PLEASE HELP! 30 POINTS! Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each statement with the equation that represents it.
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In the given scenarios: 1. Car speed (x) determines distance covered (y) in 30 minutes (y = 30x). 2. Tina's age (y) is 5 years more than Tim's age (x) (y = x + 5). 3. Chair cost (x) relates to table cost (y) as y = 2x. 4. Baking time for chocolate muffins (y) is 2 minutes longer than for vanilla muffins (x) (y = x + 2). These equations establish connections between variables in different real-world situations.
In these scenarios, we encounter different situations where certain variables and their relationships are described. Let's elaborate on each scenario and express it in a more detailed manner:
1. **Car Speed and Distance:** The speed of a car is represented by the variable 'x' in miles per hour. The total distance covered by the car in 30 minutes, denoted as 'y,' can be expressed using the formula: y = 30x. This equation relates the speed 'x' to the distance 'y' covered in a specific time period.
2. **Sibling Ages:** Tim's age, represented by 'x,' and Tina's age, represented by 'y,' are related. Tina's age is 5 years more than Tim's age, which can be expressed as y = x + 5. This equation defines the age difference between the siblings.
3. **Cost of Furniture:** In this scenario, the cost to produce a chair is 'x,' and the cost to produce a table is 'y.' The relationship is that the cost of producing a table is two times the cost of producing a chair, which can be expressed as y = 2x. This equation shows the cost relationship between chairs and tables.
4. **Muffin Baking Times:** The time required to bake a vanilla muffin is 'x,' and the time required to bake a chocolate muffin is 'y.' The relationship is that the time to bake a chocolate muffin is 2 minutes more than the time to bake a vanilla muffin, which can be expressed as y = x + 2. This equation establishes the time difference between baking these two types of muffins.
In summary, these scenarios involve different relationships and equations that connect variables and quantities in various real-world contexts, such as car speed and distance, sibling ages, furniture production costs, and muffin baking times. These equations help describe and quantify these relationships, making them useful for solving practical problems.
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Related Questions
help me with this because I have problem doing it
Answers
Answer:
A 12+6i
----------
5
Step-by-step explanation:
6
-----------
2-i
Multiply by the complex conjugate
6 2+i
----------- *------------
2-i 2+i
12 +6i
-------------
4 -2i +2i -i^2
12+6i
----------
4 - (-1)
12+6i
--------------
5
which of the following trigonometric expressions is equivalent to the y coordinate of the terminal point (√3/2, 1/2)?
Answers
The trigonometric expressions sin(π/6) is equivalent to the y coordinate of the terminal point (√3/2, 1/2) option (B) is correct.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have:
y coordinate of the terminal point (√3/2, 1/2)
Terminal point = (√3/2, 1/2)
sin(a) = 1/2
a = sin⁻¹(1/2)
a = π/6
a is the angle.
y coordinate is sin(π/6)
Thus, the trigonometric expressions sin(π/6) is equivalent to the y coordinate of the terminal point (√3/2, 1/2) option (B) is correct.
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Final answer:
The trigonometric expression equivalent to the y-coordinate (1/2) of the given terminal point (√3/2, 1/2) is sin(30°) or sin(π/6).
Explanation:
The student is asking for the trigonometric expression equivalent to the y-coordinate of the terminal point (√3/2, 1/2). In trigonometry, the y-coordinate of a point on the unit circle corresponds to the sin of the angle from the positive x-axis to the radius that ends at the point. Since the terminal point given is in the first quadrant and matches the coordinates for a 30° (or π/6 radians) angle in standard position on the unit circle, the y-coordinate is equal to sin(30°) which is 1/2. Therefore, the trigonometric expression equivalent to the y-coordinate 1/2 is sin(30°) or sin(π/6).
Please help! see attached
Answers
Answer:
The lowest value of the confidence interval is 0.5262 or 52.62%The highest value of the confidence interval is 0.5538 or 55.38%Step-by-step explanation:
Here you estimate the proportion of people in the population that said did not have children under 18 living at home.It can also be given as a percentage.
The general expression to apply here is;
[tex]C.I=p+-z*\sqrt{\frac{p(1-p)}{n} }[/tex]
where ;
p=sample proportion
n=sample size
z*=value of z* from the standard normal distribution for 95% confidence level
Given;
n=5000
Find p
From the question 54% of people chosen said they did not have children under 18 living at home
[tex]\frac{54}{100} *5000 = 2700\\\\p=\frac{2700}{5000} =0.54[/tex]
To calculate the 95% confidence interval, follow the steps below;
Find the value of z* from the z*-value tableThe value of z* from the table is 1.96
calculate the sample proportion pThe value of p=0.54 as calculated above
Find p(1-p)[tex]0.54(1-0.54)=0.2484[/tex]
Find p(1-p)/nDivide the value of p(1-p) with the sample size, n
[tex]\frac{0.2448}{5000} =0.00004968[/tex]
Find the square-root of p(1-p)/n[tex]=\sqrt{0.00004968} =0.007048[/tex]
Find the margin of errorHere multiply the square-root of p(1-p)/n by the z*
[tex]=0.007048*1.96=0.0138[/tex]
The 95% confidence interval for the lower end value is p-margin of error
[tex]=0.54-0.0138=0.5262[/tex]
The 95% confidence interval for the upper end value is p+margin of error
[tex]0.54+0.0138=0.5538[/tex]
Answer: 0.5262 - 0.5538
Step-by-step explanation:
1) Find the standard deviation with the given information:
n=5000
p=54% ⇒ 0.54
1-p = 1 - 0.54 = 0.46
[tex]\sigma =\sqrt{\dfrac{p(1-p)}{n}}\\\\\\.\ =\sqrt{\dfrac{0.54(0.46)}{5000}}\\\\\\.\ =\sqrt{\dfrac{0.2484}{5000}}\\\\\\.\ =\sqrt{0.00004968}\\\\\\.\ =0.007048[/tex]
2) Find the margin of error (ME) with the given information:
C=95% ⇒ Z = 1.960
σ=0.007048
ME = Z × σ
= 1.96 (0.007048)
= 0.01381
3) Find the confidence interval with the given information:
p = 0.54
ME = 0.01381
C = p ± ME
= 0.54 ± 0.01381
= (0.5262, 0.5538)
Answer this question thanks
Answers
First add 3 to both sides (what you do on one side you must do to the other). Since 3 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the right side and bring it over to the left side.
2 < u - 3
2 + 3 < u - 3 + 3
5 < u - 0
5 < u
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
5 < u OR u > 5
aka 5 is less then u OR u is greater then 5
This means that the graph will have an empty circle and the arrow will go to the right of 5. Look at image below.
Hope this helped!
~Just a girl in love with Shawn Mendes
Find the slope of the line
A. 4/3
B. -4/3
C. -3/4
D. 3/4
Answers
Answer:
-3/4
Step-by-step explanation:
You could identify two points and used the slope formula given two points.
OR
You can just count from one point to another.
First step: Identify two points where the line crosses nicely.
I see one at the y-intercept (0,1) and another at (4,-2). So starting at the y-intercept, how much do we need to travel down to get to (4,-2). Hopefully you say down 3, so the rise is -3. Now how much to the right after traveling down 3 from (0,1) to we need to travel to get to (4,-2) . Count the spaces...4 units right so the run is 4.
The slope is -3/4
Declan draws triangle WXY. He then constructs a perpendicular bisector from vertex W that intersects side XY at point Z. What can Declan conclude, based on his drawing?
Answers
Answer:
YZ = XZ
Step-by-step explanation:
Perpendicular Bisector:
A perpendicular bisector of a line segment 'l' is a line that is perpendicular to the line segment 'l' and cuts the line segment 'l' into two equal parts.
Given:
1. A triangle WXY.
2. A perpendicular bisector from vertex W that intersects XY at point Z.
Conclusion based on the drawing:
a. Z is the midpoint of the line segment XY because point Z lies on the perpendicular bisector of XY.
b. Hence, XZ = YZ.
Answer:
Option D.
Step-by-step explanation:
Given information: WXY is a triangle.
Steps of construction:
1. Draw a triangle WXY.
2. Constructs a perpendicular bisector from vertex W that intersects side XY at point Z.
If a line cuts a line segment exactly in half by a 90 degree angle, then it is called a perpendicular bisector.
WZ is a perpendicular bisector on XY. It means point Z divides the side XY in two equal parts.
[tex]YZ=XZ[/tex]
Therefore, the correct option is D.
Both the red and blue line segments stretch from the center of the circle to a point on the circle. The length of the blue segment is 5. How long is the red line segment?
Answers
Answer:
5
Step-by-step explanation:
We are given that there are two line segments, red and blue, that stretch from the center of the circle to a point on the circle.
Given that the length of the blue segment is 5, we are to determine the length of the red segment.
Since both the line segments stretch from the center of the circle to its circumference so they must be equal.
Therefore, length of the red line segment is 5.
Answer:
the answer is 5
Step-by-step explanation:
Enter the values needed to find the length EF (Simplify your answer)
Please Help Me!!!
Answers
Answer:
The missing term is 3b
Step-by-step explanation:
step 1
Find the coordinates of point F
Find the midpoint AB
[tex]F(\frac{-3a+3a}{2},\frac{b+b}{2})\\ \\F(0,b)[/tex]
step 2
Find the coordinates of point E
Find the midpoint AC
[tex]E(\frac{-3a-a}{2},\frac{b-5b}{2})\\ \\E(-2a,-2b)[/tex]
step 3
Find the distance EF
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute
[tex]EF=\sqrt{(b+2b)^{2}+(0+2a)^{2}}[/tex]
[tex]EF=\sqrt{(3b)^{2}+(2a)^{2}}[/tex]
therefore
The missing term is 3b
Answer:
its 3b thats the answer
Pleaseeeeeee help me ASAP
The figure below shows the letter T and four of its transformed images—A, B, C, and D:
Which of the four images was formed by a reflection of the letter T?
Answers
C
It's a reflection over the y-axis.
A box contains 7 plain pencils and 3 pens. A second box contains 3 color pencils and 3 crayons
One item from each box is chosen at random. What is the probability that a pen from the first
box and a crayon from the second box are selected?
Write your answer as a fraction in simplest form.
Answers
Answer:
[tex]\frac{3}{20}[/tex]
Step-by-step explanation:
Box 1:
Number of pens = 3
Total number of items = pencils + pens = 7 + 3 = 10
Probability that a pen will be picked, P(Pen) = [tex]\frac{3}{10}[/tex]
Box 2:
Number of crayons = 3
Total number of items = color pencils + crayons = 3 + 3 = 6
Probability that a crayon will be picked, P(Crayon) = [tex]\frac{3}{6}[/tex]
P(pen from 1st box and crayon from 2nd box),
= P(Pen) x P(Crayon)
= [tex]\frac{3}{10}[/tex] x [tex]\frac{3}{6}[/tex]
= [tex]\frac{3}{20}[/tex]
There are 8 brooms and 6 mops in a janitor's closet. What is the ratio of the
number of mops to the number of brooms?
Answers
The ratio of the number of mops to the number of brooms is,
⇒ Ratio = 3 : 4
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
There are 8 brooms and 6 mops in a janitor's closet.
Hence, The ratio of the number of mops to the number of brooms is,
⇒ Ratio = number of mops / number of brooms
⇒ Ratio = 6 / 8
⇒ Ratio = 3 / 4
⇒ Ratio = 3 : 4
Thus, The ratio of the number of mops to the number of brooms is,
⇒ Ratio = 3 : 4
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The length and width of a rectangle are
consecutive odd integers. The area of the
rectangle is 15 square units. What are the
length and width of the rectangle?
Separate the answers with a comma.
Answers
Answer:
3,5
Step-by-step explanation:
Represent the width by W and the length by L. L = W + 2 (because L and W are consecutive odd integers).
Then L * W = 15 units^2, and after substitution this becomes:
(W + 2) * W = 15, or W^2 + 2W - 15 = 0.
This factors as follows: (W + 5)(W - 3) = 0, and the positive root is W = 3.
The length and width of the rectangle are 3 and 5 respectively.
Note that 3 and 5 are consecutive odd integers, and that 3 * 5 = 15 units^2.
Final answer:
The length and width of the rectangle are consecutive odd integers that equate to an area of 15 square units, which are 3 units and 5 units, respectively.
Explanation:
The question at hand involves finding the consecutive odd integers that represent the length and width of a rectangle with an area of 15 square units.
Since the area of a rectangle is the product of its length and width, and in this case both are odd integers, we can list the odd number pairs whose product is 15.
The only odd numbers that multiply together to equal 15 are 3 and 5.
Therefore, the dimensions of this rectangle with the consecutive odd integer sides are: length of 5 units and width of 3 units, or vice versa depending on the interpretation, but typically, length is considered to be greater than width in geometry.
Which pairs of angles in the figure below are verticle angles? Check all that apply.
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Answer:
correct answer options are ; C and D
Step-by-step explanation:
By definition, vertical angles are those that are opposite each other when two lines cross and are equal.
Observing the given options;
C. ∠LRE and ∠FRA
D.∠TRF and ∠NRL
In the other options given, it could have been correct if stated as;
A. ∠ARS and ∠ERO
B. ∠NRA and ∠TRE
Which ordered pair describes the location of the point shown on the coordinates system below
Answers
Answer:
Option D (-1,-2)
Step-by-step explanation:
we know that
The ordered pair is 1 unit to the left of the origin and 2 units down from the origin
so
(x,y) ------> (0-1,0-2)
(x,y) ------> (-1,-2)
therefore
The coordinates of the ordered pair is (-1,-2)
Answer: c: (-1,-2)
Step-by-step explanation:
Just got it right on the quiz
Need help!!!
In the diagram of circle o, what is the measure of ABC?
Answers
Answer:
54 degrees
Step-by-step explanation:
I would turn this into a quadrilateral by connecting C to O and O to A.
The angles of a quadrilateral add up to 360 degrees.
So we have 90+90+126+angleABC=360
180+126+angleABC=360
306+angleABC=360
angleABC=360-306=54
Answer:
ABC = 54°
Step-by-step explanation:
Two tangent have been drawn from an external point B to the circle O.
These tangents touch the circle at points A and C.
Now as per Theorem of arcs and angles.
∠ABC = [tex]\frac{1}{2}[/tex] [m(major arc AC) - m(minor arc AC)]
= [tex]\frac{1}{2}[/tex] [234 - 126]
= [tex]\frac{1}{2}[/tex] × (108)
= 54°
Therefore, ABC = 54°
which expression is equivalent to (look at picture)
Answers
The answer is 1/2^15
For this case we must indicate an expression equivalent to:
[tex](2 ^ 3) ^ {-5}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
We also have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Rewriting the expression we have:
[tex](2 ^ 3) ^ {-5} = 2 ^ {-15} = \frac {1} {2 ^ {15}}[/tex]
Answer:
Option A
Solve the system of equations and choose the correct ordered pair.
5x+2y= 19
4x-3y = 6
Answers
Answer:
(3, 2)
Step-by-step explanation:
First, we have to eliminate a variable:
3(5x+2y = 19 )
2(4x-3y = 6)
------------------
15x+6y = 57
8x-6y = 12
Now we add the system of equations together:
15x+8x+6y-6y = 57+12
23x = 69
/23 /23
x = 3
Now we can plug this value back into one of the equations to get y:
5(3)+2y = 19
15+2y = 19
-15 -15
2y = 4
/2 /2
y = 2
Therefore, the solution to these system of equations is (3, 2)
Answer:
The solution of given system of equation is (3,2).
Step-by-step explanation:
The given system of equations is
[tex]5x+2y=19[/tex] .... (1)
[tex]4x-3y=6[/tex] .... (2)
Solve the system of equations using elimination method.
Multiply equation (1) by 3 and multiply equation (2) by 2.
[tex]15x+6y=57[/tex] .... (3)
[tex]8x-6y=12[/tex] .... (4)
Now, add the equations (3) and (4), to eliminate y.
[tex]15x+8x=57+12[/tex]
[tex]23x=69[/tex]
Divide both sides by 23.
[tex]x=3[/tex]
The value of x is 3. Substitute x=3 in equation (1), to find the value of y.
[tex]5(3)+2y=19[/tex]
[tex]15+2y=19[/tex]
Subtract 15 from both the sides.
[tex]2y=19-15[/tex]
[tex]2y=4[/tex]
Divide both sides by 2.
[tex]y=2[/tex]
The value of y is 2.
Therefore the solution of given system of equation is (3,2).
Anita Alvarez sells clothing for Toddler’s Shop. Baby blankets sell for $29.99 after a markup rate based on cost of 109%. Find the markup.
Answers
Answer:
The markup is $2.48
Step-by-step explanation:
* Lets explain the problem
- There is a cost price we don't know it
- There is a selling price we know it
- There is a markup we want to find it
- The relation between the cost price , the selling price and the markup
is ⇒ selling price - cost price = markup
∵ The percentage of the selling price is 109%
∵ The percentage of the cost price is 100%
- That means the markup rate = 109% - 100% = 9%
∵ The selling price is $29.99
- Lets use the ratio to find the cost price
∵ selling price / cost price = selling price% / cost price%
∴ 29.99 / cost price = 109 / 100
- By using cross multiplication
∴ cost price × 109 = 29.99 × 100
∴ cost price × 109 = 2999
- Divide both sides by 109
∴ cost price = $27.51
∵ The markup = selling price - cost price
∴ The markup = 29.99 - 27.51 = $2.48
* The markup is $2.48
The menu at a Pizza For Two has 23 choices. Fifteen of them contain Ham and 14 have Chicken and three are vegetarian.
a. If Monica dislikes Ham, how many choices does she have to order from?
b. If Andrew likes meet but dislikes mixed meets, how many choices does he have to order from?
Answers
Answer:
a)8
b)11
Step-by-step explanation:
given to 23-14
23-3=contains meat
a. Monica has [tex]8[/tex] choices to order from because she dislikes Ham.
b. Andrew has [tex]32[/tex] choices to order from because he likes meat but dislikes mixed meats.
a. Since Monica dislikes Ham, she cannot choose any of the 15 choices that contain Ham. She has [tex]\(23 - 15 = 8\)[/tex] choices left to order from.
b. Andrew likes meat but dislikes mixed meats, which means he can choose from the choices that contain only one type of meat (Ham or Chicken) or the vegetarian options. There are [tex]15[/tex] choices with Ham, [tex]14[/tex] choices with Chicken, and [tex]3[/tex] vegetarian choices.
[tex]\text{Total choices with only one type of meat}: \(15 + 14 = 29\)[/tex]
[tex]\text{Total choices with only one type of meat or vegetarian}: \(29 + 3 = 32\)[/tex]
Andrew has [tex]32[/tex] choices to order from.
help with the first one only
Answers
slope is [tex]\frac{rise}{run}[/tex] or [tex]\frac{vertical}{horizontal}[/tex]
Look at the image below:
The red (4) is the rise and the blue (1) is the run
this means the slope is...
[tex]\frac{4}{1}[/tex]
4
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the value of p ?
Answers
Answer:
p = 35
Step-by-step explanation:
180 - 125 = 55
180 - 90 = 90
55 + 90 = 145
180 - 145 = 35
p = 35
The remainder obtained when
x^4 + 3x^2 - 2x + 2 is divided by (x + b) is the square of the
remainder obtained when x^2 – 3 is divided by (x + b). Find the values of b.
Answers
Use the polynomial remainder theorem: the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is [tex]p(c)[/tex].
[tex](-b)^4+3(-b)^2-2(-b)+2=b^4+3b^2+2b+2[/tex]
[tex]((-b)^2-3)^2=b^4-6b^2+9[/tex]
Now
[tex]b^4+3b^2+2b+2=b^4-6b^2+9\implies9b^2+2b-7=0[/tex]
[tex]\implies(9b-7)(b+1)=0[/tex]
[tex]\implies b=\dfrac79\text{ or }b=-1[/tex]
What’s the answer ? Plz help
Answers
Answer:
Option C
Step-by-step explanation:
we know that
The solution of the system of inequalities is the shaded area above the dashed line y=4 and above the dashed line y=x
therefore
The system of inequalities is equal to
y>4
y>x
How do you solve this?
Answers
[tex]\dfrac{1}{4}+x=\dfrac{20}{3}\Big|\cdot12\\\\3+12x=80\\\\12x=77\\\\x=\dfrac{77}{12}[/tex]
Answer:
x = 77/12 or 6 5/12
Step-by-step explanation:
To solve this one step equation you have to isolate the variable. To isolate the variable you need to to do the inverse of addition which is subtraction.
So you have to subtract 1/4 by 1/4
And what you do to one side of the equation you have to do to the other side.
So 20/3 - 1/4 = 77/12
So x = 77/12 or change it to a mixed number 6 5/12.
Hope this helped you!!
Can the triangles be proven similar using the SSS or SAS similarities theorems?
Answers
Answer:
Both!
Step-by-step explanation:
By both!
You have all 3 corresponding sides are proportional so you have SSS. That is
24/8=15/5=18/6
You also have SAS because 15/5=18/6 and you have the angle between the sides that I'm referring to in that proportion.
The SSS (Side-Side-Side) theorem can prove triangle similarity if all sides of two triangles are proportional, whereas the SAS (Side-Angle-Side) can prove similarity if two sides and the included angle of one triangle are proportional to those of another triangle. However, these theorems are only applicable if these conditions are met.
Explanation:In mathematics, particularly in geometry, we often deal with proving the similarity or congruence of shapes, especially triangles. The SSS (Side-Side-Side) and SAS (Side-Angle-Side) theorems are two of those methods used to establish similarity between triangles. However, these theorems need specific conditions to be applicable.
The SSS Similarity theorem states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar. In other words, if you can match up the sides of one triangle to the sides of the other in such a way that every pair of corresponding sides has the same ratio, then the triangles are similar.
On the other hand, the SAS Similarity theorem states that if an angle of one triangle is congruent to an angle of a second triangle, and the sides including these angles are in proportion, then the triangles are similar.
Given the exact measures of the sides and angles of the triangles, it's possible to use either the SSS or SAS theorem to establish similarity. If, however, these specifics are not available or do not meet the conditions required for SSS or SAS, we cannot use these theorems to prove similarity.
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Calculate the volume Radius 4cm height 10 cm
Answers
Answer:
Step-by-step explanation:
you need to double the radius which is 8 cm
then you do 10 * 8 * 3.14 = 251.2
Find the equation of the line that is perpendicular to the line x = −5 and passes through the point (1, π). A) y = π B) y = πx C) y = 1 5 πx D) y = −5πx
Answers
Answer:
A) y = πStep-by-step explanation:
[tex]\text{The equation of a horizontal line:}\ y=a.\\\\\text{The equation of a vertical line:}\ x=a\\\\a-any\ real\ number\\\\\text{We have}\ x=-5.\ \text{It's a vertical line.}\ \text{The line that is perpendicular}\\\text{to the vertical line is a horizontal line.}\\\\\text{The line passes through the point}\ (1,\ \pi)\to x=1,\ y=\pi.\\\\\text{Therefore the equation is}\ y=\pi[/tex]
Which function could be a stretch of the exponential decay
function shown on the graph?
f(x) = 2(6)
f(x) = 1/2(6)
f(x) = 2[1/6]
f(x) = 1/2[1/6]
Answers
Answer:
(x) = 2(1/6)^x
Step-by-step explanation:
To easily solve this problem, we can graph each option using a graphing calculator, or any equation plotting tool.
Case 1
f(x) = 2(6)^x
Case 2
f(x) = 1/2*(6)^x
Case 3
f(x) = 2(1/6)^x
Case 4
f(x) = 1/2*(1/6)^x
By looking at the pictures below, we can tell that the correct option is
Case 3
f(x) = 2(1/6)^x
Since the stretch is done by a factor of 2
I don't know why the answer can be 3 OR 7. Please help me.
Answers
Answer:
see explanation
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (1, a)
d = [tex]\sqrt{(1-3)^2+(a-5)^2}[/tex]
= [tex]\sqrt{(-2)^2+(a-5)^2}[/tex]
= [tex]\sqrt{4+(a-5)^2}[/tex]
Equating d to [tex]\sqrt{8}[/tex], gives
[tex]\sqrt{4+(a-5)^2}[/tex] = [tex]\sqrt{8}[/tex]
Squaring both sides
4 + (a - 5)² = 8 ( subtract 4 from both sides )
(a - 5)² = 4 ( take the square root of both sides )
a - 5 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 5 to both sides )
a = 5 ± 2, that is
a = 5 - 2 = 3 OR a = 5 + 2 = 7
What is x3+3x2−16x−48 divided by x−1?
Answers
Answer:
x² + 4x - 12, remainder - 60
Step-by-step explanation:
Using synthetic division to divide
Since dividing by x - 1, evaluate for x = 1
1 | 1 3 - 16 - 48
↓ 1 4 - 12
---------------------------
1 4 - 12 - 60 ← degree 2 polynomial
quotient = x² + 4x - 12, remainder = - 60
Hence
[tex]\frac{x^3+3x^2-16x-48}{x-1}[/tex] = x² + 4x - 12 - [tex]\frac{60}{x-1}[/tex]
The division of the given polynomials x³ + 3x² - 16x - 48 by x - 1 using synthetic division results in the polynomial x² + 4x - 12 - 60/(x - 1) with a remainder of -60.
Explanation:The division of two polynomials can be performed using polynomial long division or synthetic division. In this case, we have a cubic polynomial divided by a linear polynomial: x³ + 3x² - 16x - 48 divided by x - 1.
We can use synthetic division to solve this. Place the coefficients of the dividend (1, 3, -16, -48) in a row and place the zero from the divisor (x - 1= 0, x = 1) to the left. Add down the columns and multiply the result by x in each row, placing the result in the next row.
Following these steps, the coefficients become 1, 4, -12, and -60 which translates to the polynomial x² + 4x - 12 - 60/(x - 1). The remainder (-60) divided by the divisor (x - 1) is added as the last term.
Learn more about Polynomial Division here:https://brainly.com/question/36507743
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