Height: 4 units
Width 2√/2
Explanation:
Start by sketching y = 6 - ². Then draw a rectangle beneath it. You will notice that the width is 2x and the height is 6 ². Area is given by length - times width, so the area function will be A=2x (6 - x²) = 12x - 2x³.
Now you differentiate to find the maximum.
A' = 12 - 6x²
Find critical numbers by setting A' to 0.
x = ± √/2
The derivative is negative at x = 2 and positive at x = 1, which justifies that the rectangle with width of √2 has maximal area.
The height will be y (√2) = 6 – (√2)²) = 4
x + 3 ? 3 = x what factor do I use in between 3 and 3
Answer:
1 or 3
Step-by-step explanation:
factors of 3 r 1 and 3
that's why 3 is a prime number
if each of the following quadrilaterals are trapezoids find the missing measures. show your work.
What is the equation of the line??
Answers:
m = -2/3
b = 1
equation: y = (-2/3)x + 1
This is the same as writing [tex]y = -\frac{2}{3}x+1[/tex]
===========================================================
Explanation:
There are a few approaches, but I like to start at the y intercept whenever it is an integer. The y intercept is where the diagonal line crosses the vertical y axis. In this case, that location is (0,1) telling us that b = 1 is the y intercept.
From that starting anchor point, we need to find a way to get to another point on this line. There are a few ways to do this, but we can move down 2 and to the right 3 units to go from (0,1) to (3,-1). This "down 2 right 3" motion directly leads to the slope of rise/run = -2/3
---------------
Alternatively, you can start at something like (-3,3) and move down 4 and move right 6 to arrive at (3,-1). Note how rise/run = -4/6 = -2/3. No matter where you start, moving along this line will involve a "down 2 right 3" movement pattern. Be sure to reduce any fractions as much as possible.
Yet another alternative is to apply the slope formula using any two points on the line. Preferably they have integer coordinates.
----------------
However you determine the slope, it's m = -2/3 after fully reducing. It along with b = 1 is plugged into y = mx+b to get y = (-2/3)x+1 as the equation of this line. It's in slope intercept form.
Simon is driving his car on a highway at a constant speed. The below table shows the relationship between the amount of
gasoline left in his car and the distance traveled on the highway.
Answer:
ccccccccccccccccccccccccccc
A seed sprouted and grew 2/3 of a foot in 3 months. What was its rate of growth in feet per month?
Answer:
2.6 inches repeating per month
Answer:
2/9
Step-by-step explanation:
A soccer player runs a total of 12 miles during a 4 hour game.
What is the unit rate?
Answer:
3
Step-by-step explanation:
12 divited by 4 =3
Pls answer questions 1-4 on this pic
(must include the math work)
i will give brainlist for the most helpful answer
#1
Breadth=
[tex]\\ \sf\longmapsto 1\dfrac{3}{4}in=\dfrac{7}{4}in=7(2)ft=14ft[/tex]
Length=
[tex]\\ \sf\longmapsto 1in=8ft[/tex]
#2.
Length=
[tex]\\ \sf\longmapsto 2\dfrac{1}{4}in=\dfrac{9}{4}in=9(2)=18ft[/tex]
Breadth=
[tex]\\ \sf\longmapsto 2in=16ft[/tex]
#3
Length(Left side)
[tex]\\ \sf\longmapsto 2\dfrac{1}{4}+1+2\dfrac{3}{4}=\dfrac{9}{4}+1+\dfrac{11}{4}=6in=6(4)=24ft[/tex]
Length (right side)
[tex]\\ \sf\longmapsto 1\dfrac{3}{4}+2+3\dfrac{1}{4}=6in=24ft[/tex]
Breadth
[tex]\\ \sf\longmapsto 1\dfrac{3}{4}+2\dfrac{1}{4}4in=16ft[/tex]
___________
[tex]\:[/tex]
Answer in the picture.
Determine the inverse of the function f(x) = 3(x - 4)^2 + 5.
f(x) as given has no inverse. We see that, for instance, f(1) = f(7) = 32; that is, two different values of x give the same value of f(x), so f is not one-to-one.
We can however restrict the domain over which f is defined to extract an invertible function. One such choice would be to restrict to the interval x ≥ 4, which I'll demonstrate below.
Recall the definition of function inverse:
f(f^(-1)(x)) = x
Then for this function, we have
3 (f^(-1)(x) - 4)² + 5 = x
3 (f^(-1)(x) - 4)² = x - 5
(f^(-1)(x) - 4)² = (x - 5)/3
√((f^(-1)(x) - 4)²)= √((x - 5)/3)
For all x, √(x²) = |x|. Then √((f^(-1)(x) - 4)²) = |f^(-1)(x) - 4|, but by restricting x ≥ 4, or x - 4 ≥ 0, we have the condition that f^(-1)(x) - 4 ≥ 0, and so by definition (of the absolute value function) the absolute value reduces to the positive case. In short, we end up with
f^(-1)(x) - 4 = √((x - 5)/3)
and hence the inverse
f^(-1)(x) = √((x - 5)/3) + 4
Write numbers least to greatest
Answer:
[tex]-6,-pi,-0.5,\frac{5}{8} ,\frac{2}{3}[/tex]
Josh runs 6 miles in 44 minutes. At the same rate, how many minutes would he take to run 9 miles?
Answer:
66 minutes
Step-by-step explanation:
Method I - proportion
x/44 = 9/6
multiply both sides by 44
x = 9 / 6 * 44
x = 66 minutes
--------------------------
Method II - rate
44/6 = 7.3333333 minutes / mile
9 * 7.3333333 = 66 minutes
if a shirt is 50$ and is on sale for 20% off how much wil you pay with 6% sales tax
Answer:
42.4 is the correct answer to this question
Help please!!!
A radio telescope has a parabolic dish. Radio signals are collected at the focal point (focus) of the parabola.
The distance from the vertex of the parabolic dish to the focus is 20 feet. The vertex of the dish is located at a point 30 feet above the ground and 80 feet to the east of a computer that reads and records data from the telescope. The diameter of the dish is 120 feet
What is the depth of the parabolic dish?
Answer:
45 feet deep
Step-by-step explanation:
First the formula for Parabola is: 4py=x2, we will make it as if it were in the center of the graph.
Now P is the distance from the vertex to the focus or to the directrix which is equal to 20.
4(20)y=x2
80y=x2
Now we just have to use one knwon value of X in the maximum point of the dish, is the diameter of the dish is 120 feet that is the maximum x, and we know that 120 feet is te distance between the widest -x and x, so those would be: -60 and 60.
We will use 60 as our value:
[tex]80y=x^{2} \\80y=60^{2} \\80y=3600\\y=\frac{3600}{80} \\y=45[/tex]
So we know that the depth of the parabolic dish is 45 feet.
In this exercise we have to use the knowledge of depth to be able to calculate the depth that is being seen by the telescope, in this way we can say that:
[tex]45 \ feet \ deep[/tex]
First, knowing that the formula for the parabola is:
[tex]4py=x^2[/tex]
Now P is the distance from the vertex to the focus or to the directrix which is equal to 20, we can say that:
[tex]4(20)y=x^2\\80y=x^2[/tex]
Now we just should use individual knwon financial worth of X fashionable the maximum point of the dish, exist the measurement across object of the eating receptacle exist 120 extremities that is to say the maximum x, and we understand information that 120 extremities is heavy distance middle from two points the expansive -x and x, so those hopeful: -60 and 60.
[tex]80y=x^2\\80y=60^2\\80y=3600\\y=45[/tex]
See morea bout depth at brainly.com/question/694922
1)cot a/2 -tan a/2 = 2 cot a
2) cot b/2 + tan b/2= 2 cosec b
prove
Jaxon's start-up business makes a profit of $500 during the first month. However, the company records a profit of -$50 per month for the next eight months and a profit of $175 for the final month. What is the total profit for the first ten months of Jaxon's business?
Answer: 275$
Step-by-step explanation:
500
-50 x 8 = -400
500 - (-400) = 100
100 + 175 = 275$
================================================================
Explanation:
The first month has a profit of +500 or simply 500.
The next 8 months have a profit of -50 per month, so we have -50*8 = -400 in profit here. A negative profit indicates debt. So far, the profit is 500 + (-400) = 500 - 400 = 100 dollars. This result is positive, so the company is in good shape so far.
It gets in better shape when adding on the final 175 profit from the tenth month. The final profit is 100+175 = 275 dollars
Abigail has been saving her earnings from her lemonade stand. Abigail has 30 dollars to spend. If she buys a new hat for 15 dollars, how many ribbons can she buy with the remaining money if they cost 4 dollars each?
Simplify the expression
Answer:
it would equal 12x + 12
:)))
Correct = brainiest
Answer:
∠AOC = 98°
∠BOC = 82°
∠DOE = 39°
Step-by-step explanation:
∠DOE = 180 - (43 + 98)
= 39°
∠BOC = 180 - ∠DOB
= 180 - 98
= 82°
∠AOC = ∠DOB (they are vertical angles which are equal)
Find the perimeter of the rectangle
= 2(2 + 3) units
= 2 × 5 units
= 10 units.
Answer:The perimeter of the rectangle is 10 units.
Hope it helps.
Do comment if you have any query.
is -3/2 parallel to 2/3
Answer: The parallel slope of 2/3 is 2/3 . m=2/3
Step-by-step explanation: Parallel slopes have the same slopes.
If a slope is 2/3, the parallel slope will be the same. So, the parallel slope will also be 2/3.
Therefore, the answer is m=2/3
Answer:
No.
Step-by-step explanation:
Parallel lines have the same slope. Perpendicular lines have opposite reciprocal slopes. In this instance, -3/2 is perpendicular to 2/3, not parallel.
A 95% confidence interval for the mean lead concentration in the urine of adult men working with lead (for smelting) is 8.22 to 11.98 micrograms per
liter (g/l). The numerical value of the margin of error for this confidence interval is ______Mg/1.
Write the slope-intercept equation of the line that passes through the given point and is perpendicular to the given line.
(0, -4) and x = -3y - 2
Answer:
y=mx+c
Step-by-step explanation:
check if u get it or not
How many groups of 1/4 are in 7.
There is 28.
7 ÷ 1/4 = 28
What are two different ways to show which is bigger ether 3/4 or 2/3
Answer:
Either through decimals or finding common denominators.
Step-by-step explanation:
When you get decimals you can clearly see which is bigger and with common denominators, you can just cancel out the denominator and see which is bigger. If you'd like me to provide an example just let me know :)
PLEASE HELP ITS DUE NOW!!!!!!
WILL MARK BRAINLIEST!!!!!
Answer:
(- 4, - 10 )
Step-by-step explanation:
y = 5x + 10 → (1)
y = 4x + 6 → (2)
Substitute y = 5x + 10 into (2)
5x + 10 = 4x + 6 ( subtract 4x from both sides )
x + 10 = 6 ( subtract 10 from both sides )
x = - 4
Substitute x = - 4 into either of the 2 equations and evaluate for y
Substituting into (1)
y = 5(- 5) + 10 = - 20 + 10 = - 10
solution is (- 4, - 10 )
__________
[tex] \: [/tex]
[tex] \sf{y = 5x + 10...(1)}[/tex]
[tex] \sf{y = 4x + 6...(2)}[/tex]
Subtitute (1) to (2)[tex] \sf{y = 4x + 6}[/tex]
[tex] \sf{5x + 10 = 4x + 6}[/tex]
[tex] \sf5x - 4x = 6 - 10[/tex]
[tex] \sf{x = - 4}[/tex]
.
Subtitute x = -4 to (1)[tex] \sf{y = 5x + 10}[/tex]
[tex] \sf{y = 5( - 4) + 10}[/tex]
[tex] \sf{y = - 20 + 10}[/tex]
[tex] \sf{y = - 10}[/tex]
.
[tex] \longmapsto \sf{( - 4 , - 10)}[/tex]
Which of the following is most likely the next step in the series?
Answer:
D.
Step-by-step explanation:
Quadrilateral: 4 sides
Pentagon: 5 sides
Hexagon: 6 sides
Now we expect 7 sides.
Answer: D.
Answer:
D
Step-by-step explanation:
The first shape has 4 vertices (quadrilateral), the second has 5 vertices (pentagon), the third shape has 6 vertices (hexagon) so the fourth would most likely have 7 vertices (heptagon).
Hope this help!
Write an equation that could be used to convert X miles into Y inches.
Answer:
y = 63360x
Step-by-step explanation:
we know 1 mile = 63360 inches
So: y = 63360x
x mile
& y inch
I can use structure to decide where to place the first digit in a quotient. A strongly agree B. agree C. disagree qD. strongly disagree
Answer: For this question, it's just like a self-survey. If you understand this concept strongly or not really, you go with that answer like strongly agree, agree, etc.
Write an expression that represents the perimeter of the triangle.
Answer:
(3m - 2) + (2m + 7) + (5m - 3)
Step-by-step explanation:
Perimeter is found by combining all side measurements together to find the total measurement. In this case, combine the sides:
(3m - 2) + (2m + 7) + (5m - 3) is your answer.
If you need a simplified expression, simply combine all the like terms together. Like terms are terms with the same as well as same amount of variables:
(3m + 2m + 5m) + (7 - 2 - 3)
(10m) + (2)
10m + 2 is your answer.
~
need help, im confused
Answer:
Part A: correct
Part B: $20
Step-by-step explanation:
Part B:The amount Vanessa pays for her printer and 2 cartridges is ...
$90 +2(25) = $140
The amount Tia pays for her printer and 2 cartridges (c=2) is ...
t = 80 +20(2) = 120 . . . . dollars
Then the difference in the amounts they pay is ...
$140 -120 = $20
Question 2 (Essay Worth 10 points)
(07.02 MC)
An equation is shown below:
3(2x - 7) = 3
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work. (6 points)
Answer:
Part A: 1 solution
Part B:
3(2x-7)=3
6x-21=3
+21 +21
6x=24
/6 /6
x=4
Step-by-step explanation:
First you distribute 3(2x-7)=3 to 6x-21=3. Next you do inverse operations by adding 21 to both sides of the equation to get 6x=24. Finally you divide both sides by 6 to get x=4
