Answer:
(-13)^3 = -2197
Step-by-step explanation:
(-13)^3 = -2197
Re-write the quadratic function below in Standard Form
y= 2(x - 2)2 – 7
Answer:
Standard form: y = 2x² - 8x + 1
Step-by-step explanation:
We are given the following quadratic function, y = 2(x - 2)² - 7, for which we must transform in its standard form.
Definition: Quadratic Function in Vertex Form:The vertex form of a quadratic function is y = a(x - h)² + k (which is the format of the given equation).
The vertex of the parabola occurs at point (h, k). The value of "a" determines the direction of the graph's opening (reflection across the x-axis); it also indicates the wideness or narrowness of the graph (vertical stretch or compression).⇒ If the value of "a" is positive, then the vertex is its minimum or lowest point on the graph.
⇒ If the value of "a" is negative, then the vertex is the maximum or highest point on the graph.
Quadratic Function in Standard Form:The standard form of a quadratic function is y = ax² + bx + c, where a ≠ 0.
Solution:Step 1: Expand the binomial, (x - 2)²:
The first step in rewriting the given equation into its standard form is expanding the binomial using the FOIL method, which transforms it into a perfect square trinomial.
y = 2(x - 2)² - 7
⇒ (x - 2)(x - 2)
⇒ [ x² - 2x - 2x + 4 ]
Step 2: Substitute the perfect square trinomial into the vertex form:y = 2(x - 2)² - 7
y = 2(x² - 2x - 2x + 4) - 7
Step 3: Distribute "2" into the parenthesis:y = 2(x² - 2x - 2x + 4) - 7
y = 2x² - 4x - 4x + 8 - 7
Step 4: Combine like terms and constants, then simplify:y = 2x² - 8x + 1.
Final Answer:Therefore, the quadratic function in standard form is y = 2x² - 8x + 1, where a = 2, b = -8, and c = 1.
_____________________________
Keywords:Quadratic equations
Parabola
Quadratic functions
Vertex form
Functions
______________________________
Learn more about quadratic functions here:
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Answer:
[tex]\displaystyle y = 2x^2 - 8x + 1[/tex]
Step-by-step explanation:
All you are doing is perfourming order of operations and using the Distributive Property. Here is how it is done:
[tex]\displaystyle y = 2(x - 2)^2 - 7 \hookrightarrow y = 2(x^2 - 4x + 4) - 7 \hookrightarrow y = 2x^2 - 8x + 8 - 7 \\ \\ \boxed{y = 2x^2 - 8x + 1}[/tex]
I am joyous to assist you at any time.
Simplify 6 x − x + 5 y − 2 y
Answer:
Add and subtract similar variables
Step-by-step explanation:
(6x-x) + 5y - 2y
5x + (5y-2y)
=5x + 3y
Answer: 5x + 3y
Step-by-step explanation: You want to work with m variables that are the same so any item with an x is grouped together so 6x - x = 5x and the ys are grouped together 5y - 2y = 3y so your final answer would be 5x+3y
Joe bought 15 items for $135. If the 15 items consisted of notebooks that cost $4.50 each and calculators that cost $12.00 each, how many of each did he buy?
n + c = 15
4.5n + 12c = 135
c = 15 - n
12c = 180 - 12n
180 - 12n + 4.5n = 135
-7.5n = - 45
15n = 90
notebook = 6
6 + c = 15
calculator = 9
A 3-column table with 5 rows. The first column has entries empty, distance travelled (meters), time (initial) (seconds), time (final) (seconds), elapsed time (seconds), average speed (meters per second). The second column labeled Trial A has entries 4. 0, 2. 0, 2. 5, 1. 5, 2. 7. The second column labeled Trial B has entries 4. 0, 1. 5, 4. 5, empty, empty. Use the data table on the left to complete the calculations. What is the elapsed time for Trial B? s What is the average speed for Trial B? m/s.
Speed is the ratio of distance and time
The elapsed time is 3 secondsThe average speed is 1.33 meters per secondHow to calculate the elapsed timeThe elapsed time is the difference between the final time and the initial time.
So, we have:
Time elapsed = 4.5 seconds - 1.5 seconds
Evaluate the difference
Time elapsed = 3 seconds
Hence, the elapsed time is 3 s
How to calculate the average speedThe average speed is the quotient of the distance and the elapsed time.
So, we have:
Average speed = 4 meters/ 3 seconds
Evaluate the quotient
Average speed = 1.33 meters per second
Hence, the average speed is 1.33 m/s
Read more about speed at:
https://brainly.com/question/4931057
Answer:
Speed is the ratio of distance and time
The elapsed time is 3 seconds
The average speed is 1.3 meters per second
Dalia purchased a T.V. on sale for 15% less than the original price. If the original price was $200 how much money did Dalia save?
Express x² -5x-14 as the product of two binomials
Answer:
(x-2)(x-7)
Step-by-step explanation:
[tex]x^{2} -5x-14\\\\x^{2} -7x+2x-14\\\\x(x-7)+2(x-7)\\\\\(x+2)(x-7)[/tex]
square DEFG is inscribed in equilateral triangle ABC with a side length of 3+2√3.
Find: area of the square
Answer:
9 units²
Step-by-step explanation:
**Refer to the attached diagram**
The angles in the right triangle FAD (and HBE) are 30-60-90 which means that its sides will be in the ratio 1 : √3 : 2
Let x = the smallest side
Therefore, the sides of the right triangle FAD are in the ratio x : √3x : 2x
This means that:
the side length of the square = √3xthe side length of the triangle = x + √3x + x = (2 + √3)xWe are told that the side length of the triangle is 3 + 2√3, so:
[tex]\implies 3 + 2\sqrt{3} =(2 + \sqrt{3} )x[/tex]
[tex]\implies x=\dfrac{3 + 2\sqrt{3}}{2 + \sqrt{3} }[/tex]
[tex]\implies x=\sqrt{3}[/tex]
As the side length of the square is √3x, and x = √3,
⇒ side length of the square = √3 x √3 = 3
Now we know the side length of the square, we can calculate the area:
⇒ area of a square = side length x side length = 3 x 3 = 9 units²
Please answer!! I’m stuck
Answer:
B. $3
Step-by-step explanation:
A single 6-pound package is approximately $5 shipping fee.
A 2-pound package is approximately $3.50 shipping fee.
A 4-pound package is approximately $4.50 shipping fee.
The question stated, "What is the approximate difference (this means we are most likely subtracting) in cost of shipping a 2-pound and a 4 pound package(the and means we are adding both 4-pound and 2-pound together) opposed to a single 6-pound package?"
As calculated above, we should add the 2-pound package and the 4-pound package together.
3.5 + 4.5 = 8
One single 6-pound package is $5, so we need to subtract the 8 with the 5.
8 - 5 = 3
Answer pls
Who knows the answer
Answer:
(i) (b) RC
(ii) (d) 1/4 ar(ΔABC)
(iii) (b) 39 cm
(iv) (a) 90°
Step-by-step explanation:
(i) (b) RC
(ii) (d) 1/4 ar(ΔABC)
(iii) (b) 39 cm
(iv) (a) 90°
Marguerite sailed 4 hours on Saturday and 3 hours on Sunday. Each day, she sailed at a rate of 11 miles per hour. Which statements are true? Check all that apply.
She sailed for 4 hours.
She sailed for 7 hours.
She sailed 44 miles in all.
She sailed 77 miles in all.
round 1588 to the nearest hundred
Answer:
1600
Step-by-step explanation:
By rounding 1588 to the nearest hundredth we get 1600.
A)2/7+3/7=
B)3/5 -1/5=
C)3/8+6/8=
D)1/3+2/5=
E)3/2+3/4=
Answer:
A) 5/7
B)2/5
C)9/8 =1 1/8
D)11/15
E)9/4=2 1/4
Does anyone mind helping?
x = 7 OR x = -3
I hope this helped
8 kilómetros a metros
Answer:
8 kilómetros son 8000 metros
Calculate each unit rate.
a) A bus traveled 288 km in 4 hours.
b) A fish swam 75 m is 25 s.
c) Seven lemons cost $1.40.
d) $250 for a 5-day car rental.
Answers:
a) 72 km per hourb) 3 meters per secondc) 0.20 dollars or 20 cents per lemond) 50 dollars per day====================================
Explanation:
a) Divide the distance over time to get the unit rate, which is the speed in this case. Speed = distance/time = 288/4 = 72 km per hour. b) Like before, divide the distance over time to get 75/25 = 3 meters per second.c) We want the cost of 1 lemon. So we'll divide the total cost over 7 to get (1.40)/7 = 0.20 dollars = 20 cents per lemond) Divide the total cost over the 5 day period. This will get the cost of each day. So we have a unit cost of 250/5 = 50 dollars per day.Please need help with number 9 and 10!! With solution needed please!!
Answer:
9. m = 710. z = (-12)Step-by-step explanation:
9.[tex]8(m + 3) = 5(m + 9) \\ 8m + 24 = 5m + 45 \\ 8m - 5m = 45 - 24 \\ 3m = 21 \\ \frac{3m}{3} = \frac{21}{3} \\ m = 7 \\ [/tex]
10.[tex] \frac{z - 6}{2z} = \frac{3}{4} \\ 4(z - 6) = 3(2z) \\ 4z - 24 = 6z \\ - 24 = 6z - 4z \\ - 24 = 2z \\ \frac{ - 24}{2} = \frac{2z}{2} \\ ( - 12) = z \\ [/tex]
Which equation matches the graph of the greatest integer function given below?
A. y= [x] + 3
B. y= [x] -3
C. y= [x] +2
D y= [x] -2
Answer:
D y= [x] -2
Step-by-step explanation:
The "floor" or "greatest integer" function graphs as a step function with a solid dot at the left end of each step. The point (0, 0) is one of those solid dots. When 2 is subtracted from the function value, the graph is shifted down 2 units so that it looks like the one given.
The given graph is of the equation ...
[tex]\boxed{y=\lfloor x\rfloor -2}[/tex]
_____
Additional comment
The ceiling function ...
[tex]y=\lceil x\rceil[/tex]
graphs as a step function with a solid dot at the right end of each step. There is a solid dot at (0, 0) for this function, as well.
Note that the function symbols have "hooks" above or below the argument to indicate ceiling or floor (respectively). The use of a square bracket [ ] for either of these functions would need to be accompanied by an explanation of the intended meaning. By itself, a square bracket has "hooks" both at the top and bottom, so does not represent either function unambiguously.
-10(2x+1/5) in standard form
Answer:
-20x-2
Step-by-step explanation:
7. Arrival of the Normandy Train
Claude is waiting to meet the train from Normandy at Gare Saint-Lazare in Paris. He
tells Marie the hour of the train's arrival and he tells Jean at which minute it arrives. He
also tells them both that the train arrives between 0600 and 1000.
They consult the timetable and find the following services between those times:
0620, 0639, 0650; 0717, 0746; 0825, 0839; 0917, 0925, 0950.
Marie then says, “I don't know when Claude's train arrives, but I'm sure that neither does
Jean."
Jean replies, “I didn't know his train, but now I do."
Marie responds, “Now I do as well!"
When is Claude's train and how do you know?
Answer:
The train is 0839
Step-by-step explanation:
First off, 0620 and 0746 are not available options, as Jean would've immediately know, as they're the only one with non-repeated minutes.
Now, when Marie says "I'm sure neither does Jean", it means she didn't get 06 or 07, as those are the number that has 0620 and 0746, which then she cannot ensure that Jean doesn't know the train arrival.
We're left with 0825, 0839, 0917, 0925 and 0950
After that, Jean said he knows the train number. So, he couldnt've gotten 25, as it is repeated in the 5 options we pick. => we're left with 0839, 0917 and 0950.
And then, Marie responds now she does as well, which it cannot be 09, as it is repeated.
So, the train number is 0839.
Thank you for helping!!
Answer:
$324.80
Step-by-step explanation:
16*7= the area so
16*7=112
112sq yards
112*2.90=324.80
PLEASE HELP GIVING BRAINLIEST 50 POINTS
Answer:
Data set is second attached diagram
Step-by-step explanation:
1. See attached diagram for line plot
To graph data on a line plot, we put a dot (or an X) above each number in the data set. If a number appears twice in the data, we put two dots above that number.
2. Largest amount of snow is the largest value = [tex]3 \frac34[/tex] in
3. Least amount of snow is the smallest value = [tex]1 \frac34[/tex] in
4. 2 days as there are 2 values of [tex]3 \frac14[/tex] in
5. If the difference between the largest and smallest value is now 3, and the smallest value is [tex]1 \frac34[/tex] in then the new piece of data is:
[tex]1 \frac34 + 3=4 \frac34[/tex] in
In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft.
Answer: 334
Step-by-step explanation: so basically, I just looked up the answer 2 this and got this question and saw no 1 answered it so I got it wrong for u
please give brainliest I got a low score for u
also
if you do k12 this is the answers to the whole test
1. 334
2. 192
3. 1259
4. 72
5. 8
Answer:
258
Step-by-step explanation:
18x21=378
18-8=10
10x20=120
378-120=258
Max has 4 more dollars than Jacob. If y is the amount of money that Jacob has, write an expression to show how much money Max has.
Your answer:
Answer:
8
Step-by-step explanation:
4 and jacob has 4. v. ...................
hola como estas espero que bien y que te hice el deposito de
What is the solution to |2x-8|=6?
A. x /= -1
B. 1 /= 7
D. -7 = x = -1
Answer:
x = 1
Step-by-step explanation:
|2-8| = 6
|-6| = 6
Answer:
Step-by-step explanation:
|2x-8|=6
2x - 8 = 6
+ 8 + 8
2x = 14
/2 /2
x = 7
2x - 8 = -6
+ 8 +8
2x = 2
/2 /2
x = 1
I'm going sure what the options are, as they are confusing.
When you post the update you question, I'll update my answer :)
I have to turn this in by tonight
Answer:
x = -11
Step-by-step explanation:
Convert fraction into negative exponential form: [tex](36^-^1)^x^-^4=(216^-^1)^x^+^1\\[/tex]
Simplify using exponent power rule: [tex](a^n)^m=a^n^m:36^-^x^+^4=216^-^x^-^1[/tex]
Convert both sides of the equation into terms with same base:[tex](6^2)^-^x^+^4=(6^3)^-^x^-^1[/tex]
Simplify using exponent power rule:
[tex](a^n)^m=a^n^m:6^-^2^x^+^8=6^-^3^x^-^3[/tex]
Based on the given conditions, corresponding exponents are equal:
[tex]-2x=8=-3x-3[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]-2x+3x=-3-8[/tex]
Combine like terms: [tex]x=-3-8[/tex]
Calculate the sum or difference: [tex]x = -11[/tex]
Thurs, x = -11
[RevyBreeze]
A triangle has vertices at L(-7,0), M(2,1), and N(-3,5). Verify that is it a right isosceles triangle.
Please help me with this problem QUICK.
Using Postulates and/or Theorems, determine whether ABC~AXY.
explain why the triangles are similar or why they are not.
Answer:
They are not similar
Step-by-step explanation:
To see whether the triangles are similar or not we can compare their side lengths:
AB = 24
AX = 6
AX/AB = 1/4 is the ratio now let's compare this to AY/AC
AY/AC = 10/25 if we simplify this the result will be 2/5 as we can see the side lengths are not proportional so the triangles are not similar.
Which temperature is colder -30 degrees or -10 degrees?
Answer:
-10 degrees celsuius is less than - 20 degrees its cold but not as cold as -10
Step-by-step explanation:
Answer:
- 30 degrees
Step-by-step explanation:
- 30 degrees
Let's look at this flipped
When the temperature is higher, the weather is hotter.
The same rule applies for the cold. When the temperature is lower, the weather is colder.
Hope this helps!
Renaldo has a
budget of $500 to buy gift boxes for a party.
Large boxes cost $65 and small boxes cost
$35. Write and graph an inequality that
represents the number of each type of gift
box that Renaldo can buy. If Renaldo buys
5 small gift boxes, how many large gift boxes
can he afford to buy?
Renal can buy a box that is $35
Step-by-step explanation:
The inequality is 35 × 5 + 65y ≤ 500. Then the number of large gift boxes will be 5.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Renaldo has a budget of $500 to buy gift boxes for a party. Large boxes cost $65 and small boxes cost $35.
Let 'x' be the number of small boxes and 'y' be the number of large boxes. Then the inequality is written as,
35x + 65y ≤ 500
If Renaldo buys 5 small gift boxes. Then the number of large gift boxes will be given as,
35 × 5 + 65y ≤ 500
175 + 65y ≤ 500
65y ≤ 325
y ≤ 5
The inequality is 35 × 5 + 65y ≤ 500. Then the number of large gift boxes will be 5.
More about the inequality link is given below.
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HELP HOW DO I SOLVE THIS
Josie wants to buy Internet access. One service provider charges a flat rate of $34.95/month. A second charges $25/month plus 33c/h. For what number of hours per month should Josie choose the flat rate?
ansewer:
25+.33h=34.95 solving for h gives h=(34.95-25)/.33 =30.15 hours. So if you are going to use more than 30 hours it better to go with the flat rate company.
Step-by-step explanation:
You want to find, h, the number of hours of usage that will make the costs for the two equal so