Answer:
Overestimate
Step-by-step explanation:
We draw five rectangles from x = 1 to x = 6, so each rectangle has a width of 1:
(6 - 1) / 5 = 1
We're using right endpoints to determine the height of each rectangle. The first rectangle is from x=1 to x=2, so the height of the rectangle is f(2) = 6. So on and so forth for the other rectangles.
The result is this:
desmos.com/calculator/vrl67vpigt
As we can see, these rectangles have areas outside of the curve, so their total area will be greater than the area under the curve. So this will be an overestimate.
Write a formula to help Jaheed determine the
number of cartons of juice he needs to
buy to make the punch.
Let's let
n = number of cartons of juice
m = number of liters in each carton
Enter the correct answer.
Answer:
n=m(x)
Step-by-step explanation:
n is the dependent variable m is the independent variable.
how many cartons, depends on how many liters are in a carton.
how many he needs to buy= the amount in carton× how ever much is in his recipe
for example
if they're are let's say 1.5 liters per carton than m=1.5. and if he needs 15 liters than n= 15
than the equation is
[tex]15 = 1.5 \times x[/tex]
x is how many cartons he needs to buy
solve for x by dividing both sides of the equation by 1.5
[tex]15 \div 1.5 = x[/tex]
and x=10 in this scenario
solve the system of linear equations separate the x- and y- values with a comma. -13x = -54 - 20y and -10x= 60 + 20y
[tex]\bf \begin{cases} -13x=-54-20y\\ -10x=60+20y \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{-13x=-54-20y}\implies -13x+20y=-54\implies \boxed{20y}=13x-54 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 2nd equation}}{-10x=60+\left( \boxed{13x-54} \right)}\implies -10x=6+13x\implies -10x-6=13x[/tex]
[tex]\bf -6=23x\implies \blacktriangleright -\cfrac{6}{23}=x \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{-13\left( -\cfrac{6}{23} \right)=-54-20y}\implies \cfrac{78}{23}=-54-20y[/tex]
[tex]\bf \stackrel{\textit{multipying both sides by }\stackrel{LCD}{23}}{23\left( \cfrac{78}{23} \right)=23(-54-20y)}\implies 78=-1242-460y\implies 1320=-460y \\\\\\ \cfrac{1320}{-460}=y\implies \blacktriangleright -\cfrac{66}{23}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( -\frac{6}{23}~,~-\frac{66}{23} \right)~\hfill[/tex]
How does -1.125 + 1.2 = 0.075 instead of 0.925?
Answer:
.0075 (hope this help; let me know if not)
Step-by-step explanation:
The operation is + and the signs of the numbers are opposite so we have to subtract. The bigger number has positive sign in front if so we do 1.2-1.125=1.200-1.125
I'm going to line up
1.200
-1.125
---------
If you have 200 and you take about 125... 75 should beleft
so
1.200
-1.125
---------
0.075
(Do not use spaces. Use to represent exponents. Example 2^3 is 22.)
Answer: y=6^x-3
It is a exponent form of graph, so first:
y=a^x-b
When b=0, the asymptote is y=0 but as the asymptote given is y=-3, b=-3
Second:
the y value increases 6, when x changes 0 to 1, so a=6
help Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
[tex]\bf f(x)=\stackrel{\stackrel{m}{\downarrow }}{4} x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \begin{array}{ccll} x&g(x)\\ \cline{1-2} 2&5\\4&7\\6&9 \end{array}~\hfill \begin{array}{llll} (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-5}{6-2}\implies \cfrac{4}{4}\implies \stackrel{\stackrel{m}{\downarrow }}{1} \end{array}[/tex]
well, clearly 4 > 1.
Answer:
f(x) has a greater slope.
Step-by-step explanation:
The slope of a function in the form of y=Mx+C is represented by the letter M, so the slope in the function F(x) =4.
Now when you have a function but you only have a table to evaluate it, to calculate the slope you have the next formula:
[tex]m=\frac{y^{2}- y^{1}}{x^{2} -x^{1} }[/tex]
You just have to pick two points from the table to use in the formula, we´ll use (4,7) as our point 1 and
(6,9) as our point 2.
This means that:
[tex]x^{1}=4[/tex] [tex]y^{1}=7[/tex]
[tex]x^{2}=6[/tex] [tex]y^{2}=9[/tex]
Now you just put it into the formula:
[tex]m=\frac{9-7}{6-4}[/tex]
[tex]m=\frac{2}{2}[/tex]
[tex]m=1[/tex]
Now that you have both slopes, you can see that the slope of g(x)=1 and the slope of f(x)=4, and you can see that f(x) has a greater slope thatn g(x).
Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?
Answer:
20000*(0.85)^x
Step-by-step explanation:
Answer:
The function f(x) representing the value of car after x years is given by
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
Step-by-step explanation:
Since value of car depreciates by 15% each year
Value of car after 1 year
[tex]f(1)=value of new car \times(1-\frac{15}{100})[/tex]
=>[tex]f(1)=\$ 20,000\times(1-\frac{15}{100})[/tex]
Value of car after 2 year
[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})^{2}[/tex]
Value of car after 3 year
[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})^{3}[/tex]
Similarly value of car after x years is
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
find the difference between (7,-1) and (-8,-9)
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-7]^2+[-9-(-1)]^2}\implies d=\sqrt{(-8-7)^2+(-9+1)^2} \\\\\\ d=\sqrt{225+64}\implies d=\sqrt{289}\implies d=17[/tex]
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
According to the data we have:
[tex](x_ {1}, y_ {1}) :( 7, -1)\\(x_ {2}, y_ {2}): (- 8, -9)[/tex]
Substituting:
[tex]d = \sqrt {(- 8-7) ^ 2 + (- 9 - (- 1)) ^ 2}\\d = \sqrt {(- 15) ^ 2 + (- 9 + 1) ^ 2}\\d = \sqrt {(- 15) ^ 2 + (- 8) ^ 2}\\d = \sqrt {225 + 64}\\d = \sqrt {289}\\d = 17[/tex]
Thus, the difference or distance between the points is 17
Answer:
[tex]d = 17[/tex]
Rewrite this radicand as two factors, one of which is a perfect square. √60
Answer:
√4 * √15.
Step-by-step explanation:
√60
=√(4 * 15)
= √4 * √15
Answer:
our answer is [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form
as [tex]2*\sqrt{15}[/tex]
Step-by-step explanation:
[tex]\sqrt{60}[/tex]
We need to solve the above expression
Factors of 60:
1X60, 2X30, 3X20, 4X15, 5X12, 6X10
We need two factors one of which is perfect square
From the above factors only 4X15 full fills our condition as 4 is a perfect square
[tex]\sqrt{60}\\ =\sqrt{4 * 15}\\ We\,\,know\,\, \sqrt{a*b}= \sqrt{a}*\sqrt{b}\\ =\sqrt{4}*\sqrt{15}\\[/tex]
Solving, we get
[tex]2*\sqrt{15}[/tex]
So, our answer is [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form
as [tex]2*\sqrt{15}[/tex]
What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0? units
Answer:
2
Step-by-step explanation:
Center: (−4,3)
Radius: 2
Answer:
radius = 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
Given
x² + y² + 8x - 6y + 21 = 0
Use the method of completing the square to obtain standard form
Collect the x- terms and y- terms together and subtract 21 from both sides
x² + 8x + y² - 6y = - 21
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(4)x + 16 + y² + 2(- 3)y + 9 = - 21 + 16 + 9
(x + 4)² + (y - 3)² = 4 ← in standard form
with centre (- 4, 3) and radius = [tex]\sqrt{4}[/tex] = 2
What is the value of
[tex]\displaystyle\\\sum_{n=2}^6\dfrac{(n-1)!}{2}=\dfrac{(2-1)!}{2}+\dfrac{(3-1)!}{2}+\dfrac{(4-1)!}{2}+\dfrac{(5-1)!}{2}+\dfrac{(6-1)!}{2}=\\\\=\dfrac{1}{2}+\dfrac{2}{2}+\dfrac{6}{2}+\dfrac{24}{2}+\dfrac{120}{2}=0.5+1+3+12+60=76.5[/tex]
Answer:
D. 76.5
Step-by-step explanation:
The summation sign means that it is the sum of the expression for all values of n upto 6.
n = 2 below the summation sign means that n starts from 2.
∑(n-1)!/2 from n= 2 to n=6
= (2-1)!/2 + (3-1)!/2 + (4-1)!/2 + (5-1)!/2 + (6-1)!/2
= 1!/2 + 2!/2 + 3!/2 + 4!/2 + 5!/2
= 1/2 + 2*1/2 + 3*2/2 + 4*3*2/2 + 5*4*3*2/2
= 1/2 + 2/2 + 6/2 + 24/2 + 120/2
= 0.5 + 1 + 3 + 12 + 60
= 76.5
in 3 games sherrys bowling scores were 109, 98 and 135. her highest score was how much more than her Lowest scores
To find out the difference between her highest score and lowest score, we can deduct the amount of highest score by lowest score.
Her highest score: 135
Her lowest score: 98
Her highest score is higher than the lowest score by:
135 - 98
=37
Therefore, her highest score is 38 more than her Lowest score.
Hope it helps!
What’s the median of the data 24,2,13,12,2,5,10,18
Answer:
11
Step-by-step explanation:
arrange from smallest to greatest:
2,2,5,10,12,13,18,24
The median is the middle name.
If you have two middles, the median is the average of them.
So you have 2 middles, 10 and 12.
The average of 10 and 12 is given by (10+12)/2=11
Hello There!
The median is the middle number of the data set so let’s find it!
Step 1. Order your numbers from least to greatest so after we have done that, our numbers would be 2,2,5,10,12,13,18,24
Step 2. We want to cross of a number at the beginning so Starting with 2 and the last number 18 and do that either until we get to one number in the middle or two numbers.
Step 3. There is no one number in the middle but we have the numbers 10 and 12 so we add them together which gives us a sum of 22 and then divide 22 by 2 and we get a quotient of 11.
Our median is 11.
The triangles to the right are congruent. Which of the following statements must be true
Answer:
It is the last one, bc=df
The true statement is one that derives from the condition that ΔABC and
ΔDEF are congruent.
Response:
The statement that must be true is; ∠A ≅ ∠DHow can the true statement be found?Given that the tringles are congruent, we have;
The length of the corresponding sides are equal
Similarly, the measure of the corresponding are equal
The side [tex]\mathbf{\overline{AC}}[/tex] ≅ Side [tex]\overline{DE}[/tex]
Side [tex]\mathbf{\overline{AB}}[/tex] ≅ Side [tex]\overline{EF}[/tex]
Which gives;
∠A ≅ ∠D
Given that ΔABC ≅ ΔDEF, we have;
Side [tex]\mathbf{\overline{BC}}[/tex] ≅ Side [tex]\overline{DF}[/tex]
Which gives;
∠C ≅ ∠F
Therefore;
∠B ≅ ∠D
The correct option is therefore; ∠A ≅ ∠DLearn more about congruent triangles here:
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Please answer from the question above :)
Answer:
205/6
Step-by-step explanation:
The question simply asks us to plug in 45 minutes into the given equation. In the graph, we see that y-axis is defined to be time. Therefore we set y=45 and solve for x.
45=-6/5x+86
-41=-6/5x (subtract 86 from both sides)
-41*(-5)=-6/5x*(-5) (multiply both sides by -5)
205=6x (divide both sides by 6)
205/6=x
Will mark Brainlist
Which variable expression represents the following word phrase?
four times the sum of five and a number
4.5+n
4n + 5
4(5 + n)
n. 5+4
Answer:
The correct option is C) 4(5 + n).
Step-by-step explanation:
Consider the provided phrase.
Four times the sum of five and a number
Let the number is n and the sum of five and a number can be written as:
[tex]n+5[/tex]
Thus, four times the sum of five and a number can be written as:
[tex]4(n+5)[/tex]
Hence, the required expression is [tex]4(n+5)[/tex]
Therefore, the correct option is C) 4(5 + n).
Find the circumference of the circle. Round your answer to two decimal places, if necessary.
Given: AB= 4
AD= 6
Which points are in the exterior of both circles?
E and G
H and F
H and G
Answer:
A
Step-by-step explanation:
The answer would be E and G. Points E and G are both OUTSIDE both circles
Hope this helped!
~Just a girl in love with Shawn Mendes
Find the decimal equivalent of 6/9
Answer:
0.66666666666666666 ( goes on forever )
Step-by-step explanation:
This simplifies to 2/3, which is known to be 0.666666666666 and so on.
Answer:
0.66666667
Step-by-step explanation:
The numbers just keep going on and on and on, but the 7 in the number stops it.
The graph below shows an airplane's speed over a period of time. Describe the events.
Answer:
The airplane gains speed when it takes off. Then it begins to lose speed at the same rate. The plane then stays at the same speed the rest of the time.
A flock of 200 birds were flying south for the winter. Every day, the amount of birds in the flock increased by an average of 4%.
The amount of birds in the flock, b, can be represented by an exponential function, where d represents the number of days since the 200 birds started. What is the equation of this exponential function?
b = 1.04 · 200d
Answer:
[tex]b=200(1.04)^{d}[/tex]
Step-by-step explanation:
we know that
The exponential function is of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
In this problem we have
a=200 birds
b=100%+4%=104%=104/100=1.04
substitute
[tex]y=200(1.04)^{x}[/tex]
Let change of variables
[tex]b=200(1.04)^{d}[/tex]
where
b is the amount of birds in the flock
d is the number of days since the 200 birds started
The equation has no solution.
A. 13y + 2 - 2y = 10y + 3 - y
B. 9(3y +7) - 2 = 3(-9y + 9)
C. 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
D. 5(2.2y + 3.4) = 5(y - 2) + 6y
Option D which simplifies to 11y +17 = 11y -10 has no solution since the left and right sides of the equations aren't equal after simplifying.
Explanation:We are tasked with determining which equation has no solution among the given options: A) 13y + 2 - 2y = 10y + 3 - y, B) 9(3y +7) - 2 = 3(-9y + 9), C) 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1 and D) 5(2.2y + 3.4) = 5(y - 2) + 6y. The equation without a solution will be the one in which the variables cancel out and the remaining numbers are not equal.
Solving the equations, starting with A, by combining like terms, we have 11y + 2 = 9y + 3, this eventually gives us y = 0.5. Option B, simplifying gives us 27y + 63 = -27y + 27, therefore y = -1.33. For C, we simplify to 34.5y + 3.1 = 34.5y - 5.1. Because both sides of the equation have equal coefficients for y, this results in 34.5y = 34.5y, which holds true for any value of y. Hence, the equation has infinitely many solutions. Option D simplifies to 11y +17 = 11y -10. Here, we see that 11y = 11y is true, however, the constants are not equal (i.e. 17 does not equal -10). Thus, option D is the equation with no solution.
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The model represents x2 – 9x + 14. Which is a factor of x2 – 9x + 14?
Answer:
(x-2)(x-7)
Step-by-step explanation:
x2 – 9x + 14 = x² - 2x - 7x + 14
= x(x-2) - 7(x-2)
= (x-2)(x-7)
Answer:
Factor of x² – 9x + 14 is:
(x-2)(x-7)
Step-by-step explanation:
We have to find the factors of:
x² – 9x + 14
On splitting the middle term, we get
x² -7x -2x +14
which could also be written as:
x(x-7)-2(x-7)
which is equivalent to:
(x-2)(x-7)
Hence, Factor of x² – 9x + 14 is:
(x-2)(x-7)
What is [(x^2y^3)^1/3]/ [^3 √x^2y] in exponential form?
Answer:
answer for question 1 is A and question 2 is B
Step-by-step explanation:
i literally just took the assignment
[tex](x^{2} y^{3})^{1/3}[/tex]/∛x²y in exponential form [tex]x^{2/3}y^{1}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex].
The correct option is (A)
What is power and exponents?
power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and
exponent denotes the number of times the same base number is multiplied.
Given function is:
[tex](x^{2} y^{3})^{1/3}[/tex]/∛x²y
Now, using rules of exponents and power
=[tex]x^{2/3} y^{3/3}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex] [(a²)³= [tex]a^{6}[/tex]]
=[tex]x^{2/3}y^{1}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex]
Hence, [tex](x^{2} y^{3})^{1/3}[/tex]/∛x²y= =[tex]x^{2/3}y^{1}[/tex]÷[tex]x^{2/3 }\;y^{1/3} }[/tex]
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Rate of change from the line
[tex]\textbf{Answer:}[/tex]
[tex]\frac{-1}{4}[/tex]
[tex]\textbf{Step-by-step explanation:}[/tex]
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\textrm{Use the formula above to determine the rate of change}[/tex]
[tex]\frac{1 - 2}{4 - 0} \rightarrow\frac{-1}{4}[/tex]
[tex]\textrm{The rate of change of this line is }[/tex] [tex]\frac{-1}{4}[/tex]
recall that all we need is two points off a straight line to get its slope, so... hmmm this one passes through (0 , 2) and (4 , 1), so let's use those
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{4-0}\implies -\cfrac{1}{4}[/tex]
if f(x)= 3x+6 which of the following is the inverse of f(x)
Answer:
f(x)^-1 = 1/3x - 2
Step-by-step explanation:
Replace f(x) with y and solve:
y = 3x + 6
Swap x and y
x = 3y + 6
Now isolate y
x/3 = 3y/3 + 6/3
1/3 x = y + 2
1/3 x - 2 = y + 2 - 2
y = 1/3x - 2 or f(x)^-1 = 1/3x - 2
For this case we have the following function:
[tex]f (x) = 3x + 6[/tex]
We must find the inverse of the function, then:
Replace f (x) with y:[tex]y = 3x + 6[/tex]
We exchange the variables:
[tex]x = 3y + 6[/tex]
We solve for "y":
Subtracting 6 on both sides of the equation:
[tex]x-6 = 3y[/tex]
Dividing between 3 on both sides of the equation:
[tex]y = \frac {x} {3} - \frac {6} {3}\\y = \frac {x} {3} -2[/tex]
We change y by [tex]f ^ {- 1} (x)[/tex], and finally we have:
[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]
ANswer:
[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]
how to find a slope of a line on a graph
Answer:
change of y/ change of x
Step-by-step explanation:
What is 1,242/99 rounded to the nearest integer? Explanation please?
Answer:
13 is the answer.
Step-by-step explanation:
In this question the given fraction is
Now we have to simplify the fraction to the nearest integer.
Since the integers are whole number not in fraction therefore 12.5 can be written as 13 as the nearest integer.
Step-by-step explanation:
Please mark brainliest and have a great day!
To find 1,242 divided by 99 and rounded to the nearest integer, we do the division and then round the result. The result of the division is 12.545..., and when rounded to the nearest integer, we get 13.
Explanation:The question is asking us to divide 1,242 by 99 and round the result to the nearest integer. First, we do the division: 1,242 ÷ 99 = 12.545454545.... Since we need to round to the nearest integer, we look at the digits following the decimal point. Because the digit immediately after the decimal point is 5 or more, we round up the integer part. So, 1,242 ÷ 99 rounded to the nearest integer is 13.
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20 Points! if pencils cost $2.40 for twelve, what is the unit price per pencil?
Answer:
$0.20
Step-by-step explanation:
A dozen of pencils = $2.40
1 pencil = $2.40 ÷ 12 = $0.20
PLEASE DO MARK ME AS BRAINLIEST UWU
ALSO, DO HAVE A GREAT DAY ;)
The unit price per pencil is determined by dividing the total cost of the pencils ($2.40) by the total number of pencils (12), giving a result of $0.20 per pencil.
Explanation:To find the unit price per pencil, you would divide the total cost by the total number of items.
In this case, the total cost is $2.40 and there are twelve pencils, so the calculation is $2.40 ÷ 12.
This will give you the unit price per pencil.
Using the numbers provided, $2.40 (the total cost) divided by 12 (the total number of pencils) equals $0.20.
So, the unit price of a pencil is $0.20.
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Which set of coordinates, paired with (-3, -2) and (-5, -2), result in a square?
The set of coordinates which paired with (-3,-2) and (-5,-2) are (-4,0) and (-4,0).
What are coordinates?The coordinates are the points with the help of which we can draw any figure on the graph.
How to find coordinates?We know that all the sides of a square are equal to each other.
Let ABCD be a square.
Coordinates of A(-3,-3) and C be(-5,-2)
Let the coordinates of B and D be (x1,y1) and (x2,y2)
To be a square AB=CD=BC=AD
AB=BC
[tex]\sqrt{(x1+3)^{2}+(y1+2)^{2} }[/tex]=[tex]\sqrt{(-5-x1)^{2} +(-2-y1)^{2} }[/tex]
solving this we will find
x1=-4
because y1 is not in the solution so y1 be equal to 0.
AD=DC
[tex]\sqrt{(-5-x2)^{2} +(-2-y2)^{2} }[/tex]=[tex]\sqrt{(x2+3)^{2} +(y2+2)^{2} }[/tex]
solving this we will find x2=-4 and y2=0
Hence the coordinates are (-4,0),(-4,0)
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Final answer:
The coordinates that form a square when paired with (-3, -2) and (-5, -2) are (-3, 0) and (-5, 0). The sides of the square are 2 units long, and by moving perpendicularly up by 2 units from each given point, we find the other two vertices of the square.
Explanation:
The student has asked which set of coordinates, when paired with (-3, -2) and (-5, -2), would result in a square. To find the coordinates that complete the square, we need to consider that the diagonals of a square are equal in length and bisect each other at right angles. The two given points (-3, -2) and (-5, -2) form a side of the square that is parallel to the x-axis and 2 units long. Since a square has all sides equal, the other two vertices of the square will be 2 units away from these points but in a perpendicular direction.
Here's how we calculate it step by step:
First, we determine the length of the side of the square by calculating the distance between the points (-3, -2) and (-5, -2), which is 2 units.
Next, we move 2 units perpendicularly from each point which can be done by either keeping the x-coordinate constant and changing the y-coordinate or vice versa. Since we want to be perpendicular to the x-axis, we change the y-coordinate.
The change in the y-coordinate could be either upwards (+2) or downwards (-2). Considering the y-value of the given points, one possible set of coordinates for the other two vertices are (-3, 0) and (-5, 0).
Therefore, the coordinates (-3, 0) and (-5, 0), when paired with (-3, -2) and (-5, -2), form a square.
In your last 14 basketball games, you attempted 65 free throws and made 47. Find the experimental probability that you make a free throw. Write the probability as a percent, to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
% = (sucesses / attempts) * 100
% = (47/65) * 100
% = 0.723 * 100
% = 72.3 %
Answer: 72.3%
Step-by-step explanation:
Given statements : The number of basketball games = 14
The number of free throws attempted = 65
The number of made = 47
Now, the experimental probability that you make a free throw is given by :-
[tex]\dfrac{\text{47}}{65}=0.72307\approx0.723[/tex]
In percent , [tex]0.723\times100=72.3\%[/tex]
Hence, the experimental probability that you make a free throw =72.3%