Answer: y = (5832/25)*(5/18)^x
==========================================================
Explanation:
Any general exponential function is of the form
y = a*b^x
Plug in (x,y) = (3,5) and we get
y = a*b^x
5 = a*b^3
If you plug in (x,y) = (2,18), then we'll get this other equation
18 = a*b^2
-------------------
So we have this system of equations
[tex]\begin{cases}5 = ab^3\\18 = ab^2\end{cases}[/tex]
From here, we divide the two equations straight down. The left hand sides divide to 5/18. The right hand sides divide to (ab^3)/(ab^2) which simplifies to b. The 'a' terms cancel and we subtract the exponents for the b terms.
Overall, we end up with b = 5/18
---------------------
Use that value of b to find 'a'
18 = a*b^2
18 = a*(5/18)^2
18 = a*(25/324)
18*(324/25) = a
a = 5832/25
You could use the other equation as well to find 'a'
----------------------
Therefore, the equation in y = a*b^x form is y = (5832/25)*(5/18)^x
To verify this, plugging in x = 3 should lead to y = 5. Similarly, plugging in x = 2 should lead to y = 18.
PLEASE HELP MEEEEEEEEEEEEEE
triangle area ?
Answer:
A= 21.65063509
Step-by-step explanation:
triangle area is =base*hight/2
Because we have a right triangle we can apply the trigonometric functions
sin30 =base/hypothenuse = base/10
cos 30 = hight/hypothenuse =hight/10
sin30 = base /10 ; multiply both sides by 10
base = 10*sin30
cos 30 = hight /10 ; multiply both sides by 10
hight = 10 cos 30
A= 10*sin30*10*cos30/2 =
100*sin 30*cos 30/2=
50*sin30*cos30 = ; use calculator make sure is set up in degrees
A= 21.65063509
Help pleaseeeee ASAP
Answer:
9 cm
Step-by-step explanation:
The volume of a square based pyramid is given as :
V = 1/3a²h
Where ; a = base edge ; h = Height
Volume, V = 48 cm³ ; a = 4cm
48 = 1/3 * 4² * h
48 = 1/3 * 16h
48 * 3 = 16h
144 = 16h
h = 144 / 16
h = 9 cm
Height = 9cm
help me find the answer
Find an expression which represents the difference when (-4x – 3y) is subtracted
from (-2x – 10y) in simplest terms.
Answer: (-2x-10y)-(-4x-3y)
-2x-10y-(-4x-3y)
-2x-10y+4x+3y
-2x+4x-10y+3y
-2x+4x-10y+3
Answer =2x-7y
Step-by-step explanation:
What is the volume of a cube whose sides are each 1 3/4 ft?
Answer:
5.4 (rounded)
Step-by-step explanation:
the volume of a cube is length*width*height so here all three are 1 3/4 (same as 1.75) and so you multiply 1.75 * 1.75 * 1.75 and that gives you 5.4 when rounded.
Tessellations (image below)
9514 1404 393
Answer:
regular octagon
Step-by-step explanation:
In order for a shape to tessellate a plane, there must be a way to arrange the shapes so that the sum of angles at a node is 360°. An arrangement of kites is shown in the attachment. Of course, squares are used to tile planes all the time, as their four 90° corners fit together nicely.
An octagon has internal angles of 135°, which is not a sub-multiple of 360°. Hence there is no way for octagons to fit together to tile a plane.
Octagons will not tessellate a plane.
ratios that are equivalent to 7/6
Answer:
14 : 12 , 21 : 18 and 28 : 24 .
Step-by-step explanation:
Answer:
14 : 12 , 21 : 18 and 28 : 24 .
Step-by-step explanation:
Therefore, 14 : 12 , 21 : 18 and 28 : 24
A circle has a circumference of 100 m. Find its area
Area of circle=796.5m²
Answer:
Solution given:
circumference of circle=100m
2πr=100m
r=100/(2π)
r=15.92m
now
area of circle=πr²=π×15.92²=796.5m²[approximately]
Answer:
A =796.1783439 m^2
Step-by-step explanation:
circumference = 2 * pi *r
100 = 2 * pi *r
Divide by 2
50 = pi r
Divide by pi
50/pi = r
Using 3.14 for pi
50/3.14 = r
15.92356688=r
Now we can find the area
A = pi r^2
A = 3.14 ( 15.92356688)^2
A =796.1783439 m^2
PLEASSE HELP ME WILL MARK YOU!
Problem 1
Answer: It is possible to draw a triangle
-------------------------
Explanation:
We use the triangle inequality theorem. Consider a triangle with sides a,b,c
A triangle is only possible if and only if the following three inequalities are all true
a+b > cb+c > aa+c > bBasically, if we can add any two sides to get a sum larger than the third side, then we can form a triangle.
If a = 3, b = 4, and c = 5, then
a+b = 3+4 = 7 which is indeed larger than c = 5 b+c = 4+5 = 9 which is larger than a = 3a+c = 3+5 = 8 which is larger than b = 4All three conditions are met, therefore we have a triangle possible.
=======================================================
Problem 2
Answer: No, a triangle is not possible
-------------------------
Explanation:
For this problem, and the next two problems, we'll use the triangle inequality theorem also.
Notice that a+b = 4+5 = 9 but this is not larger than c = 9
So the condition a+b > c is not true, and therefore we do not have a triangle possible.
=======================================================
Problem 3
Answer: No, a triangle is not possible
-------------------------
Explanation:
Similar to problem 2. A triangle isn't possible because a+b = 5+6 = 11 which is not larger than c = 12.
=======================================================
Problem 4
Answer: It is possible to draw a triangle
-------------------------
Explanation:
A triangle is possible here because
a+b = 3.5+4.5 = 8 which is larger than c = 7b+c = 4.5+7 = 11.5 which is larger than a = 3.5a+c = 3.5+7 = 10.5 which is larger than b = 4.5=======================================================
Problem 5
Answer: a, c, b
-------------------------
Explanation:
Here are two rules we'll use here
The smallest angle is always opposite the smallest sideThe largest angle is always opposite the largest sideThis applies to triangles only.
From the diagram, we can see that the 28 inch side is the longest. Angle 'a' is opposite this, making angle 'a' to be the largest angle.
Then we see that angle b is opposite the smallest side, so angle b is the smallest angle. Angle c is somewhere in between angles 'a' and b. So that's why we get the order a, c, b when sorting the angles from largest to smallest.
onathan collects postcards and stamps. The number of postcards in his collection is 12 more than the number of stamps. He has 39 postcards in all. If Jonathan has x stamps, which equation represents this situation and how many stamps does he have?
equation: 39 - 12 = x
x = 27 (stamps)
Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the
approximate volume of the toy ice cream cone? Use 3.14 for x.
52 Step-by-step explanation:
the scale is 7 millimeters = 1 meter. what is the scale factor?
Answer:
1 meter =1,000 millimeters. So, the scale is:
7 mm:1,000 mm Divide both sides by 7
1 mm:142 6/7 mm - This is the scale that was used
Step-by-step explanation:
What’s the slope. Jackie charges her phone over night. This graph shows how much the battery depletes on an hour basis
Answer:
slope (m) = 5
Step-by-step explanation:
rise/run, -10/-2 = 5
Definition: A number greater than 0 is called ____.
Answer:
a positive number as 0 is a neutral.
A manufacturer knows that 9% of the products it produces are defective. Find the probability that among 6 randomly selected products, at least one of them is defective.
Answer:1%
Step-by-step explanation:
If the trapezoid on the grid below is translated by using the rule (x,y)-> (x-4,y-3) what will be the coordinates of B’?
Answer:
B'(3, 5)
Step-by-step explanation:
Rule for the translation of a point (x, y) by 'h' units left and 'k' units upwards,
(x, y) → (x - h, y + k)
If h = 4 and k = 3,
[tex](x, y)\rightarrow(x-4,y+3)[/tex]
Following this rule coordinates of the image point of B will be,
B(7, 2) → B'(7 - 4, 2 + 3)
→ B'(3, 5)
Therefore, coordinates of the image point B' will be,
B'(3, 5)
1. if csc β = 7/3 and cot β = - 2√10 / 3, Find sec β
2. find cos y and tan y if csc y = -√6 / 2 and cot y > 0.
3. Find tan x and sin x if sec x = 6/5 and sin x > 0.
Step-by-step explanation:
1.
[tex] \tan \beta = \frac{1}{ \cot \beta } = - \frac{3}{2 \sqrt{10} } = - \frac{3 \sqrt{10} }{20} [/tex]
[tex] \csc \beta \tan \beta = \frac{1}{ \cos \beta } = \sec \beta [/tex]
Therefore,
[tex] \sec \beta = ( \frac{7}{3} )( - \frac{3 \sqrt{10} }{20} ) = - \frac{7 \sqrt{10} }{20} [/tex]
2.
[tex] \csc y = \frac{1}{ \sin y} = - \frac{ \sqrt{6} }{2} [/tex]
[tex] = > \sin y = - \frac{ \sqrt{6} }{3} [/tex]
Use the identity
[tex] \cos y = \sqrt{1 - \sin ^{2} y} \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{1 - {( - \frac{ \sqrt{6} }{3}) }^{2} } = - \frac{ \sqrt{3} }{3} [/tex]
We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:
[tex]\tan \beta = \frac{ \sin y}{ \cos y} =( - \frac{ \sqrt{6} }{3} )( - \frac{3}{ \sqrt{3} } ) = \sqrt{2} [/tex]
3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,
[tex] \sin x = \sqrt{1 - \cos ^{2} x} = \sqrt{ \frac{11}{6} } [/tex]
Solving for tan x:
[tex] \tan x = \frac{ \sin x}{ \cos x} = (\frac{ \sqrt{11} }{ \sqrt{6} } )( \frac{6}{5} ) = \frac{ \sqrt{66} }{5} [/tex]
Solve the quadratic equation by using a graphic approach. Round your answer to the hundredths place,
x² - 2x -
40
a. x= 3.24 or x = -1.24
b. x = 2.73 or x = -0.73
c. x = 4.24 or x = -0.24
d. x = 5.24or x = -1.24
Pls help and explain I’m having a hard time understanding the lesson
Answer:
Step-by-step explanation:
Well, I really don’t like graphic approaches in math, so hear ya go a formula:
Although there are easier ways that work for some quadratics, but this formula works for them all. (It is atached, have a look)
So,
( -(-2)+- square root of ((-2)^2-4(1)(-40)) ) / 2(1)
Note that for a hear I use one, since there is nothing in front of x.
( 2 + (12.8) ) / 2 < with plus
( 2 -(12.8) ) / 2 < with minus
X = 7.4
Or
X = -5.4
(Quad equations have 2 answers)
Which of the expressions below could be factored quickly using the "difference of squares"? Select all that apply.
O 81x² - 12
O x^2 + 25
O 4x^2 – 25
O 9x^2 – 16
O x^2-50
O x^2-81
O x^2-100
Answer:
81x² - 12, no as 12 is not a perfect square x^2 + 25, no as it is a sum of squares 4x^2 - 25, yes 9x^2 - 16, yes x^2 - 50, no as 50 is not a perfect square x^2 - 81, yes x^2 - 100, yesWhich expression represents the length, in inches,
of the framed picture?
Answer:
No solution is posible from the information provided
Step-by-step explanation:
Answer:
1. B
2. C
3. 8, 36
4 lemons required to make 6 cups of lemonade
Answer:
If you are looking for a fraction, it would be 2/3 lemon per cup of lemonade
Step-by-step explanation:
If you simplify 4/6 it would be 2/3
HELP Will mark brainlist
Answer:
Its B since the decimals are lower than the data.
Does -5 + 7 - 8 = 6?
Answer:
-6
Step-by-step explanation:
-5+7=2
2-2=0
0-the remaining 6 of the 8=-6
what are the possible zeros of f(x)= x^3-3x^2+x+5
Answer:
the only zero should be -1
(a) If (x - 2)(x-5) <0 and x e N then find x.
Answer:
x = 3 or x = 4.
Step-by-step explanation:
We are given the following inequality:
[tex](x - 2)(x - 5) < 0[/tex]
It is a product, and a product is negative when one term is positive and the other is negative.
First case:
[tex]x - 2 > 0 \rightarrow x > 2[/tex]
And
[tex]x - 5 < 0 \rightarrow x < 5[/tex]
Thus, in the natural set: x = 3 and x = 4.
Second case:
[tex]x - 2 < 0 \rightarrow x < 2[/tex]
And
[tex]x - 5 > 0 \rightarrow x > 5[/tex]
Empty set.
Union of the cases:
Second case is the empty set, so we only count the first case. Thus x = 3 or x = 4.
HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPP
Answer:
4. 52 ft^2
5. 25 ft^2
Step-by-step explanation:
15 -11 To get the width of scrapbooking which is = 4
4 * 13 = 52 ft^2
9 - 4 = 5 ft
5 * 5 = 25ft
In each turn of a game you toss two coins. If 2 heads come up, you win 2 points and if 1 head comes up you win one point
Answer:
I don't understand pls explain
Elizabeth has $26 left after shopping at the mall. She bought 2 shirts for $22.99 each, a drink for $2.02, and 2 books for $16 each. How much money did she start with?
Step-by-step explanation:
22.99 × 2 + 2.02 + 16 × 2 + 26= $106
how can i get a cientific form number
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
Scientific notation is helpful when dealing with really large numbers with a lot of zeroes because you can express them with smaller numbers, and it looks a lot more simple. It's just a different way to express numbers.
Here's an example : Let's say someone asked me to put the number
650,000,000 into scientific notation.
That would be 6.5 ✕ 10^8
Hope this helps, please mark brainliest if possible. Have a nice day.
find two numbers whose ratios is 3 to 5 and whose sum is 88
Answer:
33 and 55
Step-by-step explanation:
[tex]\frac{x}{y}: \frac{3}{5}[/tex]
x + y = 88
3 + 5 = 8
[tex]y(\frac{x}{y}): y(\frac{3}{5})[/tex]
[tex]x= \frac{3}{5}y[/tex]
[tex]y+\frac{3}{5}y=88[/tex]
[tex]\frac{8y}{5}=88[/tex]
[tex]5(\frac{8y}{5})=5(88)[/tex]
8y = 440
8y ÷ 8 = 440 ÷ 8
y = 55
x + y = 88
x + 55 = 88
x + 55 - 55 = 88 - 55
x = 33
