Answer:
The slope is 2.
Step-by-step explanation:
The given line has equation: [tex]f(t)=2t-6[/tex].
This is a linear equation in [tex]t[/tex].
The slope is the coefficient of the independent variable [tex]t[/tex].
The coefficient of [tex]t[/tex] in [tex]f(t)=2t-6[/tex] is 2.
Therefore the slope is 2.
Alternatively, [tex]f(t)=2t-6[/tex] is of the form [tex]f(t)=mt+c[/tex], where [tex]m=2[/tex] is the slope.
Answer:
Step-by-step explanation:
The slope is 2 and the y intercept is -6
A school day starts at 07:15. There are three periods of 40 minutes, four periods of 35 minutes and two periods of 50 minutes. There is a long break of 20 minutes and a short break of 10 minutes. Calculate the time that the school day ends.
Answer:
the school day ends at 1:45
Step-by-step explanation:
7:15 40 x 3 = 120
+2 hours =
9:15 35 x 4 = 140
+2 hours & 20 mins =
11:35 50 x 2 = 100
+1 hour & 40 mins
1:15 20 + 10 = 30
1:45
you're welcome((:
What are the coordinates of point C on the directed segment from A (-8,4) to B (10,2) that partitions the segment such that AC:CB is 2:1?
To find the coordinates of point C, divide the x- and y-coordinates of AB in the ratio 2:1.
Explanation:To find the coordinates of point C, we can use the concept of dividing a line segment in a given ratio. Given that AC:CB is 2:1, we can divide the x- and y-coordinates of the line segment AB in the same ratio.
The x-coordinate of point C is calculated by dividing the difference between the x-coordinates of points A and B by the sum of the ratio (2+1).
The y-coordinate of point C is calculated by dividing the difference between the y-coordinates of points A and B by the sum of the ratio (2+1).
Therefore, the coordinates of point C are (-2, 3).
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The correct option is d. [tex]\((4, 0)\)[/tex]. The coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].
To find the coordinates of point [tex]\(C\)[/tex] that partitions the segment [tex]\(AB\)[/tex] in the ratio [tex]\(AC:CB = 2:1\)[/tex], we use the section formula. Given points [tex]\(A(x_1, y_1)\)[/tex] and [tex]\(B(x_2, y_2)\)[/tex] with a ratio [tex]\(m:n\)[/tex], the coordinates [tex]\((x, y)\)[/tex] of the point dividing the segment in the ratio [tex]\(m:n\)[/tex] are given by:
[tex]\[x = \frac{mx_2 + nx_1}{m + n}, \quad y = \frac{my_2 + ny_1}{m + n}\][/tex]
For this problem:
- [tex]\(A(-8, 4)\)[/tex]
- [tex]\(B(10, -2)\)[/tex]
- Ratio [tex]\(m:n = 2:1\)[/tex]
Plugging in the values:
[tex]\[x = \frac{2 \cdot 10 + 1 \cdot (-8)}{2 + 1} = \frac{20 - 8}{3} = \frac{12}{3} = 4\][/tex]
[tex]\[y = \frac{2 \cdot (-2) + 1 \cdot 4}{2 + 1} = \frac{-4 + 4}{3} = \frac{0}{3} = 0\][/tex]
Thus, the coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].
The complete question is:
What are the coordinates of point C on the directed segment from A(−8,4) to B(10,−2) that partitions the segment such that AC:CB is 2:1 ?
A. (1,1)
B. (−2,2)
C. (2,−2)
D. (4,0)
What is the y-intercept of the line perpendicular to the line y = 4/3x + 1 that includes the point (4, 1)?
[tex]\bf y=\stackrel{\downarrow }{\cfrac{4}{3}}x+1\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 \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}[/tex]
so then, we know this line has a slope of -3/4 and runs through (4 , 1)
[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies -\cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=-\cfrac{3}{4}(x-4)\implies y-1=-\cfrac{3}{4}x+3[/tex]
[tex]\bf y=-\cfrac{3}{4}x\stackrel{\downarrow }{+4}\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}~\hfill \stackrel{\textit{y-intercept}}{(0,4)}[/tex]
What is the simple interest on rs 650 for 14 weeks at 6% per annum
Answer:
rs 10.5 .
Step-by-step explanation:
Simple Interest = PRT/100 where P = sum invested, R = the rate per annum, T = the time in years.
14 weeks = 14/52 years so it is:
650* 6 * (14/52) / 100
= rs 10.5.
Answer:
10.50
Step-by-step explanation:
The simple interest (I) is calculated as
I = [tex]\frac{PRT}{100}[/tex]
where P is the principal ( amount deposited), R is the rate of interest and T the time in years.
note that 14 weeks = [tex]\frac{14}{52}[/tex] of a year, hence
I = [tex]\frac{650(6)}{100}[/tex] × [tex]\frac{14}{52}[/tex]
= [tex]\frac{650(6)(14)}{100(52)}[/tex]
= [tex]\frac{54600}{5200}[/tex] = 10.50
During the worst periods of hyperinflation in a certain country, the price of food increase at a rate of 10% per month. State whether this increases was linear or exponential. If your food bill was 100 in one month during this period, what was it three months later?
Answer:
The increase was exponential
After three months his expense was: $133.1
Step-by-step explanation:
The increase was exponential, because if we call x the initial price, then after the first month the new price p is:
[tex]p = x (1 + \frac{10\%}{100\%})\\\\p=x(1+0.1)[/tex]
After the second month, the new price is 10% of the price of the previous month, that is:
[tex]p = [x (1 + 0.1)](1 + 0.1)\\\\p = x (1 + 0.1) ^ 2[/tex]
After month n, the price is:
[tex]p = x (1 + 0.1) ^ n[/tex]
Note that the equation has the form of an exponential growth function, where x is the initial price and n is the number of months elapsed.
In this case [tex]x = 100[/tex] and [tex]n = 3[/tex]. So:
[tex]p = 100 (1 + 0.1) ^ 3\\\\p=\$133.1[/tex]
What is the equation of the line graphed below?
Answer:
The equation is y = 2x. The slope is two and the line is a direct variation
Find the value of y.
Answer:
The answer should be the last one.
Step-by-step explanation:
Answer:
=2√2 the fourth choice.
Step-by-step explanation:
We can use the Pythagoras theorem to calculate the value of y.
a²+b²=c²
a=1
b=y
c=3
Therefore substituting for the values in the theorem above we get:
1²+y²=3²
Leave y on one side.
y²=3²-1²
y²=9-1
y²=8
y=±2√2 in surd form.
Since we expressing length, a scalar quantity, we take the modulus of our answer. Thus y=2√2
One triangle has the hypotenuse of 26 and the shortest side is 10, what is the other side?
a. 22
b. 25
c. 24
d. 23
Answer:
C. 24
Step-by-step explanation:
In a right triangle, the sum of the squares of the two legs of the triangle is equivalent to the square of the hypotenuse.
a²+b²=c²
a=10
b=?
c=26
Let us substitute with the values given in the question.
10²+b²=26²
100+b²=676
b²=676-100
b²=576
b=√576
=24
The other leg of the triangle is 24 units long.
Answer: option c.
Step-by-step explanation:
You need to use the Pythagorean Theorem. This is:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are legs of the triangle.
In this case you know that:
[tex]a=26\\b=10[/tex]
Then, you need to substitute values into [tex]a^2=b^2+c^2[/tex] and then solve for "c".
So, this is:
[tex]26^2=10^2+c^2\\\\26^2-10^2=c^2\\\\576=c^2\\\\\sqrt{576}=c\\\\c=24[/tex]
Find the formula for (f + g)(x) and simplify your answer.
f(x) = 3x and g(x) =
[tex] \sqrt{x - 4} [/tex]
[tex](f+g)(x)=3x+\sqrt{x-4}[/tex]
Ana has a rope that is 5 feet long. She divides her rope into 9 equal pieces. What is the length, in feet, of each piece of rope?
Final answer:
When a 5 feet long rope is divided into 9 equal pieces, each piece is approximately 0.56 feet long after performing the division and rounding to the nearest hundredth.
Explanation:
To find the length of each piece of rope when a 5 feet long rope is divided into 9 equal pieces, we need to divide the total length of the rope by the number of pieces. This is a division problem in arithmetic.
Division: 5 feet ÷ 9 pieces = 0.5555... feet per piece.
Since we typically want to represent a length in a more practical way, we can round this number. Rounding to the nearest hundredth, we get approximately 0.56 feet for each piece of rope.
Final answer:
To determine the length of each rope piece when a 5-foot long rope is divided into 9 equal parts, divide the total length by the number of parts, resulting in pieces that are approximately 0.5556 feet long.
Explanation:
To find the length of each piece of rope when a 5-foot long rope is divided into 9 equal pieces, we need to divide the total length of the rope by the number of pieces. Therefore, we use the division:
Length of each piece = Total length of rope ÷ Number of pieces
Length of each piece = 5 feet ÷ 9
Upon doing the division, we find that the length of each piece is approximately 0.5556 feet.
What of b make y = 2x plus b the same as y=2x? What does that value mean?
Pls answer:)
Answer:
No
Step-by-step explanation:
The short answer is no. b stands for some number. Once that number is fixed, it does not change. So the equation would look something like
y = 2x + 6 Now if you look at that again, that 6 is fixed.
If you want to put something in for x like x = 5 you get
y = 2(5) + 6
y = 10 + 6
y = 16 b = 6 did not change.
What does y = 2x equal
y = 2*5
y = 10
10 does not equal 16.
The only exception to what I've written is b = 0. Then both equations mean the same thing. But that is an exception.
What is the y-intercept of the function,represented by the table of values below?
Answer:
So the y-intercept is 10.
Step-by-step explanation:
So your table doesn't out right say the y-intercept. If it did it would be (x=0,y=something).
So let's see if this is linear. I'm going to see if we have the same rise/run ratio per pair of points as shown in the attachment:
These ratios are all the same -6/3 = -2/1 = -4/2 = -6/3 . These are all equal to -2.
So this is a line.
Linear equations in the form y=mx+b is called slope-intercept form where m is the slope and b is the y-intercept.
We just found m to be -2.
So our equation is now in the form y=-2x+b.
We can find b, the y-intercept, by using a point on this line. I like (4,2) from the table.
(x,y)=(4,2) with y=-2x+b will give us the information we need to find b.
2=-2(4)+b
2=-8+b
2+8=b
10=b
b=10
So the y-intercept is 10.
why does 7 9/7 = 8 2/7?
Firstly see what they are in mixed fraction form:
[tex]7 \frac{9}{7} = \frac{58}{7} [/tex]
therefore, 7 9/7 is equal to 58/7
[tex]8 \frac{2}{7} = \frac{58}{7} [/tex]
Three vertices of a square are (–1, 2), (2, 2), and (2, –1).
What is the fourth vertex of the square?
(–1, –1)
(–1, –2)
(2, 1)
(5, 1)
Question 5
Three vertices of a square are (–1, 2), (2, 2), and (2, –1).
What is the fourth vertex of the square?
(–1, –1)
(–1, –2)
(2, 1)
(5, 1)
Answer:
(-1,-1)
Step-by-step explanation:The square needs to be all side with the same value when you graph the vertices on x-y plot, you obtain (x is the dot that correspond a vertice and y the forth vertice )
x 2 | x
1 |
|
-2 -1 | 1 2
y -1| x
-2 |
If you draw a line between vertices the value it will be 2 + (-1) so the forth vertice has to be (-1,-1)
Find the area of a circle that has a diameter of 11 inches. Approximate Π as 3.14. Round your answer to the nearest hundredth.
A =
in. 2
Answer: 94.99 in^2
Step-by-step explanation: The equation for the area of a circle is A=πr^2. To solve this, we need to find the radius. The diameter is the whole circle, whole the radius is half. So divide the diameter by 2.
11/2 = 5.5
The radius is 5.5 inches. Plug the radius into the equation.
A=π5.5^2
Square the 5.5 first. You will get 30.25.
A=π30.25
Plug in 3.14 for pi.
A=3.14 x 30.25
Multiply.
A=94.985
Round to the nearest hundredth.
A=94.99
The area of the circle is 94.99 in^2.
94.99 in^2
hope this helps somebody
PLEASE HELP
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
Answer:
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct
Step-by-step explanation:
step 1
Find the area of the base of the rectangular pyramid
we know that
The volume of the rectangular pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the pyramid
we have
[tex]V=40\ units^{3}[/tex]
[tex]H=6\ units[/tex]
substitute and solve for B
[tex]40=\frac{1}{3}B(6)[/tex]
[tex]120=B(6)[/tex]
[tex]B=120/6=20\ units^{2}[/tex]
step 2
Find the volume of the rectangular prism with the same base area and height
we know that
The volume of the rectangular prism is equal to
[tex]V=BH[/tex]
we have
[tex]B=20\ units^{2}[/tex]
[tex]H=6\ units[/tex]
substitute
[tex]V=(20)(6)=120\ units^{3}[/tex]
therefore
The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct
Answer:
C
Step-by-step explanation:
Got it right one the test! <3
The first diagram shows an equilateral triangle and a
square with the same side length S. Find the area of the
triangle Ar in terms of the area of the square As
Answer:
Ar = ¼√3 As
Step-by-step explanation:
Area of an equilateral triangle is:
Ar = ¼√3 s²
Area of a square is:
As = s²
Substituting:
Ar = ¼√3 As
Which product is equivalent to 25x2 – 16?
Answer:
The correct answer would be 34
Step-by-step explanation:
When solving an expression, we would first solve the operator with the highest precedence. In mathematics, there are four basic operators. Addition, subtraction, multiplication and division. The precedence of Division and multiplication is higher than the precedence of Addition and subtraction. So by solving this with the precedence, we would first solve the multiplication operator which is 25 * 2, it will give 50, then we will subtract 16 from it like 50-16, which will give us 34.
Answer:
(5x+4)(5x-4)
Step-by-step explanation:
The product expression can be obtained by factorizing the expression 25x²-16 provided in the question.
The expression is a difference of two squares whose factors are generally
(a-b)(a+b)
√25x² is 5x
√16 is 4
Therefore the product required is (5x+4)(5x-4)
25x²-16 is equivalent to (5x+4)(5x-4)
which equation represents the data in the table? check all that apply
Answer:
[tex]y-6=-\frac{5}{4}(x+2)[/tex]
[tex]y-1=-\frac{5}{4}(x-2)[/tex]
[tex]y-3.5=-1.25x[/tex]
Step-by-step explanation:
step 1
Find the slope of the linear equation
with the points (-2,6) and (2,1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{1-6}{2+2}[/tex]
[tex]m=-\frac{5}{4}[/tex]
step 2
Find the equation of the line into point slope form
The equation of the line in slope point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{5}{4}[/tex]
1) with the point (-2,6)
substitute
[tex]y-6=-\frac{5}{4}(x+2)[/tex]
2) with the point (2,1)
substitute
[tex]y-1=-\frac{5}{4}(x-2)[/tex]
3) with the point (0,3.5)
substitute
[tex]y-3.5=-\frac{5}{4}(x-0)[/tex]
[tex]y-3.5=-\frac{5}{4}x[/tex] -------> [tex]y-3.5=-1.25x[/tex]
Answer:
A, D, E
Step-by-step explanation:
The results of a survey of customers at a pet supply store showed 36 owned mice, 32 owned parrots, and 14 owned both mice and parrots. How many owned either a mouse or a parrot?
54 people owned either a mouse or a parrot
Venn diagramA Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
Number of people that owned only mice = 36 - 14 = 22
Number of people that owned only parrot = 32 - 14 = 18
Number of people that owned either a mouse or a parrot = 22 + 18 + 14 = 54
54 people owned either a mouse or a parrot
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By using the principle of inclusion-exclusion to find the total number of pet store customers who owned either a mouse or a parrot, we calculated that 54 customers owned at least one of the pets, taking into account that 14 customers owned both.
Explanation:To determine the total number of store customers who owned either a mouse or a parrot, we need to apply the principle of inclusion-exclusion. This principle allows us to find the union of two sets without counting elements (customers) that are common to both sets more than once. The formula is ∑(A ∪ B) = ∑(A) + ∑(B) - ∑(A ∩ B), where ∑ denotes the number of elements in a set, A represents the group of mouse owners, B represents the group of parrot owners, and A ∩ B represents the group that owns both mice and parrots.
Applying this to our situation:
∑(A) = 36 (mouse owners)∑(B) = 32 (parrot owners)∑(A ∩ B) = 14 (owners of both mice and parrots)Using the principle of inclusion-exclusion:
∑(A ∪ B) = 36 + 32 - 14 = 54
This means that 54 customers owned either a mouse or a parrot or both.
solve 2/5+1/4+7/10= in simplest form
Answer:
1.35 or 27/20
Step-by-step explanation:
(2/5) + (1/4) + (7/10)
= 0.4 + 0.25 + 0.7
= 1.35 or 27/20
Which only lists multiples of 16? 1, 2, 4, 8, 16 16, 24, 32, 40 16, 32, 48, 64 1, 2, 4, 8, 12, 16
Answer:
16, 32, 48, 64
Step-by-step explanation:
Factors of a number are the numbers another number can be divided by. Multiples are numbers that can be divided by a number. Therefore, all the numbers in the list consist of 16 X 1, 16 X 2, 16 X 3, and so on.
The multiple of 16 is,
The multiples of 16 are 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, etc.
Multiple numbers:
It is a sequence where the difference between each next number and the preceding number, i.e. two consecutive multiples or products, is equal to 16. In simple words, multiples of a number are the products obtained by multiplying the given number by other natural numbers.
So, the required lists are,
16,32,48 and 64.
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what is equivalent to 10/10^3/4
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{10}{10^{\frac{3}{4}}}\implies \cfrac{10^1}{10^{\frac{3}{4}}}\implies \cfrac{10^{\frac{4}{4}}}{10^{\frac{3}{4}}}\implies 10^{\frac{4}{4}}\cdot 10^{-\frac{3}{4}}\implies 10^{\frac{4}{4}-\frac{3}{4}}\implies 10^{\frac{1}{4}}\implies \sqrt[4]{10}[/tex]
. Let A = {x: x ϵ R, x2 – 5x + 6 = 0 } and B = { x: x ϵ R, x2 = 9}. Find A intersection B and A union B
[tex]x^2 – 5x + 6 = 0\\x^2-2x-3x+6=0\\x(x-2)-3(x-2)=0\\(x-3)(x-2)=0\\x=3 \vee x=2\\A=\{-2,3\}\\\\x^2=9\\x=-3 \vee x=3\\B=\{-3,3\}\\\\A\cap B=\{3\}\\A\cup B=\{-3,-2,3\}[/tex]
If f(x) = 5x, what is f^-1(x)?
o f^-1(x) = -5x
o f^-1(x)= -1/5x
o f^-1(x) = 1/5x
o f^-1(x) = 5x
Answer:
Third choice
Step-by-step explanation:
They are asking us to find the inverse of y=5x. To do this you just switch x and y and then remake y the subject of the equation (solve for y.)
y=5x
x=5y (I switch x and y)
x/5=y ( I divided both sides by 5)
Then you just replace y with the f^-1(x) thing
f^-1(x)=x/5
or
f^-1(x)=1/5x
If f(x) = 5x, then the inverse of the function, f⁻¹(x) is x/5.
Given that :
f(x) = 5x
Let y = f(x).
So, y = 5x
Now, interchange the values for x and y.
Then,
x = 5y
Now, solve for y.
Divide both sides of the equation by 5.
x/5 = y
So, the inverse of the function is x/5.
Hence f⁻¹(x) = x/5.
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Find the value of x in the picture please
Answer:
Option B. The value of x is 20
Step-by-step explanation:
we know that
The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal.
so
In this problem
[tex](x)(x-11)=(x-8)(x-5)\\x^{2}-11x=x^{2}-5x-8x+40\\-11x=-13x+40\\2x=40\\x=20[/tex]
What is the distance between the points (2, 8) and (-7, -4) in the coordinate plane?
The distance between the points (2, 8) and (-7, -4) is 15 units.
Using the distance formula derived from the Pythagorean theorem, the distance between the points (2, 8) and (-7, -4) is found to be 15 units.
The distance between two points in the coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. For points (2, 8) and (-7, -4), the distance can be calculated as follows:
Subtract the x-coordinates: 2 - (-7) = 9.Subtract the y-coordinates: 8 - (-4) = 12.Square each result: 92 = 81 and 122 = 144.Add the squares together: 81 + 144 = 225.Take the square root of the sum: \\sqrt{225}\ = 15.Therefore, the distance between the points (2, 8) and (-7, -4) is 15 units.
Which table contains the vertex of the graph represented by y=x^2-6x+4?
A
x y
-2 20
0 4
2 -4
4 -4
B
x y
-1 11
1 -1
3 -5
6 4
C
x y
-3 31
-1 12
0 4
2 12
D
x y
0 5
2 7
3 5
5 7
Answer:
Table B
Vertex is (3,-5)
Step-by-step explanation:
We are given with an equation of a parabola [tex]y=x^2-6x+4[/tex]
Let is convert it into standard form of a parabola
[tex]y=x^2-6x+4[/tex]
adding and subtracting 9 in the right hand side of the =
[tex]y=x^2-6x+9-9+4[/tex]
[tex]y=x^2-2\times 3\times x+ 3^2-9+4[/tex]
the first three terms of the right hand side forms the expression of square of difference
[tex]a^2-2 \times a \times b+b^2 = (a-b)^2[/tex]
Hence
[tex]y=(x-3)^2-5[/tex]
adding 5 on both sides we get
[tex](y+5)=(x-3)^2[/tex]
Comparing it with the standard equation of a parabola
[tex]X^2=4\times \frac{1}{4} \times Y[/tex]
where [tex]X=x-3[/tex] and [tex]Y=y+5[/tex]
The vertex of [tex]X^2=4\times \frac{1}{4} \times Y[/tex] will be (0,0)
and thus vertex of
[tex](y+5)=(x-3)^2[/tex] will be (3,-5)
Hence the Table B is our right answer
drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. solve for x and match the solutions
The solutions to the linear equations in variable x and unknown constant [tex]\alpha[/tex] are [tex]\frac{-\alpha}{6}[/tex], [tex]\frac{3}{\alpha}[/tex] and [tex]\frac{-6}{\alpha}[/tex].
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
We are given linear equations in variable x with an unknown constant [tex]\alpha[/tex] and we have to solve for x.
[tex]4 = \frac{6}\alpha}x + 5\\\\\frac{6}{\alpha}x = - 1\\\\x = \frac{-\alpha}{6}[/tex].
[tex]7 + 2\alpha{x} = 13.\\\\2\alpha{x} = 6.\\\\x = \frac{3}{\alpha}[/tex]
[tex]-\alpha{x} - 20 = -14.\\\\-\alpha{x} = 6.\\\\x = \frac{-6}{\alpha}[/tex]
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Prove that the diagonals of a rectangle bisect each other.
The midpoint of AC is _____
Answer:
answer is a,b
Step-by-step explanation:
I have answered ur question
The mid-point of AC is (a, b). So, option D is correct. In a rectangle, the two diagonals bisect each other at their mid-point.
How to prove that the diagonals of a rectangle bisect each other?Find the mid-points of both the diagonals of the rectangleMid-point = ((x1+x2)/2, (y1+y2)/2)If the midpoints of both the diagonals are the same then they are said to bisect each other. If they are not the same, then they are not bisecting each other.Calculation:The given rectangle is ABCD
Its vertices have coordinates as
A - (0, 0)
B - (0, 2a)
C - (2a, 2b)
D - (2a, 0)
The diagonals are AC and BD.
Finding their mid-points:
Mid-point of the diagonal AC = ((0 + 2a)/2 , (0 + 2b)/2)
⇒ (2a/2, 2b/2)
⇒ (a, b) ... (1)
Mid-point of the diagonal BD = ((0 + 2a)/2, (2a+0)/2)
⇒ (2a/2, 2b/2)
⇒ (a, b) ...(2)
From (1) and (2), the midpoints of both the diagonals are equal. So, the diagonals of the rectangle ABCD bisect each other.
Hence, proved.
Therefore, the mid-point of the diagonal AC is (a, b).
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