Answer:
a) R = 3.6
b) A = 2
Step-by-step explanation:
To find the value, start by modeling the inverse proportionality by using the base equations with the original givens.
y = k/x
12 = k/1.5
18 = k
Now we use that to model the equation
R = 18/A
And we can now use that to solve parts a) and b)
a)
R = 18/A
R = 18/5
R = 3.6
b)
R = 18/A
9 = 18/A
2 = A
Evaluate the expression under the given conditions. sin(θ − ϕ); tan(θ) = 4/3 , θ in Quadrant III, sin(ϕ) = − 10/10 , ϕ in Quadrant IV
Answer: -0.6
Step-by-step explanation:
First thing to do is to solve for θ and ϕ from the given information
tan(θ) = 4/3,
θ = tan-¹4/3,
θ = 53.1°
Since tan is positive in quadrant III, θ = 53.1°
Also,
sin(ϕ) = − 10/10 ,
ϕ = sin-¹-1
ϕ = 270°
If ϕ is in the fourth quadrant, that gives 360 - ϕ i.e 360 - 270 = 90°
Substituting the values of θ and ϕ into sin(θ − ϕ), we have;
Sin(53.1 - 90)
= sin (-36.9°)
= -0.6
The given expression sin(θ - ϕ), with tan(θ) = 4/3, θ in Quadrant III, sin(ϕ) = -10/10, and ϕ in Quadrant IV, is evaluated by using trigonometric principles and identities. Upon calculations, sin(θ - ϕ) comes out to be -3/5.
Explanation:The question is asking us to evaluate the expression sin(θ − ϕ), given that tan(θ) = 4/3, θ is in Quadrant III, sin(ϕ) = -10/10, and ϕ is in Quadrant IV. In trigonometry, tan θ = sin θ/cos θ. We have tan θ = 4/3 and we know that in Quadrant III, tangent is positive but sine and cosine are negative. So, we can make a right triangle where the opposite side is 4 (basing this on the absolute value of the tan θ) and the adjacent side is 3. The hypotenuse then, by using Pythagoras theorem, comes out to be 5. Then sin θ = -4/5 and cos θ = -3/5.
For sin(ϕ), we are given that it equals -1. In Quadrant IV, sine is negative and cosine is positive, so cos ϕ = √(1 - (-1)^2) = 0.
Finally, utilizing the formula sin (a ± ß) = sin a cos ß ± cos a sin ß, we plug in our values to come to the solution sin(θ - ϕ) = (sin θ cos ϕ) - (cos θ sin ϕ) = ((-4/5)*0) - ((-3/5)*-1) = -3/5
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HELP!! Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n) = 20 · bn, where n is the number of hours and b is an unknown positive base.
Based on the model, there were initially (answer space) bacteria.
If b = 1.85, the hourly percent growth rate of the bacteria would be
(answer space) %.
Answer:
20
85%
Step-by-step explanation:
You are given the function [tex]S(n)=20\cdot b^n.[/tex]
If n is the number of hours, then initially n=0 and
[tex]S(0)=20\cdot b^0=20\cdot 1=20.[/tex]
If S(n) is the function of exponential growth, then it can be represented as
[tex]S(n)=I\cdot (1+r)^n,[/tex]
where I is the initial amount, r -is the percent growth rate and n is the number of hours.
If b = 1.85, we can represent it as b = 1 + 0.85. Thus, the hourly percent growth rate of the bacteria would be 0.85=85%.
s(n) = 20b^n
n is the time in hours. At the beginning, the time is zero hours, so n = 0.
s(0) = 20 * b^0
s(0) = 20 * 1
s(0) = 20
The initial amount was 20.
For b = 1.85,
s(n) = 20(1.85)^n
s(n) = 20(1 + 0.85)^n
The hourly growth is 0.85.
0.85 * 100% = 85%
The hourly percent change is 85%.
What is the trigonometric function's period?
Question 3 options:
pi
2 pi
3 pi
4 pi
➷ Find the difference from one peak ( highest point) to the next
In this case, it is 2 pi
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
2 pi
Step-by-step explanation:
Help with this question, please! I need help!
Answer:
$357Step-by-step explanation:
We have a rectangle measuring 25 feet × 9 feet. Remove from the rectangle two regular hexagons with a side length equal to 2 feet.
The formula of an area of a rectangle:
[tex]A_r=lw[/tex]
l - length, w - width.
Substitute l = 25 ft and w = 9 ft:
[tex]A_r=(25)(9)=225\ ft^2[/tex]
The formula of an area of a regular hexagon:
[tex]A_h=6\cdot\dfrac{a^2\sqrt3}{4}[/tex]
a - side
Substitute a = 2 ft:
[tex]A_h=6\cdot\dfrac{2^2\sqrt6}{4}=6\sqrt3\ ft^2[/tex]
The area of the wall:
[tex]A=A_r-2A_h[/tex]
Substitute:
[tex]A=225-2(6\sqrt3)=225-12\sqrt3\approx225-20.785=204.215\ ft^2[/tex]
Paiting the wall costs $1.75 per ft². Calculate:
[tex](\$1.75)(204.215)\approx\$357[/tex]
Gray and Brenda and Jack went bowling together. Bryant's score was 55. Jacks score was exactly double bryant's. Brenda has 13 fewer points than Jack. What was Brenda's score?
Bryant's score is 55 (given)
Jack's score is twice the score of Bryant, so it's
[tex]55\cdot 2 = 110[/tex]
Brenda's score is 13 less than Jack, so it's
[tex]110-13 = 97[/tex]
Please help me out.....................
. A soccer team played 32 games. If they won 25% of them, how many games did the team win?V
Answer:
[tex]8\ games[/tex]
Step-by-step explanation:
Let
x----->number of games won by the football team
we know that
[tex]25\%=25/100=0.25[/tex]
so
[tex]x=0.25(32)=8\ games[/tex]
On Monday Paula has $20 is her bank account. She spends $25 and then spends another $10. How much money does she need to add into her account (deposit) to return to the original amount she started with on Monday?
Answer:
15
Step-by-step explanation:
10 + 25= 35 and 35-20 = 15
please give branlest
Answer:
Step-by-step explanation: She Needs To Deposit $35 Dollars To Return To The Orginal Ammount She Started With On Monday.
Find the coordinates of the midpoint of a line segment with end points (-3,4) and (7,9)
Answer: (2, 6.5)
Step-by-step explanation:
[tex]Midpoint_{x,y}=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{-3+7}{2},\dfrac{4+9}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{4}{2},\dfrac{13}{2}\bigg)\\\\\\.\qquad \qquad \quad=\large\boxed{(2,6.5)}[/tex]
Twenty is fourteen more than 3 times a number. What is the number?
Answer:
2
Step-by-step explanation:
Let's disect the problem. Three times a particular number plus fourteen equals 20. Let's make an equation, and replace the number with x.
3x + 14 = 20The "3x" represents the 3 times the number,the 14 represents the 14 added to make 20.Let's solve the equation!We'll first minus 14 from each side to balance the equation, but with the intention of isolating the variable, x.
3x = 6We have almost successfully isolated the variable. To isolate the variable, we can divide by three on each side.
x = 2The number is 2.Solve the equation. Round to the nearest hundredth. Show work.
[tex]6e^{2x} - 5e^{x} = 6[/tex]
Answer:
The value of x = 0.41
Step-by-step explanation:
∵ [tex]6e^{2x}-5e^{x}=6[/tex]
Let [tex]e^{x}=y[/tex]
∴ [tex]e^{2x}=y^{2}[/tex]
∴ 6y² - 5y = 6
∴ 6y² - 5y - 6 = 0 ⇒ factorize
∴ (3y + 2)(2y - 3) = 0
∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3
∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2
∵ [tex]y=e^{x}[/tex]
∴ [tex]e^{x}=\frac{-2}{3}[/tex] ⇒ refused
([tex]e^{ax}[/tex] never gives -ve values)
∵ [tex]e^{x}=3/2[/tex] ⇒ insert ln in both sides
∵ [tex]lne^{ax}=axlne=ax[/tex] ⇒ ln(e) = 1
∴ [tex]xlne=ln(3/2)[/tex]
∴ x = ln(3/2) = 0.41
Simplify the expression.
sec x/tan x
Answer:
Option b
Step-by-step explanation:
We know that, by definition:
[tex]secx = \frac{1}{cosx}[/tex]
We also know that:
[tex]tanx = \frac{sinx}{cosx}[/tex]
Applying these identities we can simplify the given expression
[tex]\frac{secx}{tanx} = \frac{\frac{1}{cosx}}{\frac{sinx}{cosx}}\\\\\frac{secx}{tanx} = \frac{cosx}{sinxcosx}\\\\\frac{secx}{tanx} = \frac{1}{sinx}[/tex]
We know that, by definition:
[tex]\frac{1}{sinx} = cscx[/tex]
Final answer:
To simplify sec x/tan x, we use trigonometric identities to show that sec x/tan x equals csc x, which is the cosecant of x.
Explanation:
To simplify the expression sec x/tan x, we need to recall the trigonometric identities for secant (sec) and tangent (tan). We know that sec x is equal to 1/cos x and tan x is equal to sin x/cos x. When we divide sec x by tan x, we are essentially dividing 1/cos x by sin x/cos x. This simplifies to:
sec x/tan x = (1/cos x) / (sin x/cos x)Multiply the numerator by the reciprocal of the denominator: (1/cos x) * (cos x/sin x)The cos x terms cancel out, leaving us with: 1/sin xThe expression 1/sin x is the definition of cosecant (csc x), thus:sec x/tan x = csc xTo summarize, the simplified form of the expression sec x/tan x is csc x.
The sum of the measures of angleUWV and angleUWZ is 90°, so angleUWV and angleUWZ are angles.
Answer:
Angles UWV and UWZ are complementary
Step-by-step explanation:
we know that
If the sum of the measures of two angles is equal to 90 degrees, then, the angles are complementary
so
In this problem
[tex]m<UWZ+m<UWV=90\°[/tex]
therefore
Angles UWV and UWZ are complementary
Which of the following statements is true? a. sin 18° = cos 72° b. sin 55° = cos 55° c. sin 72° = cos 18° d. Both a and c. Please select the best answer from the choices provided A B C D
D
generally,
[tex] \sin( \alpha ) = \cos(90 - \alpha )[/tex]
you can visualize this by drawing a right triangle with acute angles a and 90-a
Answer:
D. Both a and c are true.
Step-by-step explanation:
a . sin 18 = cos (90 - 18) = cos 72 so a is True.
b. this is not true.
c. sin 72 = cos(90 - 72) = cos 18, so c is true.
A bakery has 63 donuts and 36 muffins for sale. What is the ratio of muffins to donuts?
The ratio of muffins to donuts in the bakery is 4:7, calculated by dividing the number of muffins (36) by the number of donuts (63).
To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts.
Given:
- Number of donuts: 63
- Number of muffins: 36
Ratio of muffins to donuts:
[tex]\[ \text{Ratio} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]
[tex]\[ \text{Ratio} = \frac{36}{63} \][/tex]
We can simplify this ratio by finding the greatest common divisor (GCD) of 36 and 63, which is 9.
[tex]\[ \text{Ratio} = \frac{\frac{36}{9}}{\frac{63}{9}} \][/tex]
[tex]\[ \text{Ratio} = \frac{4}{7} \][/tex]
So, the ratio of muffins to donuts is 4:7 .
The ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].
To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts:
[tex]\[ \text{Ratio of muffins to donuts} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]
Given that the bakery has 63 donuts and 36 muffins, we can substitute these values into the formula:
[tex]\[ \text{Ratio of muffins to donuts} = \frac{36}{63} \][/tex]
Now, we can simplify this fraction:
[tex]\[ \frac{36}{63} = \frac{4 \times 9}{7 \times 9} = \frac{4}{7} \][/tex]
So, the ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].
Find the value of x in the polygon.
Answer:
x = 25 mm
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w) where l is the length and w is the width
We know the perimeter is 60 mm and the width is 5 mm and the length is x
60 = 2(x +5)
Divide each side by 2
60/2 = 2/2(x+5)
30 = x+5
Subtract 5 from each side
30-5 = x+5-5
25 =x
x = 25 mm
[tex]\huge\bold\red{Answer}[/tex]
☑The diagram which is shown above is a rectangle.
✍ Perimeter= 60mm
✍ breadth = 5mm
➡ Perimeter of rectangle = 2(l+b)
✍ 60 = 2(l +5)
✍ 60/2 = l+5
✍ 30 - 5 = l
✍ 25 = l
☑ L = 25mm
❣..hope it helps you..❣
Each month, Kaisorn deposits $50.00 onto her public transportation card. It costs her $2.50 per trip to ride the subway. Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2.5x = y 40 − 2x = y 50 + 2.5x = y 40 + 2x = y 50 − 2.5y = x 40 − 2y = x 50 + 2.5y = x 40 + 2y = x
Answer:
For Kaisorn: [tex]y=50-2.50x[/tex]
For Thom: [tex]y=40-2x[/tex]
Step-by-step explanation:
Each month, Kaisorn deposits $50.00 onto her public transportation card.
It costs her $2.50 per trip to ride the subway. Means 2.50x
Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. Means 2x
Let x represents the number of trips
Let y represents the amount remaining in each account.
Then the system of equations represents their transportation costs are :
For Kaisorn: [tex]y=50-2.50x[/tex]
For Thom: [tex]y=40-2x[/tex]
Of 500 students going on a class trip 350 are student band members and 65 are athletes 25 band members and student athletes what is the probability that one of the students on the trip is an athlete or a band memeber?
Answer:
0.78
Step-by-step explanation:
There are 500 students in total. Thus,
350 students are band members;65 students are athlets;25 students are both band members and athlets;350-25=325 students are only band members. not athlets;65-25=40 students are only athlets, not band members.The probability that one of the students on the trip is an athlete or a band memeber is
[tex]Pr=\dfrac{325+40+25}{500}=\dfrac{390}{500}=0.78.[/tex]
A rectangular pyramid is sliced such that the cross section is perpendicular to its base and the cross section does not intersect its vertex.
What is the shape of the cross section?
square
trapezoid
triangle
rectangle
The vertex, would be the tip of the pyramid. If it was sliced at the vertex, the shape would be a triangle. Since the slice doesn't intersect the vertex, the point of the pyramid would net be included, it would be as if the tip was cut off.
You would then have a trapezoid, because the top would be a straight horizontal line parallel with the bottom line.
(9Q) Solve the log.
Answer:
D
Step-by-step explanation:
If a single six sided die is rolled once, what are the odds that you will roll a number less than 3?
Answer:
1/3
Step-by-step explanation:
1/3 since there are two numbers less than three, and there are 6 possible outcomes, so 2/6 = 1/3.
Given f(x)=7x^9 , find f^1(x). Then state whether f^1f(x) is a function.
a : y=(x/7)^1/9 ; f^1(x) is a function.
b : y=(x/7)^9 ; f^1(x) is not a function
c : y=(x/7)^1/9 ; f^1(x) is not a function
d : y=(x/7)^9 ; f^1(x) is a function
Answer:
A
Step-by-step explanation:
Edge 2021
The inverse function of f(x) = 7x^9 is found to be f^{-1}(x) = (x/7)^{1/9}. By substituting f(x) into its inverse, we can verify that f^{-1}(f(x)) = x, which shows that the composition is indeed a function. Therefore, the correct answer is option a.
The student has asked to find the inverse function of f(x) = 7x^9 and determine if the composition of the original function and its inverse is a function. The inverse function, denoted as f^{-1}(x), undoes the action of the original function. To find the inverse, we replace f(x) with y, switch the roles of x and y, and then solve for y:
Start with y = 7x^9.Switch x and y to get x = 7y^9.Divide both sides by 7 to get x/7 = y^9.Take the ninth root of both sides to solve for y, yielding y = (x/7)^{1/9}.This gives us option a: y = (x/7)^{1/9}. To check if f^{-1}(f(x)) is a function, we substitute f(x) into the inverse, resulting in f^{-1}(7x^9) = (7x^9/7)^{1/9} = x, which is indeed a function. Therefore, f^{-1}(x) is a function, and option a is correct.
Please help me out........ :)
Answer:
x = 5
Step-by-step explanation:
For the parallelogram to be a square we use the property
The diagonals of a square are congruent, hence
12x - 23 = 4x + 17 ( subtract 4x from both sides )
8x - 23 = 17 ( add 23 to both sides )
8x = 40 ( divide both sides by 8 )
x = 5
In the trapezium, a = 7cm , b = 10.4cm h = 6.7cmwork out the area of the trapezium
Please answer this question, will give brainliest!
Answer:
9.9 cm
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of CY
a^2 + b^2 = c^2
CY^2 + YZ^2 = CZ^2
YZ = XY since CZ is the perpendicular bisector
YZ = 5
CZ = 7
CY ^2 + 5^2 = 7^2
CY^2 +25 = 49
Subtract 25 from each side
CY^2 = 49-25
CY^2 = 24
Take the square root of each side
sqrt(CY^2) = sqrt(24)
CY = 4.898979
CY = 4.9 cm
We want the length of WY
WY = WC + CY
WC is a radius which is 5 cm
WY = 5cm + 4.9cm
WY = 9.9 cm
Answer:
We should work backwards we need to find YC+CW to get YW
angle bisector theorem means that ZC and XC are equal
then we can use the Pythagorean theorem to get YC
5^2 + x = 7^2
YC= √13
CW = 7 because they are both the radius of a circle
YW= 7+√13
YW=10.60 (rounded)
if f(x)=sqrt x+12 and g(x)= 2 sqrt x what is the value of (f – g)(144)?.
Answer:
the answer is 0
Step-by-step explanation:
There are 36 gold cards and 36 silver cards in a deck. The gold cards are numbered 1,3,5,... 71 and the silver cards are numbered 2.4.6,... 72. The cards are throughly shuffled and one card is randomly selected.
A. Find the probability of selecting a gold card or a card with a multiple of 12 on it. Show your work
B. Find the probability of selecting a silver card or a card with a multiple of 9 on it. Show your work.
A) multiples of 12 up to 72 ( 72 total cards)
12, 24, 36, 48, 60, 72 = 6 cards.
36 are gold.
Total gold cards and multiple of 12 = 36 + 6 =42
Probability of getting one of them is 42/72, which reduces to 7/12
B) 36 silver cards
Multiples of 9: 9, 18, 27, 36, 45, 54,63 = 7 cards
Silver cards are even and there is 3 even cards that are also multiples of 9, so subtract 3 from 7 to get 4.
Total silver cards and multiples of 9 = 36 + 4 = 40
Probability = 40/72 which reduces to 5/9
Answer:
Step-by-step explanation:
A.
Because there is no overlap between good card and card with a multiple of 12,
P(gold card or a card with a multiple of 12)
= P(gold card) + P(a card with a multiple of 12)
P(gold card)
= no. of gold cards / total no. of cards
= 36 / (36 + 36)
= 36 / 72
= 1/2
P(a card with a multiple of 12)
= no. of cards with multiples of 12 / total no. of cards
= (12, 24, 36, 48, 60, 72) / 72
= 6/72
= 1/12
P(gold card or a card with a multiple of 12)
= 1/2 + 1/12
= 7/12
B. There ARE overlaps between a silver card and a card with a multiple of 9,
P(silver card or a card with a multiple of 9)
= P(silver card) + P(a card with a multiple of 9) - P(silver card AND a multiple of 9)
P(silver card)
= no. of silver cards / total no. of cards
= 36 / (36 + 36)
= 36 / 72
= 1/2
P(a card with a multiple of 9)
= no. of cards with multiples of 9 / total no. of cards
= (9, 18, 27, 36, 45, 54, 63, 72) / 72
= 8/72
= 1/9
P(silver card AND a multiple of 9)
= no. of silver cards AND a multiple of 9 / total no. of cards
= (18, 36, 54, 72) / 72
= 4/72
= 1/18
P(silver card or a card with a multiple of 9)
= 1/2 + 1/9 - 1/18
= 10/18
= 5/9
What is the volume of a rectangular prism with the dimensions: base 3 1 2 cm, height 1 1 2 cm, and length 5 1 2 cm?
Answer:
The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=BHL[/tex]
Convert the given dimensions to an improper fractions
[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]
[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]
[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]
substitute in the formula
[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]
Convert to mixed number
[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]
Item 16 Simplify the expression. 5+8(3+x)
First, to simplify the expression 5 + 8(3 + x), distribute the 8 to everything inside the parentheses to get 5 + 24 + 8x. Then, combine the numerical terms to get the answer 29 + 8x.
Explanation:The expression you are asked to simplify is 5 + 8(3 + x). To do this, you'll need to use the distributive property, which allows you to multiply a number outside a set of parentheses by every term inside the parentheses.
Start with the expression: 5 + 8(3 + x)
Before adding, you'll need to multiply eight by every term inside the parentheses, three, and x:
5 + 8*3 + 8*x
That changes your expression to:
5 + 24 + 8x
Now, you need to combine like terms (add together the numbers that are not attached to variable x):
5 + 24 = 29
So, the simplified version of the expression is:
29 + 8x
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Solve for x for 0 ≤ x < 2 π .
cotxcosx - cotx = 0
0
Pi/2
Pi
3Pi/2
2Pi
[tex]\bf cot(x)cos(x)-cot(x)=0\implies cot(x)[cos(x)-1]=0 \\\\[-0.35em] ~\dotfill\\\\ cot(x)=0\implies \cfrac{cos(x)}{sin(x)}=0\implies cos(x)=0\\\\\\ x=cos^{-1}(0)\implies \boxed{x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ cos(x)-1=0\implies cos(x)=1\implies x=cos^{-1}(1)\implies \boxed{x=0}[/tex]
Answer:
x = π/2, 3π/2
Step-by-step explanation:
cot(x)cos(x) - cot(x) = 0
Factor out cot(x)
cot(x)[cos(x) -1] = 0
Solve each part separately
cot(x) = 0 cos(x) - 1 = 0
x = π/2, 3π/2 cos(x) = 1
x = 0
There are three possible solutions:
x = 0, π/2, 3π/2
However, the function is undefined for x = 0.
∴ x = π/2, 3π/2