Answer:
Summation notation:
[tex]\frac{1}{2}\sum_{k=1}^6f((.5k))[/tex]
or after using your function part:
[tex]\frac{1}{2}\sum_{k=1}^6(-(.5k)^2+2(.5k)+4)[/tex]
After evaluating you get 11.125 square units.
Step-by-step explanation:
The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.
The distance between x=0 and x=3 is (3-0)=3.
We want to divide that length of 3 units by 6 which gives a length of a half per each base length.
We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).
The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).
The next will be at x=2.5-.5=2, and the third rectangle will have a height of f(2).
The fourth rectangle will have a height of f(2-.5)=f(1.5).
The fifth one will have a height of f(1.5-.5)=f(1).
The last one because it is the sixth one will have a height of f(1-.5)=f(.5).
So to find the area of a rectangle you do base*time.
So we just need to evaluate:
[tex]\frac{1}{2}f(3)+\frac{1}{2}f(2.5)+\frac{1}{2}f(2)+\frac{1}{2}f(1.5)+\frac{1}{2}f(1)+\frac{1}{2}f(.5)[/tex]
or by factoring out the 1/2 part:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
To find f(3) replace x in -x^2+2x+4 with 3:
-3^2+2(3)+4
-9+6+4
1
To find f(2.5) replace x in -x^2+2x+4 with 2.5:
-2.5^2+2(2.5)+4
-6.25+5+4
2.75
To find f(2) replace x in -x^2+2x+4 with 2:
-2^2+2(2)+4
-4+4+4
4
To find (1.5) replace x in -x^2+2x+4 with 1.5:
-1.5^2+2(1.5)+4
-2.25+3+4
4.75
To find f(1) replace x in -x^2+2x+4 with 1:
-1^2+2(1)+4
-1+2+4
5
To find f(.5) replace x in -x^2+2x+4 with .5:
-.5^2+2(.5)+4
-.25+1+4
4.75
Now let's add those heights. After we obtain this sum we multiply by 1/2 and we have our approximate area:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
[tex]\frac{1}{2}(1+2.75+4+4.75+5+4.75)[/tex]
[tex]\frac{1}{2}(22.25)[/tex]
[tex]11.125[/tex]
Okay now if you wanted the summation notation for:
[tex]\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))[/tex]
is it
[tex]\frac{1}{2}\sum_{k=1}^{6}(f(.5+.5(k-1)))[/tex]
or after simplifying a bit:
[tex]\frac{1}{2}\sum_{k=1}^6 f((.5+.5k-.5))[/tex]
[tex]\frac{1}{2}\sum_{k=1}^6f((.5k))[/tex]
If you are wondering how I obtain the .5+.5(k-1):
I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)
PQ is the perpendicular
bisector of AB
In the construction shown, the two arcs with points P and Q have the same radius. What must be true of PO?
Answer:
PQ must bisect AB
Step-by-step explanation:

Transversal  cuts parallel lines  and  at points X and Y as shown in the diagram. If m∠CXP = 106.02°, what is m∠SYD?
A.
73.98°
B.
90°
C.
106.02°
D.
180°
Answer:
m<SYD = 106.02°. Reason: alternate exterior angles are equal.
Step-by-step explanation:
Answer:
m<SYD = 106.02°. Reason: alternate exterior angles are equal.
Step-by-step explanation:
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week.
Answer:
Step-by-step explanation:
Let 'c' be the number of child bikes c=20
and 'a' be the number of adult bikes. a=6
According to the problem
The restriction of building time for a week is 4c+6a≤120 hours.........(1)
and the restriction of testing time for a week is 4c+4a≤100 hours..........(2)
Lets check whether company can build c=20 and a=6 bikes in a week by putting these values in (1) and (2).
4c+6a≤120 hours.........(1)
4(20)+6(6)≤120
80+36≤120
116≤120 (true)
4c+4a≤100 hours..........(2)
4(20)+4(6)≤100
80+24≤100
104≤100 (true)
Hence, the company can build 20 child bikes and 6 adult bikes in the week....
for the function f(x)=3(x-1)^2+2 identify the vertex, domain, and range.
Answer:
The vertex of the function is (1 , 2)
The domain is (-∞ , ∞) OR {x : x ∈ R}
The range is [2 , ∞) OR {y : y ≥ 2}
Step-by-step explanation:
* Lets revise the standard form of the quadratic function
- The standard form of the quadratic function is
f(x) = a(x - h)² + k , where (h , k) is the vertex point
- The domain is the values of x which make the function defined
- The domain of the quadratic function is x ∈ R , where R is the set
of real numbers
- The range is the set of values that corresponding with the domain
- The range of the quadratic function is y ≥ k if the parabola upward
and y ≤ k is the parabola is down ward
* Lets solve the problem
∵ f(x) = 3(x - 1)² + 2
∵ f(x) = a(x - h)² + k
∴ a = 3 , h = 1 , k = 2
∵ The vertex of the function is (h , k)
∴ The vertex of the function is (1 , 2)
- The domain is all the real number
∵ The domain of the quadratic function is x ∈ R
∴ The domain is (-∞ , ∞) OR {x : x ∈ R}
- The leading coefficient of the function is a
∵ a = 3 ⇒ positive value
∴ The parabola is opens upward
∴ The range of the function is y ≥ k
∵ The value of k is 2
∴ The range is [2 , ∞) OR {y : y ≥ 2}
Which of the following correlation coefficients represents the strongest correlation?
O 0.043680937
0 -0.313535265
O-0.922107932
O 0.854423006
Answer:
Option C (-0.922107932)
Step-by-step explanation:
Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. This means that closer the correlation to 1, stronger the positive relationship, and closer the correlation to -1, stronger the negative relationship. It can be seen that Option C (-0.922107932) is the correlation coefficient which is the largest in terms of the magnitude. Therefore, Option C is the correct choice!!!
Ms. Lund placed a 7 foot ladder against a wall with the base of the ladder 4 feet away from the wall . she decided that a different , 10 foot ladder needed to be used . for if Ms. Lund wants the longer ladder to rest against the wall at the same angle as the shorter ladder , about how far away from the wall should she place its base ?
ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)
[tex] \frac{7}{10} = \frac{4}{x} \\ x = \frac{40}{7} [/tex]
The distance the wall should place its base will be 5.71 feet.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.
ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between the wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)
The distance will be calculated as below:-
( 7 / 10 ) = ( 4 / x )
x = ( 10 x 4 ) / 7
x = 5.71 feet
Therefore, the distance the wall should place its base will be 5.71 feet.
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Solve the following system of equations: 3x − 2y = 6 6x − 4y = 12 (0, 0) (6, 12) Infinitely many solutions No solutions
Answer:
The correct answer option is: infinitely many solutions.
Step-by-step explanation:
We are given the following system of equations:
[tex] 3 x - 2 y = 6 [/tex] --- (1)
[tex] 6 x - 4 y = 1 2 [/tex] --- (2)
Dividing equation (2) by 2 to get:
[tex] 3 x - 2 y = 6 [/tex] --- (3)
As the equation (3) is same as the equation (1), therefore the system will have infinitely many solutions.
Answer:
infinitely many solutions
Step-by-step explanation:
Note that if you multiply the first equation by 2, you get 6x - 4y = 12, which is exactly the same as the second equation. These two lines coincide, and so there are infinitely many solutions.
The function f(x) = 2.54 can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the
multiplicative rate of change of the function?
Answer:
So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.
Step-by-step explanation:
I think your function is off... but I can look at your ordered pairs.
(1,10)
(2,50)
(3,250),..
As the x increases by 1 the y is being multiply by a factor of 5 each time.
So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (fxg)(-5).
a. -59
b. 3
c. 26
d. -6
Answer:
78
Step-by-step explanation:
The given functions are:
[tex]f(x) = - 2x - 7[/tex]
and
[tex]g(x) = - 4x + 6[/tex]
[tex](f \times g)(x) = f(x) \times g(x)[/tex]
[tex](f \times g)(x) = ( - 2x - 7)( - 4x + 6)[/tex]
When we plug in x=-5, we get:
[tex](f \times g)( - 5) = ( - 4 \times - 5 + 6)( - 2 \times - 5 - 7)[/tex]
[tex](f \times g)( - 5) = ( 20 + 6)( 10 - 7)[/tex]
[tex](f \times g)(5) = ( 26)( 3) =7 8[/tex]
Refer to the figure and match the theorem that supports the statement.
1. If chords are =, then arcs are =. If BC = DE, then Arc BC = Arc DE
2. If arcs are =, then chords are =. If AX is perpendicular to BC, then BX = XC
3. Diameters perpendicular to chords bisect the chord If Arc BC = Arc DE, then BC = DE
The principles of circle geometry dictate that: if chords are equal then their corresponding arcs are equal; if arcs are equal then their chords are equal; and diameters perpendicular to chords bisect the chord. However, some of the proposed arguments in the question are not matching these principles.
Explanation:The three statements highlighted in this question are the principles of circle geometry.
1. If chords are equal, then arcs are equal: This theorem states that if two chords in a circle are equal in length, then their corresponding arcs (the part of the circumference that the chord subtends) are also equal. If BC = DE as stated, then Arc BC = Arc DE.
2. If arcs are equal, then chords are equal: This is the converse of the first theorem. If two arcs of a circle are equal, then the chords subtending these arcs are equal. However, this principle is not relevant for the condition if AX is perpendicular to BC, then BX = XC.
3. Diameters perpendicular to chords bisect the chord: This theorem states that if a diameter of a circle is perpendicular to a chord, then it bisects the chord. Therefore the statement if Arc BC = Arc DE, then BC = DE is not relevant to this theorem.
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What is the location of the point on the number line that is 3/5 of the way from a=2 to b=17
Answer:
11
Step-by-step explanation:
The distance that a is to b is b-a=17-2=15.
The line segment from a=2 to b=17 has length 15.
We need to know what is 3/5 of 15.
3/5 of 15 means what is 3/5 times 15?
(3/5)(15)=3(3)=9
So this means we are looking to make a line segment that is 9 units from 2 which is 2 to 11.
So 11 is 3/5 the way from a=2 to b=17.
Let's check from 2 to 11 that is a length of 9 and from 2 to 17 that is a length of 15.
Is 9/15 equal to 3/5?
Yes, 9/15 can be reduced to 3/5.
If (5^0)^x = 1, what are the possible values of x?
Answer:
x can be any value
Step-by-step explanation:
(5^0)^x = 1,
5^0 =1
1^x =1
X can be any value
For this case we have the following expression:
[tex](5^{ 0})^{x} = 1[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^{n * m}[/tex]
Then, rewriting the expression:
[tex]5 ^ 0 = 1[/tex]
Thus, the variable "x" can take any value:
Answer:
The variable "x" can take any value
riangle XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′?
Answer:
5 units
Step-by-step explanation:
According to the given statement Δ XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z' which means that each point in ΔXYZ is moved 4 units up and moved 3 units left.
To find the distance of each corresponding point we will use the Pythagorean theorem which states that the square of the length of the Pythagorean of a right triangle is equal to the sum of the squares of the length of other legs
The square of the required distance = 4^2+3^2 = 16+9 =25
By taking root of 25 we get:
√25 = 5
Thus, we can conclude that the the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′ is 5 units. ..
Which relationship in the triangle must be true?
sin(B) = sin(A)
sin(B) = cos(90 - B)
cos(B) = sin(180 - B)
COS(B) = COS(A)
Mark this and return
Save and Exit
Sube
Answer:
sin(B)=cos(90-B)
Step-by-step explanation:
sin(B)=cos(90-B) is a co-function identity.
We can also prove it using the difference identity for cosine.
Let's do that:
cos(90-B)
equals
cos(90)cos(B)+sin(90)sin(B)
0cos(B)+1sin(B)
0+sin(B)
sin(B)
Therefore cos(90-B)=sin(B).
What is the seventh term of the geometric sequence where a1=128 and a3=8
[tex]\bf \begin{array}{lll} term&value\\ \cline{1-2} a_1&128\\ a_2&128r\\ a_3&128rr\\ &128r^2 \end{array}~\hspace{5em}\stackrel{a_3}{128r^2}=\stackrel{a_3}{8}\implies r^2=\cfrac{8}{128}\implies r^2=\cfrac{1}{16} \\\\\\ r=\sqrt{\cfrac{1}{16}}\implies r=\cfrac{\sqrt{1}}{\sqrt{16}}\implies r=\cfrac{1}{4}\qquad \leftarrow \textit{common ratio} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=7\\ a_1=128\\ r=\frac{1}{4} \end{cases}\implies a_7=128\left( \frac{1}{4} \right)^{7-1} \\\\\\ a_7=128\left( \frac{1}{4} \right)^6\implies a_7=128\cdot \cfrac{1}{4096}\implies a_7=\cfrac{128}{4096}\implies a_7=\cfrac{1}{32}[/tex]
X+1
-
and h(x) = 4 - X, what is the value
Oil CD
Nior
wla
olo
Answer:
8/5
Step-by-step explanation:
[tex](g\circ h)(-3)[/tex] means [tex]g(h(-3))[/tex].
Start with the inside first: h(-3).
h(-3) means use the function called h and replace the x with -3. The expression that is called h is 4-x.
4-x evaluated at x=-3 gives us 4-(-3)=4+3=7.
So the value for h(-3) is 7, or h(-3)=7.
Now this is what we thus far:
[tex](g\circ h)(-3)=g(h(-3))=g(7)[/tex].
g(7) means use the function called g and replace x with 7. The expression that is called g is (x+1)/(x-2).
(x+1)/(x-2) evaluated at x=7 gives us (7+1)/(7-2)=(8)/(5)=8/5.
This is our final answer:
[tex](g\circ h)(-3)=g(h(-3))=g(7)=\frac{8}{5}[/tex].
PLEEEEEEASE HELP ME:D
Answer:
{ (1,1),(2,9),(4,8) } is the right answer. Mentioned relation has all the ordered pairs of x and y in the form of set, shown in the table.
Step-by-step explanation:
Tables can be used to describe functions. i.e. in given table two coordinates x,y used as ordered pairs and their values mentioned, the value x-coordinate comes first and than value of its corresponding y-coordinate .According to the table, if we take value of x=1 than we need to take corresponding value of y=1 written as ( 1,1 ), Similarly for if x=2, its corresponding value of 'y' will be y=3 written as ( 2,3 ) and so onThe entire table expressed in ordered pair gives set { (1,1),(2,9),(4,8) }.Answer details
Grade: Middle
Subject: Mathematics
Chapter: Representing Functions and relations
Keywords: relations, ordered pairs, tables and functions, set etc
Use the discriminant to describe the roots of each equation. Then select the best description.
x2 - 4x + 4 = 0
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 : a ≠ 0, then
The nature of it's roots can be determined by the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then roots are real and distinct
• If b² - 4ac = 0 then roots are real and equal
• If b² - 4ac < 0 then roots are not real
For x² - 4x + 4 = 0 ← in standard form
with a = 1, b = - 4, c = 4, then
b² - 4ac = (- 4)² - (4 × 1 × 4) = 16 - 16 = 0
Hence roots are real and equal
This can be shown by solving the equation
x² - 4x + 4 = 0
(x - 2)² = 0
(x - 2)(x - 2) = 0, hence
x - 2 = 0 or x - 2 = 0
x = 2 or x = 2 ← roots are real and equal
What is the explicit formula for this sequence?
-7,-3, 1, 5,...
A. an = -7 + (n - 1)(-4)
B. an = 9+ (n - 1)(-4)
C. an = -7 + (n - 114
D. an= -4 + (n - 1)(-7
Answer:
[tex]a_n=-7+4(n-1)[/tex]
or
[tex]a_n=-7+(n-1)(4)[/tex]
Step-by-step explanation:
-7,-3,1,5,... is a arithmetic sequence.
Arithmetic sequences have a common difference. That is, it is going up by 4 each time.
When you see arithmetic sequence, you should think linear equation.
The point-slope form of a line is [tex]y-y_1=m(x-x_1)[/tex].
m is the common difference, the slope.
Any they are using the point at x=1 in the point slope form. So they are using (1,-7).
So let's put this into our point-slope form:
[tex]y-(-7)=4(x-1)[/tex]
[tex]y+7=4(x-1)[/tex]
Subtract 7 on both sides:
[tex]y=-7+4(x-1)[/tex]
So your answer is
[tex]a_n=-7+4(n-1)[/tex]
The explicit formula for the sequence -7, -3, 1, 5,... is an = -7 + (n - 1)(4), which corresponds to an arithmetic sequence with a common difference of 4.
The student is looking for the explicit formula for the sequence -7, -3, 1, 5,.... To find the explicit formula for a linear sequence, we look for a pattern in the increments between successive terms. In this sequence, each term increases by 4 from the previous term (-7 + 4 = -3, -3 + 4 = 1, etc.), so the common difference is 4. Using the formula for an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference, we can find the explicit formula:
an = -7 + (n - 1)(4)
Since the common difference in the question is positive and we are adding it to the first term which is negative, it is clear that choice A is the correct formula representing the given sequence:
an = -7 + (n - 1)(4)
what is the slope of the line that passes through the points (1, −3) and (3, −5)
Answer:
Slope = -1
Step-by-step explanation:
Use the following formula:
slope (m) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (1 , -3)
(x₂ , y₂) = (3 , -5)
Plug in the corresponding numbers to the corresponding variables. Simplify:
m = (-5 - (-3))/(3 - 1)
m = (-5 + 3)/(3 - 1)
m = -2/2
m = -1
The slope of the line is -1.
~
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have as data the following points:
[tex](x_ {1}, y_ {1}) :( 1, -3)\\(x_ {2}, y_ {2}): (3, -5)[/tex]
Substituting the values:
[tex]m = \frac {-5 - (- 3)} {3-1}\\m = \frac {-5 + 3} {3-1}\\m = \frac {-2} {2}\\m = -1[/tex]
Thus, the slope is -1.
Answer:
The slope is -1
Which of the following does not factor as a perfect square trinomial? A. 16a^2-72a+81 B. 169x^2+26xy+y^2 C. x^2-18x-81 D. 4x^2+4x+1
Answer:
The correct option is C.
Step-by-step explanation:
Lets solve each option one by one
A) 16a^2-72a+81
According to whole square formula:
a²-2ab+b² =(a-b)²
We have to take the square root of first and third term of each equation.
a² shows the first term = 16a^2
The square root of 16a^2 is 4a.. because 4 is the number which can be multiplied two times to give 16 and when we multiply a two times it gives us a².
b² shows the third term = 81
The perfect square of 81 is 9.
2ab shows the middle term.
2ab = 2(4a)(9) = 72a
Thus we can factor it as a perfect square trinomial:
a²-2ab+b² =(a-b)²
16a²-72a+81 =(4a-9)²
B) 169x^2+26xy+y^2
a²+2ab+b² =(a+b)²
The square root of 169x² is 13x
Square root of y² is y
The middle term 26xy =2ab= 2(13x)(y)= 26xy
Thus we can factor it as a perfect square trinomial:
a²+2ab+b² =(a+b)²
169x^2+26xy+y^2 = (13x+y)²
C) x^2-18x-81
We can not factor it as a perfect square trinomial because the third term is negative.
D) 4x^2+4x+1
a²+2ab+b² =(a+b)²
The square root of 4x² is 2x
Square root of 1 is 1
The middle term 4x=2ab=2(2x)(1)= 4x
Thus we can factor it as a perfect square trinomial:
a²+2ab+b² =(a+b)²
4x^2+4x+1 = (2x+1)²
Thus the correct option is C....
The set of ordered pairs in the graph below can be described as which of the following? A. a relation B. a function C. a relation and function D. neither a relation nor function
Answer:
a relation and function ⇒ answer C
Step-by-step explanation:
* Lets revise the relation and the function
- The relation is between the x-values and y-values of ordered pairs.
- The set of all values of x is called the domain, and the set of all values
of y is called the range
- The function is a special type of relation where every x has a unique y
- Every function is a relation but not every relation is a function
* Lets solve the problem
∵ The graph is a parabola
∵ The parabola is a function because every x-coordinates of the
points on the parabola has only one y-coordinate
- Ex: some ordered pairs are (-5 , -5) , (-2 , 5) , (0 , 7) , (2 , 5) , (5 , -5)
∵ Every x-coordinate has only one y-coordinate
∴ The graph represents a function
∵ Every function is a relation
∴ The set of ordered pairs in the graph below can be described as
a relation and function
x = -2y - 5
4x – 3y = 2
How to solve this linear system?
Which information would best fill the blanks in row 3?
1.metallic bond and low melting point
2.metallic bond and high melting point
3. covalent bond and low melting point
4.covalent bond and high melting point
Answer:
covalent bond and low melting point- 3.
Answer:
C)
Step-by-step explanation:
egdenuity 2020
A television video game company has the following total expenses E and total incomes I for producing x number of games.
E=200+11x
I=120+x2
Write an equation to represent the profit p for selling x videos.
JK Rowling is autographing some of the new Harry Potter books. A store sells 56 books and she is able to autograph 5/8 of the books sold. How many books will have her autograph?
Answer:
35 books
Step-by-step explanation:
56/8 = 7
7 x 5 = 35
5/8 of 56 = 35
J.K. Rowling will autograph 35 of the 56 books sold, which is calculated by multiplying the total number of books by 5/8.
To find out how many books J.K. Rowling will autograph, we need to calculate 5/8 of the 56 books sold. Here's the step-by-step calculation:
Find out what 5/8 of the total amount is by multiplying the total number of books (56) by 5/8.
To do this, first multiply 56 by 5, which equals 280.
Then divide that number by 8, which equals 35.
Therefore, J.K. Rowling will autograph 35 books.
COMPLETE
the equation x2 - 9 = 0 has
real solution(s).
Answer:
Step-by-step explanation:
x^2-9 = 0
x^2 = 0+9
x^2=9
Take square root at both sides:
√x^2 =+/-√9
x =+/- 3
This equation has 2 real solutions, x=3 , x=-3....
Find the distance from Point A (4,2) to Point B (-3,2).
Answer:
7
Step-by-step explanation:
You can use the distance formula, but since both points have the same y-coordinate, they lie on a horizontal line. Just find the difference between the x-coordinates and take the absolute value.
distance = |-3 - 4| = |-7| = 7
Answer:
The distance is:
[tex]d=7[/tex]
Step-by-step explanation:
The distance d between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is calculated using the following formula:
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
In this case the points are:
A (4,2), B (-3,2).
Then the distance is:
[tex]d=\sqrt{((-3)-4)^2 + (2-2)^2}[/tex]
[tex]d=\sqrt{((-7)^2 + (0)^2}[/tex]
[tex]d=\sqrt{49}[/tex]
[tex]d=7[/tex]
How can you estimate 33 percent of 87?
Answer:
28.71
Step-by-step explanation:
The easiest way I do this is by taking the smaller number (33) changing it to a decimal form of .33, and then multiplying it by 87 to get 28.71
rewrite the fraction using the least common denominator
4/9 7/15
Answer:
20/45 & 21/45
Step-by-step explanation:
Find a common denominator. What you do to the denominator, you do to the numerator. In this case, the smallest denominator is 45.
(4/9)(5/5) = 20/45
(7/15)(3/3) = 21/45
The two fractions you have is:
20/45 for 4/9
21/45 for 7/15
~
Answer:
20/45 for 4/9 and 21/45 for 7/15
Step-by-step explanation:
The least common denominator of 4/9 is 20/45.
The least common denominator of 7/15 is 21/45.