Using a center of dilation at the origin, Point A with coordinates (-3, 7) is dilated with a scale factor r = 2/3. What are the coordinates of Point A’?
A) (-2, 14/3)
B) (2, -7/3)
C) (-2, 7/3)
D) (3, 14)
Answer:
The co-ordinates of A' is
A) [tex](-2,\frac{14}{3})[/tex]
Step-by-step explanation:
Given point:
(-3,7)
The point is dilated with a scale factor [tex]r=\frac{2}{3}[/tex] with the center of dilation at the origin.
To find the co-ordinates of the dilated point A'.
Solution:
Any point dilated with the center of dilation at the origin with a scalar factor [tex]k[/tex] is given by:
[tex]D(x,y)\rightarrow D(kx,ky)[/tex]
Thus, the point (3,-7) dilated with a scale factor [tex]r=\frac{2}{3}[/tex] with the center of dilation at the origin is given as :
[tex]A(-3,7)\rightarrow A'(\frac{2}{3}\cdot -3,\frac{2}{3}\cdot 7)[/tex]
[tex]A(-3,7)\rightarrow A'(-2,\frac{14}{3})[/tex]
Thus, the co-ordinates of A' is [tex](-2,\frac{14}{3})[/tex].
What the answer to this is
Answer:
1 and 2 or A
Step-by-step explanation:
it is only what macks seans
How is the sum expressed in sigma notion? Multiple choice
Answer:
The given sum expressed in sigma notation is
[tex]\sum\limits_{i=1}^{5}4^{i-4}[/tex]Therefore [tex]\sum\limits_{i=1}^{5}4^{i-4}=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]Step-by-step explanation:
Given series is [tex]\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]
The given sum expressed in sigma notation is
[tex]\sum\limits_{i=1}^{5}4^{i-4}[/tex]Now verify that the sigma notation [tex]\sum\limits_{i=1}^{5}4^{i-4}[/tex] is correct or notNow expand the series [tex]\sum\limits_{i=1}^{5}4^{i-4}=4^{1-4}+4^{2-4}+4^{3-4}+4^{4-4}+4^{5-4}[/tex] [tex]=4^{-3}+4^{-2}+4^{-1}+4^{0}+4^{1}[/tex] ( using the properties [tex]a^{-m}=\frac{1}{a^m}[/tex] and [tex]a^0=1[/tex] )[tex]=\frac{1}{4^3}+\frac{1}{4^2}+\frac{1}{4^1}+1+4[/tex][tex]=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]Therefore [tex]\sum\limits_{i=1}^{5}4^{i-4}=\frac{1}{64}+\frac{1}{16}+\frac{1}{4}+1+4[/tex]Hence verified
Answer:
Option 2
Step-by-step explanation:
1/64 = 4^-3
1/16 = 4^-2
1/4 = 4^-1
1 = 4^0
4 = 4^1
Allie and Sarah decided that they want to purchase renters insurance for the apartment they share. They made a list of all of the items to be covered by the insurance policy, along with their estimated values. If the items to be covered total more than $3000, the insurance company charges an annual premium of 23% of the total value of the items. If the items to be covered total $3000 or less, the insurance company charges an annual premium of 20% of the total value of the items. Using the list of items Allie and Sarah provided, determine their monthly renters insurance premium. Allie's Stuff Sarah's Stuff TV ($250) Stereo ($75) Stereo ($150) Bicycle ($250) CD's ($225) CD's ($130) DVD's ($385) DVD's ($300) Bicycle ($400) IPOD ($80) Microwave ($30) Computer ($675) Laptop Computer ($950) a. $65.00 b. $74.75 c. $325.00 d. $780.00
Answer:
The answer is b. $ 74.75
Step-by-step explanation:
First, we need to gather the data from the question.Data:
Let x be the value of items to be insured.
1. if the items are more than $ 3 000 it means that x is greater than $ 3000 and the annual premium will be 23 % of the total value.
2. if the items are less or equal to $ 3 000, it means that x ≤ $ 3 000 ( in other words, x is less than or equal to $ 3 000)
Second, we find the total worth of all the items. Adding up all the values gives $ 3900 which is more than $ 3 000. Therefore, rule 1 applies.The annual premium for the goods will be:
annual premium = 23 % × $ 3900
= $ 897
However, the premium is supposed to be paid monthly. Divide the total premium by 12 to get:
$ 897/12 = $ 74.75
This is option c.
There are 16 ounces in 1 pound Chanda picked 9 pounds of cherries from her tree this year find the number of ounces of cherries
Answer:
16 x 9 = 144 144 is the answer.
Step-by-step explanation:
If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of (StartFraction f Over g EndFraction) (x)?
all real values of x
all real values of x except x = 5
all real values of x except x = –5
all real values of x except x = 5 and x = –5
Answer:
all real values of x except x=5
Step-by-step explanation:
If [tex]f(x) = x2 – 25 and g(x) = x – 5,[/tex]
Then the domain is all real values of x except [tex]x=5[/tex].
What is domain in math?The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
What are all real numbers in math?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5), and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Learn more about the domain in math here: https://brainly.com/question/24539784
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What are the roots of the equation x^2 + -9=0
Answer:
x = 3 or x = -3
Step-by-step explanation:
If x^2 - 9 = 0 we transfer 9 to the right side of the equation and it's change negative sign to positive while doing so
now we have x^2 = 9 the square of a number must be equal to a positive number in real numbers
but the root can be either negative or positive so we say x = 3 or x = -3
What is the value of x to the nearest tenth?
Answer:0.8
Step-by-step explanation:
Answer:
37.0
Step-by-step explanation:
Half of x is the longer leg of the right triangle shown. That leg length can be found using the Pythagorean theorem:
x/2 = √(24.6² -16.2²) = √(605.16 -262.44) = √342.72
x ≈ 2×18.513 ≈ 37.025 . . . . . . rounding to 3 decimal places
x ≈ 37.0
What is the circumference of circle P?
Express your answer in terms of π.
The circumference of circle P is 6π ft. This corresponds to option (b) in the choices provided.
Understanding the Problem: The problem provides the length of the line segment PA, which is considered the radius of circle P.
Circumference Formula: The circumference of a circle is the distance around its edge. The formula to calculate it is C = 2πr, where C is the circumference and r is the radius.
Identifying the Radius: In this problem, PA is given as 3 ft. This represents the radius of circle P.
Substituting Values into the Formula: We substitute the given radius into the circumference formula:
C = 2π ˣ 3 ft
Calculating: We perform the multiplication to find the circumference:
C = 6π ft
Complete Question:
What is the circumference of circle P?
PA = 3 ft
Express your answer in terms of π.
a. 3π ft
b. 6π ft
c. 12π ft
d. 24π ft
PLEASE HELPPPP WITH THISSSSS
Answer:
2) Option 9.4 is correct
Therefore the length of the given line segment is [tex]s=9.4[/tex] units
3) Option (1,1) is correct
Therefore the midpoint of the given line segment is M=(1,1)
Step-by-step explanation:
2) Given that the line segment CD with endpoints C at (-3,1) and endpoint at D (5,6)
To find the length of the given line segment :
That is to find the distance of the end points using distance formula
[tex]s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] units
Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-3,1) and (5,6) respectively
Substitute the points in the distance formula we have
[tex]s=\sqrt{(5-(-3))^2+(6-1)^2}[/tex] units
[tex]=\sqrt{(5+3)^2+(5)^2}[/tex] units
[tex]=\sqrt{8^2+5^2}[/tex]
[tex]=\sqrt{64+25}[/tex]
[tex]=\sqrt{89}[/tex]
[tex]=9.4[/tex]
Therefore [tex]s=9.4[/tex] units
Option 9.4 is correct
Therefore the length of the given line segment is [tex]s=9.4[/tex] units
3) Given that the line segment PG with point P at (-6,4) and point at G (8,-2)
To find the midpoint of the given line segment :
Midpoint formula is [tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-6,4) and (8,-2) respectively
Substituting the points in the midpoint formula we get
[tex]M=(\frac{-6+8}{2},\frac{4-2}{2})[/tex]
[tex]=(\frac{2}{2}+\frac{2}{2})[/tex]
[tex]=(1,1)[/tex]
Therefore M=(1,1)
Therefore option (1,1) is correct
Therefore the midpoint of the given line segment is (1,1)
Raquel attended a volleyball game that began at 9:30am and ended at 11:45 am she began her lunch at 12:00 pm and ended lunch at 1:00 pm. how much time raquel spend at the game and lunch
Answer:
Raquel spend 2 hr 15 Minutes at the volley ball game and 1 hour at the lunch
Step-by-step explanation:
Time Spent at the Volley ball match
The difference of 11:45 and 9 :30 is 2:15 which indicate she spend 2 hour and 15 minutes at the lunch.
sameway , from 12 pm to 1 pm , it encounter a difference of 1 Hour.
hence , she spent 1 hr at lunch.
What is the equation of the line that has a slope of 4 and passes through the point (3,-10)
Answer:
y=4x-22
Step-by-step explanation:
y-y1=m(x-x1)
y-(-10)=4(x-3)
y+10=4x-12
y=4x-12-10
y=4x-22
Solve: x + 1.5= 5.7
How do I solve this?
Answer:
4.2
Step-by-step explanation:
5.7-1.5=4.2
Answer: x = 4.2
Explanation: If we're asked to solve for x in the equation x + 1.5 = 7.5, what we're really being asked to do is get x by itself on one side of the equation.
So if we take a look at the left side of our equation, notice that 1.5 is being added to x so in order to get x by itself, we must subtract 1.5 from the left side of the equation. Now remember your first rule of solving equations. If we subtract 1.5 from the left side of the equation, we must also subtract 1.5 from the right side of the equation.
So on the left side our +1.5 and -1.5 cancel out and we're simply left with x. On the right side of the equation,
5.7 - 1.5 simplifies to 4.2 so our answer is x = 4.2.
The nice thing about solving equations is that you can always check your answer by plugging it back in to the original equation.
So here, we're gonna plug a 4.2 back in for x in the original equation and we get (4.2) + 1.5 = 5.7.
Since 4.2 + 1.5 = 5.7 is a true statement, our answer checks and we know that it's right.
The slope of a line is -3 and the y-intercept is (0,4). What is the equation of the line in slope-
intercept form?
Answer:
y=-3x+4
Step-by-step explanation:
y-y1=m(x-x1)
y-4=-3(x-0)
y-4=-3(x)
y-4=-3x
y=-3x+4
What is eight more than the number of children is 24 as a word equation
Answer:
Eight plus twenty four equals thirty two
have an amazing day! (❁´◡`❁)
Step-by-step explanation:
The word equation for "eight more than the number of children is 24" can be written as:
Number of children + 8 = 24
Let's break it down step by step:
1. Identify the unknown: The unknown in this equation is the number of children. Let's represent it as "x".
2. Translate "eight more than the number of children" into mathematical language: "Eight more than" means adding 8 to the number of children.
3. Write the equation: The equation becomes x + 8 = 24.
To find the value of x, we need to isolate it on one side of the equation. We can do this by subtracting 8 from both sides:
x + 8 - 8 = 24 - 8
Simplifying further:
x = 16
Therefore, the number of children is 16.
It's important to note that the word equation can be translated into different mathematical expressions. For example, another way to represent "eight more than the number of children is 24" would be:
Number of children = 24 - 8
This equation would also yield the same answer: 16.
Remember, word equations help us represent real-life situations in mathematical form, allowing us to solve problems and find solutions.
Please help fast!! A, B, C or D?
Answer:
the answer would be is 6
Answer:
a
Step-by-step explanation:
Solve: 2(23 + a) = 34
Answer:
a = −6
Step-by-step explanation:
Step 1: You should divide both sides by 2.
[tex]23+a=\frac{34}{2}[/tex]
Step 2: then simplify [tex]\frac{34}{2}[/tex] into 17.
23 + a = 17
Step 3: next, you need to subtract 23 from both sides.
a = 17 − 23
Step 4: lastly, Simplify 17 − 23 to −6 and you're done!
a = −6
Answer:
a = -6
Step-by-step explanation:
2 (23 + a) = 34
46 + 2a = 34
2a = 34 - 46
2a = - 12
a = - 12/2
a = - 6
How do you get 24 using 1, -6, -7, -3
Answer:
24
Step-by-step explanation:
We want to set up an expression involving 1, -6, -7, -3.
-6*-3--7+1
We use BODMAS to simplify:
We multiply to get:
18--7+1
We now add to obtain:
18--6
Note that negative negative gives addition.
Therefore:
18+6
This finally simplifies to:
24
Explain how to evaluate a + b ÷ c, when a = 1 2/5, b = 2 2/5, and c = 3/4. You do not have to compute the values.
Answer:
The correct answer is: [tex]4\frac{3}{5}[/tex]
Step-by-step explanation:
According to the rule of BODMAS, division is done before addition.
So, in a + b ÷ c, we will first calculate, b ÷ c
Given b = [tex]2\frac{2}{5}[/tex] = [tex]\frac{12}{5}[/tex] , c = [tex]\frac{3}{4}[/tex] .
So, [tex]\frac{b}{c}[/tex] = [tex]\frac{12}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex]
So, [tex]\frac{b}{c} = \frac{12}{5} \times\frac{4}{3}[/tex] , as the numerator and denominator gets reversed as division is changed to multiplication.
So, [tex]\frac{b}{c} = \frac{16}{5}[/tex] .
Next the value of a to [tex]\frac{b}{c}[/tex] , where, [tex]a = 1\frac{2}{5} = \frac{7}{5}[/tex], we get,
[tex]\frac{7}{5} +\frac{16}{5} = \frac{23}{5} = 4\frac{3}{5}[/tex].
Find the length of the apothem of a regular polygon that has a perimeter of 50 cm.
Answer:
72
Step-by-step explanation:
72 i did the math
Ann has a business mowing lawns
in her neighborhood. On Mondays
she makes $18, on Tuesdays she
makes $25, and on Thursdays she
makes $19. If Ann makes this
much money every week, how
much will she have made in 3
weeks?
What is one expression that equals 1
Answer:
2-x=1
2-1=1
Step-by-step explanation:
1 + 1 - 1 x 1 / 1.
Uses all 4 basic symbols.
Simplify.
14y+112+2−134y−12
I would appreciate it if i get an answer quickly, please and thank you.
Answer:
answer is 148y + 102
Step-by-step explanation:
First add like terms 14y + 134y = 148y
then add the whole numbere 112 + 2 = 114
then subtract 114 - 12 = 102
and you get 148y + 102
Write 2/5 and 1/3 as an equivalent fraction using a common denominator
Answer:
Step-by-step explanation:
2/5=6/15
1/3=5/15
Answer:
6/15 and 5/15
Step-by-step explanation:
multiply 2/5 by 3 and 1/3 by 5
solve the system of equations by graphing. x+y=-9 4x+y=-19
For this case we have the following system of equations:
[tex]x + y = -9\\4x + y = -19[/tex]
We multiply the first equation by -4:
[tex]-4x-4y = 36[/tex]
We have the following equivalent system of equations:
[tex]-4x-4y = 36\\4x + y = -19[/tex]
We add the equations:
[tex]-4x + 4x-4y + y = 36-19\\-3y = 17\\y = - \frac {17} {3}[/tex]
We find the value of the variable "x":
[tex]x = -9-yx = -9 - (- \frac {17} {3})\\x = -9 + \frac {17} {3}\\x = \frac {-27 + 17} {3}\\x = - \frac {10} {3}[/tex]
Thus, the solution of the system is:
[tex](x, y): (- \frac {10} {3}, - \frac {17} {3})[/tex]
See the graphic in the attached image
ANswer:
[tex](x, y): (- \frac {10} {3}, - \frac {17} {3})[/tex]
See the graphic in the attached image
Answer: D
Step-by-step explanation:
Edge 2021
Solve The inequality
-p-4p>-10
-p - 4p > -10
-5p > -10
p < 2
Hope this helps! ;)
the value of x varies with y and when x=1/3 y=12 write an equationto represent the variation
Answer:
y = 36x
Step-by-step explanation:
Given that x and y vary directly then the equation relating the is
y = kx ← k is the constant of variation
To find k use the condition x = [tex]\frac{1}{3}[/tex], y = 12, then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{\frac{1}{3} }[/tex] = 12 × 3 = 36
y = 36x ← equation of variation
write the missing decimal so that each pair adds to 1
2/5 as a decimal and 9/10 as a decimal
Answer:
2/5+0.6=1 and 9/10+0.1=1
Step-by-step explanation:
1-2/5=3/5
3/5=0.6
1-9/10=1/10
1/10=0.1
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa hi plz help me
Answer:
36
Step-by-step explanation:
Easy math all you have to do is look at he problem
Kayla counted 40 chairs in the auditorium. In each row, there were 4 chairs on each side of am aisle. How many rows of chairs were there?
Answer:
10
Step-by-step explanation:
Divide 40 by 4, and you get 10. 10 rows.