Answer:
15
Step-by-step explanation:
Write a proportion:
60 cups / 12 gallons = x cups / 3 gallons
Cross multiply:
12x = 180
Divide:
x = 15
He should use 15 cups.
Jesse should use 15 cups of mushrooms to make 3 gallons of mushroom soup, based on the restaurant's recipe. Devon will be making 37.5 liters of soup for the party of 100 guests.
Explanation:To solve Jesse's question about how many cups of mushrooms he should use to make 3 gallons of mushroom soup, we need to find the proportion between the amount used in the restaurant's recipe and the desired amount for Jesse's smaller batch.
The restaurant uses 60 cups of mushrooms to make 12 gallons of soup. To find out how many cups are needed for 1 gallon, we divide the number of cups by the number of gallons:
60 cups / 12 gallons = 5 cups per gallon
Jesse wants to make 3 gallons of soup. Multiplying the amount needed for one gallon by 3 gives us the answer:
5 cups/gallon × 3 gallons = 15 cups of mushrooms.
Devon, on the other hand, is preparing soup for a party. Calculating the total amount for 100 guests using 375 milliliters per person, we get:
375 milliliters/guest × 100 guests = 37500 milliliters.
Since 1 liter is equivalent to 1000 milliliters, we can convert the milliliters to liters:
37500 milliliters / 1000 = 37.5 liters of soup for 100 guests.
ASAP ANSWER
Bobby has 4 ½ gallons of soda to share. Each serving is 1 pint. How many servings does he have to share?
each gallon has 8 pints
4 [tex]\frac{1}{2}[/tex] * 8 = 36
so there would be 36 servings
Which geometric term is best described as a straight path between two points?
A. Angle
B. Point
C. vertex
D. Line Segment
Answer:
the answer is d
Step-by-step explanation:
A line segment is best described as a path between two points.
What is a line segment?A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.
We can choose the correct answer below:Four options are given.
We have to find the geometric term that is best described as a straight path between two points.
From the given options, the only term that satisfies these conditions is a line segment.
A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.
Therefore, we have found that a line segment is best described as a path between two points. The correct answer is option D.
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I need help please
Answer:
b
Step-by-step explanation:
it makes sense because they all are going down by 1 side each time
B) the triangle because each figure is loosing one side
Which trigonometric function is being used if we get the fraction 6/10 as our answer? Question 3 options: sin(A) cos(A) tan(A) tan(gerine)
Answer:
cos(A)Step-by-step explanation:
For angle A we have
opposite = 8
adjacent = 6
hypotenuse = 10
sin A = opposite/hypotenuse
cos A = adjacent/hypotenuse
tan A = opposite/adjacent
cot A = adjacent/opposite
6/10 = adjacent/hypotenuse = cos A
The trigonometric function of the triangle is given by cos A = 6/10
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔABC
where the measure of ∠ABC = 90°
Now , from the trigonometric relations ,
cos θ = adjacent / hypotenuse
So , on simplifying , we get
The measure of BC = 6 units
The measure of AB = 8 units
The measure of AC = 10 units
cos A = 6 / 10
Hence , the measure of cos A of triangle is cos A = 6 / 10
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Find the image of (–7, –3) reflected across the x-axis. A. (–7, 3) B. (7, –3) C. (7, 3) D. (–7, –3)
Answer:
(-7, -3) (Answer A)
Step-by-step explanation:
We start with the point (-7, -3). The x-coordinate does not change at all if we reflect this point across the x-axis. Whereas the y-value of (-7, -3) is -3, we end up with +3 after this reflection. The desired image is (-7, +3) (Answer A)
The coordinates of the point (-7, - 3) reflected along the x-axis is
(- 7, 3).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
We know reflection along the x-axis of a point (x, y) converts it into a
point (x, - y).
Given, A points (-7, - 3) is reflected along the x-axis.
Therefore, The new coordinates of the points (-7, - 3) reflected along the x-axis is (- 7, 3).
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the factored form of a quadratic equation is x (x-4). the ordered pair (0,0) represents one of the zeros of the associated quadratic function. which ordered pair represents the other zero?
Answer:
the other zero is represented by the ordered pair (4, 0)
Step-by-step explanation:
We have the factored expression
[tex]x (x-4)[/tex]
We must find out for what values of x this function is equal to zero.
Then we equal the function to zero and solve for the variable x
[tex]x (x-4)=0[/tex]
The function is equal to zero when one of the two terms of the product is equal to zero.
So
[tex]x =0[/tex] We already know that this is a solution
or
[tex]x-4=0\\x =4[/tex]
Then the other zero is represented by the ordered pair (4, 0)
find the value of n such that b^2 + 16b + n is a perfect square trinomial
Answer:
64
Step-by-step explanation:
To complete the square
add ( half the coefficient of the b- term )² to b² + 16b
b² + 2(8)b + 8²
= b² + 16b + 64 = (b + 8)²
Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are .
If point D divides in the ratio 4 : 5, the coordinates of point D are .
Reset Next
Answer:
Point B is (10 , -4)
Point D is (10/9 , 1)
Step-by-step explanation:
* Lets revise the rule of the point which divides of a line segment in
a ratio
- If point (x , y) divides the line segment AB, where A is (x1 , y1) and
B is (x2 , y2) in the ratio m1 : m2
∴ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ y = [m2(y1) + m1(y2)]/(m1 + m2)
* Now lets solve the problem
- Point C (3.6 , -0.4) divides AB in the ratio 3 : 2, where A is (-6 , 5)
# x = 3.6 , y = -0.4
# A is (x1 , y1) , B is (x2 , y2)
∴ x1 = -6 , y1 = 5
∵ m1 : m2 = 3 : 2
- Substitute these values in the rule
∵ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ 3.6 = [2(-6) + 3(x2)]/(3 + 2)
∴ 3.6 = [-12 + 3x2]/5 ⇒ multiply both sides by 5
∴ 18 = -12 + 3x2 ⇒ add 12 to both sides
∴ 30 = 3x2 ⇒ divide both sides by 3
∴ 10 = x2
* The x-coordinate of B is 10
∵ y = [m2(y1) + m1(y2)]/(m1 + m2)
∴ -0.4 = [2(5) + 3(y2)]/(3 + 2)
∴ -0.4 = [10 + 3y]/5 ⇒ multiply both sides by 5
∴ -2 = 10 + 3y2 ⇒ subtract 10 from both sides
∴ -12 = 3x2 ⇒ divide both sides by 3
∴ -4 = y2
* The y-coordinate of B is -4
∴ Point B is (10 , -4)
- Point D divides AB in the ratio 4 : 5 where A (-6 , 5) and B (10 , -4)
- To find the coordinates of point D use the same rule above
# D is (x , y)
# A is (x1 , y1) and B is (x2 , y2)
# m1 : m2 is 4 : 5
∵ x1 = -6 and y1 = 5
∵ x2 = 10 and y2 = -4
∵ m1 = 4 and m2 = 5
- Substitute these values in the rule
∵ x = [m2(x1) + m1(x2)]/(m1 + m2)
∴ x = [5(-6) + 4(10)]/(4 + 5) ⇒ multiply the numbers
∴ x = [-30 + 40]/9 ⇒ add
∴ x = [10]/9 ⇒ Divide
∴ x = 10/9
* The x-coordinate of D is 10/9
∵ y = [m2(y1) + m1(y2)]/(m1 + m2)
∴ y = [5(5) + 4(-4)]/(5 + 4) ⇒ multiply the numbers
∴ y = [25 + -16]/9 ⇒ add
∴ y = [9]/9 ⇒ Divide
∴ y = 1
* The y-coordinate of point D is 1
∴ Point D is (10/9 , 1)
Need help fast do not understand this one. Solve: (x+5) / (x+8)=1+(6) / (x+1) showing all work.
Answer: [tex]x=-\frac{17}{3}[/tex]
Step-by-step explanation:
Given the equation [tex]\frac{(x+5)}{(x+8)}=1+\frac{6}{(x+1)}[/tex], you need to make the addtition indicated on the right side of the equation:
[tex]\frac{(x+5)}{(x+8)}=\frac{(x+1)+6}{(x+1)}\\\\\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}[/tex]
Now, multiply both sides of the equation by (x+8) and (x+1):
[tex](x+1)(x+8)\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}(x+1)(x+8)\\\\(x+1)(x+5)=(x+7)(x+8)[/tex]
Now, apply Distributive property:
[tex]x^2+5x+x+5=x^2+8x+7x+56[/tex]
Simplifying, you get:
[tex]6x+5=15x+56[/tex]
Subtract 5 and 15x from both sides:
[tex]6x+5-15x-5=15x+56-15x-5\\\\-9x=51[/tex]
Finally, divide both sidesby -9:
[tex]\frac{-9x}{-9}=\frac{51}{-9}\\\\x=-\frac{17}{3}[/tex]
im taking the flvs test and need the answer asapppppp
During a certain time of the year, the angle of the sun's rays at location C is smaller than the angle of the sun's rays at location D. Which location experiences cooler temperatures at that time?
Location C, because the smaller angle means the sunlight is spread out over more area
Location D, because the larger angle means the sunlight is spread out over more area
Location C, because Earth is tilted away from the sun at this time
Location D, because Earth is tilted towards the sun at this time
Answer:
d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I just finished the quiz, and this was my only incorrect one. The correct answer is A. Also, think logically. If the sun is spread out over more area, then it must be at a smaller angle. This leads to cooler temperatures, of course.
The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below:
Step 1: 8 + 12x
Step 2: 4(2) 4x2)
Step 3: 4(4 + 8x)
Step 4: Dimensions of the rectangle are 4 and 4 + 8x
In which step did the student first make an error and what is the correct step?
Step 2: 4(2) + 4x(2)
Step 2: 4(2) + 4(3x)
Step 3: 4 + (4+8x)
Step 3: 4 + (4• 8x)
Answer:
Step 2: 4(2) + 4(3x)
Step-by-step explanation:
By definition, the area of a rectangle is given by:
Area = Length × Width
In this case, we know that:
Area = 8 + 12x
Width = 4
Therefore:
Step 1: 8 + 12x
Step 2: 4(2) + (4)(3x)
Step 3: 4(2 + 3x)
Therefore, the dimensions of the rectangle are 4 and 2 + 3x.
The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be 4(2) + 4(3x). Which is the second option.
PLEASE ANSWER THIS AND EXPLAIN HOW YOU GOT THE ANSWER.
9 - 3 ÷ 1/3 + 1 =
Answer:
Step-by-step explanation:
If you use pemdas, you would do 3÷1/3 which equals 9. Then do 9-9, which equals 0. Then, do 0+1, which equals 1. Hope this helps! <3
[tex]9 - 3 \div \frac{1}{3} + 1 = [/tex]
Divisions go first, to do it we have to reverse the fraction and turn ÷ into ×
[tex] = 9 - 3 \times 3 + 1 = [/tex]
Now the multiplication
[tex] = 9 - 9 + 1 = [/tex]
[tex] = 1[/tex]
Compare the monthly payment amount of Annabelle's dream car at two different car dealerships.
Dealership A: The car costs $30,000, and the loan has an annual interest rate of 4.8%.
Dealership B: The car costs $29,800, and the loan has an annual interest rate of 5.4%.
Determine the monthly payment for each dealership, and decide which is cheaper. Both interest rates are compounded
monthly. Both loans are for 5 years, or 60 months. Assume that there is no down payment.
Answer:
Dealership A is cheaper. Hope it helps.
Answer:
By comparing both the payments we can say that Dealer A is cheaper by $4.50.
Step-by-step explanation:
Dealership A: The car costs $30,000, and the loan has an annual interest rate of 4.8% for 5 years.
The EMI formula is :
[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
Now, p = 30000
r = [tex]4.8/12/100=0.004[/tex]
n = [tex]5\times12=60[/tex]
Putting values in formula we get;
[tex]\frac{30000\times0.004\times(1+0.004)^{60} }{(1+0.004)^{60}-1 }[/tex]
=> [tex]\frac{30000\times0.004\times(1.004)^{60} }{(1.004)^{60}-1 }[/tex]
EMI is = $563.34
Dealership B: The car costs $29,800, and the loan has an annual interest rate of 5.4% for 5 years.
p = 29800
r = [tex]5.4/12/100=0.0045[/tex]
n = [tex]5\times12=60[/tex]
Putting values in formula we get;
[tex]\frac{29800\times0.0045\times(1+0.0045)^{60} }{(1+0.0045)^{60}-1 }[/tex]
=> [tex]\frac{29800\times0.0045\times(1.0045)^{60} }{(1.0045)^{60}-1 }[/tex]
EMI = $567.84
By comparing both the payments we can say that Dealer A is cheaper by $4.50.
#5! And #4 revisions!
Answer:
4. Your working and answers are correct: x = 44, y = 43.
5. GH = 60°
Step-by-step explanation:
5. Arc GH is double the inscribed angle GFH, so we have ...
2(4x+2) = 9x-3
8x +4 = 9x -3 . . . . . simplify
7 = x . . . . . . . . . . . . add 3-8x
Then the arc's measure is ...
(9·7 -3)° = (63 -3)° = 60°
Answer:
Step-by-step explanation:
Your working and answers are correct: x = 44, y = 43.
5. GH = 60°
if Mark wants to see how the price of gas has increased over the last five years, which type of graph would best illustrate this data line graph circle graph bar graph pictograph
Line graph because it shows differences
Which of the following is a list of equivalent numbers?
A. 1.25,114,12.5%
B. 0.125,14,12.5%
C. 12.5,1212,125%
D. 1.25,114,125%
ANSWER
D. 1.25,1¼,125%
EXPLANATION
The number 1.25 can be rewritten as a fraction to obtain:
[tex]1 \frac{1}{4} [/tex]
We can covert 1.25 into percentage by multiplying by 100%
This implies that,
[tex]1.25 = 1.25 \times 100\% = 125\%[/tex]
Therefore the equivalent numbers are:
1.25,1¼,125%
The correct answer is D
Which of the following is an even function?
Answer:
I believe it is the third one (C)
Step-by-step explanation:
Hello There!
Your answer would be the first one.
f(x) = \x/
F of x has to equal f of -x
Determine which diagram could be used to prove ABC - EDC using similarity transformations.
Answer: A The first Answer to the left
Step-by-step explanation:
The diagram could be used to prove that ABC-EDC using similarity transformations is option A.
The first Answer to the left
We have given that,
The diagram could be used to prove ABC - EDC using similarity transformations.
What is the transformation?
A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation.
We have to determine which diagram could be used to prove ABC-EDC.
Therefore the answer is the first diagram.
The diagram could be used to prove that ABC-EDC using similarity transformations is option A.
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Write an equation for the perpendicular line in slope intercept form for (-3,5);y=1/3x-2
Hey there! :)
We're given the equation : y = 1/3x - 2 & coordinates : (-3, 5)
If we're looking for an equation for a perpendicular line, then we know that the slope of our new equation MUST be the negative reciprocal of the original slope. This means that you flip the slope and add or remove a negative. Example : slope = -2 ⇒ negative reciprocal slope = 1/2
Before using this information, we must first find the slope of our original equation.
Using slope-intercept form, which is : y=mx+b ; where m=slope, b=y-intercept
Ask yourself : which value is in the "m" spot and which value is in the "b" spot?
Using this, we now know that 1/3 is our slope, and -2 is our y-intervept.
So, our negative reciprocal is -3.
Use point-slope form to find the y-intercept, and coordinates (-3, 5)
Point-slope = y - y1 = m(x - x1)
y - 5 = -3(x - (-3))
Simplify.
y - 5 = -3(x + 3)
Simplify.
y - 5 = -3x - 9
Add 5 to both sides.
y = -3x + 4 ⇒ slope-intercept form
~Hope I helped! :)
(08.01)
Line R is represented by the following equation: x + y = 2
Which equation completes the system that is satisfied by the solution (1, 1)?
2x + y = 2
4x − 2y = 2
2x − 2y = 2
x + y = 4
Answer:
B: 4x − 2y = 2
B: 4x − 2y = 2 equation completes the system that is satisfied by the solution (1, 1).
What is a linear equation?A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.solving this we will get the valve of Y if x is given.
explanation:
line R = x + y = 2
putting the value of X=1 & y=1 as given (1,1)
x+y =2
1+1= 2
therefore, 4x - 2y = 2
4(1) - 2(1)= 2 answer
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What is the slope of this line?
Answer: [tex]-\frac{8}{5}[/tex]
Remember: RISE/RUN (y/x). Lines that are increasing have a positive slope, and lines that are decreasing have a negative slope.
You can find the slope in two ways:
1. Useful if the line is graphed: count the units between 2 points on the line.
Let's use the points (-1, 4) and (4, -4).(-1, 4) is 8 units higher than (4, -4) and 5 units to the left of (4, -4).Because the line is decreasing, the slope is negative.Therefore, the slope is [tex]-\frac{8}{5}[/tex].2. Useful if the line is not graphed: find the difference between the y-coordinate values divided by the difference of the x-coordinate values.
Let's use the points (-1, 4) and (4, -4).[tex]\frac{-4 - 4}{4 - (-1)} = \frac{-8}{5}[/tex]Therefore, the slope is [tex]-\frac{8}{5}[/tex].Answer:
[tex]m=-\frac{8}{5}[/tex]
Step-by-step explanation:
Let
[tex]A(-1,4),B(4,-4)[/tex]
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-4-4}{4+1}[/tex]
[tex]m=\frac{-8}{5}[/tex]
[tex]m=-\frac{8}{5}[/tex]
anyone can solve this question?
Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
x² + y² = 5 → (1)
2x + y = 4 → (2)
Rearrange (2) expressing y in terms of x by subtracting 2x from both sides
y = 4 - 2x → (3)
Substitute y = 4 - 2x in (1)
x² + (4 - 2x)² = 5 ← expand factor on left side
x² + 16 - 16x + 4x² = 5
5x² - 16x + 16 = 5 ( subtract 5 from both sides )
5x² - 16x + 11 = 0 ← in standard form
(5x - 11)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
5x - 11 = 0 ⇒ 5x = 11 ⇒ x = [tex]\frac{11}{5}[/tex]
Substitute each of these values into (3) for corresponding values of y
x = 1 : y = 4 - 2 = 2 ⇒ P(1, 2)
x = [tex]\frac{11}{5}[/tex] : y = 4 - [tex]\frac{22}{5}[/tex] = - [tex]\frac{2}{5}[/tex]
Hence Q( [tex]\frac{11}{5}[/tex], -[tex]\frac{2}{5}[/tex] )
Can someone answer this for me ASAP please ?
Answer:
The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{(5 + x)}[/tex] ⇒ 2nd answer
Step-by-step explanation:
* Lets explain the meaning of the composition of functions
- Composition of functions is when one function is inside of an another
function
# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside
g(x) and (h ° g)(x) means g(x) is inside h(x)
* Now lets solve the problem
∵ h(x) = 5 + x
∵ k(x) = 1/x
- We need to find (k ° h)(x), that means put h(x) inside k(x)
* Lets replace the x of k by the h(x)
∵ k(x) = [tex]\frac{1}{x}[/tex]
∵ h(x) = 5 + x
- Replace the x of k by 5 + x
∴ k(5 + x) = [tex]\frac{1}{5 + x}[/tex]
∴ The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{5+x}[/tex]
Simplify 12a2b3 / 3ab
[tex] \frac{12 {a}^{2} {b}^{3} }{3ab } \\ = \frac{3 \times a \times b \times 4 \times a \times {b}^{2} }{3ab} \\ \\ cancelling \: common \: factors \\ \\ = 4a {b}^{2} [/tex]
Hence answer is 4ab²
Hope it helps...
Hope it helps...Regards;
Hope it helps...Regards;Leukonov/Olegion.
Leila is considering buying her first home. The house she is interested in buying is priced at $125,000. Leila can put down a $20,000 payment, and she qualifies for a 30-year mortgage at 6%. What will her monthly mortgage payment be?
Answer:
* The monthly mortgage payment is $629.53 ⇒ answer C
Step-by-step explanation:
* Lets explain how to solve the problem
- Leila is considering buying her first home
- The house she is interested in buying is priced at $125,000
∴ She can put $20000 down payment
* Lets find the balance to be paid off on mortgage
∴ The balance = 125000 - 20000 = 105000
- She qualifies for a 30-year mortgage at 6%
* Lets find the rule of the monthly payment
∵ [tex]pmt=\frac{\frac{r}{n}[P(1+\frac{r}{n})^{tn}]}{(1+\frac{r}{n})^{tn}-1}[/tex] , where
- pmt is the monthly mortgage payment
- P = the initial amount
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per unit t
- t = the time the money is invested or borrowed for
∵ P = 105000
∵ r = 6/100 = 0.06
∵ n = 12
∵ t = 30
∴ [tex]pmt=\frac{\frac{0.06}{12}[105000(1+\frac{0.06}{12})^{30(12)}}{(1+\frac{0.06}{12})^{30(12)}-1}[/tex]
∴ [tex]pmt=\frac{0.005[105000(1.005)^{360}]}{(1.005)^{360}-1} =629.528[/tex]
* The monthly mortgage payment is $629.53
PLEASEE HEELPPP I NEED THIS QUESTION ANYONE HELP!!!
Answer:
4u= - 4i - 24j
u +w = -9i - 3j
Step-by-step explanation:
The question is on operation of vectors
Given u= -i -6j and w= -8i+3j
Then 4u = 4{ -i-6j}
4u= - 4i - 24j
u+w= -i -6j + -8i+3j......................collect like terms
= -i -8i + -6j +3j
= -9i + -3j
= -9i - 3j
Evaluate the following expression (-5+7x1)-9x5
Final answer:
To evaluate the expression (-5+7x1)-9x5, follow the order of operations: calculate inside the parentheses, multiply, and then subtract, resulting in a final answer of 47.
Explanation:
To evaluate the expression (-5+7×1)-9×5, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Let's break down the expression step by step:
Inside the parentheses: -5 + (7 × 1) = -5 + 7 = 2.
Multiply: -9 × 5 = -45.
Subtract the value obtained from step 2 from the result of step 1: 2 - (-45).
Change the subtraction of a negative value to addition: 2 + 45 = 47.
Thus, the expression (-5+7×1)-9×5 evaluates to 47.
The number of frogs in a certain lake is inversely related to the number of snakes in the lake. If x represents the number of snakes in the lake, then y = 100/x represents the number of frogs in the lake. Describe the reasonable domain and range values. Graph the function.
1. Domain: The set of natural numbers / Range: The set of natural numbers
2. Shown below
Step-by-step explanation:1. Domain and Range.In this problem, we have that the number of frogs in a certain lake is inversely related to the number of snakes in the lake. Hence we are facing an Inverse Variation, so this means that if the number of snakes in the lake increases then the number of frogs in the lake decreases, because snakes eat frogs! The function that describes this is a rational function defined as:
[tex]y=\frac{100}{x}[/tex]
Where:
[tex]x: \ represents \ the \ number \ of \ snakes \ in \ the \ lake \\ \\ y: \ represents \ the \ number \ of \ frogs \ in \ the \ lake[/tex]
As you can see, [tex]x[/tex] is in the denominator, therefore [tex]x\neq 0[/tex]. Since we need to provide a reasonable domain, we say that the domain is the set of natural numbers and this doesn't include the number 0. Why aren't negative values included in the domain as well? Well, although negative values are included in the function, they aren't reasonable because [tex]x[/tex] represents the number of snakes and you always get positive numbers when counting things.
To get the range, let's take the inverse of this function, so:
[tex]y=f(x)=\frac{100}{x} \\ \\ \\ Interchange \ x \ and \ y: \\ \\ x=\frac{100}{y} \\ \\ \\ Isolate \ y: \\ \\ y=\frac{100}{x} \\ \\ f^{-1}(x)=\frac{100}{x}[/tex]
So the domain of [tex]f^{-1}(x)[/tex] is the range of our given function [tex]y=f(x)[/tex]. As you can see the inverse function is the same as our given function, then the range is the set of natural numbers as well.
2. Graph.First of all, we can define the pattern of the rational function as:
[tex]y=g(x)=\frac{1}{x}[/tex]
So our function will be:
[tex]f(x)=100g(x)=100\frac{1}{x}=\frac{100}{x}[/tex]
So the graph of [tex]f(x)[/tex] will be the same graph of [tex]g(x)[/tex] but it's been stretched vertically by a constant of 100, that is, each y-value is multiplied by 100. Also, since [tex]x \neq 0[/tex] and [tex]y \neq 0[/tex] then at [tex]x=0[/tex] there is a vertical asymptote and at [tex]y=0[/tex] there is an horizontal asymptote. Finally, the graph is shown below for [tex]x>0 \ and \ y>0[/tex], but remember: Whenever [tex]x \ and \ y[/tex] are natural numbers.
Answer:
Both the number of snakes and the number of frogs will be positive, so positive values are reasonable for the domain and range.
Step-by-step explanation:
Write an equation to describe the variation. Use k for the constant of proportionality.
y varies directly as u and inversely as p^4
[tex]\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{y} varies directly as \underline{u} and inversely as }p^4}{y=\cfrac{ku}{p^4}}[/tex]
What is the series using summation notation?
36+69+102+...+267
first term =36
second term=69
So common difference=69-36=33
checking. 69+33=102
36=3+33
so the series in AP Becomes as...
(3+33) ,(36+33) ,(36+2(33)) ... (36+7(33))
So The Answer is...
(refer above attachment.)
Hope it helps...
Regards,
Leukonov/Olegion.