mrs. jo is purchasing food she is given two options for financing the $900 purchase option A is a 5 year term at a rate of 8% option B is a 2 year term at a rate of 10% which is the better option and how much will mrs. jo save by going with the better option
Using the simple interest formula it is seen that Mrs Jo saves an amount of $180 when she chooses option B over option A.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
To determine which option is better, we need to compare the total amount of interest paid for each option.
Option A -
The principal amount is $900 and the interest rate is 8%. The term is 5 years.
Using the formula for simple interest -
Interest = Principal × Rate × Time
Interest = $900 × 0.08 × 5
Interest = $360
Total amount paid = Principal + Interest
Total amount paid = $900 + $360
Total amount paid = $1260
Option B -
The principal amount is $900 and the interest rate is 10%. The term is 2 years.
Using the formula for simple interest -
Interest = Principal × Rate × Time
Interest = $900 × 0.10 × 2 = $180
Total amount paid = Principal + Interest
Total amount paid = $900 + $180
Total amount paid = $1080
Therefore, option B is the better option because it has a lower total amount paid by choosing option B.
Mrs. Jo will save -
$1260 - $1080 = $180
Therefore, Mrs. Jo will save $180 by choosing option B instead of option A.
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One day after school, two students begin tracking the number of steps they took each minute while walking home. They each write a function, () S ( m ) , that they think can be used to track the amount of steps after m minutes. Use the drop-down menus to explain why each function does or does not represent the amount of steps after m minutes.
The function S (m) = 105m represents the amount of steps after m minutes.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable) is known as a function.
We are given two functions.
Tim's function : S (m) = [tex]105^{m}[/tex]
This function cannot be used to find the amount of steps taken after m minutes.
Each minute, they take an additional 105 steps. Equal differences represent a linear relationship.
Kristin's function: S (m) = 105m
This function can be used to find the amount of steps taken after m minutes.
For every minute that passes, 105 more steps are take.
Hence, the function S (m) = 105m represents the amount of steps after m minutes.
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Help me! I need help with my homework! Ty! :)
Answer:763.02
Step-by-step explanation:
r=9
R=r+9=18
[tex]A=R^{2}\pi-r^{2}\pi = \pi (R^{2}-r^{2})=\pi =243\pi \\\pi =3.14\\243\pi=763.02[/tex]
Answer:
763.02
Step-by-step explanation:
Area of a circle is πr²
so the area of the whole circle is the sum of both radius
9+9 = 18
so Area = 3.14 × 18² = 1017.36
then we subtract the white part to leave the shaded part
area of the white circle = 3.14 × 9² = 254.34
then 1017.36 - 254.34 = 763.02
54000 rounded to the nearest ten
54,000 rounded to the nearest ten is 54,000 because the zeros after the 4 are insignificant
What is approximation?Rounding off in math is the process of approximating a number to a certain degree of accuracy. This involves changing the value of a number to one that is simpler or easier to work with, while still maintaining an acceptable level of accuracy.
For example, rounding off 3.75 to the nearest whole number would give you 4, while rounding off 3.75 to the nearest tenth would give you 3.8.
Rounding off 54000 to the nearest ten is still 54000 because the zeros after the 4 are insignificant
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Linas builds a 4 × 4 × 4 cube using 32 white and 32 black 1 × 1 × 1 cubes. He arranges
the cubes so that as much of the surface of his large cube is white. What fraction of the
surface of his cube is white?
Answer: We can start by noticing that the total number of small cubes used is 64, which is the same as the total number of unit squares on the surface of the large cube. To maximize the white surface area, we want to arrange the cubes in a way that maximizes the number of white faces on the surface.
Each small cube has 6 faces, so there are a total of 6 x 64 = 384 faces. Half of these faces are white and half are black, since we have an equal number of white and black cubes. Therefore, there are 192 white faces and 192 black faces.
Now, let's consider how the small cubes can be arranged to maximize the white surface area. If we arrange all the white cubes together in a 4 x 4 x 4 block, then all the faces of this block that are adjacent to a black cube will be black, and all the faces that are adjacent to another white cube will not contribute to the surface area. This leaves only 16 white faces that contribute to the surface area.
On the other hand, if we alternate white and black cubes in each layer of the cube, then all the faces that are adjacent to a black cube will be white, and all the faces that are adjacent to another white cube will be black. This maximizes the white surface area. Specifically, there are 6 layers of the cube, and each layer has 16 white faces (4 along the top and bottom and 4 along each side). Therefore, there are a total of 6 x 16 = 96 white faces that contribute to the surface area.
So the fraction of the surface that is white is:
96 white faces / 384 total faces = 1/4
Therefore, one quarter of the surface area of the cube is white.
Step-by-step explanation:
Carmen's front porch is 7 feet wide and 12 feet long. Carmen wants to stain the wood on the porch next weekend. The stain costs $0.70 per square foot. How much will it cost to buy enough stain for the whole porch?
Answer: It will cost $58.80 to buy enough stain for the whole porch.
Step-by-step explanation: The area of Carmen's front porch is:
Area = length x width
Substituting the given values, we get:
Area = 12 ft x 7 ft
Area = 84 square feet
To find the cost of the stain, we need to multiply the area of the porch by the cost per square foot:
Cost of stain = Area x Cost per square foot
Cost of stain = 84 square feet x $0.70/square foot
Cost of stain = $58.80
An artist recreated a famous painting using a 6:1 scale. The dimensions of the scaled painting are 24 inches by 36 inches. What are the dimensions of the actual painting?
4 inches by 6 inches
18 inches by 30 inches
30 inches by 42 inches
144 inches by 216 inches
By using scale and prοpοrtiοn, the dimensiοns οf the actual painting are 144 inches² by 216 inches².
What are the scale and prοpοrtiοn?Scale refers tο the relatiοnship between the dimensiοns οf a scaled οbject and the cοrrespοnding dimensiοns οf the οriginal οbject. If an οbject is scaled dοwn tο half its οriginal size, then the dimensiοns οf the scaled οbject will be half οf the dimensiοns οf the οriginal οbject.
Prοpοrtiοn, οn the οther hand, refers tο the relatiοnship between twο οr mοre quantities that have the same ratiο. In οther wοrds, if twο quantities are in prοpοrtiοn, then their ratiο is cοnstant.
Tο find the dimensiοns οf the actual painting, we need tο "undο" the 6:1 scale.
If the scaled painting is 6 times smaller than the actual painting, then the actual painting is 6 times larger than the scaled painting.
Sο we can find the actual dimensiοns by multiplying the scaled dimensiοns by 6:
Actual width = 24 inches x 6 = 144 inches
Actual height = 36 inches x 6 = 216 inches
Therefοre, the dimensiοns οf the actual painting are 144 inches² by 216 inches².
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Write C/d = π.
Then show how this equation can be rewritten in two steps to write a formula for the circumference of a circle in terms of its radius.
The fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.
What is circumference οf a circle?The perimeter οf a circle οr ellipse is its circumference. That is, if the circle were οpened up and straightened οut tο a line segment, the circumference wοuld be the length οf the arc.
The equatiοn C/d = π relates the circumference (C) οf a circle tο its diameter (d) using the cοnstant pi (π).
we can use the relatiοnship between the diameter and the radius:
d = 2r
We can substitute 2r fοr d in the equatiοn C/d = π, giving us:
C/(2r) = π
We can then multiply bοth sides by 2r tο isοlate C:
C = 2πr
Therefοre, the fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.
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16 sin 10° sin 30° sin 50° sin 70° sin 90°
Answer:
2 √3
Step-by-step explanation:
The value of sin 90° is 1, so we can simplify the expression as:
16 sin 10° sin 30° sin 50° sin 70° sin 90° = 16 sin 10° sin 30° sin 50° sin 70°
We can use the identity sin (90 - x) = cos x to rewrite sin 70° as cos 20°:
16 sin 10° sin 30° sin 50° sin 70° = 16 sin 10° sin 30° sin 50° cos 20°
We can use the identity sin (180 - x) = sin x to rewrite sin 170° as sin 10°:
16 sin 10° sin 30° sin 50° cos 20° = 8 sin 10° [2 cos 20° sin 30° sin 50°]
We can use the identity sin (2x) = 2 sin x cos x to simplify the expression inside the brackets:
8 sin 10° [2 cos 20° sin 30° sin 50°] = 8 sin 10° [sin 100° - sin 20°]
We can use the identity sin (180 - x) = sin x to rewrite sin 20° as sin 160°:
8 sin 10° [sin 100° - sin 20°] = 8 sin 10° [sin 100° - sin 160°]
We can use the identity sin (x + y) = sin x cos y + cos x sin y to rewrite sin 100° as sin (60° + 40°):
8 sin 10° [sin 100° - sin 160°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 160°]
We can use the identity sin (180 - x) = sin x to rewrite sin 160° as sin 20°:
8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°] = 8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]
Now, we can use the values of sin 60°, cos 40°, and sin 20°, which are:
sin 60° = √3/2
cos 40° = √[(1+cos 80°)/2] = √[(1+sin 10°)/4]
sin 20° = sin (60° - 40°) = sin 60° cos 40° - cos 60° sin 40° = (√3/2)(√[(1+sin 10°)/4]) - (1/2)sin 10°
Substituting these values into the expression, we get:
8 sin 10° [sin 60° cos 40° + cos 60° sin 40° - sin 20°]
= 8 sin 10° [√3/2 × √[(1+sin 10°)/4] + 1/2 × sin 10° - (√3/2) × √[(1+sin 10°)/4]]
= 2 √3 sin 10° √[(1+sin 10°)/2]
Therefore, the value of the expression is:
16 sin 10° sin 30° sin 50° sin 70° sin 90° = 2 √3
BOOMER GENERATION: At 84%, Boomers are the highest amongst all the generations that want to shop in-store.
In a sample size of 75 people in the Boomer Generation, estimate how many of them prefer to shop in-store.
Sketch a visual to represent this data.
To estimate how many Boomers prefer to shop in-store, we can use the percentage given and apply it to the sample size of 75 people.
84% of 75 = 0.84 x 75 = 63
Therefore, we can estimate that approximately 63 Boomers out of a sample size of 75 prefer to shop in-store.
To represent this data visually, we can create a simple bar graph. The x-axis can represent the different generations and the y-axis can represent the percentage of people who prefer to shop in-store. We can then plot the data for Boomers as a bar that reaches 84% on the y-axis.
Find the area of the shaded region.
Answer:
18.2 square miles
Step-by-step explanation:
r = radius of circle
= 4 miles
Area of shaded region = Area of sector
= [tex]\frac{AngleOfSector}{360}[/tex] ×[tex]\pi r^{2}[/tex]
= [tex]\frac{130}{360}[/tex] × [tex]\pi (4)^{2}[/tex]
= 18.2 [tex]mi^{2}[/tex] (Rounded to 3 significant figures)
Complete the sentences about simplifying this expression once you given a value for b. 24 + b/b + 24 x 53.72
Answer:
Step-by-step explanation:
To simplify the expression 24 + b/b + 24 x 53.72,
we first need to substitute the given value of b into the expression.
For example, if b is equal to 5, we can replace all instances of b with 5 to get 24 + 5/5 + 24 x 53.72.
Next, we can simplify the division by evaluating 5/5, which equals 1.
Then, we can multiply 24 and 53.72 to get a product of 1288.28.
Finally, we can add the simplified terms to get a final result of 1312.28.
Therefore, the simplified expression, given that b is equal to 5, is 1312.28.
Find the area of the shaded region. Round to the nearest tenth.
(you will not be able to enter the units - just the number answer)
25 ft
Answer:
Step-by-step explanation:
its 10.7
1x1 *why is that ok ut number
(Giving brainlist for the right answer)
Consider the continuous extraction of benzoic acid from a mixture of benzoic acid and toluene, using water as the extracting solvent. The acidic- toluene mixture in the rate of 100 L/min and the and water in the rate of 110 L/min are fed into a tank where they are stirred efficiently, and the mixture is then pumped into a second tank where it is allowed to settle into two layers. The concentration of acid in the inlet mixture is 0.12 kg/L, and the volume of the tank is 120 L. The upper organic phase and the lower aqueous phase are removed separately.
The amount of acid in water is linear with amount of acid in the toluene as y=5x
Determine the acid has passed into the solvent phase after 20 minutes.
A list of simplifications for the idealized problem (model) follows:
1. Combine the two tanks into a single stage.
2. Express stream-flow rates on solute-free basis.
3. Assume steady flow rate for each phase.
4. Assume that toluene and water are immiscible.
5. Assume that feed concentration is constant.
6. Assume that the mixing is efficient enough such that the two streams leaving the stage are always in equilibrium with each other and can be expressed as y=mx , where m is the distribution coefficient, x is the concentration of benzoic acid leaving the stage in the organic phase, and y is the aqueous phase benzoic mass concentration.
Answer:
Amount of benzoic acid in the solvent phase = 0.303 kg/L * 100 L/min * 20 min = 606 g.
Step-by-step explanation:
To determine the amount of benzoic acid that has passed into the solvent phase after 20 minutes, we need to use the given simplifications to set up a mass balance equation.
Let's express the stream-flow rates on a solute-free basis, which means that we consider only the flow rate of the solvent (water) and the flow rate of the toluene (ignoring the mass of benzoic acid in each stream). Let Fw be the flow rate of water and Ft be the flow rate of toluene.
Since the toluene and water are immiscible, we can assume that the volume of the two phases leaving the tank is the same as the volume of the mixture entering the tank (which is 100 L/min). Let V be this volume, which is also equal to the volume of the tank (120 L).
Let x be the concentration of benzoic acid leaving the stage in the organic phase (i.e., the solvent phase), and y be the mass concentration of benzoic acid in the aqueous phase.
From the given simplification, we have:
y = 5x
Let's use the mass balance equation to relate the flow rate of benzoic acid entering the tank to the flow rate of benzoic acid leaving the tank:
FtCt,in = VxCt,out + (FwCw,in - Fw*Cw,out)*y
where Ct,in and Cw,in are the concentrations of benzoic acid in the toluene and water entering the tank, respectively, and Ct,out and Cw,out are the concentrations of benzoic acid in the toluene and water leaving the tank, respectively.
We can assume that the feed concentration is constant, so Ct,in = 0.12 kg/L. We also know that the flow rate of the toluene and water entering the tank are 100 L/min and 110 L/min, respectively.
The concentration of benzoic acid in the water leaving the tank is given by:
Cw,out = y/5 = x/5
Since the flow rate of each phase is steady, we can assume that the concentration of benzoic acid in the toluene leaving the tank is the same as the concentration of benzoic acid in the toluene entering the tank, which is also 0.12 kg/L.
Substituting these values into the mass balance equation, we get:
1000.12 = 120x*0.12 + (110 - 120)*y
Simplifying, we get:
12 = 14.6x + 10y
Substituting y = 5x, we get:
12 = 39.6x
x = 0.303 kg/L
Therefore, the concentration of benzoic acid leaving the tank in the organic phase is 0.303 kg/L.
To find the amount of benzoic acid that has passed into the solvent phase after 20 minutes, we need to multiply the concentration by the flow rate of the toluene:
Amount of benzoic acid in the solvent phase = 0.303 kg/L * 100 L/min * 20 min = 606 g.
We can use the mass balance equation to solve this problem. Let x be the concentration of benzoic acid leaving the stage in the organic phase (in kg/L) and y be the concentration of benzoic acid in the aqueous phase (in kg/L). Then we have:
Mass of benzoic acid entering the stage per minute = Mass of benzoic acid leaving the stage per minute
The mass of benzoic acid entering the stage per minute is:
100 L/min x 0.12 kg/L = 12 kg/min
The mass of benzoic acid leaving the stage per minute can be expressed in terms of x and y as:
100 L/min x (0.12 kg/L - x) + 110 L/min x y = (100 + 110) L/min x m x x
Simplifying and using the given linear relationship between y and x, we get:
12 - 100x + 110(5x) = 210x
Solving for x, we get:
x = 0.034 kg/L
Therefore, the concentration of benzoic acid in the organic phase after 20 minutes is 0.034 kg/L.
5x-12 ≤3x-4 solve it and gimme the response
Answer:
x ≤ 4
Step-by-step explanation:
5x-12 ≤3x-4
collect like terms
5x - 3x ≤ -4 + 12
2x ≤ 8
2x/2 ≤ 8/2
x ≤ 4
Answer:
x [tex]\leq[/tex] 4
Step-by-step explanation:
5x - 12 [tex]\leq[/tex] 3x - 4 Subtract 3x from both sides
2x - 12 [tex]\leq[/tex] -4 Add 12 to both sides
2x [tex]\leq[/tex] 8 Divide both sides by 2
x [tex]\leq[/tex] 4
Helping in the name of Jesus.
A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 4 stocks?
If you own 4 stocks, there are 81 possibilities that could occur, according to the provided assertion.
The probability calculation is what?In most cases, the probability is described as the ratio of favourable outcomes to all results in the survey region. Probability of an occurrence P(E) = (Number of positive events) is how it is stated (Sample space).
For each of the 4 stocks, there are 3 possibilities - up, down, or unchanged. Therefore, the total number of possibilities for owning 4 stocks is 3 x 3 x 3 x 3, which is equal to 81.
So there are 81 possible scenarios if you own 4 stocks.
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Micah bought 1 pair of jeans for $24 and 3 shirts for $9 each. How much did Micah spend in all?
the answer to this question..
Answer idek
Step-by-step explanation: why
please help me with this
Step-by-step explanation:
the total cost is $200.
the given function calculates the total costs.
so, all we need to do is set the function result and calculate backwards to the necessary value of m :
200 = 0.75m + 50
150 = 0.75m
m = 150/0.75 = 200
the van must have been rented for 200 miles to have cost $200.
CAN SOMEONE HELP WITH THIS QUESTION?✨
By answering the presented question, we may conclude that As a result, function the value of f'(-1) is -9.
what is function?Mathematicians examine numbers and their variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "function" refers to the relationship between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible functions are on functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions.
We are given the function f(x) = -3x3 - 4 and asked to calculate the value of f' (-1).
To determine f'(-1), calculate the derivative of f(x) with respect to x and evaluate it at x = -1.
f(derivative )'s is provided by:
[tex][-3x3 - 4] f'(x) = d/dx = -9x^2[/tex]
We can now calculate f'(-1) by entering x = -1:
[tex]f'(-1) = -9(-1) (-1)\\a^2 = -9[/tex]
As a result, the value of f'(-1) is -9.
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which function has the same end behavior as f = -x -4 - 1?
The end behavior of the function f(x) = -1/x - 4 is given as follows:
As x -> ∞, f(x) -> -4.
How to obtain the end behavior of a function?The end behavior of a function refers to the behavior of the function as the input variable (usually denoted as "x") approaches positive or negative infinity. To obtain the end behavior of a function, we look at the highest degree term in the function, which will determine the general shape of the graph.
The function for this problem is defined as follows:
f(x) = -1/x - 4.
As x goes to infinity, the term 1/x goes to zero, hence the end behavior of the function is defined as follows:
f(x) = 0 - 4
f(x) = 4.
Missing InformationThe problem is incomplete, hence I found the end behavior of the function f(x) = -1/x - 4.
You should use the same procedure to find the end behavior of the function in your problem.
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A plumber charges $ 65 for a diagnostic check. After the check it was $85 per hour for the work. With $320 in your wallet, how many hours can you afford?
Answer:
3 hours
Step-by-step explanation:
65 - 85x = 320
85x = 320 - 65
85x = 255
x = 255 / 85
x = 3
Which of the following expressions can you multiply using the FOIL Method? Check all that apply
3x(2x^2+5x-4)
(x-1)(x^2+2x*5)
(6x-5)(x+4)
(x+g)(x-h)
Answer:
Option C
Step-by-step explanation:
(a) find the critical numbers of (if any), (b)
find the open interval(s) on which the function is increasing or
decreasing, (c) apply the First Derivative Test to identify all
relative extrema, and (d) use a graphing utility to confirm your
results
(a) OIne critical number that is x = 1
(b) Function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).
(c) at x = 1, this critical number corresponds to a relative minimum.
(d) The graph is given in the attachment.
What is derivative of function?The rate change of the function at a specific point
a) The values of x where the derivative of the function equals zero or does not exist.
f'(x) = -4x + 4
Setting f'(x) equal to zero gives:
-4x + 4 = 0
-4x = -4
x = 1
So the critical number is x = 1.
(b) we need to examine the sign of the derivative on either side of the critical number.
When x < 1, f'(x) is negative, indicating that the function is decreasing.
When x > 1, f'(x) is positive, indicating that the function is increasing.
Therefore, the function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).
(c) all relative extrema, we examine the sign of the derivative in the neighborhood of the critical number x = 1. Since f'(x) changes sign at x = 1, this critical number corresponds to a relative minimum.
(d) The graph is given in the attachment.
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70 POINTSS)NEED FAST ANSWERS)
A square with a side length of 42 meters was created from a square with a side length of 3.5 meters using a scale factor. What is the scale factor?
12:1
24:1
144:1
147:1
Answer:
multiply all of them then add all of them then divide by the lowest number
12:1 is the scale factor
3.5 ÷ 3.5 = 1 and 142 ÷ 3.5 =123.5 so 42:123.5 ratio simplified is 12:1
Looking at the question, to find the scale factor we are going to divide 42 by 3.5 which is 12. To check our work we will do 1 times 3.5 which is 42.
Why is it not 147:1? Well, scale factoring means that in two similar geometric figures, the scale factor is the ratio of their corresponding sides, dividing the two corresponding lengths of the sides will gives the ratio
To check go to:
https://www.ginifab.com/feeds/cm_to_inch/scale_factor_calculator.html
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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
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John ordered 330 units of a product for $495 then he reduced his order to 270 units how much money does John have to pay for is 270 units
Answer:
405$
Step-by-step explanation:
First we need to find out what is the price of one unit:
330 units - 495$
1 unit - x $
Use the property of proportion to find x:
x = 1 × 495 / 330 = 1,5$ (for one unit)
Then multiply this price by 270 (since it's the new quantity of units):
270 × 1,5 = 405$
A 984-foot tree has grown at a constant rate each year. In the equation below, t is the age of the tree in years.
24t = 984
What is the unit rate in the equation above?
A.
24 feet per year
B.
41 feet per year
C.
984 feet per year
D.
960 feet per year
The unit rate of 24t = 98 is A. 24 feet per year.
What is unit rate?Unit rate is the rate of increase or decrease of a unit of item
Now, since a 984-foot tree has grown at a constant rate each year. Since we have the equation 24t = 984, wheret is the age of the tree in years.
To determine the unit rate, we compare it with the function y = mx where m = gradient
Now, the gradient is the rate of change of y per unit of x.
Now, comparing y = mx with 24t = 984,
y = 984, m = 24 and t = xSince m = 24 which is the gradient which is also the unit rate.
So, the unit rate of 24t = 98 is A. 24 feet per year.
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what is an irrational number between 5.25and 5.26
Answer:
One example of an irrational number between 5.25 and 5.26 is:
√139 ≈ 11.78982612...
Since the decimal representation of √139 goes on forever without repeating, it is an irrational number.
Step-by-step explanation:
Nakia is an architect designing a house with a peaked roof. She is trying to decide what the limitations are on her design. If AB is 8 feet and triangle ABC will be isosceles, describe the possible lengths for AC.
The possible calculated length of the segment AC is a length of any value that exceeds around 7.15 feet.
How to use Pythagoras Theorem?If triangle ABC is an isosceles triangle, then the length of AC must be equal to the length of BC.
Let's denote the length of AC as "x".
To find the length of the diagonal line segment referred to as BD, which represents the height of the peaked roof, we can use the Pythagorean theorem:
BD² = AB² - (AC/2)²
BD² = 8² - (x/2)²
BD² = 64 - x²/4
In order for the roof to be peaked, BD must be less than x, otherwise the roof would be flat.
Therefore, we can set up the inequality:
x√(64 - x²/4) < x
64 - x²/4 < x²
Multiplying both sides by 4 gives:
256 - x² < 4x²
5x² > 256
Dividing both sides by 5 gives:
x² > 51.2
x > √(51.2)
x > 7.15 feet
As a result, any value greater than the square root of 51.2 (approximately 7.15 feet) is a possible length for AC.
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The possible lengths for AC are any values greater than 7.15 feet.
How to use Pythagoras theorem?We are given that the triangle ABC is an isosceles triangle. This means that the length of segment AC must be equal to the length of segment BC.
Let x denote the length of AC.
With the aid of the Pythagorean theorem, the length of the diagonal line segment BD which denotes the height of the peaked roof is:
BD² = AB² - (AC/2)²
BD² = 8² - (x/2)²
BD² = 64 - x²/4
If the roof is to be peaked, then the length of segment BD must be less than x. Thus, we generate the inequality:
BD < x
√(64 - (x²/4)) < x
Square both sides to get:
64 - x²/4 < x²
256 - x² < 4x²
5x² > 256
x² > 51.2
x > √(51.2)
x > 7.15 ft
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can someone solve this question for me? hurry please
The graph of the system of linear inequality is attached below
What is the graph of the inequalitya. Graphing the system of linear inequality, the solutions are (0.7, -3.35)
b. To prove that the inequality remains true at any given point, we can use a test point. We will choose the point (0,0) as our test point.
For the first inequality, plugging in (0,0) gives:
4(0) + 8(0) ≤ -24
0 ≤ -24
This is clearly false, so (0,0) is not a solution to the first inequality. This means that any point below the line 4x + 8y = -24 will not satisfy the inequality.
For the second inequality, plugging in (0,0) gives:
12(0) - 4(0) < 5
0 < 5
This is true, so (0,0) is a solution to the second inequality. This means that any point to the left of the line 12x - 4y = 5 will satisfy the inequality.
Therefore, the system of inequalities will only be satisfied by points that are both below the line 4x + 8y = -24 and to the left of the line 12x - 4y = 5. We can verify this visually by graphing the two lines and shading in the appropriate regions. Any point in the shaded region will satisfy both inequalities, and any point outside of the shaded region will not satisfy at least one of the inequalities.
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