Answer:
8√30
Step-by-step explanation:
The length of the third side is 32 - 8 - 11 = 13. s (which is half of the perimeter) is 32 / 2 = 16 so the answer is:
√s(s-a)(s-b)(s-c) = √16 * (16 - 8) * (16 - 11) * (16 - 13) = √16 * 8 * 5 * 3 = √1920 = 8√30
The profit ,P dollars, earned by students at a high school selling boxes of chocolates is approximated to be P= -60x^2+600x , where x dollars is the selling price of one box of chocolates. What selling price gives the maximum profit?
Answer:
Selling price of 5 gives the maximum profit
Step-by-step explanation:
What we do here is to find the first derivative, since at maximum points, the profit will be set to zero.
Mathematically, we have;
dp/dx = -120x + 600
We now equate this to zero
0 = -120x + 600
120x = 600
x = 600/120
x = 5
Triangle ABE is similar to triangle ACD. AED and ABC are straight lines. EB and DC are parallel. AE = 5 cm, BC = 4.5 cm, BE = 4 cm, CD = 9 cm The area of quadrilateral BCDE is x cm2 The area of triangle ABE is y cm2 Find an expression for y in terms of x . Give your answer as simply as possible. (3 marks)
Answer:
y = 16x/65
Step-by-step explanation:
Given:
Triangle ABE is similar to triangle ACD. AED and ABC are straight lines
EB and DC are parallel
The area of quadrilateral BCDE = xcm²
The area of triangle ABE = ycm²
Find attached the diagram from the above information.
In similar triangles, the ratio of their corresponding angles are equal.
Also, the ratio of the area of the two triangles = square of ratio of the corresponding sides of the two triangles.
Area ∆ACD/area of ∆ABE = (DC/EB)²
Area ∆ACD/area of ∆ABE = [(area of quadrilateral BCDE +
area of ∆ABE)]/(area of ∆ABE)
(x+y)/y = (DC/EB)²
(x+y)/y = (9/4)²
x+y = (81/16)y
x = (81/16)y - y
x = (81y - 16y)/16
x = 65y/16
Making y subject of formula
16x = 65y
y = 16x/65
An expression for y in terms of x:
y = 16x/65
An expression for y in terms of x is :
y = 16x/65
Given:
Triangle ABE is similar to triangle ACD. AED and ABC are straight lines . EB and DC are parallel The area of quadrilateral BCDE = xcm² The area of triangle ABE = ycm²Consider, the image attached:
In similar triangles, the ratio of their corresponding angles are equal.
Also, the ratio of the area of the two triangles = square of ratio of the corresponding sides of the two triangles.
Thus,
Area ∆ACD/area of ∆ABE = (DC/EB)²
Area ∆ACD/area of ∆ABE =
[(area of quadrilateral BCDE + area of ∆ABE)]/(area of ∆ABE)
On substituting the given values:
(x+y)/y = (DC/EB)²
(x+y)/y = (9/4)²
x+y = (81/16)y
x = (81/16)y - y
x = (81y - 16y)/16
x = 65y/16
In terms of y:
16x = 65y
y = 16x/65
Therefore, an expression for y in terms of x: y = 16x/65
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Find the Y-intercept of the line graph. (Please help!)
Answer:
-2
Step-by-step explanation:
The y intercept is where the graph crosses the y axis. The graph crosses the y axis at (0, -2), so the y intercept is -2.
The y intercept is useful in slope intercept form, (y=mx+b), where b is the y intercept.
Answer: -2
Step-by-step explanation: The y-intercept of a graph is where the graph crosses or intersects the y-axis.
Notice that the graph shown here hits the y-axis at -2.
So the y-intercept of this graph is -2.
Select all angle measures for which sin(∅) = - ( (√2) /2)
a) 3π/4
b) 5π/4
c) 7π/4
d) 9π/4
e) 13π/4
I do not understand the steps to take, thank you for any help
Answer:
b) 5π/4
c) 7π/4
e) 13π/4
Step-by-step explanation:
sin θ = -½√2
There's really no algebra to be done here. There are two ways you can solve. One, you can use a calculator. Two, you can memorize your unit circle.
Either way, it helps to draw the unit circle. sin θ is the y coordinate, so you're looking for points on the circle where y = -½√2. This happens at two places: θ = 5π/4 and 7π/4.
Next, we need to check the options that are greater than 2π.
9π/4 is the same as π/4.
13π/4 is the same as 5π/4.
So the three correct answers are 5π/4, 7π/4, and 13π/4.
Answer:
B
C
D
Step-by-step explanation:
Order The numbers from least to greatest
0.453, 0.35, 4/5
Answer:
Step-by-step explanation:
0.35
0.453
4/5
The distance between points (1, 2) and (x 1 ,y 1 ) is the square root of (x 1 -1)^ 2 +(y 1 -2)^ 2
Answer:
True
Step-by-step explanation:
The distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].
The given points are (1, 2) and [tex](x_{1} , y_{1})[/tex] .
We to find the distance between the given points.
What is the formula to find the distance between points?The formula to find the distance between points is [tex]\sqrt{(x_{1}-x_{2} )^{2}-(y_{1}-y_{2} )^{2} }[/tex].
Now, [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex]
Therefore, the distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].
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which words have vertical symmetry for all of the letters in the word?
Answer:
palindromes
Step-by-step explanation:
palindromes are spelled the same forward and backward, thus have vertical symmetry.
Melinda and Paula shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paula shoveled for 25 minutes to complete 345 square feet of driveway. 30x + 30y = 450 20x + 25y = 345 How much more can Paula shovel in 1 minute than Melinda?
Answer:
3 more square feet.
Step-by-step explanation:
x = The amount Melinda can shovel in 1 minute
y = The amount Paula can shovel in 1 minute
So make two equations:
30(x + y) = 450 x + y = 15 x = 15 - y
20x + 25y = 345 4x + 5y = 69
Plug in:
4(15 - y) + 5y = 69
60 - 4y + 5y = 69
y = 9
x = 6
9 - 6 = 3
Answer:
Answer is A
Step-by-step explanation:
Took it on Edg.
Which is equivalent to (9 y squared minus 4 x)(9 y squared + 4 x), and what type of special product is it?
Answer:
[tex](9y^2-4x)\,(9y^2+4x)=81y^4-16x^2[/tex]
and it is the special factor product that leads to a difference of squares
Step-by-step explanation:
The product: [tex](9y^2-4x)\,(9y^2+4x)[/tex]
is a product of the form:
[tex](a-b)\,(a+b) = a^2-b^2[/tex]
which leads as shown to a difference of squares. So they binomials [tex](a-b)[/tex] and [tex](a+b)[/tex] are the factors of the difference of squares [tex]a^2-b^2[/tex].
In our case, the product:
[tex](9y^2-4x)\,(9y^2+4x)= (9y^2)^2-(4x)^2=81y^4-16x^2[/tex]
Answer:
B
Step-by-step explanation:
When you multiply a function by -1 what is the effect on its graph?
Answer:
Step-by-step explanation:
Depends on what you mean by multiplying by - 1. I assume you are not going to multiply the y or f(x) term by - 1.
If that is so, take an example. Suppose you have a graph that is y=x^2
That's a parabola that opens upwards and it has a line going through its focus which is a point on the +y axis.
When you multiply the right hand side by - 1, the graph you get will be y = - x^2.
That opens downward and the focus is on the - y axis.
That means that the effect of the graph is that it flips over the x axis, which I think is the third answer.
Answer:
c
Step-by-step explanation:
ape x
Work out m and c for the line: y = 8 x
Answer:
m = 8 and c = 0
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 8x ← is in slope- intercept form, that is y = 8x + 0
with m = 8 and c = 0
What is the length of segment GH?
Answer:
4√5
Step-by-step explanation:
Distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
Coordinates given:
H(8, 1)
G(0, -3)
d = [tex]\sqrt{(8-0)^2 + (1+3)^2}[/tex] = 4√5
Answer:
StartRoot 80 EndRoot
80 square root is the answer
Step-by-step explanation:
|GH|² = (8 - 0)² + (1 - (-3))²
|GH|² = 64 + 16
|GH|² = 80
GH = sqrt(80)
pls mark as brainliest
Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6? x = 6, x = –5 x = 5, x = –5 x = 7, x = –6 no solution
Answer:
Step-by-step explanation:
This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:
-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us
-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us
| 2x + 2 | = -10.
Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative is distance, there is no solution to this equation.
Answer:
no solution
Step-by-step explanation:
This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:
-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us
-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us
| 2x + 2 | = -10.
Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative
Really need help :( struggling
Answer:
B
Step-by-step explanation:
The original amount will be the coefficient of (1 + 0.04)^r which is $728.00.
Solve log x = 4. x = 4 x = 40 x = 1,000 x = 10,000
Answer:
x = 10000
Step-by-step explanation:
log x = 4
Raise each side to the base of 10
10^log x = 10 ^4
x = 10 ^4
x = 10000
Answer:
x = 10,000
Step-by-step explanation:
I got it right on the test.
Un grup de ciclistes han de fer una excursió a una casa rural que es troba a 72 quilòmetres del seu poble. El primer dia recorren 2/3 del camí. El segon dia recorren 1/4 del camí i el tercer dia arriben a la casa rural. Calcula els quilòmetres que recorren cada dia.
Answer:
29.76 milles
11.16 milles
44.64 milles
Step-by-step explanation:
Van haver de fer una excursió a una casa rural que està a 72 quilòmetres del seu poble.
El primer dia viatgen 2/3 de camí. Aquest dia, van viatjar:
2/3 * 72 = 48 quilòmetres
En el segon dia viatgen 1/4 de camí. Aquest dia, van viatjar:
1/4 * 72 = 18 quilòmetres
A el tercer dia arriben a la casa de camp. Aquest dia, van viatjar 72 quilòmetres.
Hem de convertir cada un d'ells en milles.
1 km = 0.62 milles
El primer dia:
48 km = 0.62 * 48 = 29.76 milles
El segon dia:
18 km = 0.62 * 18 = 11.16 milles
El tercer dia:
72 km = 0.62 * 72 = 44.64 milles
What is the numerical solution to the equation five less than three times a number equals four more than eight times the numbers?
A. -9/5
B. 1/11
C. -1/5
D. 1/5
Answer:
Option A
Step-by-step explanation:
Let us first consider the equation at hand. We are given that this equation is as follows, five less than three times a number equals four more than eight times the numbers. Convert this into a numerical format;
[tex]3x - 5 = 4 + 8x[/tex]
where x = " the number "
[tex]3x - 5 = 4 + 8x,\\- 5 = 4 + 5x,\\- 9 = 5x,\\\\x = - 9 / 5 \\\\Solution - Option A[/tex]
If you wish, take a look at this verbal explanation. To solve the equation 3x - 5 = 4 + 8x, one would first subtract 3x on either side of the equation, resulting in the simplified equation - 5 = 4 + 5x. Subtracting - 4 from either side, - 5 - 4 = - 9, and so we receive - 9 = 5x. Dividing 5 on either side, x = - 9 / 5, Option A.
What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work. y = 2x + 17 y = 1/2x + 8 y = -2x - 7 y = -1/2x + 2
Answer:
y = -1/2x + 2
Step-by-step explanation:
If two lines are perpendicular then the product of their slopes are -1
m1*m2 = -1
where m1 amd m2 is slope of two lines.
_______________________________________
Given line
y = 2x-3\
it is in form of y = mx+c (slope intercept form)
where m is slope and c is y intercept
Thus, slope of line y = 2x-3 is 2
Now we know that product of two lines are -1
let m be slope of other line
then m*2 = -1
m = -1/2
thus, slope of required line is -1/2
let the line be y = mx+c but m = -1/2
thus
y = -1/2 x + c
given that point(-6,5) lies on it
we use -6 in plca of x and 5 in place of y
5 = -1/2 *-6 + c
=>5 = 3 +c
=> c = 5-3 = 2
Thus, equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5) is y = -1/2x + 2
Using the graphing method, which of the following choices is the
solution of system: 3y = x-9
y = -x + 1
Answer:
y=x_1 is the solution of system
The Naturally Made Bath and Body store pays $550 a month for rent and utilities. The average cost for its products to be manufactured is about $3.00 an item. If the average price for a product sold in the store is $5.50, what will the break-even point be? Let x represent the number of products sold. The break-even point occurs when the cost function equals the revenue function. 550 + 3.00x = 5.50x Naturally Made needs to sell products to break even. The cost or revenue when it sells the break-even number of products will be $
Answer:
220 products need to be sold to break it even.
Step-by-step explanation:
550 + 3.00x = 5.50x
550 = 2.50x
220 = x
if the perimeter of regular hexagon is 10 cm, what is the radius of the circle curcumscribing the polygon?
Answer:
60
Step-by-step explanation:
hexagon is 6 sided shape. 10 * 6=60
Solve for X
A) 9
B) 16
C) 4
Answer:
B) 16
Step-by-step explanation:
8/x= cos 608/x= 1/2x= 8*2x= 16Answer:
B. 16
Step-by-step explanation:
CAH = Adjacent/Hypotenuse
cos60=8/x
xcos60=8
x= 8/cos60
x=8/0.5
x= 16
Solve for x h(x)=−7x ; h(x)=63
Answer:
x = -9
Step-by-step explanation:
-7x = 63
Divide -7 into both sides.
-7x/-7 = 63/-7
x = 63/-7
x = -9
Put x as -9 in the function to check.
h(x) = -7x
h(-9) = -7(-9)
h(-9) = 63
Answer:
x = -9
Step-by-step explanation:
h(x)=−7x ; h(x)=63
Set the two equal
-7x = 63
Divide by -7
-7x/-7 = 63/-7
x = -9
The area of a rectangle, A = l • w is represented by the expression 24x6y15. Which could be the dimensions of the rectangle?
Answer:
l=[tex]24\*x^{6}[/tex]
w=[tex]y^{15}[/tex]
Step-by-step explanation:
We know that the area of rectangle can be determined by the multiply the length to the width i.e
A = l • w..................Eq(1)
Here A represented the area .
l= Length of rectangle
w= Width of rectangle
Here A= [tex]24x^{6} y^{15}[/tex]...
It can be written as [tex]A= 24x^{6} \ *y^{15}[/tex]..............Eq(2)
Comparing the Eq(2) to the Eq(1)
[tex]l=24x^{6}\\ w=y^{15}[/tex]
Answer:
the right answer A. 2x^5y^8 and 12xy^7
Step-by-step explanation:
Pls answer i will mark as branliest
Answer:
Part A:
x = 80 degrees
Part B:
A => Corresponding Angles (They correspond to each other)
Hope This Helps!
Don't hesitate asking anything regarding this!
Write -1/19, 7/4, -4/7 from least to greatest
Answer:
-4/7, -1/19, 7/4
Step-by-step explanation:
The fractions converted into decimals would be -0.05, 1.75, -0.57
Which is the scale factor of the dilation?
Answer:
needs more information!
Step-by-step explanation:
need more information
10 people have pink cups. then 5 of those 10 people got red cups and threw the pink cups away. how many people have pink cups?⇒⇒
Answer:
5 people have pink cups
Step-by-step explanation:
10-5=5
:D
Answer:
5
Step-by-step explanation:
10-5=5
^--^
Find the 96th term of the arithmetic sequence -16, -28, -40, ...
Answer:
1124.
Step-by-step explanation:
The common difference (d) is -16 - (-28) = 12, ( also -28 - (-40) = 12).
The nth term of an A.S. is a1 + d(n - 1) where a1 = first term, d=common difference.
so the 96th term of the given A.S. is:
-16 + 12(96 - 1)
= -16 + 12*95
= 1124.
-1156Answer:
Step-by-step explanation:
The expression below is a sum of cubes.
64x3 + 125
O A. True
O B. False
Answer:
true it's A....
Answer:
A
Step-by-step explanation:
64x³ + 125
∛(64x³ + 125)
= 4x + 5
The expression is a sum of cubes.