Answer:
Remember that a triangle rectangle of length L and width W has an area:
A = W*L
In our rectangle, we have two sides along the x and y axes.
So one of the vertices of our triangle rectangle is the point (0, 0)
And the other vertex, is along the line:
y = -4x + 20
So, if the opposite vertex is at the point:
(x₁, y₁)
We can define the length as the difference between the x-values of each vertex.
L = (x₁ - 0) = x₁
And the width, similarly, as:
W = (y₁ - 0) = y₁
Such that the point (x₁, y₁) is a solution for the equation y = -4x + 20, then we have:
y₁ = -4x₁ + 20
Then we can rewrite the width as:
W = -4x₁ + 20
Now, we can write the area of our rectangle as:
A = (x₁)*(-4x₁ + 20)
A = -4*x₁^2 + 20*x₁
Now we want to maximize the area, notice that the area is given by a quadratic equation with a negative leading coefficient.
Thus, the maximum will be at the vertex of that quadratic equation.
Remember that for a general quadratic equation:
y = a*x^2 + b*x + c
The x-value of the vertex is:
x = -b/(2*a)
so, in our case, the x-value of the vertex will be:
x₁ = -20/(-4*2) = 20/8 = 5/2
Now we can evaluate this in our area equation:
A = -4*(5/2)^2 + 20*(5/2) = 49.36
This is the maximum area of the rectangle.
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞
Answer:
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Step-by-step explanation:
The minimum value of the curve = (1.9, -5.7),
The maximum value = (0, 2)
The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)
The point the function crosses the y-axis (the y-intercept) = (0, 2)
The given points can be plotted using MS Excel, from which we have;
F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5
The correct option is therefore, F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Answer:
A. F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
Step-by-step explanation:
Slope -1/4, passes through (12,-4)
Answer:
y = - [tex]\frac{1}{4}[/tex] x - 1
Step-by-step explanation:
Assuming you require the equation of the line
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
To find c substitute (12, - 4) into the partial equation
- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1
y = - [tex]\frac{1}{4}[/tex] x - 1 ← equation of line
Miguel can use all or part of his $25 gift card to make a music purchase. Each song costs $1.50, and there is a $1.00 per account activation fee.
Which inequalities can represent this situation if m is the number of songs he can buy? Select two options.
1 + 1.5 m less-than-or-equal-to 25
Answer:
A, E or 1, 5
Step-by-step explanation:
Its not A, D
The perimeter of a rectangle is 18cm . if the length is (x+2), find it's width.
Answer:
W = 7 - x
Step-by-step explanation:
The perimeter is P= 2L + 2×W , where L is the length and W is the width.
If L = (x+2) , replacing L with the expression x+2 we have
P= 2×(X+2) + 2W ⇔ 18 = 2x + 4 + 2W ⇔ 2W =18 - 2x - 4 ⇔ 2W = 14 - 2x
⇔ W = 7 - x
Help fast!
Describe at least two ways to find or
estimate the year the population of the town
will be 40 thousand. (You don't have to
actually find the value.)
Write an equation of a circle given the center (-4,4) and radius r=5
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y - k)² = r² where (h,k) is the center.
Center( -4 , 4) and r = 5
(x -[-4])² + (y - 4)²= 5²
(x + 4)² + (y-4)² = 25
x² + 2*4*x +4² + y² - 2*y*4 + 4² = 25
x² +8x + 16 + y² - 8y + 16 = 25
x² + 8x + y² - 8y + 16 + 16 -25 = 0
x² + 8x + y² - 8y +7 = 0
We have that the an equation of a circle given the center (-4,4) and radius r=5 is mathematically given as
(x-4)^2+(y-4)^2=5^2
Equation of a circle
Question Parameters:
Given the center (-4,4) and radius r=5
Generally the equation for the Equation of a circle is mathematically given as
(x-x')^2+(y-y')^2=r^2
Therefore, The resultant equation will be
(x-x')^2+(y-y')^2=r^2
(x-4)^2+(y-4)^2=5^2
Hence,an equation of a circle given the center (-4,4) and radius r=5 is
(x-4)^2+(y-4)^2=5^2
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Please someone tell me the answer of these questions
Answer:
VERTICALLY OPP ANGLES
Step-by-step explanation:
arshad's father bought x sweets .(x-4)were eaten by children and 20 were left.how many sweets did his father bring
Answer:
24
Step-by-step explanation:
20+4
simple
x-4=20
x=20+4
x=24
mark me as brainliest
Answer:
24 sweets
Step-by-step explanation:
Remaining sweets = 20
x - 4 = 20
Add 4 to both sides.
x = 20 +4
x = 24
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
I believe it is A. 1,1150.6cm^3
Step-by-step explanation:
To solve for the volume of a cone:
[tex]V = \pi radius^{2} \frac{height}{3}[/tex]
pls help, and explain. I will give brainliest
Answer:
Nicole should take 13 1/8 cups of snack mix.
Step-by-step explanation:
If a serving size is 7/8 and Nicole wants to take 15 serving sizes (15 7/8's), then we must multiply 7/8 by 15:
15 × 7/8
Write 15 over 1 (15 = 15/1) to make the calculations easier:
15/1 × 7/8
Multiply the numerators and denominators separately:
15 × 7 / 1 × 8
105 / 8
Instructions don't say you have to do this but I will convert this improper fraction into a mixed number:
105/8 = 13 1/8
Please help me solve this problem
Answer:
-4
they wanted you to compute using x as 3
-2*3 + 2 = -4
Step-by-step explanation:
Vanessa and her friends are watching three movies consecutively. The first movie is 2 hours and 17 minutes long. The second movie is 84 minutes long, and the last movie is 99 minutes long. How much time will they spend watching the movies?
Answer:
320 minutes (5 hours and 20 minutes).
Step-by-step explanation:
2 hours and 17 minutes = 137 minutes
137 + 84 + 99 = 320
Therefore, they will spend 320 minutes (5 hours and 20 minutes) watching movies.
what is 2/3 divide by 2/9
Answer:
3
Step-by-step explanation:
(2/3)/(2/9) = (2/3) * (9/2) = 3
In the figure below j ll h find the values of x and y
Answer:
26
Step-by-step explanation:
Given: Lines J and H are parallel lines. O intersects both lines equally.
Since two angles equal 180, that will be what (4y + 12) and 64 will be equal to.
(4y + 12) + 64 = 180
76 + 4y = 180
-76 -76
-------------------
4y = 104
y = 26
x and y is both 26 because they are vertical angles.
Hope this helped.
(6 1/4)^4
Answer fast or i will report you
Answer:6
Step-by-step explanation: The rules of exponential says (a^x)^y=a^xy.
Therefore you will multiply 1/4 with 4 to get an exponent of 1. So the answer is 6^1 which is also written as 6
Write 0.2 repeating as a fraction in simplest form (The 0.2 is repeating, so the 2 has the repeating bar above it, just need someone to solve this, it would help a lot thanks.)
If x is the number 0.222…, then 10x = 2.222…. Subtracting x from 10x eliminates the fractional part, so that
10x - x = 2.222… - 0.222…
==> 9x = 2
and solving for x gives x = 2/9.
If you could answer them all It would really be helpful PLEASE marking brainliest
Answer:
1. the area of the triangle minus the area of the small, inner rectangle. what did you not understand there ?
the standard formula (hi, internet !) for the area of a triangle is baseline×height/2.
the standard formula (hi, first grade !) for the area of a rectangle is length×width.
that's it.
1.a.
the volume of an object regularity shaped like a silo is always ground area times height.
for this object we only need to imagine to stand the object up sideways on the triangle side.
and don't forget - an area is always a square unit (like cm²,m², ft², ...). and a volume is always a cubic unit (like cm³, m³, ft³, ...).
so then, the triangle area is the ground area. and the original long side line of the object is is height.
as we said in 1. above, the area of a triangle is baseline×height (of the triangle, not of the overall object) divided by 2.
so, we have here 6×4/2 = 6×2 = 12 m²
and now the ground area × object height = 12×8=96 m³
b.
the standard formula for the volume of a ball (hi, internet !) is pi×r³.
so, we have here pi×9³. can you calculate that with your calculator ? that is pi×729 = 2290.221 cm³
2a.
the height of the cone is (as the drawing already suggests) determined via the right-angled triangle of the radius (half of the diameter) of the ground circle, the height of the cone and the length of the sideline on the outside mantle of the cone. this sideline is the Hypotenuse (the baseline of the triangle opposite of the 90 degree angle).
so, we use Pythagoras
c² = a² + b² (c being the Hypotenuse, a and b being the sides).
11² = 8² + h²
121 = 64 + h²
h² = 57
h = 7.55 cm
2b.
the standard formula for the volume of a cone (hi, internet !) is
pi×r²×h/3
pi×8²×7.55/3 = pi×64×7.55/3 = 506 cm³
Step-by-step explanation:
all of that you could easily search on the internet and since it yourself way faster than putting things in here and waiting for responses.
as there is really nothing to explain but just to use the standard formulas with the given numbers.
the tub started with gallons of water
Answer:
huh?
Step-by-step explanation:
SOMEONE PLEASE ANSWER THIS ASAP!!
The population of Arlington High School can be modeled using the equation P(t) = 3,500(1.027)^t , where t represents the number of years since 2010
Is the population of Arlington High increasing or decreasing? Explain how you can tell using the equation.
How do you interpret the statement that P(6)= 4,107
SOMEONE PLEASE ANSWER THIS
Step-by-step explanation:
Arlington is increasing because it has 1.027, if it was 0.27 it would be decreasing
If p(6)= 4107 that means after 6 years there would be a total population of 4107
In XYZ, what is the cosine ratio of X?
Answer:
c) 12/15 = 4/5
Step-by-step explanation:
imagine we mirror the triangle up, so that Z is on top.
then you can clearly see that 6 is cos(X) times r (and r is then 7.5).
XY is sin(X)×7.5
and again, 7.5 is r (the line making the X angle).
so, the cosine ratio of X is
6 = cos(X)×7.5
cos(X) = 6/7.5 or then 12/15. or simplified 4/5.
solve for the measure of a
Answer:
Step-by-step explanation:
The supplement of the exterior angle is 180 - 75 = 105
In a cyclic quadrilateral (a four sides figure where all the vertices touch the circumference of a circle), the opposite angles are supplementary. Therefore <a = 180 - 105 = 75
But I think you already knew that.
Find the volume of this cylinder please..
Answer: 825
Step-by-step explanation:
Plug in the values for v = π*r²*h
So, your new equation is v = π*5²*11 (I got 5 because 10 is the diameter, the radius is half the diameter, therefore r = 5.)
The question is also telling us to replace π with 3.
now we solve, after gathering all of our information.
v = 3*5²*11
v=3*25*11
v=75*11
v=825
Alec pulled a couch 3 meters, using a force of 400 N. The couch weighed 200 N. How do you calculate the work done by Alec?
A . Add 400 to 200
B . Divide 400 by 3
C . Multiply 200 by 3
D . Multiply 400 by 3
Answer:
D
Step-by-step explanation:
It is because work is done when a force cause an object to move in the direction of the applied force.
so work is equal to force × distance
What is the name of an investment that pools money from many investors in
order to acquire a large variety of stocks, bonds, and other investments?
A. Derivative
B. Mutual fund
C. Annuity
Answer:
Mutal fund because its a formerly greatest instruments
The name of an investment that pools money from many investors in order to acquire a large variety of stocks, bonds, and other investments is Mutual fund.
What is investment?Investment is traditionally defined as the "commitment of resources to achieve later benefits
A mutual fund is a type of investment vehicle that pools money from multiple investors to invest in a diversified portfolio of stocks, bonds, and other securities.
Mutual funds are managed by professional fund managers who use the pooled funds to purchase a range of investments, with the goal of generating a return for the investors.
Investors in mutual funds own shares in the fund, and the value of their investment is based on the performance of the underlying securities held by the fund.
Mutual funds offer investors the benefits of diversification, professional management, and ease of investment, as well as the ability to invest in a variety of asset classes with relatively low minimum investment requirements.
Hence, the name of an investment that pools money from many investors in order to acquire a large variety of stocks, bonds, and other investments is Mutual fund.
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HELPPP HELP PLS PRONTO ASAP
Ahmed is working at a restaurant. His boss pays him $16.00 per hour and
promises a raise of $1.25 per hour every 6 months. Which sequence
describes Ahmed's expected hourly wages, in dollars, starting with his current
wage?
Answer:
B
Step-by-step explanation:
each of the numbers is just adding 1.25 on to it
Answer: Choice B
16.00, 17.25, 18.50, 19.75, ...
==========================================================
Explanation:
We start with $16.00 as the first term, as this is the amount the boss pays him initially. Then we add on 1.25 to get 16+1.25 = 17.25 to represent the next wage after that first raise.
Then after the second raise he gets, he'll then earn 17.25+1.25 = 18.50 an hour. This process theoretically can go on forever, but realistically the boss will likely set some kind of limit.
We say that this sequence { 16.00, 17.25, 18.50, 19.75, ... } is arithmetic with the first term of 16.00 and common difference 1.25
The common difference is the gap width between any two neighboring terms, and it's the amount the wage goes up each time he gets a raise.
Wendy went to the salon and had 2 1/6 inches of hair cut off. The next day she went back
and asked for another 2 1/6 inches to be cut off. How much hair did she have cut off in all?
Write your answer as a fraction or as a whole or mixed number.
inches.
Answer:
4 1/3 of her hair
Step-by-step explanation:
Just add 2 1/6 + 2 1/6 and there you go
There is the total amount of her hair she cut
RS=7y+4, ST=3y+6, and RT=90
Answer:
If it is a straight line then ;
RT= RS+ST
90=(7y+4) + (3y+6)
90 = 10y + 10
10y= 90 – 10
10y = 80
y= 80 / 10
y =8
ST = 3y+6= 3(8)+6= 24 +6 = 30
RS = 7y +4 = 7(8) + 4 = 56 +4 = 60
I hope I helped you^_^
what must be added to a + b to get a
Answer:
we have to add (-b) to get (a)
Step-by-step explanation:
a+b+(-b)=a
a+b-b=a
a=a
Hence verified.
Hope this helps you. Have a nice day^_^
How to find interquartilte range
============================================================
Explanation:
Each x represents a data point location.
So, for example, having an x over 60 means 60 is part of the set.
The set of values we're working with is
{59,60,61,63,63,64,66,68,70,71,71,73}
The repeated values are due to the fact we have a stack of two 'x' markers, and they occur at 63 and 71.
To find the IQR (interquartile range), we'll first need to find the median of this set. That's the middle most value.
Count out the number of values to find that there are n = 12 values.
The list splits into two halves that are n/2 = 12/2 = 6 items each
Between slots 6 and 7 is where the median is located.
The value in slot 6 is 64 and the value in slot 7 is 66. Average those two items to get (64+66)/2 = 65
The median is 65
---------------------------------
Next, we'll form two groups L and U such that
L = set of items lower than the median
U = set of items larger than the median
Because n is even, we simply just break the original set into two equal groups (6 items each)
L = {59,60,61,63,63,64}
U = {66,68,70,71,71,73}
The values of Q1 and Q3 represent the medians of L and U in that order.
The median of set L is (61+63)/2 = 62, so Q1 = 62
The median of set U is (70+71)/2 = 70.5, which is Q3
-----------------------------------
To summarize everything so far, we have found
Q1 = 62Q3 = 70.5Subtract those items to get the IQR
IQR = Q3 - Q1
IQR = 70.5 - 62
IQR = 8.5 which points us to choice C as the final answer.
If f(x) = 3x^2-2x+4 and g(x) = 5x^2+6x-8, find (f-g)(x)
Answer:
-2x^2-8x+12
Step-by-step explanation:
f(x) = 3x^2-2x+4
g(x) = 5x^2+6x-8
(f-g)(x)= 3x^2-2x+4 -(5x^2+6x-8)
Distribute the minus sign
(f-g)(x)= 3x^2-2x+4 -5x^2-6x+8
Combine like terms
=-2x^2-8x+12
Answer: (f+g)(x)=8x^2+4x-4
Step-by-step explanation:
