To reflect a point over the y-axis, you have to reverse the sign of the x-coordinate, the y-coordinate remains the same.
For example for a point P with coordinates (x,y) the reflection is
Original point → y-axis reflection
P(x,y) → P'(-x,y)
For the point (2,-4) the reflection over the y-axis is:
(2,-4) → (-2,-4)
use the distributive property to write an equivalent expression-(3x-7)= ?
For the expression
- ( 3x - 7)
The distributive property equivalent expression is obtained by multiplying both terms by minus (-) sign i.e
- (3x) -(-7)
-3x +7
Thus,
-(3x - 7 ) = -3x +7
The variable y varies directly with x. If y=22 when x=17, what is y when x=31?
Answer:
40.12
Explanation:
y varies directly with x
This is written as:
[tex]y\propto x[/tex]Introducing the constant of proportion k, we have:
y = kx
If y=22 when x=17
[tex]\begin{gathered} 22=17k \\ k=\frac{22}{17} \end{gathered}[/tex]Therefore, the equation connecting y and x is:
[tex]y=\frac{22}{17}x[/tex]When x=31
[tex]\begin{gathered} y=\frac{22}{17}\times31 \\ y=40.12 \end{gathered}[/tex]I need help write an algebraic expression to represent the following sentences.NUMBER 4
Given the statement: "17 more than the product of 5 and a number", notice the second part "the product of 5 and a number" can be written like this:
[tex]5x[/tex]Since we have "17 more than the product...", this means that the expression would be:
[tex]5x+17[/tex]Therefore, the algebraic expression is 5x+17
order the numbers from least to greatest -4.5 and -3 and 1/2 4 point 1/2 -2.5 negative 3
The numbers are:
[tex]-4.5,-3,\frac{1}{2},4\frac{1}{2},-2.5,-3[/tex]In this list, the least will be the negative numbers.
The ones with biggest absolute value, within the negatives, will be the least.
After that will be the positive numbers. We have only two positive numbers.
Then, the list from least to greatest is:
[tex]-4.5,-3,-3,-2.5,\frac{1}{2},4\frac{1}{2}[/tex]1.) rotation 180° about the origin J(-3,3), K(-3, 4), L(-2, 4)2.) reflection across x = -1 Q(-2,5)3.) translation: (x, y) to (x - 2), G(-1, 2)IF YOU DONT KNOW PLEASE DON'T ANSWER! if you can explain pleasee do
1) The rule for a 180 ° rotation from the origin is
[tex](x,y)\rightarrow(-x,-y)[/tex]Then,
[tex]\begin{gathered} J\text{ }\Rightarrow(-3,3)\text{ }\rightarrow(-(-3),-3)=(3,-3) \\ K\text{ }\Rightarrow(-3,4)\text{ }\rightarrow(-(-3),-4)=(3,-4) \\ L\text{ }\Rightarrow(-2,4)\text{ }\rightarrow(-(-2),-4)=(2,-4) \end{gathered}[/tex]2) The rule for reflection about the x-axis is
[tex](x,y)\rightarrow(x,-y)[/tex]Then
[tex]Q\Rightarrow(-2,5)\rightarrow(-2,-5)[/tex]3) As the statement indicates, we only need to modify the X coordinate of the point. Then
[tex]G\Rightarrow(-1,2)\rightarrow(-1-2,2)=(-3,2)[/tex]Solve the system of equations,4.x - 2y = 83x + 4y = 17
I need help to prove CM=3! Please and thank you
The segment CD is given by the sum of the segment CM and MD.
[tex]CM+MD=CD[/tex]Since the point they connect is the midpoint of CD, both segments have the same measure
[tex]CM=MD[/tex]Since we know the measure of MD, we have the measure of CM.
[tex]MD=3\implies CM=3[/tex]the figure shows the represents the pattern of a glass ceiling based on the marketings shown. which triangles can be proven congruence?
Pay your attention to the triangles INK and KNP.
Notice that:
[tex]IK\equiv PN[/tex][tex]\angle IKN\equiv\angle KNP[/tex][tex]KN\equiv NK[/tex]For the SAS criterion, then:
[tex]\Delta IKN\cong\Delta PNK[/tex]It is apparent but not known if there are collinear points in the figure. So, this is the only congruence that we can be 100% sure about.
what is the output value for the following function if the input value is 5y=4x-34223172
step 1 : we need to put in the value of x, which is 5 into the equation so as to get the output
y = 4x - 3
y = 4(5) - 3
y = 20 -3
y = 17
Write as asimplified ratio of the pure drug form: 9% solution.
hello
the ratio of 9% is given as 9/100
the answe is 9/100
Express h in terms of P: 3h + 4 = P. 10
We are given the expression 3h+4=P and told to express h in terms of P. This means that we should apply mathematical operations to this equation, so we can "isolate" the variable h on one side of the equality sign. So, at first, we have the given equation
[tex]3h+4=P[/tex]Then, we subtract 4 on both sides, so we get
[tex]3h=P-4[/tex]Finally, we divide both sides by 3, so we get
[tex]h=\frac{P-4}{3}[/tex]What is the area of this quadrilateral? 4 ft J3R 10 ft 10 ft 3AC 4 ft O A. 36 square feet O B. 42 square feet O C. 12 square feet O D. 30 square feet
Take into account the area of the three parts of the figure.
There are two equal triangles, their areas are:
A1 = b·h/2 = (3 ft)(4 ft)/2 = 6 ft²
A2 = 6 ft²
The area of the rectangle is:
A3 = w·l = (10 ft)(3 ft) = 30 ft²
The area of the total figure is:
AT = A1 + A2 + A3
AT = 6 ft² + 6 ft² + 30 ft²
AT = 42 ft²
Select the correct answer. Identify the word form of this number: 489,570 A four hundred eighty-nine thousand, five hundred seventy в. four hundred and eighty-nine thousand, five hundred and seventy four hundred eighty-nine thousand, five hundred seven D.four hundred eighty-nine thousands, five hundred seventy
The correct way is: four hundred eighty-nine thousand, five hundred seventy (489,570)
Write an equation in slope-interpret form of the line shown?
Slope -intercept form:
y=mx+b
Where:
m= slope
b= y-intercept. (where the line crosses the y-axis)
By looking at the graph we can see that the line crosses the y- axis at y=3.
So, the y-intercept is:
b= 3
For the slope we have to apply the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Use the points form the graph:
Point 1 = (x1,y2) = (1,2)
Point 2 = (x2,y2)= (4,-1)
[tex]m=\frac{-1-2}{4-1}=\frac{-3}{3}=-1[/tex]So, the final equation:
y= -x+3
Find the area of a circle with a diameter of 97.5.
Answer : area of a circle is 7,462.41
[tex]\begin{gathered} \text{Area of a circle = }\pi\cdot r^2 \\ \text{The given diameter is 97.5} \\ \text{Diameter = 2 x radius} \\ \text{Make radius the subject of the formula} \\ \text{Radius = }\frac{diameter}{2} \\ \text{Radius = }\frac{97.5}{2} \\ \text{Radius = 48.75} \\ \text{Let }\pi\text{ = 3.14} \\ \text{Area of a circle = 3.14 x 48.75 x 48.75} \\ \text{Area of a circle = 3.14 x 2,376.56} \\ \text{Area of a circle = 7,462. 41} \end{gathered}[/tex]I know the type of angle relationship I just need help with missing angle.
Given:
The angles in figure.
Required:
Find the angle 1.
Explanation:
The relation between angles is alternate interior angles.
So,
[tex]\begin{gathered} 114^{\circ}=\angle1 \\ So, \\ \angle1=114^{\circ} \end{gathered}[/tex]Answer:
Angle 1 equals 114 degree.
Suppose that an obje
In order to factor the given expression we have to start by determining the greatest common factor (GCF) of the terms of the given function, like this:
-16t² = -1×16×t×t
128t = 8×16×t
Then, 16t is the greatest common factor, by factoring 16t out we get:
h(t) = 16t(-1×t + 8)
By factoring -1 out, we get:
h(t) = -16t(t - 8)
Then, the factored expression is h(t) = -16t(t - 8)
By evaluating the factored expression at t = 2, we get:
h(2) = -16(2)(2 - 8) = -16(2)(-6) = 192
For the base expression:
h(2) = -16(2)² + 128(2) = 192
We got 192 from both expressions at t = 2, then the factored expression was correctly formulated
laws of exponent - divisionsimplify4²—4⁵
Remember that when you have two powers with the same base dividing each other, you substract the exponents.
This way,
[tex]\frac{4^2}{4^5}\rightarrow4^{2-5}\rightarrow4^{-3}\rightarrow\frac{1}{4^3}[/tex]QuestionLet f(x) = (3)x-3. What is f(1)?Provide your answer below:ƒ(1) =
SOLUTION
We were given
[tex]f(x)=(3)^{x-3}[/tex]We want to find f(1). f(1) means we will substitute 1 for x into the function, we have
[tex]\begin{gathered} f(x)=(3)^{x-3} \\ f(1)=(3)^{1-3} \\ f(1)=3^{-2} \\ f(1)=\frac{1}{3^2} \\ f(1)=\frac{1}{9} \end{gathered}[/tex]Hence the answer is 1/9
the data set is 4 8 15 X 23 42
The mode of a data set is the value that appears the most in the set.
In order to have a mode of 23, the value of X must be 23, this way this value will appear two times in the set, and all the other values appear just one time.
So the answer is X = 23.
A bag of numbered lottery balls contains the numbers 1 through 60. What is the probability that a randomly selected ball will be a number that is not between 15 and 23, inclusive? Give your answer as a simplified fraction.
A bag of numbered lottery balls contains the numbers 1 through 60.
Total number of balls = 60
Numbers between 15 and 23 are 15, 16, 17,18, 19, 20, 21, 22, 23
Total numbers between 15 and 23 = 9
Probability of selecting number between 15 and 23 = 9/60
So, probability of not selecting number between 15 and 23 = 1- 9/60
[tex]\begin{gathered} 1-\frac{9}{60}=\frac{51}{60} \\ 1-\frac{9}{60}=\frac{17}{20} \end{gathered}[/tex]Therefore, probability of not selecting number between 15 and 23 is 17/20
Answer : 17/20
Explain to a younger student about a matrix. Include names of the parts of a matrix and a reason why the students would want to use a matrix.
A matrix (in plural it's called matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
The horizontal line of entries is called rows while and vertical lines of entries in a matrix is called columns.
The size of a matrix is defined by the number of rows and columns that it contains.
[tex]undefined[/tex]List all possible rational zeros for the function. (Enter your answers as a comma-separated list.)f(x) = x4 + 3x3 − 4x + 4x=
Given
[tex]f(x)=x^4+3x^3-4x+4[/tex]Solution
Recall
[tex][/tex]The final answer1. Which of the following equations can be used to find the missing angle, x, in the triangle below? xo 42° 42° O A.X +84 = 180 O B. x+84 = 300 O C.X + 42 = 90 O D. X + 42 = 180
Given data:
The given figure of the triangle.
The expression for the angle sum property is,
[tex]\begin{gathered} 42+42+x=180 \\ x+84=180 \end{gathered}[/tex]Thus, option (A) is corect.
The television show Lett3rs has been successful for many years. That show recently had a share of 16, which means, that among the TV sets in use, 16% were tuned to Lett3rs. An advertiser wants to verify that 16% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a Lett3rs broadcast.Find the probability that none of the households are tuned to Lett3rs.P(none) = Find the probability that at least one household is tuned to Lett3rs.P(at least one) = Find the probability that at most one household is tuned to Lett3rs.P(at most one) =
In this scenario, there are only two outcomes. It is either the household is tuned to Lett3rs or not. The outcomes are independent. This means that we can apply the binomial probability. the formula is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n = number of trials
x = number of succeses
p = probability of success
q = probability of failure
From the information given,
n = 14
p = 16% = 16/100 = 0.16
q = 1 - 0.16 = 0.84
1) P(none) = P(x = 0)
Thus,
P(none) = 14C0 * 0.16^0 * 0.84^(14 - 0)
P(none) = 0.087
2) P(at least one) = P(x ≥ 1) = 1 - P(x = 0)
P(at least one) = 1 - 0.087
P(at least one) = 0.913
P(at most one) = P(x = 0) + P(x = 1)
P(x = 1) = 14C1 * 0.16^1 * 0.84^(14 - 1) = 0.2322
P(at most one) = 0.087 + 0.2322
P(at most one) = 0.32
Select all of the stories that can be represented by the equation.If none of the stories can be represented, select "None of the above".(a) 14x-7 = 77(b) 3x+6=315
It is given that a story represents the equation given by:
[tex]14x-7=77[/tex]The correct stories for the equation is given by:
"A take-out pizza restaurant charges $14 for each pizza.Frank purchased x pizzas.There was also a delivery charge of $7 for the entire purchase.Frank spent a total of $77 including the delivery fee"
"A take-out pizza restaurant charges x dollars for each pizza.Frank purchased 14 pizzas.There was also a delivery charge of $7 for the entire purchase.Frank spent a total of $77 including the delivery fee"
Option A and B are correct stories for the problem subpart a.
It is given that a story represents the equation given by:
[tex]3x+6=315[/tex]The correct stories for the equation is given by:
"A printing press company charges x dollars per banner.There is also a one -time setup fee of $6.Jane prints 3 banners.She paid a total of $315 including the setup fee."
"A printing press company charges $3 per banner.There is also a one -time setup fee of $6.Jane prints x banners.She paid a total of $315 including the setup fee."
Option B and C are correct stories for subpart b.
y = 1/3x + 2y = -3x^2 – 5x – 4Solve the system by graphing. Can anyone please help with the second on?
Solution
For this case we can set up equal the two equations and we got:
[tex]\frac{1}{3}x+2=-3x^2-5x-4[/tex]And solving for x w ehave:
[tex]3x^2+\frac{16}{3}x+6=0[/tex]We can multiply both sides of the equation by 3 and we got:
[tex]9x^2+16x+18=0[/tex]And we can solve this using the quadratic formula and we got:
[tex]x=\frac{-16\pm\sqrt[]{16^2-4(9)(18)}}{2\cdot9}[/tex]Since the discriminant is lower than 0 we can conclude that this system has 0 solutions and we can verify with the graph given by:
A bicyclist travels the first 800 m of a trip 1.4 minutes, the next 500 m in 1.6 minutes and finishes up the final 1200 m in 2 minutes. Find the average speed (in meters/min) of the bicyclist for this trip ?
Speed = distance/time
We would apply the formula which states that
Average speed = total distance covered/total time spent
From the information given,
total distance covetred = 800 + 500 + 1200 = 2500 meters
Total time spent = 1.4 +1.6 +2 = 5 minutes
Average speed = 2500/5 = 500 meters/min
Suzanne is putting a fence around her rectangular garden. The length of the garden, xx, is 44 feet more than the width. The perimeter of the garden is 3232 feet. Write an equation to find the length of the garden.
The perimeter of the rectangle
[tex]P=2l+2w[/tex]l=lenght
w=width
l=w+44
P=3232
[tex]3232=2(w+44)+2w=4w+88[/tex][tex]4w+88=3232[/tex][tex]4w=3232-88[/tex][tex]4w=3144[/tex][tex]w=\frac{3144}{4}=786[/tex]l=786+44=830
the equation of the length
l=w+44
Solve for b: A=1/2 bh
Given the following formula:
[tex]A=\frac{1}{2}bh[/tex]We want to rewrite this expression in a way 'b' is a function of the other terms.
Multiplying both sides by 2, we have:
[tex]2A=bh[/tex]Then, if we divide both sides by 'h':
[tex]b=\frac{2A}{h}[/tex]And this is our answer.