Answer: First Option
The points have the same x-coordinate value.
Step-by-step explanation:
By definition, a relation is considered a function if and only if for each input value x there exists only one output value y.
So, the only way that the line that connects two points in the coordinate plane is not a function, is that these two points have the same coordinate for x.
For example, suppose you have the points (2, 5) and (2, 8) and draw a line that connects these two points.
The line will be parallel to the y axis.
Note that the value of x is the same x = 2. But when x = 2 then y = 5 and y = 8.
There are two output values (y = 8, y = 5) for the same input value x = 2.
In fact all the vertical lines parallel to the y-axis have infinite output values "y" for a single input value x. Therefore, they can not be defined as a function.
Then the correct option is:
The points have the same x-coordinate value.
Alicia is making cupcakes for a party she is having and wants to make sure everyone gets at least 1 cupcake
The recipe calls for 1/2 teaspoon of salt for every batch and each batch makes 21 cupcakes if the part will have a total of 84 people attending how many teaspoon of salt will Alicia need.
2 teaspoons
21+21=42 so for every 1 teaspoon there is 42 people
42+42=84 so it’s 2 teaspoons
Answer:
Let's imagine that x is the number of teaspoon of salt needed to make at least 84 cupcakes.
So we know that, 1 batch makes 21 cupcakes, and we need at least 84 cupcakes, so the number of cupcakes batch needed here should be:
84 ÷ 21 = 4 (batches)
Since we knew the number of batches that we need to make the cupcakes, we now calculate the amount of sugar needed. We have:
1/2 teaspoon of salt for every 1 batch.
x teaspoon of salt for every 4 batches.
x = (4 . 1/2) . 1 = 2 (teaspoons)
this is the rest of the first question
-7x/7 > 56/7
x < -8
Diagram with a hollow dot on 8.
Is there more wood in a 70-foot-high tree trunk with a radius of 2.1 feet or in a 60-foot-high tree trunk with a radius of 2.4 feet? Assume that the trees can be regarded as right circular cylinders.
There is
nothing
▼
ft
ft cubed
ft squared
of wood in the 70-foot-high tree and
nothing
▼
ft cubed
ft squared
ft
of wood in the 60-foot-high tree. There is more wood in the
▼
60
70
-foot-high tree
Answer:
There is more wood in a 60-foot-high tree trunk with a radius of 2.4 feet
Step-by-step explanation:
* Lets talk about the right circular cylinder
- It has two circular bases
- The volume of it = Area of the base × its height
- The area of the base = πr²
- The quantity of wood in the tree is the volume of the cylinder
* Lets calculate the volumes the two trees and compare
between them
- Volume of the first tree:
∵ Its radius = 2.1 feet
∴ The area of its base = π(2.1)² = 4.41π feet²
∵ Its height = 70 feet
∴ Its volume = 4.41π × 70 = 308.7π = 969.8 feet³
- Volume of the second tree:
∵ Its radius = 2.4 feet
∴ The area of its base = π(2.4)² = 5.76π feet²
∵ Its height = 60 feet
∴ Its volume = 5.76π × 60 = 345.6π = 1085.7 feet³
∵ 1085.7 > 969.8
∴ The volume of wood in 2nd tree > the volume of wood in 1st tree
* There is more wood in a 60-foot-high tree trunk with a radius of 2.4 feet
On May 9, 2014 Jason made a deposit of $650.00. What is his balance after this transaction?
A) $540.28
B) $832.45
C) $1190.28
D) $1548.11
C is the correct answer
A health club charges non-members $5 per day to swim and $9 per day for an exercise class. Members pay a yearly fee of $300 plus $4 per day to attend an exercise class and no swim fee. If Robert swims and takes an exercise class every time he goes to the gym, which equation shows the number of days he must use the gym to make the membership worthwhile? m
Answer:
300+4x < (9+5)*x
Step-by-step explanation:
x is number of times Robert goes to the gym
Answer:
5d+ 9d=300+4d
Step-by-step explanation:
Answer on EDGE
The diameter of a sphere is 10 cm. What is the spheres volume? Round to the nearest tenth.
4/3πr^3 is the equation to solve for volume.
Since the radius is 5 cm (10/2), we know the equation is 4/3π125
166 2/3π cm^3
or
523 1/3 cm^3
Final answer:
The volume of a sphere with a 10 cm diameter is approximately 523.6 cubic centimeters when rounded to the nearest tenth.
Explanation:
The student is asking for the volume of a sphere with a given diameter of 10 cm. To calculate the volume, you use the formula for the volume of a sphere, which is V = (4/3)πr³.
First, we need to find the radius of the sphere, which is half of the diameter, so the radius (r) is 5 cm. Plugging this into the formula gives us V = (4/3)π(5 cm)³. Now we calculate the volume: V = (4/3)π(125 cm³) ≈ 523.6 cm³ when rounded to the nearest tenth. So, the volume of the sphere is approximately 523.6 cubic centimeters.
please help me this is kinda hard
All sides of a square/cube are the same. Since this is a cube, you'll find the volume by "cubing" (get it?) 4.4m.
4.4³ or 4.4 * 4.4 * 4.4 = 85.184m³ but you can round that to 85m³
I hope that helps!
the clock in our classroom has a radius of 9 inches. if its 4:00, find the arc length and area of the sector for this time.
Answer:
6pi; 27pi
Step-by-step explanation:
Since 4:00 is 120 degrees on a clock, then it is 120/360 or 1/3 of the clock. Now let’s find the arch length! Since the radius of the clock is 9, then the circumference will be 18pi. Since 1/3 of the clock is 4:00, then the arc length is 1/3 of the circumference. SO the arc length is 6pi.
Now let’s find the area of the sector. Since the radius is 9, then the area is 81pi. So 1/3 of that is 27pi.
If each cube has edges 2 centimeters long, what is the volume of the blue-outlined prism?
A) 20 cm3
B) 40 cm3
C) 160 cm3
D) 320 cm3
Answer:
C) 160 cm3
Step-by-step explanation:
Since each cube represents 2 centimeters you need to multiply by 2 three times, since there are three dimensions. The volume of the figure is 160 cm3
Answer:
C (160)
Step-by-step explanation:
hope it helps brainliest pls
two vertices of a right angle have coordinates (3,7) and (3,10). The segment that connects these points a leg of the triangle. which set of coordinates for the third vertex would create a right triangle?
Answer:
(x,7) or (x,10)
Step-by-step explanation:
It is given that two vertices of a right triangle have coordinates (3, 7) and (3, 10), we can see that the x-coordinate is same for both vertices, therefore it is a vertical line and thus base of the right angle triangle.
We need to find the height of this triangle which will be perpendicular to this line, so the value of y-coordinate of third point must be either 7 or 10.
Example
(8,7)
9 is what percent of 50
All you have to do is divide 9/50, which equals 0.18 Move the decimal 2 units to the right to get 18% as your answer
Hope this helps you!
The 9 is 18% percent of 50.
Given that,
There are 2 numbers i.e. 9 and 50.We need to find out the percentage.Based on the above information, the calculation is as follows:
[tex]= 18\div 100\\\\= 9\div 50[/tex]
So here we can conclude that The 9 is 18% percent of 50.
Learn more: brainly.com/question/6201432
plz help god bless if do only 5 stuff to do :3
Referring to the tables above, which students have earned exactly five minutes of free time on Friday? Select all that apply.
Winslow
Amelia
Demetrius
Harley
Jackson
Tyler
Jasmine
Joe
None of the students
Referring to the tables above, which students will receive notes home on Friday? Select all that apply.
Winslow
Amelia
Demetrius
Harley
Jackson
Tyler
Jasmine
Joe
None of the students
Referring to the tables above, which students will receive no rewards or consequences? Select all that apply.
Winslow
Amelia
Demetrius
Harley
Jackson
Tyler
Jasmine
Joe
None of the students
Referring to the tables above, which students will receive at least ten minutes of free time on Friday? Select all that apply.
Winslow
Amelia
Demetrius
Harley
Jackson
Tyler
Jasmine
Joe
None of the students
Referring to the tables above, which students will receive at least fifteen minutes of free time on Friday? Select all that apply.
Winslow
Amelia
Demetrius
Harley
Jackson
Tyler
Jasmine
Joe
None of the students
Ok I got it.
Question 1 - Demetrius, Jackson, Tyler, and Amelia
Question 2 - Winslow
Question 3 - Joe
Question 4 - Harley and Jasmine
Question 5 - No one recieves fifteen minutes of free time
I hurried this one because Imma go see avengers endgame.
I hope this helps you very much.
I would appreciate making me the brainliest.
Thanks in advance
In triangle ABC, m A = 25°, m B = 55°, and a = 10.73. Use the law of sines to find b. Round your answer to the nearest tenth.
Answer:
Option A. [tex]b=20.8\ units[/tex]
Step-by-step explanation:
we know that
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]
substitute the values and solve for b
[tex]\frac{10.73}{sin(25\°)}=\frac{b}{sin(55\°)}\\ \\ b=10.73*sin(55\°)/sin(25\°)\\ \\b=20.8\ units[/tex]
Answer:
20.8 option A
Step-by-step explanation:
sine law for triangle states that
sin A / a = sin B / b = sin C / c ( equation for sine law )
where m A = 25°
m B = 55°
a = 10.73
b = unknown
from the equation for sine law
sin m A / a = sin m B / b
sin 25° / 10.73 = sin 55° / b
0.4226 / 10.73 = 0.8191 / b
0.0394 = 0.8191 / b equation 2
cross multiply equation 2 becomes
0.0394 b = 0.8191
therefore b = 0.8191 / 0.0394 = 20.789 to the nearest tenth will be 20.8
What substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation?
Answer:
The substitution is
[tex]u = x ^ 4[/tex]
[tex]u ^ 2 -3u +2 = 0[/tex]
Step-by-step explanation:
We have the 8th degree polynomial equation
[tex]x ^ 8 - 3x^4 -+2 = 0[/tex]
To rewrite the equation as a quadratic function, take the common factor of the term x with the smallest exponent, in this case it is [tex]x ^ 4[/tex].
Now make a change of variable
[tex]u = x ^ 4[/tex].
So rewriting the equation in terms of u, we have:
[tex]u ^ 2 -3u +2 = 0[/tex]
Now the initial equation became a quadratic equation
Factoring is left:
[tex](u-2) (u-1) = 0[/tex]
[tex]u = 2[/tex] and [tex]u = 1[/tex]
[tex]x ^ 4 = 2[/tex] and [tex]x ^ 4 = 1[/tex]
Answer:
substitution should be p = x⁴
Step-by-step explanation:
It is given that,
x⁸ - 3x⁴ + 2 = 0
we can rewrite the equation,
(x⁴)² - 3x⁴ + 2 =0
To find the substitution
Here we can see that x⁴ is common in two terms of the given equation
we can substitute p instead of x⁴, the equation becomes,
p² - 3p +2 = 0
Therefore substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation is p = x⁴
Part A
given that P=(5,4), Q=(7,3), R=(8,6), and S=(4,1), find the component form of the vector PQ+4RS.
a.(18,19)
b.(-2,-6)
c.(-14,-21)
d.(-18,-19)
Part B
Use the information from part A to find the magnitude of the vector PQ+4RS.
a. 2sqrt10
b. 7sqrt13
c. sqrt35
d. 637
Answer:
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:-14,-21\:>\:[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}[/tex]
Step-by-step explanation:
The given points have coordinates; P=(5,4), Q=(7,3), R=(8,6), and S=(4,1).
[tex]^{\to}_{PQ}=^{\to}_{OQ}-^{\to}_{OP}[/tex]
[tex]^{\to}_{PQ}=<\:7,3\:>\:-\:<\:5,4\:>[/tex]
[tex]^{\to}_{PQ}=<\:7-5,3-4\:>\:[/tex]
[tex]^{\to}_{PQ}=<\:2,-1\:>\:[/tex]
[tex]^{\to}_{RS}=^{\to}_{OS}-^{\to}_{OR}[/tex]
[tex]^{\to}_{RS}=<\:4,1\:>\:-\:<\:8,6\:>[/tex]
[tex]^{\to}_{RS}=<\:4-8,1-6\:>\:[/tex]
[tex]^{\to}_{RS}=<\:-4,-5\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2,-1\:>\:+4\:<\:-4,-5\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2,-1\:>\:+\:<\:-16,-20\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2-16,-1-20\:>\:[/tex]
[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:-14,-21\:>\:[/tex]
The correct answer is C
The magnitude is given by:
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{x^2+y^2}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{(-14)^2+(-21)^2}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{196+441}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{637}[/tex]
[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}[/tex]
The correct answer is B
A salesman makes 4% commission on sales. What is his commission on $8,472 worth of sales?
Answer:
The answer is $12,000 I think check to be sure...Sorry in advance I'm not the best at math guys...
Step-by-step explanation:
4% of 8472 = 338.88
The salesman will have made $338.88, which is 4% of $8,472.
the width of a rectangular flower bed is 7ft less than the length. The area is 18ftsq. Find the length and the width
Answer:
width = 2ft and length = 9ft
Step-by-step explanation:
width W = x
length L = x +7
area of a rectangle A = L * W
18 = (x + 7) * x
18 = x² + 7x
x² + 7x -18 =0
solve the equation by factorisation
x² -2x + 9x - 18 =0
x(x - 2) + 9(x - 2) =0
(x - 2)(x + 9) = 0
x = 2 and -9
therefore the width is 2ft because it is positive and the negative value is ignored
the length = 2 + 7 = 9ft
Answer:
width = 2ft and length = 9ft
Step-by-step explanation:
What is the sum of the geometric series?
Answer:
40
Step-by-step explanation:
The given geometric series is:
[tex]\sum_{n=1}^4(-2)(-3)^{n-1}[/tex].
When n=1, [tex]a_1=(-2)(-3)^{1-1}[/tex], [tex]\implies a_1=(-2)(-3)^{0}=-2[/tex]
When n=2, [tex]a_2=(-2)(-3)^{2-1}[/tex], [tex]\implies a_2=(-2)(-3)^{1}=6[/tex]
When n=3, [tex]a_3=(-2)(-3)^{3-1}[/tex], [tex]\implies a_3=(-2)(-3)^{2}=-18[/tex]
When n=4, [tex]a_4=(-2)(-3)^{4-1}[/tex], [tex]\implies a_4=(-2)(-3)^{3}=54[/tex]
The sum of the given series is:
-2+6-18+54=40
Which unit would you use to measure the height of a bird? mm cm m km
I would use the centimeter to measure the height of a bird.
I’m assuming centimeters because km is like miles and mm is for something else not for height
A pentagon has the following measurements what is interior angles: (x-8), (3x-11), (x+8), (x), and (2x+7). Which of the following could be measurements for interior angles of a pentagon.
Answer:
60°
68°
76°
193°
Step-by-step explanation:
step 1
Calculate the sum of the interior angles in a pentagon
The formula to calculate the sum of the interior angles is equal to
S=(n-2)180°
where
n is the number of sides
In this problem
n=5 sides
substitute
S=(5-2)180°=540°
step 2
Find the value of x
(x-8)+(3x-11)+(x+8)+(x+(2x+7)=540°
(8x-4)=540°
8x=540°+4°
x=544°/8=68°
step 3
Find the measures of the internal angles of the pentagon
(68-8)°=60°
(3*68-11)=193°
(68+8)=76°
68°
(2*68+7)=143°
was the answer they put right?
Let f(x) = -2x - 7 and g(x) = -4x + 3. Find (fog)(-5)
ANSWER
[tex]( f \circ \: g)( - 5)= -53[/tex]
EXPLANATION
The given functions are:
f(x) = -2x - 7 and g(x) = -4x + 3
[tex]( f \circ \: g)(x) = f(g(x))[/tex]
[tex]( f \circ \: g)(x) = f( - 4x + 3)[/tex]
[tex]( f \circ \: g)(x) = - 2( - 4x + 3) - 7[/tex]
Expand:
[tex]( f \circ \: g)(x) = 8x - 6 - 7[/tex]
[tex]( f \circ \: g)(x) = 8x - 13[/tex]
We substitute x=-5
[tex]( f \circ \: g)( - 5) = 8( - 5) - 13 = -53[/tex]
What is the solution to the equation 3x+9-7x=2(x+6)
The answer is x equals 1/2.
Answer:
X = - 1/2
Step-by-step explanation:
3x+9-7x=2(x+6)
9-4x=2x+12
6x=-3
x=-1/2
Which two transformations are applied to pentagon ABCDE to create A’B’C’D’E’?
The pentagon was reflected across the x-axis. By looking at Point A, you can see x was increased 8, x+8. Also, y was increased by 2, y+2.
Answer:
The correct option is c.
Step-by-step explanation:
From the given figure it is clear that the vertices of preimage are A(-5,-2), B(-7,-3), C(-6,-6), D(-3,-5) and E(-3,-3).
The vertices of image are A'(3,6), B'(5,5), C'(4,2), D'(1,3) and E'(1,5).
If figure translated 2 units right and 8 units up then
[tex](x,y)\rightarrow (x+2,y+8)[/tex]
The vertices of pentagon after translation.
[tex]A(-5,-2)\rightarrow A_1(-3,6)[/tex]
[tex]B(-7,-3)\rightarrow B_1(-5,5)[/tex]
[tex]C(-6,-6)\rightarrow C_1(-4,2)[/tex]
[tex]D(-3,-5)\rightarrow D_1(-1,3)[/tex]
[tex]E(-3,-3)\rightarrow E_1(-1,5)[/tex]
If the figure reflected across y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
The vertices of pentagon after translation by rule [tex](x,y)\rightarrow (x+2,y+8)[/tex] followed by reflection across y-axis are
[tex]A_1(-3,6)\rightarrow A'(3,6)[/tex]
[tex]B_1(-5,5)\rightarrow B'(5,5)[/tex]
[tex]C_1(-4,2)\rightarrow C'(4,2)[/tex]
[tex]D_1(-1,3)\rightarrow D'(1,3)[/tex]
[tex]E_1(-1,5)\rightarrow E'(1,5)[/tex]
The pentagon ABCDE translated according to the rule [tex](x,y)\rightarrow (x+2,y+8)[/tex] and reflected across the y-axis to create A'B'C'D'E'.
Therefore, the correct option is c.
the rectangular floor of a classroom is 36 ft in length and 32 ft in width and scale drawing of the floor has a length of 9 inches what is the area in square inches of the floor in scale drawing
72 square inches.
Start by finding the dimensions of the scale drawing. If 36 divided by a number equals 9, then that number is 4. 36 / 4 = 9
So, you need to divide 32 by 4 as well to get 8.
This means the scale drawing is 9 inches long and 8 inches wide.
Finally, to find the area, multiply the length and width together. 9 * 8 = 72
The area of the scale drawing is 72 square inches.
A class of 25 students took a spelling test. Two students scored 100 on each test, nine students scored 95 on each test, ten students scored 90 on each test, three students scored 80 on each test and one student scored 70. What is the average score of the spelling test rounded to one decimal place? Enter your answer in the box.
data:
2 scored 100
9 scored 95
10 scored 90
3 scored 80
1 scored 70
set of data:
70, 80, 80, 80, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 95, 95, 95, 95, 95, 95, 95, 95, 95, 100, 100
to find the average score of the spelling test, we have to add all of the numbers up and then divide by 2
all of those numbers added up would be 2,265
next, divide 2,265 by 2
2,265 / 2 = 1,132.5
finally, round 1,132.5
= 1,133 (average score of spelling test)
A class of 25 students took a spelling test. The average score of the students on the spelling test is 90.6.
How to find the average data?The average data is calculated as follows:
Add all the data elementsDivide the sum by the number of data items.Calculation:Given that,
A class of 25 students took a spelling test.
The data of scores of those students:
2 students - 100
9 students - 95
10 students - 90
3 students - 80
1 student - 70
Adding all the scores of each student:
2×100 + 9×95 + 10×90 + 3×80 + 1×70 = 2265
Dividing the sum by the number of students (25):
⇒ 2265/25
⇒ 90.6
Therefore, the average of the given data is 90.6.
Learn more about the average of the data here:
https://brainly.com/question/20118982
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For the function whose graph is shown, which is the correct formula for the function?
Answer:
y=lxl-1
Step-by-step explanation:
It goes down one.
The formula is:
y=nlx-kl+t
k translates it horizontally.
t translates it vertically.
Hw 30 surface area.
Answer:
5. LA = 301.6 sq. cm., SA = 402.1 sq. cm.
6. LA = 377.0 sq. in., SA = 603.2 sq. in.
7. LA = 113.1 sq. cm., SA = 169.6 sq. cm.
8. LA = 502.7 sq. cm., SA = 603.2 sq. cm.
9. 396 sq. in.
Step-by-step explanation:
The lateral area is the area of all the faces, except the base(s). The surface area is the area of ALL the faces of the shape.
5.
The lateral area of a cylinder is given by the formula:
LA = 2πrh
where r is the radius and h is the height of the cylinder
So, lateral area would be 2π(4)(12) = 301.6 sq. cm.
The surface are would be the lateral area (301.6) PLUS the area of 2 of the circular bases. Circle has an area of πr^2.
So 2 bases would have area of (π(4)^2)*2=100.5
Thus, the surface area = 301.6 + 100.5 = 402.1
6.
The lateral area would be LA = 2πrh
The radius is given as 6 and height as 10. Plugging it would give us:
LA = 2πrh = 2π(6)(10) = 377.0 sq. in.
For the surface area, we would need to add the top and bottom (which are 2 identical circles with area πr^2 each) with the lateral area. So we have:
2 * (π(6)^2)
=226.2
Surface area = 377.0 + 226.2 = 603.2 sq. in.
7.
The radius of the cylinder is 3 and height is 6. We will plug them into the respective formulas.
lateral area:
LA = 2πrh = 2π(3)(6) = 113.1
surface area:
area of 2 circles (top and bottom) = (πr^2)*2 = (π(3)^2)*2 = 56.5
Surface area = 113.1 + 56.5 = 169.6
8.
diameter is given as 8, so radius is half of it. Hence, radius is 4 and height given as 20.
Plugging these values into the respective formula we will get the answer.
lateral area:
LA = 2πrh = 2π(4)(20) = 502.7
surface area:
area of both the circles (top and bottom) PLUS the lateral area of 502.7.
So, surface area = 502.7 + (πr^2)*2 = 502.7 + (π(4)^2)*2 = 603.2
9.
The frosting area of area of two rectangles (left and right) + area of two rectangles (back and front) + area of rectangle (top).
So, surface area of the frosting part = 2 (4*15) + 2(4*12) + (12)(15) = 396
The image of (6, 9) under a dilation is (4, 6). The scale factor is -2 2/3 -2/3
Answer:
The scale factor is 2/3.
Step-by-step explanation:
Given data,
The given image is (6,9)
The image after dilation is (4,6)
The scale factor is calculated by dividing the resultant image by the initial image.
For example, if the initial dimensions are (x1, y1) and the final dimensions are (x2,y2). The scale factor is calculated using x2/x1 = y2/y1 = Scale Factor
In our scenario,
x1 = 6
x2 = 4
y1 = 9
y2 = 6
Scale Factor = x2/x1
=> 4/6
=> 2/3
Similarly for y axis,
Scale Factor = y2/y1
=> 6/9
=> 2/3
Therefore, the scale factor is 2/3.
Which statement describes the graph of g(x) with respect to the graph f(x)?
a. let f(x)=(x+3)^2+2
let g(x)=(x+3)^2-3
* it is translated right 5 units
* stretched horizontally by a
factor of -3
* compressed vertically by a
factor of -3
* it is translated down 5 units
b. let f(x)=x^2 +5
let g(x)=(x+1)^2+5
* it is translated right 1 unit
* it is translated left 1 unit
*it is translated up 1 unit
* compressed vertically by a
factor of 5
c. Let f(x)=(x+6)^2
let g(x)=2(x+6)^2
* it is compressed horizontally by a factor of 2
* it is translated up 2 units
* it is translated right 2 units
* it is stretched vertically by a factor of 2
show work and answer please
Answer:
a. Translated down 5 units.
b. Translated 1 to the left.
c. Stretched vertically by a factor 2.
Step-by-step explanation:
a. It is translated down by 2 - (-3) = 5 units.
b. The x in f(x) is replaced by (x + 1) to gives g(x).
It is translated left by 1 unit.
c. The 2 stretches it vertically by a factor of 2.
Using translation concepts, it is found that the correct options are given by:
a) it is translated down 5 units.
b) it is translated left 1 unit.
c) it is stretched vertically by a factor of 2.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem:
In item a, 5 was subtracted from the function, hence it was shifted down 5 units.In item b, we have that x -> x + 1, hence it was shifted left 1 unit.In item c, the function was multiplied by 2, hence it was vertically stretched 2 units.More can be learned about translation concepts at https://brainly.com/question/4521517
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The equation that measures the shape of your contact lens is -0.5x2 + 6x – 16 = 0. The lens maker cuts the lens material at the x-axis for fitting. Find the zero(s) where the lens material starts and ends.
Answer:
Step-by-step explanation:
The correct zero(s) where the lens material starts and ends are at x = 4 and x = 8.
To find the zero(s) of the quadratic equation [tex]-0.5x^2 + 6x - 16 = 0[/tex] , we can use the quadratic formula, which is given by:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c = 0.[/tex]
For the given equation, a = -0.5, b = 6, and c = -16. Plugging these values into the quadratic formula, we get:
[tex]\[ x = \frac{-6 \pm \sqrt{6^2 - 4(-0.5)(-16)}}{2(-0.5)} \][/tex]
[tex]\[ x = \frac{-6 \pm \sqrt{36 - 32}}{-1} \][/tex]
[tex]\[ x = \frac{-6 \pm \sqrt{4}}{-1} \][/tex]
[tex]\[ x = \frac{-6 \pm 2}{-1} \][/tex]
Now, we have two possible solutions for x:
[tex]\[ x = \frac{-6 + 2}{-1} = \frac{-4}{-1} = 4 \][/tex]
[tex]\[ x = \frac{-6 - 2}{-1} = \frac{-8}{-1} = 8 \][/tex]
Therefore, the zero(s) where the lens material starts and ends are at x = 4 and x = 8. These are the points where the lens maker cuts the lens material along the x-axis for fitting.