Step-by-step explanation:
f(x) = x² − 6x + 9
f(½) = (½)² − 6(½) + 9
f(½) = ¼ − 3 + 9
f(½) = 6¼
The value is 6¼, or as an improper fraction, 25/4.
Answer: The correct answer is: " 6 [tex]\frac{1}{4}[/tex] " ;
_______________________________________________
or; write as: " 6.25 " .
______________________________________________
" f([tex]\frac{1}{2})[/tex] = 6 [tex]\frac{1}{4}[/tex] " ;
= 6.26 " .
______________________________________________
Step-by-step explanation:
______________________________________________
Given the function:
______________________________________________
" f(x) = x² − 6x + 9 " ;
______________________________________________
What is: " f([tex]\frac{1}{2}[/tex]) " ?
______________________________________________
Plug in "([tex]\frac{1}{2}[/tex])" for all values of "x" in the equation;
→ to solve for: " f([tex]\frac{1}{2}[/tex]) " ; as follows:
______________________________________________
→ " f([tex]\frac{1}{2}[/tex]) " ;
= ([tex]\frac{1}{2}[/tex])² − 6*([tex]\frac{1}{2}[/tex]) + 9 ;
= ([tex]\frac{1^{2} }{2^{2}}[/tex]) − ([tex]\frac{6*1}{2}[/tex]) + 9 ;
= ([tex]\frac{1}{4}[/tex]) − ([tex]\frac{6}{2}[/tex]) + 9 ;
= ([tex]\frac{1}{4}[/tex]) − 3 + 9 ;
Note: " - 3 + 9 " = 9 + (-3) = 9 − 3 = " 6 " ;
So: Rewrite as:
______________________________________________
→ " ([tex]\frac{1}{4}[/tex]) + 6 " ;
______________________________________________
→ which equals: " 6 [tex]\frac{1}{4}[/tex] " ;
_______________________________________________
or; write as: " 6.25 " .
_______________________________________________
Hope this answer —and lengthy explanation — is helpful to you!
Wishing you the best in your academic endeavors
— and within the "Brainly" community!
_______________________________________________
Find the circumference and area of a circle with a radius 9 cm.
Answer:
C =56.52 cm
C =56.52 cm
C =56.52 cm
A =254.34 cm^2
Step-by-step explanation:
To find the circumference of a circle, we use
C = 2 * pi *r
where pi is approximated by 3.14 and r is 9
C = 2 * 3.14 *9
C =56.52 cm
To find the area of a circle, we use
A = pi *r^2
where pi is approximated by 3.14 and r is 9
A = 3.14 *9^2
A =254.34 cm^2
Your answer would be 56.52 cm (18π) for the circumference, and 254.34 cm² (81π) for the area.
The formula for the circumference of a circle is 2πr. In this case, we know that the radius is 9, so substituting it in, you get 2 * 9 * π. Solving this, we get 18π as our circumference. Your question states to use 3.14 as π, so the final step is to multiply 18 by 3.14. 18 * 3.14 = 56.52. The unit in this case would just be cm, as we are looking at circumference, or length.
The formula for the area of a circle is πr². Again, we know r = 9, so just substitute it in the equation, to get π9², which can be solved to equal 81π. Then, using 3.14 as π, we get 81 * 3.14 = 254.34 as our final answer. The unit in this case would be cm², as this is concerning area.
Hope this helps!
Can Someone Help Me With This Question??!!
Answer:
I'm pretty sure its 1
Step-by-step explanation:
because if y = 1. 1 by the power of 3 is 1, and y by the power 2 is 1. 1- 10 is -9 . -9 times 1 equals -9, and -9 equals -9 therefore it's a true statement
Step-by-step explanation:
y³ (y² − 10) = -9y
Move everything to one side:
y³ (y² − 10) + 9y = 0
Factor out common term:
y (y² (y² − 10) + 9) = 0
Distribute:
y (y⁴ − 10 y² + 9) = 0
Factor:
y (y² − 1) (y² − 9) = 0
Solve:
y = 0, ±1, ±3
Since y > 0, the two possible values for y are 1 and 3.
Create equations to solve for missing angles may be hard for me to solve. Need help on this!!
Answer: A.2x+30=90
wwww
I am having trouble with this relative minimum of this equation.
Answer:
So the approximate relative minimum is (0.4,-58.5).
Step-by-step explanation:
Ok this is a calculus approach. You have to let me know if you want this done another way.
Here are some rules I'm going to use:
[tex](f+g)'=f'+g'[/tex] (Sum rule)
[tex](cf)'=c(f)'[/tex] (Constant multiple rule)
[tex](x^n)'=nx^{n-1}[/tex] (Power rule)
[tex](c)'=0[/tex] (Constant rule)
[tex](x)'=1[/tex] (Slope of y=x is 1)
[tex]y=4x^3+13x^2-12x-56[/tex]
[tex]y'=(4x^3+13x^2-12x-56)'[/tex]
[tex]y'=(4x^3)'+(13x^2)'-(12x)'-(56)'[/tex]
[tex]y'=4(x^3)'+13(x^2)'-12(x)'-0[/tex]
[tex]y'=4(3x^2)+13(2x^1)-12(1)[/tex]
[tex]y'=12x^2+26x-12[/tex]
Now we set y' equal to 0 and solve for the critical numbers.
[tex]12x^2+26x-12=0[/tex]
Divide both sides by 2:
[tex]6x^2+13x-6=0[/tex]
Compaer [tex]6x^2+13x-6=0[/tex] to [tex]ax^2+bx+c=0[/tex] to determine the values for [tex]a=6,b=13,c=-6[/tex].
[tex]a=6[/tex]
[tex]b=13[/tex]
[tex]c=-6[/tex]
We are going to use the quadratic formula to solve for our critical numbers, x.
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}[/tex]
[tex]x=\frac{-13 \pm \sqrt{169+144}}{12}[/tex]
[tex]x=\frac{-13 \pm \sqrt{313}}{12}[/tex]
Let's separate the choices:
[tex]x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}[/tex]
Let's approximate both of these:
[tex]x=0.3909838 \text{ or } -2.5576505[/tex].
This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.
The relative maximum is at approximately -2.5576505.
So the relative minimum is at approximate 0.3909838.
We could also verify this with more calculus of course.
Let's find the second derivative.
[tex]f(x)=4x^3+13x^2-12x-56[/tex]
[tex]f'(x)=12x^2+26x-12[/tex]
[tex]f''(x)=24x+26[/tex]
So if f''(a) is positive then we have a minimum at x=a.
If f''(a) is negative then we have a maximum at x=a.
Rounding to nearest tenths here: x=-2.6 and x=.4
Let's see what f'' gives us at both of these x's.
[tex]24(-2.6)+25[/tex]
[tex]-37.5[/tex]
So we have a maximum at x=-2.6.
[tex]24(.4)+25[/tex]
[tex]9.6+25[/tex]
[tex]34.6[/tex]
So we have a minimum at x=.4.
Now let's find the corresponding y-value for our relative minimum point since that would complete your question.
We are going to use the equation that relates x and y.
I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.
[tex]y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56[/tex]
I'm shoving this into a calculator:
[tex]y=-58.4654411[/tex]
So the approximate relative minimum is (0.4,-58.5).
If you graph [tex]y=4x^3+13x^2-12x-56[/tex] you should see the graph taking a dip at this point.
Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
Answer:
Part 1) 0.65 more than -4.35 ----------> -3.70
Part 2) 0.65 more than -4.35 ---------> 5.11
Part 3) 4.34 added to -8 ---------------> -3.66
Part 4) 9.14 added to -9.14 -------------> 0
Step-by-step explanation:
Part 1) we have
0.65 more than -4.35
The algebraic expression is equal to the sum of the number -4.35 plus 0.65
[tex]-4.35+0.65=-3.70[/tex]
Part 2) we have
1.98 added to 3.13
The algebraic expression is equal to the sum of the number 3.13 plus 1.98
[tex]3.13+1.98=5.11[/tex]
Part 3) we have
4.34 added to -8
The algebraic expression is equal to the sum of the number -8 plus 4.34
[tex]-8+4.34=-3.66[/tex]
Part 4) we have
9.14 added to -9.14
The algebraic expression is equal to the sum of the number -9.14 plus 9.14
[tex]-9.14+9.14=0[/tex]
Which expression is equivalent to
Answer:
Second option: 2x^10y^12
Step-by-step explanation:
Divide
60/30 = 2
When exponents are divided, it subtracts.
20 - 10 = 10
2x^10
24-12 = 12
y^12
Simplify
2x^10y^12
Answer:
Option No. 2
[tex]2x^{10}y^{12}[/tex]
Step-by-step explanation:
Given equation is:
[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}\\=\frac{30*2 * x^{20-10}y^{24-12}}{30}\\\\=2*x^{10}*y^{12}\\=2x^{10}y^{12}[/tex]
The rules for exponents for numerator and denominators are used. The powers can be shifted from numerator to denominator and vice versa but their sign is changed.
So, the correct answer is option 2:
[tex]2x^{10}y^{12}[/tex]
five consecutive multiples of 11 have a sum of 220. what is the greatest of these numbers
A. 33
B. 44
C. 55
D. 66
Answer:
66
Step-by-step explanation:
11,22,33,44, and 55 are 5 consecutive multiples of 11.
11=11(1)
22=11(2)
33=11(3)
44=11(4)
55=11(5)
-----------------
You can see consecutive multiples of 11 where we don't know the actual multiples will look like:
11n,11(n+1),11(n+2),11(n+3),11(n+4).
Now we are given the sum of the numbers I just mentioned is 220.
This means,
11n+11(n+1)+11(n+2)+11(n+3)+11(n+4)=220
Each term 11n,11(n+1),11(n+2),11(n+3),11(n+4), and 220 all have a common factor of 11 so divide both sides by 11:
1n+1(n+1)+1(n+2)+1(n+3)+1(n+4)=20
1 times anything is still just that anything:
n+n+1+n+2+n+3+n+4=20
Combine the like terms:
n+n+n+n+n+1+2+3+4=20
Simplify the combining:
5n+10=20
Subtract 10 on both sides:
5n =10
Divide both sides by 5:
n =10/5
Simplify right hand side:
n =2
So if n=2, then the multiples of 11 in question look like this:
11n=11(2)=22
11(n+1)=11(3)=33
11(n+2)=11(4)=44
11(n+3)=11(5)=55
11(n+4)=11(6)=66
--------------------------Add up to see if sum is actually 220.
Putting into my calculator gives me a result of 220.
We are good.
Now you just have to determine what the greatest of the number 22,33,44,55, and 66 is...
The greatest listed here is 66.
If the distance across the window is 10 ft, what is the area of the semicircular part of the window? Use 3.14 for and round the answer to the nearest hundredth. 39.25 m
A boat and a plane leave from each of their ports going in the same direction at the same time. They are traveling at different speeds, but both the plane and the boat maintain their own consistent speed and direction. After a few minutes, the boat is 6 miles away from its port and the plane is 100 miles away from its port. How many miles will the plane be from its port when the boat is 54 miles away from its port?
Answer:
900 miles will the plane be from its port when the boat is 54 miles away from its port
Step-by-step explanation:
Given data
boat away = 6 miles
plane away = 100 miles
to find out
How many miles will plane be from port when boat 54 miles away from its port
solution
first we consider x distance while plane travel and boat travel 54 miles
from question given the equation will be
boat away from its port / plane away from its port = boat away from its port/ plane away from its port
54 / x = 6/100
solve this equation
6 × (x) = 54 × 100
x = 54 × 100 / 6
x = 900
so 900 miles will the plane be from its port when the boat is 54 miles away from its port
Is the following shape a right triangle? How do you know?
Answer:
C.
Step-by-step explanation:
The only information you really need in order to determine if this is a right triangle are the slopes of segments AB and BC. If the slopes of these segments are opposite reciprocals of one another, then the lines are perpendicular, and the angle is a right angle (making the triangle a right triangle!). Point A has coordinates (-5, 5), B(-3, 2), C(-6, 0).
The slope of segment AB:
[tex]m=\frac{2-5}{-3-(-5)}=-\frac{3}{2}[/tex]
The slope of segment BC:
[tex]m=\frac{0-2}{-6-(-3)}=\frac{2}{3}[/tex]
As you can see, the slopes are opposite reciprocals of one another so angle ABC is a right angle, and triangle ABC is a right triangle. Choice C is the one you want.
Answer:
Yes, two sides are perpendicular and the side lengths fit the Pythagorean theorm
Step-by-step explanation:
Because it's the answer
Which binomial could be rewritten as a difference of two squares? A) x^2 + y^2 B) 4x^2 − 11y^2 C) 7x^2 − 21y^2 D) 25x^2 − y^2
Answer:
D
Step-by-step explanation:
A: Difference means minus. A has no minuses anywhere. Not the answer.
B: Could be true if you allow irrational numbers. I'm guessing you are not allowed to give (2x - sqrt(11)y)(2x + sqrt(11)y). So B is not the answer
C: Take out the 7 as a common factor. 7(x^2 - 3y^2) If you allow C, you have to allow B so C is not the answer.
D: answer (5x - y)(5x + y)
Denver, Engle and Fido are all dogs who eat differing amounts of dog food. Denver gets 2 19 of the dog food. Engle and Fido share the rest of the food in the ratio 4 : 3 What is Fido's share of the dog food? Show your answer as a percentage, rounded to the nearest percent if necessary
Final answer:
Fido's share of the total dog food, when rounded to the nearest percent, is approximately 38% after considering the 4:3 ratio with Engle for the remaining food after Denver's part.
Explanation:
The question involves calculating Fido's share of the dog food in a ratio and expressing that share as a percentage. Denver eats 2/19 of the dog food, leaving 17/19 for Engle and Fido. Engle and Fido share this remaining dog food in a ratio of 4:3. To find out what fraction of the total dog food Fido gets, we first calculate the total parts that Engle and Fido's shares make, which is 4 + 3 = 7 parts. Fido's share is 3 parts out of these 7. We then multiply the fraction of the remaining food (17/19) by Fido's share (3/7) to get Fido's share of the total dog food.
Fido's share = (17/19) * (3/7) = (17*3) / (19*7) = 51/133
Now, we convert Fido's share to a percentage:
Percentage = (51/133) * 100% ≈ 38.35%
Rounded to the nearest percent, Fido's share is approximately 38% of the total dog food.
WANT FREE 20 POINTS + BRAINLIEST? ANSWER THIS GEOMETRY QUESTION CORRECTLY AND I GOT YOU :)
Use the given diagram to answer the question.
1. Which line is the intersection of two planes shown?
A. v
B. x
C. y
D. z
2. Which line intersects one of the planes shown?
A. w
B. x
C. y
D. z
3. Which line has points on three of the planes shown?
A. v
B. x
C. y
D. z
Answer:
1.x
2.z
3.v
Step-by-step explanation:
just took the test sorry if i'm wrong
Answer:
1. The correct option is B.
2. The correct option is D.
3. The correct option is C.
Step-by-step explanation:
1.
Let left plane is plane (1), right plane is plane (2) and horizontal plane is plane (3).
From the given figure it is clear that plane (1) and (3) intersect each other and plane (2) and (3) intersect each other.
Point B lies on the intersection of plane (1) and (3), and line x passes through the point B.
Point A lies on the intersection of plane (2) and (3), and line w passes through the point A.
So, line x and w represent the intersection of two planes. Only line x is available in the options.
Therefore the correct option is B.
2.
Line z is the which intersect plane (1) at point C. So, z is the line that intersects one of the planes.
Therefore the correct option is D.
3.
Line y passes through A and B. Points A and B are point which are lie on the intersection of planes.
The line y has points on three of the planes.
Therefore the correct option is C.
The container that holds the water for the football team is 3/10 full. After pouring in 7 gallons of water, it is 4/5 full. How many gallons can the container hold?
Step-by-step answer:
This is a problem involving subtraction of fractions.
To solve the problem, we find out the increase of the fraction of container and equate it to the amount of water added. Then we find the amount of water contained in the whole container (fraction = 1)
7 gallons = 4/5 - 3/10 = 8/10 - 3/10 =5/10 = 1/2 container
therefore, multiply by two on both sides,
14 gallons = 1 container
So container can hold 14 gallons.
The volume of a 3D object is the amount of space it contains. A fish tank, for example, is three feet long, one foot wide, and two feet tall. To get the volume, multiply the length by the breadth by the height, which is 3x1x2, or six. As a result, the fish tank has a volume of 6 cubic feet.
How to solve?Volume of cuboidal container- LBH
Given after poring 7 gallons tank is 4/5 full
Hence 7 gallon=4/5x
x=7*5/4=35/4gallon
Hence container can hold 35/4 gallon i.e=8.75gallon
Learn more about volume
https://brainly.com/question/27710307
#SPJ2
Peter paid $79.80 for renting a tricycle for 6 hours. What was the rate per hour for renting the tricycle? (Input only numeric values and decimal point, and report prices to two decimal places, such as 12.30.)
Answer:
$13.30
Step-by-step explanation:
divide your total by the hours
$79.80/6=$13.30
answer as soon as possible
Which terms complete the factorization of x2+27x+162? A 27, 9x, 18x B 9, 9x, 18x C 27, 9x, 27x D 9, 9x, 27x
Answer:
B. 9, 9x, 18x
Step-by-step explanation:
The value in each box is the product of the row heading and column heading. You can find the missing column heading by dividing the box value (162) by the row heading (18).
Answer:
The answer is B coz its completes the factorization
After plotting the data where x=area, and f(x)=the length of one side of the square, Sam determined the model to approximate the side of a square was Use the model Sam created to predict the side length of the square when the area is 86. 6
Each side of the square would be approximately 9.3 units long.
To predict the side length of the square when the area is 86.6 units, we need to use the model that Sam created. Sam likely developed a mathematical relationship between the area (x) and the length of one side of the square (f(x)). This relationship is typically expressed as a function, such as [tex]\( f(x) = \sqrt{x} \),\\[/tex] where [tex]\( x \)[/tex] represents the area and [tex]\( f(x) \)[/tex]represents the length of one side of the square.
In this model, the side length of the square is equal to the square root of the area. Therefore, to predict the side length when the area is 86.6 units, we substitute this value into the function:
[tex]\[ f(86.6) = \sqrt{86.6} \][/tex]
Now, we can calculate this:
[tex]\[ f(86.6) \approx \sqrt{86.6} \approx 9.3 \][/tex]
So, according to Sam's model, when the area is 86.6 units, the length of one side of the square is approximately 9.3 units. This means that if you were to draw a square with an area of 86.6 units, each side of the square would be approximately 9.3 units long.
With the function [tex](f(x) = \sqrt{x - 5} + 3\),[/tex] the predicted side length for an area of 86 is calculated by evaluating f(86).
This results in a side length of 12 units.
Therefore option b. 12 units is correct.
To find the predicted side length of a square when given the area, let's use the function provided by Sam:
[tex]\[f(x) = \sqrt{x - 5} + 3.\][/tex]
Here, x represents the area, and f(x) represents the predicted side length of the square.
Find f(x) for (x = 86):
1. Plug in[tex]\(x = 86\):[/tex]
[tex]\[f(86) = \sqrt{86 - 5} + 3 = \sqrt{81} + 3 = 9 + 3 = 12.\][/tex]
The predicted side length when the area is 86 is 12.
Given the function[tex]\(f(x) = \sqrt{x - 5} + 3\),[/tex] the predicted side length when [tex]\(x = 86\)[/tex] is option b. 12 units.
Question : After plotting the data where x=area, and f(x)=the length of one side of the square, Sam determined the model to approximate the side of a square was f(x)= *square root sign* x-5+3 Use the model Sam created to predict the side length of the square when the area is 86.
a. 6
b. 12
c. 81
d. 144
How to calculate the surface area of a cylinder
Geometry:
The vertices of quadrilateral EFGH are E(-2, -1), F(1, 2), G(6, 0), and H(2, -2). Find the scale factor if the image of EFGH has vertices E’(-3, -3/2), F’(3/2, 3), G’(9,0), and H’(3, -3).
Answer:
3/2
Step-by-step explanation:
Every coordinate of E'F'G'H' is 3/2 times that of EFGH, so the image is 3/2 times the size of the original.
___
For example, E'x/Ex = -3/-2 = 3/2; E'y/Ey = (-3/2)/-1 = 3/2.
The scale factor between quadrilateral EFGH and its image E'F'G'H' can be found by calculating the ratio of the lengths of corresponding sides. In this case, it is approximately 0.707.
Explanation:In this task, we are asked to find the scale factor between a quadrilateral and its image. The scale factor can be found by dividing the lengths of corresponding sides in the image by the respective side length in the original figure.
First, let's calculate the distance between the vertices E and F in the original figure using the Euclidean distance formula: sqrt[(x2-x1)^2 + (y2-y1)^2] = sqrt[(1+2)^2 + (2+1)^2] = sqrt[9+9] = sqrt[18] = approximately 4.2426.
Then, let's do the same for vertices E' and F' in the image: sqrt[(3/2+3)^2 + (3+3/2)^2] = sqrt[(9/4 + 9/4)+(9/4 + 9/4)] = sqrt[(9/2)+(9/2)] = sqrt[9] = 3.
Your scale factor, then, is the length of EF' divided by the length of EF: 3 / 4.2426, which roughly equals 0.707.
Learn more about Scale Factor here:https://brainly.com/question/35553153
#SPJ11
HELPPPPPPP ASAPPPPP
Match each graph with the logarithmic function it represents.
Answer:
f(x)=3-4 In (x-2)=graph 3
f(x)=3-In x=graph 1
f(x)=In (x+1)=graph 4
f(x)= 2In (x+3)= graph 2
Step-by-step explanation:
Use a graph tool to visualize the functions.Attached are the graphed functions respectively.
Answer:
f(x) = 3 - 4㏑(x - 2) ⇒ graph 3
f(x) = 3 - ㏑(x) ⇒ graph 1
f(x) = ㏑(x + 1) ⇒ graph 4
f(x) = 2㏑(x + 3) ⇒ graph 2
Step-by-step explanation:
* Lets look to the graphs and solve the problem
- We will use some points on each graph and substitute in the function
to find the graph of each function
- Remember: ㏑(1) = 0 and ㏑(0) is undefined
- Lets solve the problem
# f(x) = 3 - 4㏑(x - 2)
- Let x - 2 = 1 because ㏑(1) = 0, then f(x) will equal 3
∵ x - 2 = 1 ⇒ add 2 for both sides
∴ x = 3
- Substitute the value of x in f(x)
∴ f(x) = 3 - 4㏑(3 - 2)
∴ f(x) = 3 - 4㏑(1) ⇒ ㏑(1) = 0
∴ f(x) = 3
∴ Point (3 , 3) lies on the graph
- Look to the graphs and find which one has point (3 , 3)
∵ Graph 3 has the point (3 , 3)
∴ f(x) = 3 - 4㏑(x - 2) ⇒ graph 3
# f(x) = 3 - ㏑(x)
- Let x = 1 because ㏑(1) = 0, then f(x) will equal 3
- Substitute the value of x in f(x)
∴ f(x) = 3 - ㏑(1) ⇒ ㏑(1) = 0
∴ f(x) = 3
∴ Point (1 , 3) lies on the graph
- Look to the graphs and find which one has point (1 , 3)
∵ Graph 1 has the point (1 , 3)
∴ f(x) = 3 - ㏑(x) ⇒ graph 1
# f(x) = ㏑(x + 1)
- Let x = 0 because ㏑(1) = 0, then f(x) will equal 0
- Substitute the value of x in f(x)
∴ f(x) = ㏑(0 + 1) = ㏑(1) ⇒ ㏑(1) = 0
∴ f(x) = 0
∴ Point (0 , 0) lies on the graph
- Look to the graphs and find which one has point (0 , 0)
∵ Graph 4 has the point (0 , 0)
∴ f(x) = ㏑(x + 1) ⇒ graph 4
# f(x) = 2㏑(x + 3)
- Let x + 3 = 1 because ㏑(1) = 0, then f(x) will equal 0
∵ x + 3 = 1 ⇒ subtract 3 from both sides
∴ x = -2
- Substitute the value of x in f(x)
∴ f(x) = 2㏑(-2 + 3) = 2㏑(1) ⇒ ㏑(1) = 0
∴ f(x) = 0
∴ Point (-2 , 0) lies on the graph
- Look to the graphs and find which one has point (-2 , 0)
∵ Graph 2 has the point (-2 , 0)
∴ f(x) = 2㏑(x + 3) ⇒ graph 2
I need answer for this
The answer is:
If the green line has a slope of -4, the slope of the red line will also be -4.
So, the correct option is, C. -4
Why?We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.
So, if two lines are parallel, and one of them (the green line) has a slope of -4, the slope of the other line (the red one)will also be -4.
Have a nice day!
For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom layer has 81 boxes and the taop layer has only 1 box, how many boxes are in the display?
Answer:
285 boxes are in the display
Step-by-step explanation:
Given data
top layer box = 1
last row box = 81
to find out
how many box
solution
we know that every row is a square so that if the bottom layer has 81 squares it mean this is 9² and every row has one lesser box
so that next row will have 8^2 and than 7² and so on till 1²
so we can say that cubes in the rows as that
Sum of all Squares = 9² + 8² +..........+ 1²
Sum of Squares positive Consecutive Integers formula are
Sum of Squares of Consecutive Integers = (1/6)(n)(n+1)(2n+1)
here n = 9 so equation will be
Sum of Squares of Consecutive Integers = (1/6) × (9) × (9+1) × (2×9+1)
Sum of Squares of Consecutive Integers = 285
so 285 boxes are in the display
Given image A’B’C’D’E’.
If the pre-image contained Point A (-1, 5), which of the transformations resulted in image A’B’C’D’E’?
A(x, y) → (x - 3, y + 1)
A(x, y) → (x - 3, y - 1)
A(x, y) → (x + 3, y - 1)
A(x, y) → (x + 3, y + 1)
The transformations resulted in image A’B’C’D’E' is:
A(x,y) → (x-3,y-1)
Step-by-step explanation:The coordinates of the Point A is given by: A(-1,5)
and the coordinates of the Point A' is given by: A'(-4,4)
Let the translation be given by the rule:
(x,y) → (x+h,y+k)
Here
(-1,5) → (-4,4)
i.e.
-1+h= -4 and 5+k=4
i.e.
h= -4+1 and k=4-5
i.e.
h= -3 and k= -1
The transformation is:
A(x,y) → (x-3,y-1)
Solve the system of linear equations below. X + y = 4 2x + 3y = 0 A. X = -6, y = 2 B. X = -1, y = 5 C. X = 11 5 , y = 9 5 D. X = 12, y = -8
The solution to the system of linear equations X + Y = 4 and 2X + 3Y = 0 is obtained using the elimination method, resulting in X = 12 and Y = -8.
Explanation:To solve the system of linear equations X + Y = 4 and 2X + 3Y = 0, we can use the substitution or elimination method. Let's use the elimination method for this solution.
Rewrite the first equation as Y = 4 - X.Substitute the expression for Y into the second equation: 2X + 3(4 - X) = 0.Simplify and solve for X: 2X + 12 - 3X = 0 which simplifies to -X + 12 = 0, yielding X = 12.Substitute X back into the first equation: Y = 4 - 12, giving Y = -8.Therefore, the solution to the system is X = 12 and Y = -8, which corresponds to option D.
Seth is driving to a friends house that is y miles away .After driving x miles in 4 hours, he still has 612 miles to go. The equation that relates y and x is . If he is driving at a speed of d miles per hour, the equation that relates x and d is
Answer:
Step-by-step explanation:
speed x time = distance
s (1.5) = 105
1.5s=105
s = 70mph
d(t) = 70t
Answer:
The equation that relates y and x is [tex]y=x+612 mi[/tex], and the equation that relates x and d is [tex]4d=x[/tex].
Step-by-step explanation:
Step 1: First we know that the total distance is equal to y. The distance traveled in 4 hours equals x, and the distance from point x to y equals 612 miles. Adding x to the remaining 612 miles gives the total distance y.
[tex]y=x+612 mi[/tex]
Step 2: To know the relationship between x and d, we must first raise the speed during the journey to x.
[tex]v=\frac{x}{4h}[/tex]
Then, we set the speed d e equal v:
[tex]v=\frac{d}{h}[/tex]
[tex]\frac{x}{4h} = \frac{d}{h}[/tex]
Clearing x we get:
[tex]x=4h * \frac{d}{h}[/tex]
[tex]x=4d[/tex]
Have a nice day!
What is the solution of y ? 4x = 0 and 3x + 6y = 9? A. `x= 0`, `y= (3)/(2)` B. `x= (1)/(3)`, `y= (4)/(3)` C. `x = 1`, `y = -1` D. `x= (1)/(4)`, `y= (2)/(3)`
Answer:
A. `x= 0`, `y= (3)/(2)`
Step-by-step explanation:
Dividing the first equation by 4 gives ...
x = 0
Substituting that into the second equation gives ...
3·0 +6y - 9
y = 9/6 = 3/2 . . . . divide by 6, reduce the fraction
The solution of the set of equations is ...
x = 0, y = 3/2
_____
The question here asks "what is the solution of y ?". That answer is y = 3/2.
Could somebody please help me with some graphing in math?
"Consider the graphed quadratic function with one point located at point P. Plot a point on the graph that has integer coordinates and represents an average rate of change of 5 with point P."
Thank you for helping me out!
Answer:
Q(-2,-7)
See attachment
Step-by-step explanation:
We need to form a simultaneous equation and solve.
The point P has coordinates (1,8). Let the other point Q also have coordinate (x,y).
Then the average rate of change is the slope of the secant line connecting P(1,8) and Q(x,y) and this has a value of 5.
[tex]\implies \frac{8-y}{1-x}=5[/tex]
[tex]\implies 8-y=5(1-x)[/tex]
[tex]\implies y=5x-3...(1)[/tex]
This point Q also lies on the given parabola whose equation is [tex]y=-(x-2)^2+9...(2)[/tex]
Put equation (1) into (2) to get:
[tex]5x+3=-(x-2)^2+9[/tex]
[tex]5x+3=-(x^2-4x+4)+9[/tex]
[tex]5x+3=-x^2+4x-4+9[/tex]
[tex]5x+3=-x^2+4x+5[/tex]
[tex]x^2+x-2=0[/tex]
[tex](x-1)(x+2)=0[/tex]
[tex]x=1,x=-2[/tex]
When x=-2, y=5(-2)-3=-7
Therefore the required point is Q(-2,-7)
these three lengths create a triangle, true or false, will mark brainliest
Question 9:
Answer: False
Step-by-step explanation: False. These sides will not create a triangle because the longest side equals the two other sides combined. 10=7+3. This will just be a line.
Question 10:
Answer: False
Step-by-step explanation: False. These sides will not create a triangle because the longest side equals the two other sides combined. 7=2+5. This will just be a line.
What is the value of y? 18+2y+4+10+2x+10
Answer:
1) 18+2y+4+10+2x+10
2) 42+2y+2x
3) 42+2x=-2y
4) -1(42-2x=2y)
5) (42-2x=2y)/2
y=21-x
Step-by-step explanation:
1) Original equation
2) Combine like terms
3) Since the problem is asking to find the value of Y, Isolate it
4) Multiply by a negative to make Y positive
5) Since what we have left isn't in simplest form, divide by 2
What is left is y=21-x or y=-x+21
The data below shows the temperature of the water in a swimming pool over a two week period.
Week 1
Day-------Temperature (°F)
Monday 58°
Tuesday 48°
Wednesday 49°
Thursday 61°
Friday 58°
Saturday 51°
Sunday 39°
Week 2
Day--------Temperature (°F)
Monday 68°
Tuesday 74°
Wednesday 73°
Thursday 75°
Friday 70°
Saturday 67°
Sunday 63°
How many degrees greater is the mean temperature in week 2 than in week 1? A: ________
Answer:
18 °F
Step-by-step explanation:
The means are calculated in the usual way: add up the numbers and divide by the number of them. When there are a bunch of numbers, it is convenient to let a calculator or spreadsheet compute the mean for you.
In the attached, we see the mean for week 1 is 52°, and in week 2, it is 70°. The mean is 70° -52° = 18° greater in week 2.