A farmer has two pieces of land in a parallelogram shape on the same base. He grows vegetables and flowers in two triangular pieces of land as shown in diagram.
Q: Check whether the two triangular pieces of land are equal in area.
Answers
Step-by-step explanation:
In trapezoid ABCF, AB || CF.
Therefore, parallelograms ABEF & ABCD have same height and lie on the same base AB.
[tex] \therefore Ar(\parallel^{gm} ABEF) = Ar(\parallel^{gm}ABCD)\\... (1)\\\\
\because\: Ar(\parallel^{gm} ABEF) \\=Ar(\triangle AFD) + Ar(\square \: ABED)....(2) \\\\
\&\: Ar(\parallel^{gm}ABCD)\\= Ar(\triangle BCE) +Ar(\square ABED)....(3) [/tex]
From equations (1), (2) & (3), we find:
[tex] Ar(\triangle AFD) + Ar(\square \: ABED) \\ = Ar(\triangle BCE) +Ar(\square ABED)
\\ \\ \purple {\boxed {\therefore Ar(\triangle AFD) = Ar(\triangle BCE)}}
\\ [/tex]
Thus, the two triangular pieces of land are equal in area.
Hence proved.
Related Questions
What is the measure of angle x
Enter your answer in the box
Answers
x = 83°
Solution:
The reference image to the answer is given below.
Sum of the adjacent angles in a straight line = 180°
⇒ ∠1 + ∠2 + ∠3 = 180° (Refer image)
⇒ 56° + ∠2 + 41° = 180°
⇒ 56° + 41° + ∠2 = 180°
⇒ 97° + ∠2 = 180°
⇒ ∠2 = 180° – 97°
⇒ ∠2 = 83°
In the given image ∠5 and ∠2 are vertically opposite angles.
Vertical angle theorem:
Vertically opposite angles are equal.
⇒ ∠5 = ∠2
⇒ x = ∠2
⇒ x = 83°
Hence the measure of angle x is 83°.
Which choice shows the coordinates of C’ if the trapezoid is reflected across the y-axis?
On a coordinate plane, trapezoid A B C D has points (2, 1), (3, 5), (5, 3) and (3, 1).
(–5, 3)
(3, –5)
(5, –3)
(–3, 5)
Answers
The coordinates of C’ is (-5,3), the correct option is A.
How does reflection across axis work?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.
If you study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
Thus, if you're reflecting a point (x,y) along x axis, then its x
abscissa will stay same but y
ordinates will negate. Thus (x,y) turns to (x, -y)
Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)
Given;
On a coordinate plane, trapezoid A B C D has points (2, 1), (3, 5), (5, 3) and (3, 1).
Now,When a point is reflected across the y-axis, the rule is:
(x,y)→ (-x,y)
C (5.3)= C' (-5,3)
Therefore, the reflection on C will be C (5.3) C' (-5,3).
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Which describes how to graph h (x) = negative RootIndex StartRoot x + 8 EndRoot by transforming the parent function?
Reflect the parent function over the y-axis, and translate it 3 units to the right.
Reflect the parent function over the y-axis, and translate it 3 units to the left.
Reflect the parent function over the x-axis, and translate it 8 units to the right.
Reflect the parent function over the x-axis, and translate it 8 units to the left.
Answers
Answer:
Reflect the parent function over the x-axis, and translate it 8 units to the left.
Step-by-step explanation:
The given function is
[tex]y = - \sqrt{x + 8} [/tex]
The parent function is
[tex]y = \sqrt{x} [/tex]
Since there is a negative multiply the transformed function, there is a reflection in the x-axis.
Since 8 is adding, within the square root, there is a horizontal translation of 8 units to the left.
Therefore to graph the given function, reflect the parent function over the x-axis, and translate it 8 units to the left.
Take the reflection of the graph about the x-axis and then translate the graph of the function by 8 units in the left direction and this can be determined by using the rules of transformation.
Given :
Function -- [tex]\rm y = - \sqrt{x+8}[/tex]
The following steps can be used in order to determine the correct statement:
Step 1 - The parent function is given below:
[tex]\rm y = \sqrt{x}[/tex]
Step 2 - Now, draw the graph of the parent function.
Step 3 - Take the reflection of the graph about the x-axis. So, the function becomes:
[tex]y =- \sqrt{x}[/tex]
Step 4 - Now, translate the graph of the function obtained in the above step by 8 units in the left direction. So, the function becomes:
[tex]y = -\sqrt{x+8}[/tex]
Therefore, the correct option is D).
For more information, refer to the link given below:
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The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74 . Find their ages.
Answers
Answer:
The age of Noelle's dad is 54 years and that of Noelle is 20 years.
Step-by-step explanation:
Let the age of Noelle's dad is x years and that of Noelle is (74 - x) years.
{Since, the sum of their ages is 74}
Now, given that the age of Noelle's dad is 6 less than 3 times Noelle's age.
So, 3(74 - x) - 6 = x
⇒ 4x = 222 - 6 = 216
⇒ x = 54
So, the age of Noelle's dad is 54 years and that of Noelle is (74 - 54) = 20 years. (Answer)
Another submarine descent can be represented as y= -240 x where y is the elevation and x is time in hours. How long will it take this submarine to make the descent
Answers
Answer:
8.75h
Step-by-step explanation:
8.75 hours will be taken by the submarine to make the descent.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a submarine’s descent can be represented as y = -240x, where y is the elevation and x is time in hours.
We need to find the the time it will take this submarine to make the descent to the seafloor 2,100 feet below the surface
Since the submarine to make the descent to the seafloor 2,100 feet below the surface
So y = - 2100
So y = - 240x gives
- 2100 = - 240x
Divide both sides by -240
x=8.75
Hence, 8.75 hours will be taken by the submarine to make the descent
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In a short story, a character decides to distance himself
from his family by moving away. When he does, life
becomes difficult. He realizes how often he had relied on
his family for support and encouragement. In order to
respect his plea for independence, his family had refrained from contacting him. In the end, the character moves back to his hometown and is happier because of it.
Which common literary theme is best illustrated by the passage?
Answers
Answer:
A)
Step-by-step explanation:
The theme is a message that the story was trying to portray. In the story, it seems that the character realizes that his home life and family matter more to him than he thought which is why he moved back to his hometown and became happy from that. He moved away thinking that life would be better without his family and soon regrets it.
Barbara is 142 cm tall. This is 2 cm less than 3 times
her height at birth. Find her height at birth.
Answers
Final answer:
Using an algebraic approach, we found out that if Barbara is 142 cm tall, which is 2 cm less than three times her birth height, then her height at birth was 48 cm.
Explanation:
The question asks us to determine Barbara's height at birth given that she is currently 142 cm tall and that this height is 2 cm less than three times her height at birth. To find her height at birth, we can construct and solve a simple algebraic equation based on this information.
Let h represent Barbara's height at birth. The problem states that:
142 cm = 3h - 2 cm
Adding 2 cm to both sides of the equation, we get:
144 cm = 3h
Dividing both sides of the equation by 3 so we can solve for h, gives us:
h = 144 cm / 3
h = 48 cm
Therefore, Barbara's height at birth was 48 cm.
An airplane flying at a velocity of 610 m/s lands and comes to a complete stop
over a 53 second period.
a) Did this airplane speed up or slow down? Explain your reasoning.
b) Did this airplane accelerate or decelerate? Explain your reasoning.
c) Should your answer be positive or negative? Explain your reasoning.
d) Calculate the acceleration.
Answers
A) The airplane slowed down. It states that the plane lands and come to a complete stop over a 53 second period.
B) It decelerates. The speed doesn't increase. It slows down.
C) The answer should be positive. Although the deceleration is slowing down the plane, it's not going at a negative speed.
D) The answer is 11.5m/s. I divided the velocity by the amount of seconds it takes to make a complete stop.
The following information should be considered;
A) The airplane falled down. It states that the plane lands and come to a complete stop over a 53 second period.
B) It decelerates. The speed doesn't increase. It slows down.
C) The answer should be positive. The deceleration is slowing down the plane, it's not going at a negative speed.
D) The answer is 11.5m/s. I divided the velocity by the amount of seconds it takes to make a complete stop.
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Which equation represents the line shown in the graph below ? *20 points* I NEED IT ASAP !!!
Answers
Answer:
B
Step-by-step explanation:
x = 5
y = -3 What is the solution to the system of equations?
Answers
Answer:
y=5m-3
Step-by-step explanation:
The product of a non-zero rational number and an irrational number can always be
Answers
Answer:
The product of a non-zero rational number and an irrational number will always be an irrational number.
Step-by-step explanation:
Here's a proof by contradiction for this claim.
Consider an irrational number [tex]x[/tex]. Assume by contradiction that this claim isn't true. In other words, assume that there exist a non-zero rational number [tex]y[/tex] such that [tex]x \cdot y[/tex] is a rational number.
By the definition of rational numbers, a number is a rational number if and only if it can be written as the quotient of two integers.
[tex]y[/tex] is a rational number ⇔ there exist two integers [tex]a[/tex] and [tex]b[/tex] such that [tex]\displaystyle y = \frac{a}{b}[/tex].[tex]x \cdot y[/tex] is a rational number ⇔ there exist two (other) integers [tex]c[/tex] and [tex]d[/tex] such that [tex]\displaystyle x \cdot y = \frac{c}{d}[/tex].Divide [tex]y[/tex] from both sides of the equation:
[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/y[/tex].
The left-hand side of this equation is now equal to [tex]x[/tex].
Since [tex]\displaystyle y = \frac{a}{b}[/tex] by assumption, the [tex]y[/tex] on the right-hand side of this equation can be replaced with [tex]\displaystyle \frac{a}{b}[/tex]. Hence, the right-hand side of this equation would become
[tex]\displaystyle \frac{x\cdot y}{y} = \left.\frac{c}{d}\right/\frac{a}{b} = \frac{c}{d}\cdot \left(\frac{b}{a}\right) = \frac{b \cdot c}{a \cdot d}[/tex].
Combine the two sides of the equation to obtain:
[tex]x = \displaystyle \frac{b \cdot c}{a \cdot d}[/tex].
Since [tex]b[/tex] and [tex]c[/tex] are both integers, their product [tex]b \cdot c[/tex] would also be an integer. Similarly, since [tex]a[/tex] and [tex]d[/tex] are both integers, their product [tex]a \cdot d[/tex] would also be an integer.
In other words, [tex]x[/tex] can now be represented as the quotient of two integers. By the definition of rational numbers,
Hence, the original assumption that this claim isn't true, is not true. That verifies the claim that the product of a non-zero rational number and an irrational number would be an irrational number.
8 cm
5 cm
10 cm
12 cm
Find the area of the figure.
41 cm
90 cm2
95 cm
100 cm?
Answers
Answer:
its 90cm^2
Step-by-step explanation:
hope d answer will help u
what is maximum and minimum of f(x)=7x^2
Answers
Answer:
Minimum value is 0
Maximum value is undefined.
Step-by-step explanation:
The given function is [tex]f(x)=7x^2[/tex]
This function is a parabola that has its vertex at the origin.
The coefficient of the quadratic term is 7, which is greater than zero.
This means that, the graph will open up.
The graph will therefore have a minimum value of y=0
The graph of this function does not have a maximum value.
URGENT! PLEASE HELP!
Find the roots of f(x)=x^2+10x−96
Question 6 options:
x=8 or x=−12
x=6 or x=−16
x=−6 or x = 16
x =8 or x =12
Answers
Answer:
the answer is x=6 or x=-16
The correct answer is x = 6 or x = -16.
To find the roots of the quadratic function f(x) = x2 + 10x - 96, we need to solve the equation x2 + 10x - 96 = 0 using the quadratic formula.
Using the quadratic formula, x = (-b ± √(b2 - 4ac)) / 2a, where a = 1, b = 10, and c = -96, we get x = 6 or x = -16 as the roots of the function f(x).
Therefore, the correct answer is x = 6 or x = -16.
The revenue each season from tickets at the theme part is represented by t(x) = 5x. The cost to pay the employees each season is represented by r(x) = (1.5)x. Examine the graph of the combined function for total profit and estimate the profit after four seasons.
Answers
Answer:
14
Step-by-step explanation:
The revenue earned is represented by t(x)=5x. Since the equation asks for the profit after four seasons you fill in 4 for x and get 20. r(x)=(1.5)x is how much it costs to pay their employees each season so you fill in 4 for x. Now you take revenue earned and subtract it by the cost to pay employees and you get the profit.
5x - 1.5x = Profit
5(4) - 1.5(4) = Profit
20 - 6 = Profit
14 = Profit
Answer:
15
Step-by-step explanation:
Supria and Elle live 21 miles apart. They leave their respective homes at the same time to go for
a jog. They begin running toward each other with the intent of meeting. Supria runs at a
constant rate of 8 miles per hour and Elle runs at a constant rate of 8 miles per hour. A third
friend starts at Supria's house and rides her bike toward Elle's house and rides her bike toward
Elle's house at a constant rate of 10 miles per hour. How far will the bicyclist have ridden when
Supria and Elle finally meet?
Answers
Answer:
[tex]d3=13.125[/tex] [tex]miles[/tex]
Step-by-step explanation:
Given data:
[tex]total[/tex] [tex]distance = 21[/tex] [tex]miles[/tex]
[tex]s1=8[/tex] [tex]miles/hr[/tex]
[tex]s2=8[/tex] [tex]miles/hr[/tex]
[tex]s3=10[/tex] [tex]miles/hr[/tex]
First we have to find out the how much time it takes when Supria and Elle meet.
As we know,
[tex]Displacement=rate*time[/tex]
[tex]d1=s1*t[/tex]
[tex]d2=s2*t[/tex]
[tex]d1+d2=21[/tex]
[tex]8t+8t=21[/tex]
[tex]16t=21[/tex]
[tex]t=21/16[/tex]
Now we can find that how much the third friend had traveled during this time period
[tex]d3=s3*t[/tex]
[tex]d3=10*21/16[/tex]
[tex]d3=13.125[/tex] [tex]miles[/tex]
Write an equation that you can use to find the value of x. Perimeter of square: 30 mm An equation that you can use is =30.
Answers
Answer:30=4x
Step-by-step explanation:
HELP NOW PLS what is (x+6)
Answers
x+6 is x+6. It's an expression. Not sure what you need help with.
Answer:
You set the problem =0, so (x+6)=0.
Then, you do the inverse to get x alone. 6-6(cancels out) and 0-6 is -6.Now your equation should look like x=-6 and you’re done.
Step-by-step explanation:
What is the value of F(x) = 4x+9
When x= 5
Answers
Answer:
f(5) = 29
Step-by-step explanation:
Step 1: Identify the function
f(x) = 4x + 9
Step 2: Let x equal 5 in the function
f(5) = 4(5) + 9
Step 3: Multiply
f(5) = 20 + 9
Step 4: Add
f(5) = 29
Answer: 29
Answer:
[tex]F(x)=29[/tex]
Step-by-step explanation:
Given function:
[tex]F(x) = 4x+9[/tex]
Find F(x) at , [tex]x= 5[/tex]
The value of 'x' is given for which we have to find the value of F(x)
Putting the given 'x' in the function equation
[tex]F(x) = 4x+9\\\\ F(x) = 4(5)+9\\\\ F(x) = 20+9\\\\ F(x) = 29[/tex]
So , [tex]F(x)=29[/tex] at [tex]x=5[/tex]
In the linear equation y=4x +2, the value “2” represents which of the following?
Answers
Answer:
The y-intercept
Answer:
b
Step-by-step explanation:
I am thinking it would be "b" because y=mx+b so not the multiple choice but whichever one says b
A tank has 15 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)
Define a function f that determines the number of gallons of water in the tank, f ( w ) , in terms of the number of pounds of water that have drained from the tank since the tank started draining, w .
Answers
Answer:
[tex]f(w) = 15 - \frac{w}{8345}[/tex]
Step-by-step explanation:
Water begins draining from a tank when the tank has 15 gallons of water in it.
Now, if we define f(w) as a function that represents the number of gallons of water remains in the tank after w pounds of water that have drained from the tank since the tank started draining, then the function can be represented as
[tex]f(w) = 15 - \frac{w}{8345}[/tex]
Since, w pounds of water is equivalent to [tex]\frac{w}{8345}[/tex] gallons of water. (Answer)
(Recall that water weighs 8.345 pounds per gallon.)
The function f should be defined is [tex]f(w) = 15 - \frac{w}{8345}[/tex]
Important information:A tank has 15 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)
Function:Since we have to defined the function so it is f(w) that shows the number of gallons of water remains in the tank after w pounds of water.
So, the function should be [tex]f(w) = 15 - \frac{w}{8345}[/tex]
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Mutliply x - 3 and x + 3
Answers
Answer:
Step-by-step explanation:
(x-3)*(x+3)
we begin by expanding and then simplifying
= (x²+3x-3x-9)
= x² - 9
Answer:
x² - 9
Step-by-step explanation:
hello :
(x - 3 ) (x + 3) = x²+3x-3x-9
(x - 3 ) (x + 3) = x² - 9
20. Math and Science There are 6 pure
spectral colors: red, orange, yellow, green,
blue, and violet. Some animals cannot
see all of these colors. Bees cannot see
orange or red. What fraction of the pure
spectral colors can bees see?
Answers
2/1 frptrhgqhgr4tjtfix jxcfh8u5t8ofszYI7wyt439tfy7efgy5g
Final answer:
Bees can see 4 out of the 6 pure spectral colors, which simplifies to the fraction 2/3 after removing the 2 colors they cannot see, orange and red.
Explanation:
The question involves calculating a fraction, which is a basic mathematical concept. We are told there are 6 pure spectral colors: red, orange, yellow, green, blue, and violet. Bees cannot see orange or red, so we must find out what fraction of the 6 pure spectral colors bees can see. We subtract the 2 colors bees can't see (orange and red) from the total of 6, leaving us with 4 colors they can see which are yellow, green, blue, and violet.
To express this as a fraction, we take the number of colors bees can see (4) and place it over the total number of pure spectral colors (6). Therefore, the fraction of pure spectral colors that bees can see is 4/6. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Thus, the simplified fraction is 2/3.
Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is “normal”, have many of each type of animal does he have
Answers
Answer:
He have 47 ducks and 7 cows.
Step-by-step explanation:
Given:
Farmer Jones raises ducks and cows.
He looks out his window and sees 54 animals with a total of 122 feet.
Now, to find the each type of animal he have.
Let the number of ducks be [tex]x.[/tex]
And the number of cows be [tex]y.[/tex]
So, total number of animals are:
[tex]x+y=54[/tex]
[tex]x=54-y[/tex] ....( 1 )
As, the feet of cows are 4 and ducks are 2.
Now, the total number of feet are:
[tex]2(x)+4(y)=122[/tex]
[tex]2x+4y=122[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]2(54-y)+4y=122[/tex]
[tex]108-2y+4y=122[/tex]
[tex]108+2y=122[/tex]
Subtracting both sides by 108 we get:
[tex]2y=14[/tex]
Dividing both sides by 2 we get:
[tex]y=7.[/tex]
The number of cows = 7.
Now, to get the number of ducks we substitute the value of [tex]y[/tex] in equation (1):
[tex]x=54-y\\x=54-7\\x=47.[/tex]
The number of ducks = 47.
Therefore, he have 47 ducks and 7 cows.
Expand the following expression.
2/5(2x-7)
(just checking again)
Answers
Answer:
b
Step-by-step explanation:
2 x 2 = 4/5
2 x -7 = -14 / 5
Answer:
B) 4/5x-14/5
Step-by-step explanation:
2/5(2x-7)
2/5*2x= 4/5x
2/5*7=14/5
Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s).
What is the mean of the given distribution, and which type of skew does it exhibit?
{4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2}
The mean of the distribution is
, and it exhibits a
skew.
Answers
Mean = 3.25
Solution:
Step 1 : Given data:
4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2
Step 2:
Sum of the numbers
= 4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2
= 52
Sum of the numbers = 52
Number of terms = 16
Step 3:
[tex]$\text{Mean}=\frac{\text{Sum of the numbers}}{\text{Number of terms}}[/tex]
[tex]$=\frac{52}{16}[/tex]
= 3.25
Mean = 3.25
Mean of the distribution is 3.25.
Answer: Mean= 3.25 with a POSITIVE skew
Step-by-step explanation:
edmentum
Write an equation in point-slope form for the line that has a slope of 56 and contains the point (−8,−4).
Answers
Step-by-step explanation:
Given: slope of line m = 56 & line contain point is (−8,−4).
[tex] \therefore (x_1, \:\: y_1) = (-8, \:\: - 4)[/tex]
Equation of line in slope point form is given as:
[tex]y - y_1 =m(x - x_1) \\ \\ \therefore \: y - ( - 4) = 56 \{x - ( - 8) \} \\ \\ \blue{ \boxed{\therefore \: y + 4= 56 (x + 8) }}\\ ..(this \: is \: the \: equation \: of \: line \: in \: \\ slope \: point \: form)\\ \\ \therefore \: y + 4= 56x + 56 \times 8 \\ \\ \therefore \: y + 4= 56x + 448 \\ \\ \therefore \: y = 56x + 448 - 4 \\ \\ \huge \red{ \boxed{\therefore \: y = 56x + 444 }}\\ ..(this \: is \: the \: equation \: of \: line \: in \: \\ slope \: intercept \: form)[/tex]
Answer:
y+4 = 56(x+8)
Step-by-step explanation:
y-y1 = m(x-x1)
y-(-4) = 56(x-(-8))
y+4 = 56(x+8)
If needed, simply it further
y+4 = 56x+448
y = 56x+444
Write the expression in standard form.
(4f-3+2g)-(-4g+2)
Answers
To write the given expression (4f-3+2g)-(-4g+2) in standard form, change the signs of the terms subtracted and combine like terms to simplify to 4f + 6g - 5.
Explanation:To write the expression in standard form, you need to simplify the expression by combining like terms and handling the subtraction of negative numbers properly. Given the expression (4f-3+2g)-(-4g+2), you first remove the parenthesis while changing the signs of the terms inside the parenthesis being subtracted.
The expression -(-4g+2) will become +4g-2 once we apply the rule that subtracting a negative is the same as adding a positive, similarly to the example 2-(-6)=2+6=8.
Now the expression is simplified to 4f - 3 + 2g + 4g - 2. We combine like terms to get 4f + 6g - 5.
The standard form of the given expression is 4f + 6g - 5.
The expression (4f-3+2g)-(-4g+2) can be simplified using the distributive property and combining like terms.
First, distribute the negative sign to the terms inside the parentheses: (-1) * (-4g) = 4g and (-1) * 2 = -2.
The expression becomes (4f-3+2g) + (4g-2).
Next, combine like terms: 4g + 2g = 6g, and -3 - 2 = -5.
The final expression in standard form is 4f + 6g - 5.
Find the sum 5/10 + 3/100 =
Answers
Answer:
0.53
Step-by-step explanation:
5/10 + 3/100=0.53
Answer:
0.53
Step-by-step explanation:
5/10 + 3/100
by Elysium
(50 +3)/100
53/100
0.53
Write a number of your choice, using the following clues:
a two digit number
greater than 40
divisible by both 2 and 3
Answers
Answer:
42 and 72
Step-by-step explanation: