The maximum height reached is greater than 12m, hence the ball reach a height of 12m
The height of the toy cannon all launched is expressed as [tex]h(t) = -5t^2 + 20t + 4[/tex]
h is the height reached by the ball
t is the time taken by the ball to reach its maximum height
A) In order to determine whether the ball reached the height of 12m, we will have to substitute h = 12 into the formula as shown:
[tex]12= -5t^2 + 20t + 4\\ -5t^2 + 20t + 4 -12=0\\ 5t^2 - 20t +8=0\\[/tex]
Hence the equation that can be used to tell whether the ball reaches a height of 12 is [tex]5t^2-20t+8=0[/tex]
B) At the maximum height
dh/dt = 0
-10t + 20 = 0
-10t = -20
t = 20/10
t = 2
Get the maximum height reached
h(2) = -5(2)^2 + 20t + 4
h(2) = -5(4) + 20t + 4
h(2) = -20 + 20(2) + 4
h(2) = -20+40+4
h(2) = 24 m
Since the maximum height reached is greater than 12m, hence the ball reach a height of 12m
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To determine whether the ball reaches a height of 12 meters, we set the height equation equal to 12 and solve the quadratic equation. Upon solving, we find that the ball reaches 12 meters, hence the answer to whether the ball reaches 12 meters is yes.
Explanation:To determine whether the toy cannon ball reaches a height of 12 meters, we can set the height equation h(t) equal to 12 meters:
12 = -5t^2 + 20t + 4.
To solve for t, we need to rearrange the equation and solve the resulting quadratic equation:
0 = -5t^2 + 20t + 4 - 12
0 = -5t^2 + 20t - 8
This is the equation that can be used to tell whether the ball reaches a height of 12 meters. To determine if the ball does reach 12 meters, we solve for the roots of the equation:
-5t^2 + 20t - 8 = 0
Using the quadratic formula, we find the possible values for t. If there are real, positive solutions, it means the ball does reach 12 meters at those times.
Upon solving, we find that the ball indeed reaches a height of 12 meters because there are real, positive solutions for t.
Therefore, the answer to Part B is yes; the ball does reach a height of 12 meters.
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Franklin Construction Company build a sidewalk around two sides of a new library, as shown in the figure. what is the area of the sidewalk.
please help
Answer:
[tex]630.36\ ft^2[/tex]
Step-by-step explanation:
we know that
To find out the area of the sidewalk, multiply the length by the width of the sidewalk
The width of the sidewalk is equal to
[tex]113.4\ ft-110\ ft=3.4\ ft[/tex]
or
[tex]75.4\ ft-72\ ft=3.4\ ft[/tex]
The area is equal to
[tex]113.4(3.4)+72(3.4)\\385.56+244.8\\630.36\ ft^2[/tex]
Three points of a function are graphed.
A coordinate plane with 3 points plotted at (10, 18), (14, 24), and (18, 30).
Which statement describes the function through the points?
The function is a direct variation function with a constant of variation of 1.5.
The function is a direct variation function with a constant of variation of 1.8.
The function is linear but is not a direct variation function.
The function is not a linear function.
The function through the points (10, 18), (14, 24), and (18, 30) is a direct variation function with a constant of variation of 1.8.
Explanation:In this case, we have a linear function. We can determine this by checking if the changes between the x-values and the y-values are consistent. For the change in x-values: (14-10 is 4) and (18-14 is also 4), the change is constant. Similarly, check the change in y-values: (24-18 is 6) and (30-24 is also 6), thus the change is constant. Hence, the function is linear.
More so, this function is a direct variation function because it passes through the origin. In direct variation functions, the ratio of y to x remains constant. In this case, the y divided by x at each point [(18/10=1.8), (24/14=1.71), (30/18=1.67)] is approximately 1.8, which is almost constant.
So, the best description of this function is: 'The function is a direct variation function with a constant of variation of 1.8'.
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Answer:
The function is linear but not a direct variation function.
Step-by-step explanation:
A scientist measured the wavelength of an X-ray as 0.0000000065 meters. Write the number in scientific notation.
Answer:
[tex]6.5 \times 10^{-9}[/tex]
Step-by-step explanation:
The scientific notation of a number is to express the number in the form [tex]x\times 10^{y}[/tex] where x is the base of ten.
So, if we want to express the number 0.0000000065, then we can write it as
[tex]\frac{6.5}{1000000000} = 6.5 \times 10^{-9}[/tex].
So, we can write 0.0000000065 as [tex]65\times 10^{-10}[/tex] or [tex]0.65 \times 10^{-8}[/tex] but those are not the scientific notation.
Therefore, [tex]6.5 \times 10^{-9}[/tex] is the scientific notation of 0.0000000065. (Answer)
What slope passes through -3,7 and is parallel to 4x-1?
Answer:
y = 4x + 19Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ ||\ k\iff m_1=m_2\\\\\text{We have}\ k:y=4x-1\to m_1=4.\\\\\text{Therefore}\ m_2=4.\\\\l:y=4x+b\\\\\text{Put the coordinates of the point (-3, 7) to the equation of a line:}\\\\7=4(-3)+b\\7=-12+b\qquad\text{add 12 to both sides}\\19=b\to b=19\\\\\text{Finally:}\\\\y=4x+19[/tex]
The lengths of the sides of a triangle are6, 8, 10. Can the triangle be a right triangle?
Answer:
Yes
Step-by-step explanation:
Another way of stating the question: Does the Pythagorean Theorem apply here? Does 6^2 + 8^2 = 10^2?
Does 36 + 64 = 100? YES
Yes, this is a right triangle.
Answer: Yes. That is because it fits the requirements of the Pythagoream Therom:
6^2+8^2 10^2
36+64 100
100 = 100 :)
When the solution of x2 + 9x − 9 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r? x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
A: 117
B: 54
C:45
D: 9
Answer:
The answer is option A. 117
Step-by-step explanation:
The general solution of the quadratic equation is:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
The given equation is x2 + 9x − 9 is expressed as minus 9 plus or minus the square root of r, all over 2
Comparing to the general solution
∴ r = determinant = b² - 4 a c
From the given equation: a = 1 , b = 9 and c = -9
∴ r = 9² - 4 * 1 * (-9) = 81 + 36 = 117
The answer is option A. 117
Answer:
117
Step-by-step explanation:
Urgent!!! Triangle ABC has angles the following angle measures. m<A=2x+7 , m<B=10x+10 and m<C=8x+23. what is the value of x and what is the measure of each angle?
x=
m<A=
m<B=
m<C=
Answer:
The Value of x= 7.
m∠A= 21°
m∠B= 80°
m∠C= 79°
Step-by-step explanation:
Given:
m∠A = 2x+7
m∠B = 10x+10
m∠C = 8x+23
We need to find the value of x and measures of each angle.
Now by angle sum property which states that sum of all angles of a triangle are 180°.
Hence from above statement we can say in ΔABC;
m∠A+m∠B+m∠C=180
Now substituting the given values in above equation we get;
[tex]2x+7+10x+10+8x+23=180\\2x+10x+8x+7+10+23=180\\20x+40=180\\20x=180-40\\20x=140\\\\x=\frac{140}{20} =7[/tex]
Hence value of x is 7.
Substituting the value of x in all angles we get;
m∠A=[tex]2x+7=2\times7+7=14+7=21\°[/tex]
m∠B=[tex]10x+10=10\times7+10=70+10=80\°[/tex]
m∠C=[tex]8x+23= 8\times7 +23 = 56+23=79\°[/tex]
Final answer:
To find the value of x and the measure of each angle in triangle ABC, set up an equation using the given angle measures. Solve for x and substitute it back in to find the measures of each angle. Then : m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
Explanation:
To find the value of x and the measure of each angle in triangle ABC, we need to set up an equation using the given angle measures. Since the sum of the angles in a triangle is 180 degrees, we can write the equation as:
m<A + m<B + m<C = 180
Substituting the given angle measures, we have:
(2x + 7) + (10x + 10) + (8x + 23) = 180
Simplifying the equation:
20x + 40 = 180
Subtracting 40 from both sides:
20x = 140
Dividing both sides by 20:
x = 7
Now that we know the value of x, we can find the measure of each angle by substituting x into the respective expressions:
m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
Which absolute value function, when graphed, represents
the parent function, f(x) = |xl, reflected over the x-axis and
translated 1 unit to the right?
5 -4 -3 -2 -1
1
2
3
4
5
f(x) = -1 | + 1
f(x) = -x-11
f(x) = |-*1 + 1
f(x) = |-* - 11
anche
Save and Exit
Answer:
f(x) = -|x| + 1
Step-by-step explanation:
f(x) = |xl when reflected over the x-axis is f(x) = -|x|.
When reflected over x-axis a graph becomes negative in y value.
f(x) = -|x| then translate 1 unit to the right is f(x) = -|x| + 1. Adding 1 translates the graph towards the right because the positive x-axis is on the right.
7 pencils for 16 dollars
Answer:44 cents
Step-by-step explanation:
7/16 = .4375
Answer:
Step-by-step explanation: To find the unit price you could divide 7 by 16
Bills annual salary is 2/3 of Jen's annual salary.if bills salary is$64,000, what is Jen's salary?
Answer:
$96,000
Step-by-step explanation:
To find Jen's annual salary, divide Bill's annual salary of $64,000 by 2/3, resulting in Jen's salary being $96,000.
Explanation:To calculate Jen's annual salary based on the information that Bill's annual salary is 2/3 of Jen's, first express Bill's salary as a fraction of Jen's:
Let J represent Jen's annual salary.According to the problem, we have that Bill's salary equals 2/3 of Jen's, so (2/3)*J = $64,000.To find Jen's salary J, divide Bill's salary by 2/3, so J = $64,000 / (2/3).After calculation, J = $64,000 * (3/2), which simplifies to J = $96,000.Therefore, Jen's annual salary is $96,000.
y is inversely proportional to the square of x.
A table of values for x and y is shown.
a) Express y in terms of x.
b) Work out the positive value of x when y = 25
Answer:
a) [tex]y=\frac{K}{x^{2} }[/tex]b) [tex]x=\frac{2}{5}[/tex]Step-by-step explanation:
If [tex]y[/tex] is inversely propotional to the square of [tex]x[/tex], then the relation would be like
[tex]y=\frac{K}{x^{2} }[/tex]
Where [tex]K[/tex] is the constant of propotionality.
Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use [tex](1,4)[/tex]
[tex]y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4[/tex]
Replacing this constant, the expression between variables is
[tex]y=\frac{4}{x^{2} }[/tex]
Which is the answer to a).
Now, if [tex]y=25[/tex] the value of [tex]x[/tex] would be
[tex]y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}[/tex]
Therefore, the answer to b) is [tex]x=\frac{2}{5}[/tex]
In an inverse variation, y is inversely proportional to the square of x. To express y in terms of x, the equation is y = k/(x^2). To find the positive value of x when y = 25, the equation is 25 = k/(x^2), and x = sqrt(k/25) is the solution.
Explanation:In an inverse variation, a variable is inversely proportional to another variable if their product is a constant. In this case, y is inversely proportional to the square of x. We can write this relationship as y = k/x^2, where k is the constant of variation.
To express y in terms of x, we can rearrange the equation as y = k/(x^2).
To find the positive value of x when y = 25, we can substitute these values into the equation and solve for x. We have 25 = k/(x^2). Rearranging the equation gives us k = 25x^2. Since we want to find the positive value of x, we can take the square root of both sides to get x = sqrt(k/25).
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Jimmy measured four pieces of wood. their measures are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft. what's the length of the shortest piece
After converting all measurements to the same format (decimals), we can see that the shortest piece of wood Jimmy measured is 4.02 ft.
To find the shortest piece of wood, we first need to convert all the lengths to the same format, preferably in decimals for easier comparison. The lengths of the wood pieces given are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft.
Let's break it down:
4.2ft remains as it is. 9/2ft equals 4.5ft when converted to a decimal. 4.02ft remains as it is. 4 2/9ft equals approximately 4.22ft when the fraction is converted to a decimal.
So, we have pieces of wood that are 4.2 ft, 4.5 ft, 4.02 ft, and 4.22ft. Looking at these numbers, it is clear that the piece of wood that measures 4.02 ft is the shortest.
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find the value for x.
Answer: x = -13
=========================
Work Shown:
19 = 38/2
19 & 1/2 = 19 + 1/2
19 & 1/2 = 38/2 + 1/2
19 & 1/2 = (38+1)/2
19 & 1/2 = 39/2
-------
In the original equation, replace the "19 & 1/2" with "39/2" to get
(5/2)x + (1/2)x = 39/2 + (9/2)x
Each term involves a fraction with a denominator of 2. If we multiply both sides by the common denominator, then the fractions will cancel out
For example: 2*(5/2)x = (10/2)x = 5x
So after multiplying both sides by 2, you should have this new equation
5x + 1x = 39 + 9x
--------
Let's solve that latest equation for x
5x + 1x = 39 + 9x
6x = 39 + 9x
6x-9x = 39 + 9x-9x ... subtract 9x from both sides
-3x = 39
-3x/(-3) = 39/(-3) .... divide both sides by -3
x = -13
how do i solve this
Answer:
y = -2x + 3
Step-by-step explanation:
Slope-intercept equation of a line is:
y = mx + b
where m is the slope and b is the y intercept.
Here, m = -2 and b = 3.
y = -2x + 3
Brenda recorded a temperature of 19°C, and Cooper recorded a temperature 17°C higher. What temperature did Cooper record?
Answer:
Cooper recorded a temperature of 36° C.Step-by-step explanation: If you add 19 and 17 together you get 36.
Hope this helps! :)
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 cents per square
centimeter. The top will be made of glued paper, costing 0.08 cents per square centimeter. Find the dimensions for
the package that will minimize production cost.
Helpful information:
To minimize the cost of the package:
Radius:
Height:
Minimum
To minimize production cost, we need to find the dimensions of the package that will satisfy the volume equation and minimize the cost equation. Taking the partial derivatives of the cost equation with respect to the variables 'r' and 'h', and setting them equal to zero, we can find the critical points. Solving these equations, we find that the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
Explanation:To find the dimensions of the package that will minimize production cost, we need to consider the cost of the sides and bottom made of styrofoam and the cost of the top made of glued paper. Let's denote the radius of the base of the cylinder as 'r' and the height of the cylinder as 'h'.
The volume of a cylinder is given by the formula V = πr²h. We know that the volume of the package needs to be 350 cubic centimeters, so we can write the equation as πr²h = 350.
The cost of the sides and bottom of the container is given by the formula C1 = 0.03 * (2πrh + πr²), and the cost of the top is given by the formula C2 = 0.08 * πr².
To minimize the cost, we need to find the values of 'r' and 'h' that satisfy the volume equation and minimize the cost equation.
Since this is a calculus problem, we will differentiate the cost equation with respect to 'r' and 'h', and set the derivatives equal to zero to find the critical points.
Taking the partial derivatives of C1 and C2 with respect to 'r' and 'h', we get:
∂C1/∂r = 0.03 * (2πh + 2πr) = 0∂C1/∂h = 0.03 * (2πr) = 0∂C2/∂r = 0.08 * (2πr) = 0∂C2/∂h = 0Solving these equations, we find that h = 7 cm and r = 2.5 cm. Therefore, the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
what is the answer because am stuck
Answer:
30 Oranges!
Step-by-step explanation:
Given that for every 2 apples there are 3 oranges.
How many oranges would be there in a basket of 20 apples?
Since for every couple of apples we have 3 oranges we will calculate how many couples of apples are there in the basket.
Given there are 20 apples. This means that there are [tex]$ \frac{20}{2} $[/tex] = 10 pairs of apples.
Since for one pair we have three oranges, for 10 pairs we would have 3 X 10 = 30 oranges.
Therefore, we can conclude that the number of oranges in the bigger basket would be 30.
five numbers that have 3, 7, and 13 as prime factors
Step-by-step explanation:
(3)(7)(13) = 273
(3)(3)(7)(13) = 819
(3)(7)(7)(13) = 1911
(3)(7)(13)(13) = 3549
(3)(3)(3)(7)(13) = 2457
(3)(7)(7)(7)(13) = 13377
(3)(7)(13)(13)(13) = 46137
....
10. Estimate by rounding -5 2/5+9 8/11-3 5/6
Answer:
0.5
Step-by-step explanation:
-5 2/5=-27/5
9 8/11=107/11
-3 5/6=-23/6
--------------------
-27/5+107/11-23/6
-27/5-23/6+107/11
-162/30-115/30+107/11
-277/30+107/11
-3047/330+3210/330=163/330=0.493=0.5
What is the equation of the line that is perpendicular to the y-axis and contains the point (-2,7)
A: y=-x+5
B: x=-2
C: y=x+9
D: y=7
Answer:
y = 7
Step-by-step explanation:
The straight line which is perpendicular to the y-axis will be either x-axis or parallel to the x-axis.
Now, the general equation for all straight line which is either x-axis or parallel to x-axis are given by y = c ........... (1), where c is any constant.
For c = 0 the line will be x -axis. therefore, y = 0, is the equation of x-axis.
Now, if the line (1) passes through the point (-2, 7), then the equation will be y = 7. (Answer)
{Since, the point (-2,7) will satisfy the equation (1) and then c will be equal to 7.}
The height of a skydiver jumping out of an airplane is given by h=16t +3200
Answer:
The answer is yes :)
Step-by-step explanation:
Which postulate proves these two triangles are congruent ?
Answer:
HL
Step-by-step explanation:
HL is used for right triangles that are congruent. These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
Here, we have,
A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles are isosceles, scalene and equilateral triangles.
Two angles are said to be complementary if their sum is 90 degrees.
Two triangles are said to be congruent if all their corresponding sides and angles are congruent.
This means that the triangles have equal angles and equal sides.
here, we have,
HL is used for right triangles that are congruent.
These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
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no one helped me with the last question but i got it can someone help me with this
y = 2x
Step-by-step explanation:
The linear functions are given by:
y = mx+b
To find the slope, we have to find the change in x and y
The change in x is:
[tex]-14-(42) =-14+42 =28\\14+14= 28[/tex]
The change in y is:
[tex]-28-(-84) = -28+84 = 56\\28-(-28) = 28+28 = 56[/tex]
The slope is:
[tex]Slope = \frac{change\ in\ y}{Change\ in\ x}\\=\frac{56}{28}\\= 2[/tex]
Putting slope in equation of linear function
[tex]y =2x+b[/tex]
To find the value of b, we will put any pair of input and output in the slope-intercept form
So, putting (14,28)
[tex]28 = 2(14) + b\\28 = 28+b\\b = 28-28\\b = 0[/tex]
Hence,
the linear equation for function is:
y = 2x
Keywords: Linear function, slope intercept form
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20 pts! A line passes through (3, 7) and (6, 9). Which equation best represents the line?
y = 3 over 2 x + 5
y = 2 over 3 x + 5
y = 3x + 2
y = 2 over 3 x + 2
Answer:
y = 2 over 3 x + 5
Step-by-step explanation:
m= y2-y1/x2-x1
m= (9-7)/(6-3)
m=2/3
y=mx+b
y= 2/3x+b
(3,7)
7=2/3(3)+b
7=6/3+b
7=2+b
5=b
b=5
y=2/3x+5
Is the sequence -3, 1, 5, 9,... An arithmetic sequence
Answer:
Yes, it's an arithmetic sequence.
Step-by-step explanation:
Each term in this sequence is 4 more than the previous term. Therefore we have an arithmetic sequence.
You can rent time on computers at the local copy center for a a $ 7 setup charge and an additional $ 3.50 for every 10 minutes. How much time can be rented for $ 22?
Answer:
The answer should round up to 40 minutes. Do it to make sure the answer is 4 which in this case = 40
Step-by-step explanation:
[tex]22 - 7 \div 3.50[/tex]
Answer:
Computer can be rented for 42.85 minutes using $22
Step-by-step explanation:
Given:
Setup charge = $ 7
Additional charge for every 10 minutes = $ 3.50
To find:
The time for which the computer can be rented for $ 22
Solution:
Let the additional time be x
for additional charge for 10 minutes =3.50
for 1 minute , additional charge = [tex]\frac{3.50}{10}[/tex]= $0.35
According to the question
setup cahrge + additional charge= $22
[tex]7+(0.35\times x)=22[/tex]
[tex](0.35\times x)=22-7[/tex]
[tex](0.35\times x)=15[/tex]
[tex]x=\frac{15}{035}[/tex]
x=42.85
Solve using a suitable inverse operation:
A) a/5= -2
I just want to know what this means and how to do it.
Answer:
a = - 10
Step-by-step explanation:
Given
[tex]\frac{a}{5}[/tex] = - 2
a is divided by 2. The inverse operation to division is multiplication, thus
Multiply both sides by 5 to clear the fraction
a = 5 × - 2 = - 10
How can I factor 24 + 32x
Answer:
8(3+4x)
Step-by-step explanation:
it it can be pulled out of both 24 and 32.
A 14 pound bag of dog food cost $16.24 and a 30 pound bag of dog food cost $33.30 which statement is true and can be used to determine the better buy?
A.The unit rate per pound of a 14 pound bag $0.05 less than the unit rate of a 30 pound bag.
B.The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.
C.The unit rate per pound of a 14 pound bag is $0.50 less than the unit rate of a 30 pound bag.
D.The unit rate per pound of a 14 pound bag is $0.50 more than the unit rate of a 30 pound bag.
Answer:
B)
Step-by-step explanation:
16.24/14=1.16
33.3/30=1.11
1.16-1.11=0.05
The correct statement is The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
14 pound bag cost = 16.24
cost of 1 pound bag = 16.24/14
= $1.16
and,
another bag which is of 30 pound costs = 33.30
= 33.30 / 30
= $1.11
Hence, The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.
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7.66 × 0.55 i need 20 charters to ask this
Answer:
4.213
Step-by-step explanation: