Answer:
41
Step-by-step explanation:
We know that complex numbers are a combination of real and imaginary numbers
Real part is x and imaginary part y is multiplied by i, square root of -1
Modulus of x+iy = [tex]\sqrt{x^2+y^2}[/tex]
Here instead of x and y are given 9 and 40
i.e. 9+40i
Hence to find modulus we square the coefficients add them and then find square root
|9+49i| =[tex]\sqrt{9^2+40^2} =\sqrt{1681}[/tex]
By long division method we find that
|9+40i| =41
Answer: Modulus of |9+40i| =41
Step-by-step explanation:
Since we have given that
[tex]z=\mid9+40i\mid[/tex]
Here,
[tex]z=a+bi\\\\where,\\\\a=\text{real number}=9\\\\b=\text{imaginary number}=40[/tex]
We need to find the modulus of z:
[tex]\mid z\mid=\sqrt{a^2+b^2}[/tex]
[tex]\mid z\mid=\sqrt{9^2+40^2}\\\\\mid z\mid=\sqrt{81+1600}\\\\\mid z\mid=\sqrt{1681}\\\\\mid z\mid=41[/tex]
Hence, Modulus of |9+40i| =41
What is the area of this parallelogram? 4.9 cm? 12.25 cm? 17.15 cm? 24.01 cm? Parallelogram A B C D is composed of a square and two triangles. The square has a length and height of 3.5 centimeters each. There are two identical triangles. Each triangle has a base of 1.4 centimeters and a height of 3.5 centimeters.
Answer:
(C) 17.15
Step-by-step explanation:
the function f(x) varies inversely with x and f(x)=0.5 when x =0.3. what is f(x) when x=2.4?
Answer:
0.0625
Step-by-step explanation:
If the function f(x) varies inversely with x, then this function is of the form
[tex]f(x)=\dfrac{a}{x},[/tex]
where a is unknown number.
Since f(x)=0.5 when x =0.3, then
[tex]0.5=\dfrac{a}{0.3},\\ \\a=0.5\cdot 0.3=0.15.[/tex]
Therefore, the function is
[tex]f(x)=\dfrac{0.15}{x},[/tex]
Now when x=2.4,
[tex]f(2.4)=\dfrac{0.15}{2.4}=\dfrac{15}{240}=\dfrac{1}{16}=0.0625.[/tex]
In germany, VAT is at 19% jeremy buys a calculator in germany for 58.31 euros this price includes VAT find the amount of VAT paid by jeremy
€9.31
Step-by-step explanation:total = price + tax
... tax = 0.19×price . . . . . . . meaning of 19% VAT
... total = price + 0.19×price = 1.19×price
Dividing by 1.19, we can find the price in terms of the total.
... total/1.19 = price
And we can use this to find the tax
... tax = 0.19×price = 0.19×(total/1.19) . . . . . substitute for price
... tax = 0.19/1.19 × total = 19/119 × total . . . . . . simplify
... tax = 19/119 × 58.31 . . . . . . . put in total amount
... tax = 9.31 . . . . euros
What is the area of the rhombus shown below?
Answer:
B
Step-by-step explanation:
The interior of the 4 triangles in the rhombus are right angle triangles. In addition AC is bisected by BD and BD is bisected by AC. Those form the sides of the right angle triangle.
So the sides of the right angle are
1/2 17 = 8.5 and1/2 15 = 7.5The area of one right angle is
1/2 * 8.5 * 7.5 = 1/2 * 63.75 = 31.875But there are 4 of themArea of the rhombus = 4 * 31.875 = 127.5The answer is B
Answer:
B. 125.5 square units
Step-by-step explanation:
The area of a rhombus is half the product of the diagonals.
If the diagonals have lengths a and b, then the are is:
area = ab/2
area = (17)(15)/2
area = 255/2
area = 127.5
Answer: B. 125.5 square units
Which input value produces the same output value for the two functions on the graph?
X= -3
X= -1
X= 1
X= 3
Answer:
X=3
Step-by-step explanation:
We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship. This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.
Answer:
The correct option is 4.
Step-by-step explanation:
If the graph of a function represent in coordinate plane, then x-axis represents the domain of the function and y-axis represents the range of the function.
We have to find the input value that produces the same output value for the two functions on the graph.
From the given graph it is clear that the intersection point of both functions is at (3,-1).
At x=3 the output value of f(x) is -1.
At x=3 the output value of g(x) is -1.
It means both functions have same output -1 at x=3.
Therefore the correct option is 4.
Identify the domain of the graphed function.
Answer: Option A is correct
(-5,3) U (3,6]
Step-by-step explanation:
Domain of a function is the complete set of values that the independent variable can assume.
In the given graphed function we can see that the minimum value of independent variable (x) is -5 and the maximum value is 6, wherein the values -5 and 3 do not belongs to x.
This set of values is represented as
(-5,3) U (3,6]
Hope it helps.
Thank you.
The domain of the graphed function is (-5,3) U (3,6].
The correct option is A.
The domain of a function is the entire range of values that the independent variable can take.
In the given graphed function, we observe that the lowest value of the independent variable (x) is -5, and the highest value is 6.
However, it is the values -5 and 3 are not included in the domain.
So, the set of values is represented as (-5,3) U (3,6].
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Kevin takes a survey of the ages of people in the library at 10 a.m. and at 6 p.m. on a Wednesday.

Kevin wants to give a talk at the library to new drivers on the dangers of texting and driving. Which statement best describes when Kevin should make the talk and why?
At 6 p.m., because the median age of the people in the library at that time is 17 (around the age of new drivers)
At 10 a.m., because the average age of someone in the library at that time is about 30
At 10 a.m., because there are more people with cars at the library at that time
At 6 p.m., because the range of ages for this data set is less than the range of ages for the 10 a.m. data set
Answer:
Option 3rd is correct
Step-by-step explanation:
Kevin takes a survey of the ages of people in the library at 10a.m and at 6p.m on a Wednesday.
He should talk at library to new drivers on the dangers of texting and driving at the time when there are more people with the car.
So, that he can convey messages to more people in less time.
Therefore, Option 3rd is correct that is At 10 a.m., because there are more people with cars at the library at that time
Answer:
1 is correct.
Step-by-step explanation:
I had the same question and I tried the other answer and so it was wrong. And in the correction I had, it was the first one.
Solve f/a+r=m/s for m
Answer:
d. m = fs/ (a+r)
Step-by-step explanation:
f/ (a+r) = m/s
We want to isolate m, so we will multiply both sides by s
f/ (a+r) *s= m/s*s
fs/ (a+r) = m
[tex]\dfrac{m}{s}=\dfrac{f}{a+r}\qquad\text{multiply both sides by}\ s\neq0\\\\\boxed{m=\dfrac{fs}{a+r}}[/tex]
Last month, dory biked 11 times as many miles as karly. Togetherthey biked a total of 156 miles . How many miles did dory bike last month
Answer:
143 miles
Step-by-step explanation:
Let the distance Karly biked be x
Then Dory biked 11x
So x+11x=156
x=156/12=13
So Dory biked 11 ⋅ 13= 143 miles
Is this correct?
If a solid piece of an aluminium cylindrical rod has a volume of 200 cm3 and a base area of 20 cm2, what is the length of the piece of aluminium rod?
Answer: 10 cm
Step-by-step explanation:
Given: The volume of a solid piece of an aluminium cylindrical rod =[tex]200\cm^3[/tex]
The base area of cylinder = [tex]20\ cm^2[tex]
We know that the volume of cylinder is given by :-
[tex]\text{Volume]=\text{base area}\times \text{height}\\\\\Rightarrow200\=20\\times h\\\\\Rightarrow\ h=\frac{200}{20}=10[/tex]
Hence, the length of the piece of aluminium rod = 10 cm
To find the length of the aluminum rod with a volume of 200 cm³ and a base area of 20 cm², divide the volume by the base area. The length is 10 cm.
If a solid piece of an aluminum cylindrical rod has a volume of 200 cm3 and a base area of 20 cm2, to find the length of the aluminum rod, we can use the formula for the volume of a cylinder, which is Volume = Base Area imes Height (or length in this case, since it's a rod). Given the volume (V) is 200 cm³ and base area (A) is 20 cm², the length (L) can be calculated as L = V / A.
When you divide 200 cm³ by 20 cm², the result is:
L = 200 cm³ / 20 cm² = 10 cm.
Therefore, the length of the aluminum rod is 10 cm.
PLEASE ANSWER THIS QUESTION FOR BRAINLIEST AND 30 POINTS!!
Answer:
The author must sell 3000 books.
Step-by-step explanation:
The total amount earned = advance + books sold * money per book
We know they want to make 7000
The advance is 2500
They earn 1.50 for each book sold
b= number of books sold
Substituting in
7000= 2500 + 1.5b
Subtract 2500 from each side
7000-2500 = 2500-2500 + 1.5 b
4500 = 1.5 b
Divide each side by 1.5
4500/1.5 = 1.5b/1.5
3000 = b
The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?
A. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then across the y-axis.
B. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.
C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Answer:
if you still need the answer, its C.
Step-by-step explanation:
A bag contains 7 good apples and 3 bad apples. Nick takes two apples at random from the box, WITHOUT replacement.
This problem deals with dependent events in probability. The probability of picking two good apples in a row from a bag containing 7 good and 3 bad apples, without replacement, is calculated as (7/10)*(6/9), which equals 0.467.
Explanation:The subject of this question is Mathematics, specifically probability. When Nick picks two apples without replacement, we are dealing with dependent events, since the outcome of the second event depends on the outcome of the first event. Dependent events require a different calculation for the probability.
The total apples in the bag initially are 7 good + 3 bad = 10 apples. The probability of picking a good apple on the first draw is 7/10 or 0.7. When one apple is taken out, there are now 9 apples left in the bag. If the first apple was good, the probability of picking the second good apple is now 6/9 or 2/3.
Since these are dependent events, the total probability of picking two good apples in a row would be (7/10) * (6/9) which reduces to 14/30 or approximately 0.467.
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The sum of two numbers is 46 and the difference is 10 . What are the numbers?
Answer: 28 and 18
Step-by-step explanation:
I used the guess and test strategy to find that:
28 - 10 = 18
28 + 18 = 46
To find the two numbers, we need to solve a system of equations. By assigning variables to the numbers and setting up equations based on the given information, we can use the method of substitution to find the values of x and y. The two numbers are 28 and 18.
Explanation:
To solve this problem, let's assign variables to the numbers. Let's say the two numbers are x and y. We are given two pieces of information: the sum of the two numbers is 46, so we can write the equation x + y = 46, and the difference between the two numbers is 10, so we can write the equation x - y = 10.
To solve this system of equations, we can use the method of substitution. Rearrange one of the equations to solve for one variable in terms of the other. For example, we can rearrange the first equation to get x = 46 - y. Substitute this expression for x in the second equation:
(46 - y) - y = 10.
Simplify the equation:
46 - 2y = 10. Subtract 46 from both sides:
-2y = -36. Divide both sides by -2 to solve for y:
y = 18. Substitute this value of y back into one of the equations to solve for x:
x + 18 = 46. Subtract 18 from both sides:
x = 28.
So the two numbers are 28 and 18.
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A biker rode 45 miles in 180 minutes. At what speed (in miles per hour) was the biker travelling? A. 4 B. 17 C. 9 D. 12
Answer:
v = 15 miles / hour
Step-by-step explanation:
Given:
Distance covered by biker = s=45 miles
time taken by him = t=180 minutes
TO Find:
speed in miles per hour = v = ?
Solution:
As it is given that the distance covered is 45 miles
and time taken by him is 180 minutes
as one hour have 60 minutes
so time taken by rider = t = 180 /60
= 3 hours
this step is done because we have to find speed in miles per hour
Now
The formula for finding the distance is
distance = speed * time
or
s = v * t
we have to find v
so dividing both sides by t
[tex]\frac{s}{t} = \frac{v*t}{t}[/tex]
it becomes
[tex]v = \frac{s}{t}[/tex]
Putting the values
[tex]v = \frac{45}{3}[/tex]
solving it gives
v = 15 miles / hour
which is the required speed
in the given options it is not available
The speed is 15 miles per hour, not matching any of the provided answer choices.
The question asks for the speed of the biker in miles per hour when given the distance rode over a certain amount of time. To find the speed, we can use the formula: Speed = Distance / Time.
In this case, the biker rode 45 miles in 180 minutes. Since there are 60 minutes in an hour, we first convert 180 minutes into hours by dividing by 60: 180 / 60 = 3 hours.
Next, we calculate the speed: Speed = 45 miles \/ 3 hours = 15 miles per hour. But since this isn't one of the options provided, it seems there has been a typo in the answer choices. The correct answer, which should be 15 mph, is missing in the options.
Write an equation of the line that is parallel to 3x + 9y = 7 and passes through the point (6, 4).
A) y = 3x - 26
B) y = -3x + 16
C) y = 1/3 x-2
D) y = -1/3 x+6
Answer:
D) y = -1/3 x+6
Step-by-step explanation:
If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope. Knowing y= mx+b we need to find the slope of the old line.
3x+9y=7
Subtract 3x from each side
3x-3x +9y = -3x+7
9y = -3x+7
Divide each side by 9
9y/9 = -3x/9 + 7/9
y = -1/3 x + 7/9
We know the slope of the old line is -1/3, so the slope of the parallel line is -1/3.
If we know the slope of the line and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y-4 = -1/3(x-6)
Distribute the -1/3
y-4 = -1/3 x -1/3*-6
y-4 = -1/3x +2
Add 4 to each side
y-4+4 = -1/3x +2+4
y = -1/3x+6
A candy bar has 220 calories 132 calories are sugar what percent of the calories does the candy bar have?
What are the answer choices?
To find out what percent of the calories in a candy bar comes from sugar, divide the calories from sugar (132) by the total calories (220) and multiply by 100, resulting in 60% of the calories being from sugar.
To calculate what percent of the calories in the candy bar are from sugar, we can use the formula for percentage: (part / whole) x100. In this case, the part is the number of calories from sugar, and the whole is the total number of calories in the candy bar.
First, let's identify the given values:
Now, let's calculate the percentage:
Percentage of calories from sugar = (132 / 220) x 100Calculating this, we find:
Percentage of calories from sugar = 0.6 x100Percentage of calories from sugar = 60%Therefore, 60% of the calories in the candy bar are from sugar.
Find f(x) if it is known that f(x−2)=2x−4
Answer:
f(x) = 2x
Step-by-step explanation:
Remark
What I'm about to do is probably not the best way to do this question, but it is right. The plan is to take out a common factor on the right of f(x - 2) and then derive f(x) from that.
Solution
f(x - 2) = 2x - 4 Take out a common factor on the right of f(x -2)f(x - 2) = 2(x - 2) Now what that means is that in the original equation, wherever you saw an x, you put in x - 2. So the original equation must have beenCheck
f(x) = 2x To check this put x - 2 back inf(x - 2) = 2(x -2) Remove the brackets. f(x - 2) = 2x - 4 which is what it should be.Final answer:
To find f(x), replace x - 2 with y to get f(y) = 2(y + 2) - 4, simplify to f(y) = 2y, then revert y back to x to find f(x) = 2x.
Explanation:
To find the function f(x) when you know that f(x - 2) = 2x - 4, you need to replace x - 2 with y so that x = y + 2. Therefore, f(y) = f(x - 2) = 2x - 4 becomes f(y) = 2(y + 2) - 4.
Simplifying this, we get:
f(y) = 2y + 4 - 4
f(y) = 2y.
Now, to revert back to the original function, replace y with x to get f(x) = 2x. This is the function we were looking to find.
HElP Me
Multiplying by a fraction gives a _____ number.
equal
smaller
larger
Multiplying by a fraction yields a smaller number if the fraction is less than 1, and a larger number if the fraction is greater than 1.
When multiplying by a fraction, the result depends on the fraction you're multiplying by. If the fraction is less than 1 (or what we refer to as a proper fraction where the numerator is less than the denominator), then the result is a smaller number than the original number you started with. For instance, multiplying 5 by 1/2 (which is a proper fraction) will yield 2.5, which is smaller than 5. However, if you multiply by a fraction greater than 1 (an improper fraction where the numerator is greater than the denominator), such as 5/3, the result will be a larger number. So, multiplying 5 by 5/3 will yield approximately 8.33, which is larger than 5.
If a town with a population of 10,000 doubles every 14 years, what will the population be in 42 years and is it modeled by a linear function or an exponential function? A) 30,000; linear function B) 60,000; exponential function C) 72,000; linear function D) 80,000; exponential function
Answer: D) 80000; exponential function
Step-by-step explanation:
It would double 3 times in total; first from 10k to 20k, then from 20k to 40k, and finally from 40k to 80k. Hope this helps
Answer:
D)80,000; exponential function
Step-by-step explanation:
We are given that a town with a population of 10,000 doubles every 14 years
So, Initial Population = 10,000
Now we are given that what will the population be in 42 years
First determine how many times population will double : [tex]\frac{42}{14} = 3[/tex]
So, In 42 years it doubles three times .
Now Linear functions change at a constant rate per unit interval while An exponential function changes by a common ratio over equal intervals.
So, the given situation will be modeled by exponential function
So, Using exponential function : [tex]y=ab^x[/tex]
Where a is Initial Population = 10,000
b is rate of change
x = time = 3 times
So, the population will be in 42 years=[tex]10000 (2)^3[/tex]
=[tex]80000[/tex]
So, the population will be 80,000 after 42 years.
Thus Option D is correct.
D)80,000; exponential function
A triangle has two sides of lengths 4 and 15.What value could the length of the third side be? Check all that apply.. A:12 B:13 C:4 D:15 E:11 F:19
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A: 4, 12, 15
4 + 12 = 16 > 15 CORRECT :)
B: 4, 13, 15
4 + 13 = 17 > 15 CORRECT :)
C: 4, 4, 15
4 + 4 = 8 < 15 INCORRECT :(
D: 4, 15, 15
4 + 15 = 19 > 15 CORRECT :)
E: 4, 11, 15
4 + 11 = 15 INCORRECT :(
F: 4, 15, 19
4 + 15 = 19 INCORRECT :(
Answer: A: 12, B: 13, D; 15Tickets for a baseball game cost a? dollars for adults and c? dollars for children. The expression 2a+3c represents the cost (in dollars) for a family to go to the game. What is the cost for the family when an adult ticket is $17? and a child ticket is $12??
To find the total cost for the family to attend the baseball game, we substitute the given ticket prices into the expression 2a + 3c, where a is the cost of an adult ticket and c is the cost of a child ticket, resulting in a total cost of $70.
Explanation:The student is asking about the cost for a family to attend a baseball game with the given prices for adult and child tickets.
Given the cost of an adult ticket as $17 and a child ticket as $12, we use the expression provided (2a + 3c) to calculate the total cost for the family.
Substituting the given values into the expression, we get 2(17) + 3(12), which equals 34 + 36.
Summing up these two products gives us a total of $70.
Therefore, it will cost the family $70 to attend the baseball game.
Use the figure below list the sides least to greatest of triangle PRQ.
Answer:
Hence third choice RQ, RP, PQ is correct.
Step-by-step explanation:
We know that if A, B, C are the angles of the triangle and if ∠A > ∠B
a>b {Where “a” is side created by angle A and “b” is side created by angle B }.
We will use same property to decide which side is bigger.
In triangle PRQ,
∠P = 30 degree
∠R = 85 degree
then ∠P + ∠R + ∠Q = 180 {since sum of all three angle of triangle is 180 degree}
30 + 85 + ∠Q = 180
115 + ∠Q = 180
∠Q = 180 - 115
∠Q = 65
Now we know measure of all angles so we can do comparison using above property.
Smallest angle is ∠P so side RQ will be smallest.
Largest angle is ∠R so side PQ will be largest.
Hence we get RQ < RP < PQ.
Hence third choice RQ, RP, PQ is correct.
There are 120 students surveyed (30 from each grade). Use the table below to determine that probability that a student selected at random is in 11th grade or selected Math as their favorite subject?
Find P (11th or math)
a. 7/120
b. 1/2
c. 67/120
d. 59/120
Answer: 59/120 (choice D)
Add up the values in the "math" column and the "11th" row to find the total number of people who are either in 11th grade, in math, or in both.
So,
(12+10+8+7) + (14+5+3) = 59
represents the number of people who are in either category. This is out of 120 (given). This is where 59/120 comes from.
HELP!!!!!!! 100 POINTS PLS HALP
Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’s bill is 7%. How much is Isaac’s total bill? Show your work.
ANSWERED^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 84.53
If Isaac uses a coupon entitling him to a 25% discount off the purchase price before tax, how much will his bill be? Assume that a 7% sales tax is applied to the discounted price. Using words, explain how you found the discounted price.
ANSWERED ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 63.4
The shoe store’s clerks are paid on commission. If the clerk receives a 12% commission on total purchase amounts before tax is applied, how much would the commission be for Isaac’s purchase with and without a coupon?
NOT ANSWERED^^^^^^^^^^^^^^^^^^^^^^^ Pls help
Answer:
7.11 and 9.48
Step-by-step explanation:
.12 is equal to 7.11
with out coupon
.12 is equal to 9.48
with the coupon
a. Isaac's total bill is $84.53
b. Isaac's price after the discount is $63.40
c. The shoe store clerk's commission before the coupon is $9.48 and $7.11 after the coupon
Solution to the first question
Total bill = cost of shoes + tax paid
Tax paid = tax rate + cost of shoes
Cost of shoes = $37.00 + $42.00. = $79
Tax paid = $79 + 0.07 = $5.53
Total bill = $5.53 + $79 = $84.53
Solution to the second question
The discounted price of the shoes can be found by subtracting the value of the discount from the price of the shoes
Discounted price = cost of the shoes = value of the 25% discount
Value of the 5% discount = 0.25 x $79= $19.75
Discounted price = $79 - $19.75 = 59.25
Bill = discounted price x ( 1 + tax rate)
59.25 x 1.07 = $63.40
Solution to the third question
Commission before the coupon
Commission = 12% x price before the coupon
0.12 x $79 = $9.48
Commission after the coupon
Commission = 12% x price after the coupon
0.12 x 59.25 = $7.11
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What is the exact situation to the equation e^4x-1=3
(In picture)
Answer:
Short Answer: B
Step-by-step explanation:
You want to solve for x in
e^(4x - 1) = 3 Take the natural log of both sidesln(e^(4x - 1) ) = ln3 Bring the power down from the left side of the equation(4x - 1) ln(e) = ln(3) Note that ln(e) = 1(4x - 1)*1 = ln(3) Add 1 to both sides4x - 1 + 1 = ln(3) + 1 Reduce4x = ln(3) + 1 Divide by 4x = (ln(3) + 1)/4pease help, thank you
Answer: -2
=====================================================
Draw a vertical line through 4 on the x axis. This vertical line crosses the parabola at some point (which we'll call point A). Draw a horizontal line from point A to the y axis and note how it lands on y = 12. Therefore the point (4,12) is on this parabola.
Repeat the same steps as before to find that (8,4) is also on the parabola
We need to find the slope of the line through (4,12) and (8,4)
m = (y2 - y1)/(x2 - x1)
m = (4-12)/(8 - 4)
m = -8/4
m = -2
The slope of this line is -2 meaning that the average rate of change from x = 4 to x = 8 is -2.
The line goes down 2 units each time you move to the right 1 unit.
A builder uses 32 wooden slats to make 4 fence panels. Fatima wants to know how many slats are needed for 1 panel. Gerard wants to know how many slats he will need to make 8 panels. Drag an expression to answer each question.
1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Wooden slates required to make 4 fence panels = 32
To find wooden required to make 1 panel, use ratio property,
4 fence panels = 32 wooden slates
1 fence panel = 8 wooden slates
Also, to find wooden required to make 8 panels, use ratio property,
4 fence panels = 32 wooden slates
8 fence panels = 64 wooden slates
1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.
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Final answer:
Gerard needs 64 slats to make 8 panels, as it is a proportional relationship.
Explanation:
To find out how many slats are needed for one panel, we simply divide the total number of slats by the number of panels. Since a builder uses 32 slats to make 4 panels, for one panel, Fatima would need:
Number of slats for one panel = Total number of slats \/ Number of panels
Number of slats for one panel = 32 / 4 = 8 slats
For Gerard's question, if 1 panel requires 8 slats, then to make 8 panels he would need:
Number of slats for 8 panels = Slats per panel x Number of panels
Number of slats for 8 panels = 8 x 8 = 64 slats
It's a straightforward example of a proportional relationship in mathematics, where the number of slats scales directly with the number of fence panels.
What number can you multiply by −2√ to get a rational number?
Answer:
the square root of 2 times the negative square root of 2 would be -2, which is a rational number.
Ben and Jerry’s ice cream company estimates that for every 32 people that they serve their delicious ice cream to, they need to make 128 ounces of ice cream. How many people can they serve if they make 704 ounces of ice cream?
Set up a proportion and solve.
The first part of the proportion would be the known values of 32 people to 128 ounces.
The second part of the proportion is X ( the number of people) for 704 ounces.
This is written as 32/128 = X/704
To solve for X Cross multiply:
32 * 704 = 128x
Simplify:
22528 = 128x
Solve for X by dividing both sides by 128:
x = 22528 / 128
x = 176 people