Using the rule of 3
120 - 320
x - 3360
120*3,360 = 320x
403,200 = 320x
403,200/320 = x
x = 1,260
About 1,260 students are left handed.
Which of the following transformations are used when transforming the graph of the parent function f(x) = log7x to the graph of g(x) = -log7(3x)+4? Select all that apply.
In this problem, we have the transformations
option B (shift the graph of f(x) 4 units up
option C reflect the graph of f(x) over the y-axis
1. 2х^2 * 3x^3y * 3x^3y=1. 2х^2 * 3x^3*y * 3x^3*y=
Given the expressions
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y= \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}= \end{gathered}[/tex]First: we group and multiply the numbers
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y=(2\cdot3\cdot3)\cdot x^2\cdot x^3\cdot y\cdot x^3\cdot y=18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}=(2\cdot3\cdot3)x^2\cdot x^{3y}\cdot x^{3y}=18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Now we have the expressions
[tex]\begin{gathered} (A).18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Second: we multiply the expressionswith the same base adding its exponents
[tex]\begin{gathered} (A).18x^{2+3+3}\cdot y^{1+1}=18x^8y^2 \\ (B).18x^{2+3y+3y}=18x^{6y+2} \end{gathered}[/tex]Express 4√90 in simplest radical form.
ANSWER
[tex]\text{12}\sqrt[]{10}[/tex]EXPLANATION
We want to find the simplest radical form of 4√90.
To do this, we have to reduce the number in the square root in factor form and then reduce it with the square root.
We have:
[tex]\begin{gathered} 4\sqrt[]{90} \\ \Rightarrow\text{ 4 }\cdot\text{ }\sqrt[]{\text{9 }\cdot\text{ 10}}\text{ = 4 }\cdot\text{ }\sqrt[]{3\cdot\text{ 3 }\cdot\text{ 10}} \\ \Rightarrow\text{ 4 }\cdot\text{ 3 }\cdot\text{ }\sqrt[]{10} \\ \Rightarrow\text{ 12}\sqrt[]{10} \end{gathered}[/tex]That is the simplest radical form.
The graph of y = x 2 has been translated 7 units to the left. The equation of the resulting parabola is _____.y = (x - 7) 2y = (x + 7) 2y = x 2 - 7y = x 2 + 7
The translation of a function to the left or to the right is a horizontal translation. Horizontal translation can be defined as the movement toward the left or right of the graph of a function by the given units. It should be noted that the shape of the function remains the same. The horizontal translation is also known as the movement/shifting of the graph along the x-axis. For any base function f(x), the horizontal translation by a value k can be given as
[tex]f(x)=f(x\pm k)[/tex]If the function is shifted to the right, the translation function would be
[tex]f(x)=f(x-k)[/tex]If the function is shifted to the left, the translation would be
[tex]f(x)=f(x+k)[/tex]If the graph of y = x² has been translated 7 units to the left. The equation of the resulting parabola would be
[tex]y=(x+7)^2[/tex]Hence the equation of the resulting parabola is (x+7)²
Subtract this question
[tex]{ \frac{5}{3}} [/tex]
Step-by-step explanation:
[tex]{ \purple{ \sf{3 \frac{2}{6} - 1 \frac{2}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{18 + 2}{6} - \frac{3 + 2}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} - \frac{5}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} \times \frac{1}{1} - \frac{5}{3} \times \frac{2}{2}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} - \frac{10}{6}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20 - 10}{6}}}} [/tex]
[tex]{ = \purple{ \sf{ { \frac{ \cancel{10}^{ \green{ \sf{5}}} }{ \cancel{ 6_{ \green{ \sf{3}}} }}}}}}[/tex]
[tex]{ = \purple{ \boxed{ \red{ \sf{ \frac{5}{3}}}}}} [/tex]
In the following table of values, what would be the value of “b” in ax2 + bx + c?
–2
–9
–1
–1
0
9
1
21
2
35
1
9
11
22
The value of b is 11.
From the question, we have
ax² + bx + c
using (0, 9)
substituting the value we get
9 = a(0)² + b(0) + c
c = 9
Therefore,
-1 = a(-1)² + b(-1) + c
-1 = a - b + 9
-1 - 9 = a - b
a - b = - 10
using (-2, -9)
-9 = a(-2)² + b(-2) + 9
-9 - 9 = 4a - 2b
-18 = 4a - 2b
2a - b = -9
combine the equation
a - b = - 10
2a - b = -9
solving the equations we get
a = 1
Then,
1 - b = -10
b = 1 + 10
b = 11
Hence, the value of b is 11.
Subtraction:
The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.
To learn more about subtraction visit: https://brainly.com/question/2346316
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g(0) 10 Cabin Rental Cost ($) У 70 60 50 + (0,57] ) 40 30 10 1 (0.15) 0 1 2 3 4 5 6 7 8 9 10 Number of Days
f(x) = x +57
g(x) =7x+15
The solution is (7,64). To rent the cabin for 7 days cost $64
1) Let's examine the graph. We can see two linear equations.
Picking two points for f(t) = (7,64) and (0,57) and for g(t) (0,15) and (7,64) let's find out their respectives slopes:
2) For f(t) , let's plug into the slope-intercept formula, plugging one point:
(0,57)
y=mx+b
57=0x +b
57= b
So the rule for the function is, in terms of f(x) = x +57
(0,15)
y=mx +b
15=0x +b
15 =b
So the rule for the function g(t) , in terms of g(x) is g(x) =7x+15
Interpreting the solution:
The solution to this Linear System of Equations is the common point (7,64).
So filling in the blanks we have:
The solution is (7,64). To rent the cabin for 7 days cost $64
what is the only value of x not in the domain ?
The Solution:
Given:
Required:
Find the domain of the function. What is the value of x that is not in the domain of f(x).
Graphing the function, f(x), we get:
So, the domain of the function is:
[tex](-\infty,-1)\cup(-1,\infty)[/tex]To find the value of x that is not in the domain, we need to find the value of x for which the function is undefined. That is,
[tex]\begin{gathered} 6x+6=0 \\ 6x=-6 \\ \\ x=\frac{-6}{6}=-1 \end{gathered}[/tex]Thus, the value of x not in the domain is:
[tex]x=-1[/tex]
Question #5The table shows four relations.RelationRelation 2Relation 3Rolation 4-2-5-3Y-4-4-2-1- 11312372Which relations represent functions?ARelation 1 and Relation 3BRelation 2 and Relation 4СRelation 3 and Relation 2DRelation 4 and Relation 1
The RELATION 1 and 3 represent a function
Rationale
There are no x value with several y values.
For a relation to be a function, there should only one y value fot each x
Can you please solve this equation and please explain to me ^step-by-step^ (this is my homework)
In the equation
[tex]0.07(6t-4)=0.42(t-1)+0.14[/tex]to solve for t, we first expand both sides of the equation.
[tex]0.42t-0.28=0.42t-0.42+0.14[/tex]We subtract 0.42t from both sides to get
[tex]-0.28=0.42+0.14[/tex]The right side does not equal the left side of the equation; therefore, this equation has no solution and choice C is correct.
I need help with my math
Given data:
The given points are (-2,-1) and (3, -1).
The slope of the line passing through the given points is,
[tex]\begin{gathered} m=\frac{-1-(-1)}{3-(-2)} \\ =\frac{0}{5} \\ =0 \end{gathered}[/tex]Thus, the slope of the line passing through the given points is 0.
The table below shows the thickness of coins. Coin Thickness quarter i millimeters 12 millimeters dime nickel millimeters penny 13 millimeters Hailey stacks a dime on top of a penny. She estimates the thickness of the two coins to be less than 3 millimeters. Write a symbol (, or =) in the box to make the statement true. Then use the statement to tell whether Hailey's estimate is correct. 12 + 12 + 1 Is Hailey's estimate correct?
A dime has a thickness of 1 7/20 mm and a penny has 1 1/2 mm.
Stacking both coins, we will have :
[tex]1\frac{1}{2}+1\frac{7}{20}[/tex]and we have the inequality :
[tex]1\frac{1}{2}+1\frac{7}{20}\boxed{\text{ }}1\frac{1}{2}+1\frac{1}{2}[/tex]Note that 1 7/20 is less than 1 1/2, so the inequality symbol is "<"
[tex]1\frac{1}{2}+1\frac{7}{20}<1\frac{1}{2}+1\frac{1}{2}[/tex]since 1 1/2 + 1 1/2 is equal to 3mm
Therefore, the thickness of stacking coins is less than 3mm
Hailey's estimate is correct (Yes)
estimate the product by rounding to the nearest 10: 28×56×76
EXPLANATION
Given the operation:
28------> rounded to 30
56-------> rounded to 50
76 ------> rounded to 80
Now, we can mentally calculate that:
3x5= 15 so 30x50 = 1500 (two zeros)
15x8 = 120 so,
1500x80 = 120,000
The answer is 144,000.
A physical education teacher divides the class into teams of 5 to play floor hockey. There are atotal of 4 teams. How many students, s, are in the class? Solve the equation 8 + 5 = 4 to find thenumber of students.
we know that
the number of students (s) is equal to the number of teams, multiplied by the number of students in each team
so
s=4*5
s=20
answer is 20 students
The local newspaper charges $34.80 for an 8-week subscription. Paige buys an 8-week subscription. How much does it cost her each week?
Answer:
$4.35
Step-by-step explanation:
8 weeks = $34.80
1 week = x
Cross-multiply
$34.80/8
=$4.35
So, for each week, Paige will pay $4.35
$(4.35 × 8 = 34.8)
what number do you need to add/subtract/multiply/divide each side by in order to solve the problem below?[tex] \frac{5}{6} = - \frac{2}{3} x[/tex]
The equation is,
[tex]\frac{5}{6}=-\frac{2}{3}\cdot x[/tex]The equation can be solved if on right side there is only variable with any number in multiplication. So equation can be solved as,
[tex]\begin{gathered} \frac{5}{6}\cdot\frac{-3}{2}=-\frac{2}{3}x\cdot\frac{-3}{2} \\ x=-\frac{5}{4} \end{gathered}[/tex]So to eliminate -2/3
I really sure what to do for this question some help would be greatly appreciated
Given the Domain and the Range of the relation, you need to remember that the Domain is the set of all input values (x-values), and the Range is the set of all the output values (y-values).
Therefore, knowing the input values and the corresponding output values indicated in the Diagram, you can write the following ordered pairs:
[tex](1,9),(4,10),(10,3)[/tex]Notice that they have this form:
[tex](x,y)[/tex]Where "x" is the x-coordinate of the point, and "y" is the y-coordinate.
Therefore, you need to plot all the points on the Coordinate Plane in order to express the relation as a graph.
Hence, the answer is:
your gonna need a calculator for this I don't have one help please
The correct answer is the option a) because in the table we can note that the values of the weight are strictly increasing, and the only option that meets this condition is the option a).
*Will mark brainiest* Rectangle ABCD is rotated 90° clockwise about the origin to produce Rectangle A'B'CD' What is the length, in units of line segment CD'?
When the given rectangle is rotated 90° around origin point, you obtain the same rectangle, but instead of a horizonatl rectangle as before, you get a vertical rectangle with height CD' and width A'D'.
The length of the segment CD' is 6 units
Consider this prism. Enter the volume of the rectangular prism, in cubic centimeters. 3 3/4, 3 1/3, 2 1/2.
Solution
For this case we have the following dimensions:
x = 3 3/4 = 15/4
y= 3 1/3 = 10/3
z= 2 1/2 = 5/2
Then we can find the volume with the following formula:
[tex]V=x\cdot y\cdot z=\frac{15}{4}\cdot\frac{10}{3}\cdot\frac{5}{2}=\frac{125}{4}ft^3[/tex]Then we can convert to cm^3 like this:
[tex]\frac{125}{4}ft^3\cdot\frac{(30.48\operatorname{cm})^3}{1ft^3}=884901.46\operatorname{cm}^3[/tex]You went to the mall to buy a sweater that was 30% off and you had an additional 20% off coupon. The cashier took the 20% off first and then the 30% off of the reduced amount second. The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second. Would it matter which way this was done? Why or why not?
Explanation
let's check every case,
Step 1
A)The cashier took the 20% off first and then the 30% off of the reduced amount second.
let x represents the original price
to find the 20% we can use
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-20}{100}=x*(\frac{80}{100})=0.8x \\ new\text{ price =}0.8c \end{gathered}[/tex]then,the 30 % of the reduced amount, so
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.8x\rparen *\lparen}\frac{100-30}{100}=(0.8x)*(\frac{70}{100})=(0.8x)(0.7)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 2
B)The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second
so
i) 30 of the first
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-30}{100})=x*(\frac{70}{100})=0.7x \\ new\text{ price =}0.7c \end{gathered}[/tex]then, 20 % off the reduced amount
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.7x\rparen *\lparen}\frac{100-20}{100}=(0.7x)*(\frac{80}{100})=(0.7x)(0.8)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 3
so, we can conclude in both cases the final price will be the same, becuase we have a triple product
[tex]\begin{gathered} x*0.8*0.7=x*0.7*0.8 \\ 0.56x=0.56x \end{gathered}[/tex]so, the answer is
it does not matter which way the calculation is done, because the order does not affect the product
I hope this helps you
Priya rewrites the expression 8 − 24 as 8( − 3). Han rewrites 8 − 24 as2(4 − 12). Are Priya's and Han's expressions each equivalent to 8 − 24? Explain your reasoning.
The given expression is
[tex]8y-24[/tex]Priya rewrite the expression as
[tex]8(y-3)[/tex]Expanding priya's expression gives
[tex]\begin{gathered} 8(y-3)=8\times y-8\times3 \\ 8(y-3)=8y-24 \end{gathered}[/tex]Hence Priya's expression is equivalent to 8y - 24
Han's rewrite the expression as
[tex]2(4y-12)[/tex]Expanding Han's expression gives
[tex]\begin{gathered} 2(4y-12)=2\times4y-2\times12 \\ 2(4y-12)=8y-24 \end{gathered}[/tex]Hence, Han's expression is equivalent to 8y - 24
Solve using substitution. y = 7x + 3 y = 6x + 4(_ , _)
We have the following:
[tex]\begin{gathered} y=7x+3 \\ y=6x+4 \end{gathered}[/tex]solving using substitution:
[tex]\begin{gathered} 7x+3=6x+4 \\ 7x-6x=4-3 \\ x=1 \end{gathered}[/tex]for y:
[tex]y=7\cdot1+3=7+3=10[/tex]The answer is (1, 10)
what is the mean? 66, 594, 69, or 74what is the median? 74, 66, 69, or 75what is the mode? 74, 90, 21, or 66what is the range? 69, 66, 74, or 594
We have the distribution;
74, 90, 21, 68, 62, 84, 34, 87,74.
Let's arrange this from ascending to descending order, we obtain;
[tex]21,34,62,68,74,74,84,87,90[/tex]i. The mean or average of this distribution is
[tex]\begin{gathered} \frac{21+34+62+68+74+74+84+87+90}{9}=\frac{594}{9} \\ \operatorname{mean}=66 \end{gathered}[/tex]ii. The median is the central value, in this distribution, there are 9 values, so the median value is the 5th value.
[tex]\operatorname{median}=74[/tex]iii. The mode is the value with the highest frequency, this is the most occurring value, in this distribution;
[tex]\text{mode}=74[/tex]iv. The range is the difference between the highest and lowest values, this is;
[tex]\begin{gathered} 90-21=69 \\ \text{Range}=69 \end{gathered}[/tex]
-7>-10 true or false
To answer this question we need to see it on an axis.
-7> -10 , it is true. -7 it's more near to 0.
what are the coordinates of the vertex for x^2+ 5x - 24 = 0
Solution:
We are required to find the coordinates of the vertex for x^2+ 5x - 24 = 0
[tex]The\text{ x-coordinate of the vertex is x=}\frac{-b}{2a}[/tex][tex]\begin{gathered} For\text{ x}^2+5x-24=0 \\ a=1 \\ b=5 \\ x=-\frac{5}{2(1)} \\ x=-\frac{5}{2} \\ x=-2.5 \end{gathered}[/tex]To get the y coordinate, substitute x = -5/2 into the equation
[tex]\begin{gathered} \begin{equation*} \text{x}^2+5x-24=0 \end{equation*} \\ =(\frac{-5}{2})^2+5(\frac{-5}{2})-24 \\ \\ =\frac{25}{4}-\frac{25}{2}-\frac{24}{1} \\ =\frac{25-50-96}{4} \\ \\ =\frac{-121}{4} \\ \\ =-30.25 \end{gathered}[/tex]Hence, the coordinate of the vertex is (-2.5, -30.25)
I need help checking to make sure my work is correct. Start with the basic function f(x) = 2x. If you have an initial value of 1, then you end up with the following iterations:f(1) = 2 x 1 = 2f^2 (1) = 2 x 2 x 1 = 4f^3 (1) = 2 x 2 x 2 x 1 = 8The question Part 1: If you continue the pattern, what do you expect would happen to the numbers as the number of iterations grows? Check your result by conducting at least 10 iterations. I put: f^4 (1) = 2 x 2 x 2 x 2 x 1 = 16f^5 (1) = 2 x 2 x 2 x 2 x 2 x 1 = 32f^6 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 1 = 64f^7 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 128f^8 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 256f^9 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 512f^10 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 1024Part 2: Repeat the process with an initial value of -1. What happens as the number of iterations grows?
Given: The function below:
[tex]f(x)=2x[/tex]To Determine: The interation with initial value of 1
When the initial value is 1, it means that x = 1
If x =1, we can determine f(1) by the substituting for x in the function as shown below:
[tex]\begin{gathered} f(x)=2x \\ x=1 \\ f(1)=2(1)=2\times1=2 \end{gathered}[/tex][tex]f^2(1)=2^2\times1=2\times2\times1=4[/tex]Part 1:
It can be observed that as the number of iterations grow, the number increase in powers of 2
This can be modelled as
[tex]f^n=2^n\times1=2^n[/tex][tex]f^{10}=2^{10}\times1=1024[/tex]Part 2:
If we repeat the process with an initial value of -1. As the number of iterations grows, the number can be modelled as
[tex]\begin{gathered} f^{-n}=2^{-n}\times1 \\ f^{-1}=2^{-1}\times1=\frac{1}{2}\times1=\frac{1}{2} \\ \text{For initial value of -2, we would have} \\ f^{-2}=2^{-2}\times1=\frac{1}{2^2}\times1=\frac{1}{4} \end{gathered}[/tex]So, as the initial value decreases, it can be observed by the above calculations that the number would be decreasing by the the reciprocal of the power of 2.
how do I calculate the area of a partial circle?
A part of a circle is called an arc and an arc is named according to its angle.
Which of the numbers 12, 13, or 14 is the solution of 106 = 118 - x?
The given expression is
[tex]106=118-x[/tex]First, we add x on each side
[tex]\begin{gathered} 106+x=118-x+x \\ 106+x=118 \end{gathered}[/tex]Then, we subtract 106 from each side
[tex]\begin{gathered} 106-106+x=118-106 \\ x=12 \end{gathered}[/tex]The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If anastronaut weighs 215 pounds on the surface of the Earth, what will this astronaut weigh 2650 miles above the Earth? Assume that the radius of the Earth is 4000miles. Round your answer to one decimal place if necessary
Given:
F is inversely proportional to the square of the distance means that
[tex]F=\frac{k}{d^2}[/tex]So the value of "k" is:
[tex]\begin{gathered} 215=\frac{k}{4000^2} \\ k=215\times(4000)^2 \\ k=3440000000 \end{gathered}[/tex]Weigh in 2650 mile above
[tex]\begin{gathered} F=\frac{k}{d^2} \\ F=\frac{3440000000}{(2650)^2} \\ F=\frac{3440000000}{7022500} \\ F=489.85\text{ pound} \end{gathered}[/tex]