using the formula:
Area = (1/2) × base × height
In this case, we know the base is 48cm and the hypotenuse is 50cm. To find the height, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (a) is equal to the sum of the squares of the lengths of the other two sides (a and b) in the right triangle.
c² = a² + b²
So in this case, we have:
50² = 48² + b²
Solving for b, we get:
b =√ 50² - 48²
b = √2500 - 2304
b = √196
b = 14 cm
So the height of the triangle is 14cm.
Now we can use this information to find the area:
area = (1/2) ×48 ×14 = 336 cm²
Hence, we can say the area of the triangle is 336 cm²
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For what value of k is 3x² 2kx 27?.
For the roots to be real and equal, the value of k should be 9, -9.
The complete question is:
For what values of k are the roots of the quadratic equation 3x2 + 2kx + 27 = 0 real and equal?
For the roots of the equation to be real and equal, we first compare the given quadratic equation with standard form of quadratic equations, which is: [tex]ax^2+ bx+ c=0[/tex]
Thus, a = 3; b= 2k and c = 27
We know, for real and equal roots, Discriminant (D) = [tex]b^2 - 4ac[/tex] = 0
Therefore, we now substitute the values of a, b, and c in the above formula, we get
(2k)^2 - 4(3)(27) = 0
4k^2 - 324 = 0
4k^2 = 324
k^2 = 81
k= 9 or -9
Thus, the value of k is 9 or -9.
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How do you find the mean and standard deviation of the sampling distribution of the sample proportion?.
The standard deviation of the sampling distribution of a sample proportion using the formula σ^p=√p(1−p)N σ p ^ = p ( 1 − p ) N. The standard deviation of the sampling distribution of a sample proportion is about 0.054.
In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.
Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.
The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.
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which transformations were used to create congruent trapezoid W' X' Y' Z' from Trapezoid W XYZ
The translation and rotation of 180° about the origin. Then the correct option is A.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
From the graph, the trapezoid W'X'Y'Z' is derived by the translation and rotation of 180° about the origin. Then the correct option is A.
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Why the ratio of sine of angle of incidence to the sine of angle of refraction is constant?.
Ratio of sine of angle of incidence to the sine of angle of refraction is constant by Snell’s law.
According to Snell's Law, the refractive index, or n, is a constant that represents the ratio of a wave's angle of incidence to angle of refraction as it passes through a boundary between two mediums.
₁n₂=n₂/n₁=sin θ₁/sin θ₂= v₁/v₂,
where n is the refractive index,
v is the speed in different medium and θ is the angle between the normal and the ray at the surface of boundary.
If we do an experiment and measure the angles of incidence and refraction, we will discover that a straight line passing through the origin results from plotting the sine of the angles of incidence and refraction.
This shows that the sine of the angle of incidence and the sine of the angle of refraction are directly related, and that the ratio of the two will result in a constant value that we refer to as the refractive index. The ratio of the sines of the angles corresponds to the proportion of the wave speeds through the medium.
Thus, we can say that refractive index is constant for a given pair of media.
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How to solve a function?.
Step-by-step explanation:
a function with a single input variable x is usually defined like
y = f(x) = expression in x
to "solve" it means either to have a value for x and then calculate y.
or to have a value for y and find the corresponding value for x, so that f(x) = y. this usually involves finding and using the inverse function of f(x).
the details depend on the functions and operations used in the function expression.
find the value of a and b when x=12.\frac{5x^2}{2}
Answer:
when x = 12, a = 360 and b = 16.8.
Step-by-step explanation:
James buys a computer. The seller reduces the price by 30% and adds VAT at 17.5%. If James pays £1551 for the computer, what was its original price? (Give your answer to the nearest pence.)
Answer:
£1885.71
Step-by-step explanation:
Reducing by 30% is doing this: 100% - 30% = 70% = 0.7
Reducing a price by 30% is the same as multiplying the price by 0.7
Adding 17.5% is doing this: 100% + 17.5% = 117.5% = 1.175
Adding 17.5% to a price is the same as multiplying the price by 1.175
Let the original price be x.
1.175 × 0.7 × x = £1551
x = £1551/(1.175 × 0.7)
x = 1885.71
Answer: £1885.71
What is the slope-intercept form of the equation of the line graphed on the coordinate plane below?
The slope intercept form of the equation of the line graphed on the coordinate plane below will be y=-3x -1.
As we know, The slope intercept form of a straight line is y=mx + c, where m is the gradient which is the Tanθ where θ is the angle between the line and the x-axis. And C is the interception point on the y-axis.
To find the gradient, we can calculate Δy/Δx. From the graph given we can take two points on the line with the coordinates (1,-4) and (0,-1). From this, we can calculate the gradient :
⇒[tex]\frac{(y2-y1)}{(x2-x1)}[/tex]
⇒[tex]\frac{(-1)-(-4)}{0-(1)}[/tex]
⇒-3
And , from the figure we can see the line is intersecting the y-axis -at -1.
So, putting the values in y=mx+c will give us y=-3x -1
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Please help me with this!!!
Step-by-step explanation:
the area of a rectangle is
length × width.
so, it's simply a problem of multiplying 2 fractions.
it is
2 3/5 × 3 1/4
first we need to convert the numbers into true fractions.
2 3/5 = (2×5 + 3)/5 = 13/5
3 1/4 = (3×4 + 1)/4 = 13/4
the beauty of a multiplication (compared to addition) is that we don't need to bring the fractions to the same denominator. we can simply calculate with what they are.
you remember,
a/b × c/d = (a×c)/(b×d)
therefore,
13/5 × 13/4 = (13×13)/(5×4) = 169/20 =
= (8×20 + 9)/20 = 8 9/20
the area of the rectangle is 8 9/20 in²
Question 3(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
Which of the following graphs has a slope of negative three halves and a y-intercept of 3?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.
What is the point-slope form?Mathematically, the point-slope form of any straight line can be calculated by using this expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on this line:
Points on x-axis = (0, 2).Points on y-axis = (3, 0).At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 3 = (0 - 3)/(2 - 0)(x - 0)
y - 3 = -3/2(x)
y = -3x/2 + 3
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Answer:
Step-by-step explanation:
A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.
What is the point-slope form?
Mathematically, the point-slope form of any straight line can be calculated by using this expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.
x and y represents the data points.
From the information provided above, we have the following slope and data points on this line:
Points on x-axis = (0, 2).
Points on y-axis = (3, 0).
At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 3 = (0 - 3)/(2 - 0)(x - 0)
y - 3 = -3/2(x)
y = -3x/2 + 3
Can someone please help me with this math problem it is so confusing? The math problem is located in the picture, Thanks!
Domain:
Range:
The domain is the set of all x-values (or inputs) used by the function. In a graph like this, you want to see how the graph lines up with the x-axis.
As an interval, the domain is [-4,-1], as shown on the domain graph.
(Remember to write intervals from lesser-to-greater.)
The range is the set of all y-values (or outputs) used by the function. In a graph like this, you want to see how the graph lines up with the y-axis.
As an interval, the range is [-4,-2].
(Again, remember to write intervals from lesser-to-greater.)
Please help as fast as you can???
Answer:
Nabila has $25 dollars.
Hasan has $19 dollars.
Tarek has $50 dollars.
Step-by-step explanation:
Let's say Hasan has "x" dollars at first. The question tells us that Nabila has six more dollars than Hasan has. This means that Nabila has "x + 6" dollars. The last given information is that Tarek has two times what Nabila has. So, Tarek has "2x + 12" dollars, basically.
Then, we can add up all these amounts to find out the result for each person.
[tex]4x + 18 = 94\\x = 19[/tex]We found what is "x". This means that we actually found the answer.
Hasan had "x" dollars so he has $19 dollars.
Nabila had "x + 6" dollars so she has $25 dollars.
Finally, Tarek had "2x + 12" dollars or two times of what Nabila has so he has $50 dollars.
What type of triangle is a 3 4 5 triangle?.
A triangle with a right angle is a 3 4 5 triangle.
A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.
The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.
So the right angle triangle is a triangle with sides of 3, 4, and 5.
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Sally has 4 yards of a ribbon. How many 1/6 yard pieces can she cut?
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Viewer's Age Group
Excellent
Good
Average
Poor
Marginal Total
16-25
52
42
12
113
26-35
33
50
9
97
36-45
58
12
28
34
132
16-55
25
17
22
12
76
564
12
8
28
Marginal Total
180
126
70
70
446
Note: A rating of good or excellent means the audience liked the movie, while rating of poor means the audience disliked the
movie
A movie producer conducted a survey after : preview screening of her new movie to find out how the film would be received by viewers from different
age groups. The table shows the numbers of viewers in different age groups who rated the film excellent, good, average; and poor.
Out of the total respondents, the percentage of respondents from the 46-55 age group who rated the film excellent is
to two decimal places.
% Write your answer up to two decimal places.
The equation -3p + (1/8) = (- 1/4) holds true for p = 0.125.
Write your answer up to two decimal places ?The equation is as follows:
-3p + ( 1/8 ) = ( - 1/4 )
The denominators of the two terms are different on the left-hand side of the equation.
The LCM of 1 and 8 is therefore 8.
Therefore,
- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )
- 24p / 8 + 1 / 8 = - 1 / 4
( - 24p + 1 ) / 8 = - 1 / 4
Add 8 to both sides of the equation now.
We get,
[ ( - 24p + 1 ) / 8 ]
× 8 = ( - 1 / 4 ) × 8
- 24p + 1 = - 8 / 4
- 24p + 1 = - 2
Add 1 to each side of the equation, then
- 24p + 1 - 1 = - 2 - 1
-24p = - 3
Subtract 24 from each side of the equation now.
- 24p / 24 = - 3 / 24
- p = ( - 1 / 8 )
On each side of the equation, multiply by -1.
( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 ) ( - 1 )
p = 1 / 8
p = 0.125
The equation will be true for p = 0.125.
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How many terms are in the polynomial?
6-7x² + 3x
Enter only a number.
The sum of terms with the notation kxn, where k is any number and n is a positive integer, is referred to as a polynomial.
What number of terms makes up the polynomial?The following expressions are polynomials:
A. 6y^2 + 5x
D. (7y^2 + 9x) / 4
Describe polynomials.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.
Any polynomial must have variable exponents that are non-negative integers.
Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
These expressions are now:
A. 6y^2 + 5x
B. (7x^2 + 8) / 4x
C. (y^2 + 3x ^1/3) / 4
D. (7y^2 + 9x) / 4
Here, we can observe that there are just two polynomial expressions.
A. 6y^2 + 5x
D. (7y^2 + 9x) / 4
The non-polynomial expressions include,
B. (7x2 + 8/ 4x) contains a variable in the numerator.
C. (y2 + 3x 1/3) / 4 - This exponent has a fractional exponent.
Consequently, the polynomial expressions are,
A. 6y^2 + 5x
D. (7y^2 + 9x) / 4
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How much higher i checkpoint 4 than checkpoint 3. If checkpoint 4 i -99 and checkpoint 3 i -207
Checkpoint 4 will be higher than Checkpoint 3 by 108.
In our question, it is given that the Checkpoint 4 value is -99 and the Checkpoint 3 value is -207.
We will use Subtraction. What is Subtraction?
The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).
The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller. For instance, your friends consumed 7 of the 9 cupcakes you purchased for your birthday party. You are now down to two cupcakes. This can be expressed as a subtraction formula: 9 - 7 = 2, which means "nine less seven equals two." The result of subtracting 7 from 9 is 2, or (9 - 7) Here, we divided two numbers, 9, and 7, by one another to get the difference of 2.
Subtracting the value of Checkpoint 3 from Checkpoint 4, we get:
Checkpoint - Checkpoint 3 = -207 -(-99)
= -207 + 99 = 108.
Therefore Checkpoint 4 will be higher than Checkpoint 3 by 108.
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A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number greater than 4.
17 over 60
18 over 60
24 over 60
For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is, 18/60.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
Total number of tossing a number cube = 60
Here, Number of times greater than 4 comes up = 10 + 8 (frequency of is 10 and frequency of 6 is 8)
Hence, Number of times greater than 4 comes up = 18
Thus, Probability of getting number greater than 4
= (frequency of getting 5 and 6) / (total number of trials)
Hence, Probability of getting number greater than 4 = 18 / 60
Therefore, For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is 18/60.
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There were 9,600 tourists on the beach that day but only 12 of them were buried up to their neck in sand. What percent of the tourists were buried up to their neck in sand ?
Answer:
.125%
Step-by-step explanation:
Answer:
To find the percent of tourists buried up to their neck in sand, you can divide the number of buried tourists by the total number of tourists and multiply by 100.
12 buried tourists / 9,600 total tourists = 0.00125
0.00125 x 100 = 0.125 or 12.5%
So, 12.5% of the tourists were buried up to their neck in sand.
In 1940, a coat cost $25.00. Thirty years later, the price increased by 310%. How much more did a coat sell for thirty years later?
Please answer and explain the answer I will mark brainlisest
Answer:
$77.5
Step-by-step explanation:
Has risen in price BY 310% To mean its price has added 310% from the old price:
Price new = Price old + (Price old × 310%).
To calculate the difference, we just need to calculate 310% of the old price (a percentage is a hundredth):
$25 × 310% = $25 × 3.1 = $77.5
A parallelogram is a _____ polygon in which both pairs of opposite sides are parallel.
Answer:
Quadrilateral
Step-by-step explanation:
I remember learning this in math class. A parallelogram has two dimensions. Each of its four sides has two parallel pairs. The parallel sides have the same length.
How do you find the product?.
Answer: You multiply the 2 given numbers together
Step-by-step explanation: I hope this helped!
How do you write algebraic expressions and equations?.
Algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations.
Algebraic expressions: An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. For example, 3x + 2y is an algebraic expression that contains the variables x and y and the operations of addition and multiplication.
Algebraic equations: An algebraic equation is a statement that shows two algebraic expressions are equal. For example, 3x + 2y = 12 is an algebraic equation that shows the left-hand side (3x + 2y) is equal to the right-hand side (12).
To write an algebraic expression or equation, you need to follow these steps:
Identify the numbers and variables in the problem.
Write the problem using mathematical symbols and operations.
Use the correct order of operations (PEMDAS) to simplify the expression or equation.
Use the equal sign (=) to write the equation.
For example, if you are given the problem "Three times a number plus two times another number equals 12", you can write the algebraic equation as:
3x + 2y = 12
In this equation, x and y are the variables and 3 and 2 are the coefficient. The equation represents the relationship between x and y and it can be used to solve for one of the variables if the other one is known.
Therefore, In short, algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations. To write an algebraic expression or equation, you need to identify the numbers and variables in the problem, use mathematical symbols and operations, use the correct order of operations and use the equal sign (=) to write the equation.
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The product of 8 and four times m
Find an equation of the plane consisting of all points that are equidistant from (1, 4, 4) and (-4, 1, 2).
the required equation is 5x - 6y + 5z = 7
Given that;
points : (1, 4,4) and (-4, 1,2).
mid point : ( [(1-4)/2], [(4-1)/2], [(4+2)/2]
⇒ midpoint : ( -3/2, 3/2, 3 )
x₀ y₀ z₀
Direction vector n = [-4-(1)], [ 1-4], [ 2-4]
⇒ Direction vector n = < -5, -3, -2 >
General equation plane : n(x-x₀, y-y₀, z-z₀) = 0
so we substitute
⇒ (-5,-3,-2) (x-3/2, y-(-2), z-(-5/2) ) = 0
⇒ (-5,-3,-2) (x - 3/2, y + 2, z + 5/2) ) = 0
⇒ 5(x - 3/2) - 6(y + 2 ) + 5(z + 5/2) = 0
⇒ 5x - 15/2 - 6y - 12 + 5z + 25/2 = 0
⇒ 5x - 6y + 5z = 15/2 + 12 - 25/2
⇒ 5x - 6y + 5z = 7
Therefore, the required equation is 5x - 6y + 5z = 7
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Twenty five car can take the ferry acro the river at one time if 150 car took the ferry and it wa full each time how many time did the ferry cro the river
By applying the division formula, the number of times the ferry crossed the river would be 6 times.
To divide something means to split it into two or more equal pieces, areas, classes, categories, groups, or divisions. Dividing something means to give each component to a separate group, or to create equal parts from the whole. When doing division, the resulting value may or may not be an integer. The final result may occasionally be expressed as a decimal.
To calculate the division, we can use this following formula:
Dividend ÷ Divisor = Quotient + Remainder.
Where:
Dividend = the number, which is being divided
Divisor = the number, which divides the number (dividend) into equal parts
Quotient = the result of the division operation
Remainder = the leftover number in the division operation.
In this case, we are given that:
Dividend = 150
Divisor = 25
Thus, the number times the ferry crossed the river would be:
= 150 ÷ 25
= 6
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You have found the following ages (in years) of all 5 zebras at your local zoo:
8, 11, 17, 7, 19
What is the average age of the zebras at your zoo? What is the standard deviation? Round your
answers to the nearest tenth.
Average age:
years old
Standard deviation:
years
Show Calculator
Answer:Answers below
Step-by-step explanation:
The average age of the zebras at the zoo can be found by adding up all of the ages and dividing by the number of zebras.
In this case, the ages of the zebras are 8, 11, 17, 7, 19.
To find the average age, we add up all of the ages: 8 + 11 + 17 + 7 + 19 = 62
Then we divide by the number of zebras (5): 62/5 = 12.4
So, the average age of the zebras at the zoo is 12.4 years old.
To find the standard deviation, we first need to find the variance.
The variance is the average of the squared differences from the mean.
We can find the variance by taking each value, subtracting the mean, squaring the result, and dividing by the number of zebras.
The standard deviation is the square root of the variance
So, the standard deviation of the zebras age is difficult to calculate by hand, but we can use a calculator to find the standard deviation, which is approximately 4.345 years.
Rounding to the nearest tenth:
The average age is 12.4 years old
The standard deviation is 4.3 years
4 bags of candy each contain 5 butterscotch candies and some
peppermint candies.Altogether, the bags contain 52 candies.
The required number of Peppermint candies in each bag is 8.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the number of peppermint candies be x in each bag,
Butterscotch candies in 5 bags = 5 × 4 = 20 candies
Peppermint candies in 5 bags = x × 4 = 4x candies
According to the quesiton, Altogether, the bags contain 52 candies.
20 + 4x = 52
x = 8
Thus, the required number of Peppermint candies in each bag is 8.
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Elizabeth has 1 7/10 as many plants as Rosalie has in her garden. If Elizabeth has 51 plants, how many plants does Rosalie have in her garden?
10x+7y=263
4x+8y=230
Solve system of equations
Answer: (9.5, 24)
Step-by-step explanation:
10x + 7y = 263 (1)
4x + 8y = 230 (2)
Multiply (1) by 4 and (2) by 10:
40x + 28y = 1052 (3)
40x + 80y = 2300 (4)
Do (4) - (3):
52y = 1248
y = 24
x = 9.5
(x, y) = (9.5, 24) :>
