The correct option B. It is compressed horizontally by a factor of 2 and translated up 3 units.
What is meant by the term translation?The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There isn't any change in the form because it is simply moved from one location to another.For the given question;
The image function is defined as ; y = ㏒(2x) + 3
The parent function is; y = ㏒(x).
The first graph, X, is multiplied by 2 (2x), compressing it horizontally by a factor of 2.The number 3 is then added, which moves the graph up three units.Thus, the image function y = ㏒(2x) + 3 is obtained by the process as,compressed horizontally by a factor of 2 and translated up 3 units.
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The complete question is-
How is the graph of y = ㏒(2x) + 3 related to the graph of y = ㏒(x).
Options are-
A. It is stretched horizontally by a factor of 2 and translated up 3 units.
B. It is compressed horizontally by a factor of 2 and translated up 3 units.
C. It is stretched vertically by a factor of 2 and translated up 3 units.
D. It is compressed vertically by a factor of 2 and translated up 3 units.
Which step in solving this equation is justified by the Associative Property of Addition? Consider the sequence of steps to solve the equation: 6v + 3(y – 5) = 4y -- (2v + 1) Given + 3(-5) = 4y - (2v + 1) Step 16v + 3y - 15 = 4y - (2y + 1) Step 2 6y + 3y - 15 = 4y - 2 - 1 Step 3 9y - 15 = 4y – 2v-1 Step 4 9y - 15=-2y + 4y - 1 Step 5 9v - 15 = 2y - 1 Step 6 7y - 15 =-1 Step 77y=14 Step 8y=2 a. Step 7 b. Step 3 c. Step 5 d. Step 4 2. MGSE9-12.A.REI.1 Which step in solving this equation is justified by the
First consider what the associative property of addition is:
Due to such a property, the sum of three or more numbers remains the same regardless of how the numbers are grouped.
Then, from the different steps given in the question, you can notice that in the step 3, regardless the simplifcation of like terms right side or left side, the result is the same.
During the 2003-2004 season, Kevin Weekes of the Carolina
Hurricanes saved 1506 out of 1652 shots on goal. To the nearest
what part of the time did Weekes save shots on goal?
Part of the time weekes save shots on goal is 0.911.
Given,
Total number of shots on goal=1652
Number of shots saved=1506
Part of time weekes save shots on goal,
[tex]\frac{Number of shots saved}{Total number of shots on goal}\\\\\\=\frac{1506}{1652}\\ \\=0.911[/tex]
Thus, Part of the time weekes save shots on goal is 0.911.
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what line is perpendicular to the line y=2x+4 ? what line is parallel to line y + 2x+4 ? *options are for both answers*
Given the line : y = 2x + 4
the general equation of the line is y = mx + b
where m is the slope , b is the y intercept
By comparing the given line with the general form
so, the slope of the given line is :
m = 2
the slope of the perpendicular line will be = -1/m
so, the slope of the perpendicular line = -1/2
The slope of the parallel line = the slope of the given line
So, the slope of the parallel line = 2
so, the answer is:
the perpendicular line is : y = (-1/2) x + 10
The parallel line is : y = 2x + 1
How many student tickets were sold if 150 general admission tickets were sold?
After simplification, 250 tickets sold to students if 150 general admission tickets were sold.
In the given question we have to find the how many student tickets were sold if 150 general admission tickets were sold.
The cost of concert ticket for general admission is $15.
The cost of concert ticket for student is $9.
Total sales of ticket is $4500.
The total 150 ticket sold to general admission.
So the total cost of ticket that received from the general admission is
=150*15 = 2250
Let x number of ticket sold to student.
Then total cost of students ticket is 9x.
Now the expression should be
9x+2250 =4500
Subtract 2250 on both side, we get
9x = 2250
Divide by 9 on both side we get
x = 250
Hence, 250 tickets sold to students if 150 general admission tickets were sold.
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The right question is
Concert ticket cost $15 for general admission, but only $9 with student ID. Ticket ales total $4500. How many student tickets were sold if 150 general admission tickets were sold?
A fire drill occurred in the middle of a math test that Ms Ramirez was giving. She decided to add 5 points to everyone's original score. Which of the following statistical measures would adding these 5 points alter when compared to the original scores? 1. the mean score 2. the interquartile range 3. the range 4. the standard deviation
Concept
Given the data below as the original score of the student
[tex]5,10,\text{15,20}[/tex]The mean score is given as
[tex]\frac{5+10+15+20}{4}=12.5[/tex]Adding 5marks to the score we will be having the score below
[tex]10,15,20,25[/tex]Then the new mean score becomes
[tex]\frac{10+15+20+25}{4}=17.5[/tex]Hence the mean will be altered by adding
Other statistical measures will not be altered
I need helpBarbara works at a law office as an entry level lawyer. She spends 2/5 of her time at the law office doing paper work. How many hours does she have to work to spend 10 hours doing paper work.
GIVEN:
We are told that Barbara works 2/5 of her time doing paper work and this fraction represents 10 hours of her total working time.
Required;
To determine how many hours she will have to work in order to have 10 hours doing paper work.
Step-by-step solution.
Take note that her entire working hours is represented by 1 whole since, a fraction of it has already been identified as two-fifths.
This means
[tex]\frac{2}{5}\times h=10[/tex]Take note that the fraction is taken as two-fifths of the total hours h and, if multiplied by the total hours, we would get 10 hours.
Hence, if we simplify the above equation, we would get the value of h as follows;
[tex]\begin{gathered} \frac{2}{5}\times h=10 \\ \\ Cross\text{ }multiply: \\ \\ h=\frac{10\times5}{2} \\ \\ h=25 \end{gathered}[/tex]Therefore,
ANSWER:
Barbara has to work for 25 hours in order to spend 10 hours on paper work.
The diagram shows a tile in the shape of a trapezium.
12 cm
10 cm
Work out the area of the tile.
26 cm
The area of the trapezium would be 190 square centimeters.
What is the area of a trapezium?The area of trapezium is given by -
A = (1/2) x (height) x (sum of parallel sides)
We have a trapezium as shown in the image.
We have -
Sum of parallel sides = [a + b] = 26 + 12 = 38 cm
Height = [h] = 10 cm
Therefore, the area would be -
A = (1/2) x (height) x (sum of parallel sides)
A = 0.5 x 10 x 38
A = 10 x 19
A = 190 square centimeters
Therefore, the area of the trapezium would be 190 square centimeters.
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Last year at a certain high school, there were 140 boys on the honor roll and 68 girls on the honor roll. This year, the number of boys on the honor roll increased by 5% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
11.5%
Step-by-step explanation:
Last year:
Boys: 140
Girls: 68
Total: 208
This year:
Boys: 105% of 140 = 1.05 × 140 = 147
Girls: 125% of 68 = 1.25 × 68 = 85
Total: 232
percent change = (new - old)/new × 100%
percent change = (232 - 208)/208 × 100%
percent change = 11.5%
Solving Systems of linear equations by elimination
The solution of the systems of linear equations is x = 13.81 and y = 73.381. The average salaries were equal in the year 1999. The average salary that year was about $73381.
What is the system of linear equation?
A collection of two or more linear equations is a system of linear equations. The graph of a system of two equations is a pair of lines in the plane for two variables (x and y).
The intersection point of the lines is ( 13.81, 73.381).
The average salaries were equal after 14 years since 1985.
The average salaries were equal (1985 + 14) = 1999.
The average salary that year was about $73381.
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use two unit multipliers to convert 500 feet to centimeters
Answer:
15240.00 cm
Step-by-step explanation:
15240.00 cm
500 feet * 30.48x(cm)
x = centimeters per foot
Mai is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.Company A charges $97 and allows unlimited mileage.Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven.For what mileages will Company A charge less than Company B?Use m for the number of miles driven, and solve your inequality for m.
Answer:
m>60
Explanation:
Let the number of miles driven = m
Company A charges $97 and allows unlimited mileage.
[tex]\text{ Total Charge for Company A}=\$97[/tex]Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven.
[tex]\text{ Total Charge for Company B}=55+0.70m[/tex]When the charge for Company A is less than that of Company B:
[tex]97<55+0.70m[/tex]We then solve the inequality for m:
[tex]\begin{gathered} 97\lt55+0.70m \\ \text{ Subtract 55 from both sides} \\ 97-55\lt55-55+0.70m \\ 42\lt0.70m \\ \text{ Divide both sides by 0.7} \\ \frac{42}{0.70}<\frac{0.70m}{0.70} \\ 6060 \end{gathered}[/tex]Company A will charge less than Company B when the number of miles driven, m is greater than 60.
Graph the polygon with the given vertices and its image after a reflection in the given line.
J(2, 1), K(3, 5), L(6, 5), M(5, 1); x = 1
The equation of the parallel line in slope-intercept form is y=
numbers: (-2,-4) 4x+7y=11
(Pls help I have a F in math rn)
The equation of the line parallel to 4x+7y=11 and passes through (-2,-4) is y = - 4 / 7x - 36 / 7
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is parallel to 4x+7y=11.
Parallel lines have the same slope.
Hence,
4x+7y=11
7y = - 4x + 11
y = - 4 / 7 x + 11
Therefore, the slope of the line is - 4 / 7 x. Let's find the y-intercept using (-2, -4)
-4 = - 4 / 7(-2) + b
-4 - 8 / 7 = b
b = - 36 / 7
Therefore, the equation of the line is y = - 4 / 7x - 36 / 7
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Write an equation in standard form of the line that passes through the given point and has the given slope.
(-6, -10); m =
6
Answer:
Below
Step-by-step explanation:
First , write it in point (-6, -10) slope ( 6 ) form then manipulate it to standard form:
(y- -10) = 6 ( x - -6)
y+10 = 6x + 36
6x - y = -26
Mr. A drove to a city in New Jersey
that is 200 miles away. He got
there in 2 hours. What is his
2 rate of change (At what Speed
was Mr. A driving)
Answer:
100 miles per hour
Step-by-step explanation:
He drives 200 miles in 2 hours so just divide 200 by 2 to get the unit rate/ miles per hour
Please assist me with this too if you don't mind.
The equation when solved for k is of:
k = y - a(x - h)².
The domain for the relation is:
x ≥ 0.
How to solve the equation for k?The equation is defined as follows:
y = a(x - h)² + k
To solve for k, we have to isolate the variable k, moving the term a(x - h)², which doesn't have the variable k, to the other side with inverted signal, hence the solution for k is obtained as follows:
y - a(x - h)² = k.
k = y - a(x - h)².
What is the domain for a relation?The domain of a relation is the set containing all the values assumed by the input in the relation.
For the table, the input is the number of miles driven, which assumes values of zero and greater, hence the domain of the relation is defined as follows:
x ≥ 0.
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On Sunday, Steve, Jo, Lucy, Max, and Alex decide to throw aparty. On Monday, they each invite 3 friends. On Tuesday, thefriends that were invited on Monday each invite 3 more people.On Wednesday, the people who were invited on Tuesday eachinvite 3 more people.If this continues, how many people will be invited on Saturday toattend the party?
Step 1. The party will be thrown by Steve, Jo, Lucy, Max, and Alex --> 5 people.
On Monday, each invites 3 friends. So for, the number of people invited is:
[tex]5\times3=15[/tex]Step 2. On Tuesday, the friends that were invited (15) invited 3 more people each. The number of people invited now is:
[tex]15\times3=45[/tex]Step 3. On Wednesday, the 45 people invited on Tuesday, each invite 3 more people. The number of people invited again multiplies by 3:
[tex]45\times3=135[/tex]Step 4. The trend continues so for Thursday, the number of people invited on the previous day multiplies by 3:
[tex]135\times3=405[/tex]Step 5. On Friday the number of people invited is:
[tex]405\times3=1,215[/tex]Step 6. Finally, on Saturday, the day of the party, the number of people invited is multiplied one last time by 3:
[tex]1,215\times3=3,645[/tex]Answer:
3,645
Point A is at (6,1) and point C is at (2,-7)
Find the coordiantes of ppint b on line segamnt AC such that AB= 1/3BC
Answer:
A (6. 1) C (2. -7)
6-2 = 4 1- (-7) = 8
as AB= 1/3 BC = AB= 1/4 AC
so x=6-4/4 =5
y= 1-8/4 =-1
so B(5, 1)
Answer:
B(5, - 1)----------------------------------
GivenPoints A(6, 1) and C(2,- 7),Point B that partitions AC as AB : BC = 1 : 3.Find point BUse the section formula
[tex]P=(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n} )[/tex], where P- point to be found, m : n is the ratio and the (x,y) are coordinates of endpointsSubstitute and find the point B:
[tex]B=(\dfrac{1*2+3*6}{1+3} ,\dfrac{1*(-7)+3*1}{1+3} )=(20/4,-4/4)=(5,-1)[/tex]Solve for x.
−4.5(x+3.21)=−33.21
Responses
x = 4.17
x, = 4.17
x = 6.67
x, = 6.67
x = 8.09
x, = 8.09
x = 10.59
Answer:
b
Step-by-step explanation:
Answer:
x = 4.17
Step-by-step explanation:
you just solve it using BIDMAS. I'm 100% sure I'm right
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The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer: |28| |62| |90|
Mobile device: |46| |64| |110|
Column totals: |74| |126| |200|
What is the joint relative frequency of students who use a mobile device in an online class?
Answer: 32%
Step-by-step explanation:
The reason on why this answer is 32% is because in order to calculate joint relative frequency, you must have two values.
The first value is the one the question is asking you about. For this, it's mobile device in online classes, which is 64 on the table. Simply divide this number by the total of the table, which is normally on the bottom right. In this case, it's 200.
Now all that needs to be done is this:
[tex]\frac{64}{200}[/tex] = 0.32, which is 32%.
The answer is 32%, C.
The joint relative frequency of students who use a mobile device in an online class will be 32% as the "Student who use a mobile device in online class=64 and total students=200".
What is joint relative frequency?The ratio of a frequency that is not in the total row or column to the total number of values or observations is known as joint relative frequency. In a two-way frequency table, the marginal frequency is the entry in the "total" for the column and the "total" for the row. These are the frequencies in a given category divided by the total number of data values. The term "joint frequency" refers to the joining of one variable from the row and one variable from the column. The ratio of the frequency in a specific category to the total number of data values is known as joint relative frequency.
Here,
Title Traditional Online Row totals
Computer: |28| |62| |90|
Mobile device: |46| |64| |110|
Column totals: |74| |126| |200|
The joint relative frequency of students who use a mobile device in an online class,
Student who use a mobile device in online class=64
Total students=200
64/200=0.32
0.32*100=32%
As "Students who use a mobile device in an online class=64 and total students=200," the joint relative frequency of students who use a mobile device in an online class will be 32%.
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if i have figure A (R=5ft) and figure B is (R=2ft) and the volume =(88 cu ft) what is the answer
we get that
[tex]h_b=\frac{88}{4\cdot\pi}\approx7[/tex]as the figure are congruent we get
[tex]h_a=\frac{5}{2}\cdot7=17.5[/tex]so the volume is
[tex]V_a=\pi\cdot5^2\cdot17.5=1375ft^3[/tex]Factor the expression using the GCF.
84+28
Answer:
28(3 +1)
Step-by-step explanation:
You want the expression 84+28 to be factored using the GCF.
GCFThe Greatest Common Factor (GCF) of 84 and 28 can be found by looking at the remainder from division of 84 by 28.
84 ÷ 28 = 3 r 0
The remainder is 0, so 28 is a factor of 84. Since it is also the largest factor of itself, it is the GCF of the two numbers.
Distributive propertyFactoring out 28, we have ...
84 +28 = 28·3 +28·1 = 28(3 +1)
The factored expression is 28(3 +1).
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I need help on the question in the picture attached. i tried posting it but no one is answering it and this was due last week. please help fast
Answer:
Yes
Explanation:
To find our whether Marrissa's budget will be enough for the party, we need to find the linear equation relating the cost and the number of guests. The linear equation is the form
[tex]y=mx+b[/tex]where y is the cost in dollars. m is the cost per guest, and b can be interpreted as additional charges for the party facility.
The cost per guest is given by the slope of cost vs. guest graph.
Let us pick two values (100, 1325) and (50, 725) and compute the slope:
[tex]\frac{\$1325-\$750}{100-50}=\frac{\$12}{\text{guest}}[/tex]With the value of slope m in hand, we now find b by using the values x = 100, y = 1325 (the choice of these values is arbitrary)
[tex]\begin{gathered} 1325=12(100)+b \\ 1325=1200+b \\ \therefore b=125 \end{gathered}[/tex]Hence, the equation relating the cost and the number of guests is
[tex]y=12x+125[/tex]Now, for 75 guests the cost will be
[tex]\begin{gathered} y=12(75)+125 \\ y=\$1025.\text{ } \end{gathered}[/tex]Therefore, Marrissa's budget, which is $1200, is greater than the cost of the party, meaning it will be enough.
Write an equation in point slope form for the line that passes through (-3,5) with a slope of -3
The equation of line in point slope form is y = -3x -4
Given,
The points which the line passes through;
(x, y) = (-3,5)
Slope, m = -3
We have to find the equation in point slope form;
Point slope form;
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Here,
Point slope form;
y - y₁ = m(x - x₁)
Then,
y - 5 = -3(x - -3)
y - 5 = -3x -9
y = -3x - 9 + 5
y = -3x - 4
That is,
The equation of line in point slope form is y = -3x -4
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Find all points on the y-axis that are 5 units from the point (4, 6). (smaller y-value)(x, y) = (larger y-value)
Step 1:
Write the parent coordinates
(4 , 6)
Step 2
The point can bo on the positive y-axis or on the negative y-axis.
New coordinates
( 4 + 5, 6 + 5)
= (9 , 11)
Or
( 4 - 5, 6 - 5)
= (-1 , 1)
Final answer
Smaller y-value = 1
Larger y-value = 11
Jan and Jo live 1,170 miles apart. At the same time, they start driving toward each other on the same road. Jo’s constant rate is 60 mph. Jan’s is 70 mph. How long will it take them to meet?
Answer:
Step-by-step explanation:
to get the time taken for Jan and Jo to meet we proceed as follows;
Jan's speed=70 mph
Jo's speed =60 mph
distance between =1170
relative speed=70+60=130
time taken for them to meet will be:
time=(distance)/(relative speed)
=1170/130
=9 hours
the answer is 9 hours
Answer:
Option (B) is correct, 9 hours.
What is the equation of a polynomial function, R, with rational coefficients that
have a zero of 4 + √5 and 3i?
The equation of a polynomial function, R, with rational coefficients will be;
P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i
What is Quadratic equation?
An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The zeroes of the polynomial function are;
⇒ 4 + √5 and 3i
Now,
Since, The zeroes of the polynomial function are;
⇒ 4 + √5 and 3i
So, The factor of the polynomial function are;
(x - (4 + √5)) and (x - 3i)
Hence, We can formulate the polynomial function as;
P (x) = (x - (4 + √5)) (x - 3i)
= (x - 4 - √5) (x - 3i)
= x² - 3ix - 4x + 12i - √5x + 3√5i
= x² - (3i + √5 + 4)x + (12 + 3√5) i
Thus, The equation of a polynomial function, R, with rational coefficients will be;
P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i
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Sarah's truck can carry a maximum of 1351.5 pounds. She puts a 100-pound bag of cement mix in the truck. Which inequality can be used to find b, the number of 4.5-pound bricks that can also be put in the truck?
Sarah's truck can carry a maximum of 1351.5 pounds. She puts a 100 - pound bag of cement mix in the truck. Which inequality can be used to find b, the number of 4.5-pound bricks that can also be put in the truck?
___________________________________________
Maximum of 1351.5 pounds
Total ≤ 1351.5 pounds
The number on bricks = b
b*4.5 = bricks weight
100 + 4.5*b ≤ 1351.5
__________________
Can you see the updates?
___________________
Answer
100 + 4.5*b ≤ 1351.5
1351.5 ≥ 100 + 4.5*b
The centre of a circle is the point with coordinates (-1, 3)
The point A with coordinates (6, 8) lies on the circle.
Find an equation of the tangent to the circle at A.
Give your answer in the form ax+by+c=0 where a, b and c are integers.
Answer:
[tex]7x-5y-2=0[/tex]
Step-by-step explanation:
The gradient of the line from the centre to [tex]A[/tex] is [tex]\frac{8-3}{6-(-1)}=\frac{5}{7}[/tex].
Perpendicular lines have gradients that multiply to -1, so the tangent at the point A has gradient 7/5.
So, the equation is:
[tex]y-8=\frac{7}{5}(x-6) \\ \\ 5(y-8)=7(x-6) \\ \\ 5y-40=7x-42 \\ \\ 7x-5y-2=0[/tex]
what's the
measure of
LX?
HELPO PLEASEEE
Answer:
x = 40
Step-by-step explanation:
180 - 120 is 60
180 - 100 is 80
60 + 80 is 140
40 is the unknown angle
vertical angle means x is 40