Answer:
V(t) = 25000 * (0.815)^t
The depreciation from year 3 to year 4 was $2503.71
Step-by-step explanation:
We can model V(t) as an exponencial function:
V(t) = Vo * (1+r)^t
Where Vo is the inicial value of the car, r is the depreciation rate and t is the amount of years.
We have that Vo = 25000, r = -18.5% = -0.185, so:
V(t) = 25000 * (1-0.185)^t
V(t) = 25000 * (0.815)^t
In year 3, we have:
V(3) = 25000 * (0.815)^3 = 13533.58
In year 4, we have:
V(4) = 25000 * (0.815)^4 = 11029.87
The depreciation from year 3 to year 4 was:
V(3) - V(4) = 13533.58 - 11029.87 = $2503.71
The depreciation from year 3 to year 4 was $2503.71
Exponential functionThe standard exponential function is expressed as:
[tex]y=a(1\pm r)^t[/tex]
r is the rate
t is the time
Given the following parameters
a = 25000,
r = -18.5% = -0.185,
Substitute into the formula
y = 25000 * (1-0.185)^t
y = 25000 * (0.815)^t
In year 3, we have:
y(3) = 25000 * (0.815)^3 = 13533.58
In year 4, we have:
y(4) = 25000 * (0.815)^4 = 11029.87
The depreciation from year 3 to year 4 was:
y(3) - y(4) = 13533.58 - 11029.87 = $2503.71
The depreciation from year 3 to year 4 was $2503.71
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HEEEEEELP PLLLEEEEEEEZZZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Lara has a triangle that has side lengths of 26, 34, and 58. She wants to reduce the triangle by one half, so she divides each side and each angle measurement by 2.
What error did Lara make?
Lara should have multiplied each measurement by 1/2.
Lara should have only divided the angles by 2 in order to reduce the triangle.
Lara should have only divided the side lengths by 2 in order to reduce the triangle.
Lara did not make an error.
C is correct,
A is wrong as it halves both the angles and lengths by two which is the same as what she did in the first place so it cannot be correct.
B is also wrong for a similar reason, a triangle cannot have less than 180 degrees, which is impossible as the angles just change naturally which is why all triangles must have 180 degrees, which is the reason she is wrong in the first place.
And D is just incorrect, if she wanted to have shorter sides she should have only decreased all the lengths as it the the ratio of angles that determine the shape of a triangle while the sum of all angles is 180 degrees.
Answer: C
Step-by-step explanation:
On rainy days, Francesca likes to ride the stationary bike at the gym. Yesterday, she rode for 30 minutes and covered 6 miles. Today, she plans to ride 8 miles.
If she rides at the same rate, how many minutes will it take Francesca to ride today?
Answer:
6/30=0.2 so 0.2 miles per minute
8/0.2=40 minutes
You can also check 30/6=5 so the conversion is 5
8 x 5 = 40 minutes.
Step-by-step explanation:
Hope this helps can I have brainliest
If on rainy days, Francesca likes to ride the stationary bike at the gym. Yesterday, she rode for 30 minutes and covered 6 miles. Today, she plans to ride 8 miles. If she rides at the same rate, how many minutes will it take Francesca to ride today will be 40 minutes
First step is to formulate
8×30÷6
Now let determine the how many minutes will it take Francesca to ride today
Number of minutes=8×30÷6
Number of minutes=8×6
Number of minutes=40 minutes
Inconclusion if on rainy days, Francesca likes to ride the stationary bike at the gym. Yesterday, she rode for 30 minutes and covered 6 miles. Today, she plans to ride 8 miles. If she rides at the same rate, how many minutes will it take Francesca to ride today will be 40 minutes.
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What two numbers multiply to be 72 and add up to be 27
Answer:
9x8=72 and 25+2=27
Step-by-step explanation:
1x9=9
2x9=18
3x9=27
4x9=36
5x9=45
6x9=54
7x9=63
8x9=72
brainleist please i really need it
Tara is shown a picture of a dart board along with some dimensions. She knows that each triangular section in the dartboard is congruent. What is the approximate length of arc x?
Answer:
The approximated length of arc x is 4 inches ⇒ C
Step-by-step explanation:
The diameter of the outer circle is 28 inchesThere is a boundary with width 2 inchesThat means the diameter of the inner circle is less than the diameter of the outer circle by 4 inches (2 in from each side)
The diameter of the inner circle = 28 - 4 = 24 inchesThe circumference of the inner circles formed from 20 congruent arcs of length x inches
The circumference of the inner circle = 20 xNow let us find x
The formula of the circumference of a circle is C = π d, where d is the diameter of the circle
∵ The diameter of the inner circle is 24 inches
∴ d = 24
∴ C = 24 π
∵ C = 20 x
- Equate 20 x by 24 π
∴ 20 x = 24 π
- Divide both sides by 20
∴ x = 3.769911184
- Round it to the nearest unit
∴ x ≅ 4
The approximated length of arc x is 4 inches
Use Cramer's Rule to find the determinant of the coefficient matrix of this system of equations.
Answer:
Determinant = -12
Step-by-step explanation:
rewrite the system as
-2 = 2x - 3y + 0z
0 = 0x + y - 2z
1 = -3x + 2y - z
then the coefficient matrix is
{ [2, -3, 0]
[0, 1, -2]
[-3, 2, -1] }
to find determinant
{ [2, -3, 0] , 2, -3
[0, 1, -2] , 0, 1
[-3, 2, -1] }, -3, 2
determinant = 2*1*-1 + (-3 * -2 * -3) + (0*0*2) - 0 - (2*-2*2) - 0
determinant = -2 - 18 + 0 - 0 + 8 = -12
A fair coin is flipped eight times. What is the probability of the coin landing heads up exactly 2 times?
Answer:
50%
Step-by-step explanation:
no matter how many times it is flip you will get heads or tails.
Answer:
50%
Step-by-step explanation:
two sides 1/2= 50%
find the diameter of a circle with and area of 90.25 pi m square
Answer:
The diameter of the circle is 19 m
Step-by-step explanation:
The formula of the area of a circle is A = π r², where r is its radius
To find the diameter from the area of the circle equate the formula of the area by the value of the area to find r, then multiply r by 2 because the diameter of a circle is equal twice its radius
∵ The area of the circle is 90.25 π m²
∵ A = π r²
- Equate A by 90.25 π
∴ π r² = 90.25 π
- Divide both sides by π
∴ r² = 90.25
- Take √ for both sides
∴ r = 9.5
∵ The diameter of a circle is twice its radius
∴ d = 2 r
- Substitute r by 9.5
∴ d = 2(9.5)
∴ d = 19
The diameter of the circle is 19 m
Answer:
The diameter would be 19 m
Step-by-step explanation:
hope i helped
Find the length of the intercepted arc with a central angle of measure θ=π/6 on a circle with radius r = 3. Round to the nearest tenth.
Answer:
Step-by-step explanation:
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 3
θ = π/6
2π = 360 degrees
π = 360/2 = 180
Therefore,
θ = 180/6 = 30 degrees
Therefore,
Length of arc = 30/360 × 2 × 3.14 × 3
Length of arc = 1.6 to the nearest tenth
Final answer:
To find the length of the intercepted arc on a circle with radius 3 and a central angle of π/6, calculate using the formula s = rθ. The result is approximately 1.6 units after rounding to the nearest tenth.
Explanation:
The question asks to find the length of the intercepted arc given a central angle of measure θ=π/6 on a circle with radius r = 3 and to round the answer to the nearest tenth. To calculate the arc length (θ), we use the formula s = rθ, where θ is measured in radians. Given θ=π/6 and r=3, the arc length s is therefore 3*(π/6)= π/2. To get a numerical answer, substitute π with approximately 3.14159, resulting in s = (3*3.14159)/6 which simplifies to s ≈ 1.57. Rounding to the nearest tenth gives us an arc length of 1.6 units.
What is the product? StartFraction 2 y Over y minus 3 EndFraction divided by StartFraction 4 y minus 12 Over 2 y + 6 EndFraction
To simplify the expression, first rewrite the fractions:[tex]\( \frac{2y}{y - 3} \) and \( \frac{2(y - 3)}{y + 3} \)[/tex]. Then, divide the first fraction by the reciprocal of the second, yielding[tex]\( \frac{2y}{y - 3} \).[/tex]
let's simplify the expression:
[tex]\[ \frac{\frac{2y}{y - 3}}{\frac{4y - 12}{2y + 6}} \][/tex]
First, we'll simplify the fractions within the larger fractions:
[tex]\[ \frac{2y}{y - 3} = \frac{2y}{y - 3} \times \frac{(y - 3)}{(y - 3)} = \frac{2y(y - 3)}{(y - 3)^2} = \frac{2y^2 - 6y}{y^2 - 6y + 9} \][/tex]
[tex]\[ \frac{4y - 12}{2y + 6} = \frac{4(y - 3)}{2(y + 3)} = \frac{2(y - 3)}{y + 3} \][/tex]
Now, we'll divide the first fraction by the second fraction. This is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{\frac{2y^2 - 6y}{y^2 - 6y + 9}}{\frac{2(y - 3)}{y + 3}} = \frac{2y^2 - 6y}{y^2 - 6y + 9} \times \frac{y + 3}{2(y - 3)} \][/tex]
Now, let's cancel out common factors:
[tex]\[ = \frac{2y(y + 3)}{(y - 3)(y + 3)} \times \frac{y + 3}{2(y - 3)} \][/tex]
[tex]\[ = \frac{2y}{y - 3} \][/tex]
So, the simplified expression is [tex]\( \frac{2y}{y - 3} \).[/tex]
there are 9 children in the classroom each student will get 6 pencils how many pencils will the teacher have to give out
Answer: 54
Step-by-step explanation:
Answer:
The teacher will have to give out 54 pencils
Step-by-step explanation:
there 9 children in the class. each student gets 6 pencils.
9 times 6 = 54
For every four dollars that jamie saves in her account , her sister saves five dollars in her account . If Jamizne has $20.00 in her account, how much money does her sister have in her account?
Final answer:
By using the ratio of 4:5 for the amounts that Jamie and her sister save, we calculate that since Jamie has $20, her sister has $25 in her account.
Explanation:
To find out how much money Jamie's sister has in her account, we need to first understand the ratio of the amounts they save. For every four dollars that Jamie saves, her sister saves five dollars. This gives us a ratio of 4:5.
Since Jamie has $20 in her account, we can determine how many times four dollars fits into twenty dollars to find out how many 'units' of savings Jamie has made. We do this by dividing 20 by 4, which equals 5. So, Jamie has saved 5 units of 4 dollars each.
Knowing that each unit for Jamie's sister is $5, we calculate the total amount for her sister by multiplying 5 units with the sister's $5, which equals $25. Therefore, Jamie's sister has $25 in her account.
Final answer:
For every $4 Jamie saves, her sister saves $5. Jamie has $20, which is equal to 5 units of $4. Therefore, Jamie's sister has saved 5 units of $5, which amounts to $25.
Explanation:
The question asks how much money Jamie's sister would have in her account, given that Jamie has $20 and for every four dollars that Jamie saves, her sister saves five dollars. To find the amount Jamie's sister has saved, we use the ratio of their savings. Since Jamie has $20 and saves $4 for every $5 her sister saves, we can calculate the amount Jamie's sister has saved using the following steps:
First, determine how many 'four dollar' units Jamie has saved. She has saved $20, so that's $20/$4 = 5 units.
Since Jamie's sister saves $5 for each of these units, we multiply the number of units by $5 to find her savings, which is 5 units * $5/unit = $25.
Therefore, Jamie's sister has $25 in her account.
What is the interest on $3,500 borrowed for two years at 2.5% interest?
Answer:
turn the percentage into a decmial and then multiply the money
help on this please !! trig ratios
Answer: 0.72
Step-by-step explanation: I’ve drawn the triangle out and have assumed that 21 is adjacent and 29 is the hypotenuse. In that case, 21/29 = 0.724
One third of a number increased by 7 is five. What is the number?
Final answer:
To solve this problem, we can set up an equation and solve it to find the number. The number is -6.
Explanation:
To solve this problem, let's set up an equation. Let's assume the number is represented by x. The problem states that one third of the number increased by 7 is five, so we can write the equation as:
(1/3)x + 7 = 5
To solve for x, we can subtract 7 from both sides of the equation:
(1/3)x = 5 - 7
Next, we simplify the right side of the equation:
(1/3)x = -2
Finally, to isolate x, we multiply both sides of the equation by 3:
x = -2 * 3
Therefore, the number is -6.
James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a
radius of 2 cm. One tray makes 6 spheres.
What is the total volume of ice the tray can make at one time?
Either enter a exact answer in terms of IT or use 3.14 for T.
Each sphere of ice has a radius of 2cm
one tray makes 6 spheres
What is the total volume of ice the tray can make at one time?
Total volume of each sphere is 33.51 cm^3
The tray can hold 6 of these at a time
33.5 * 6
201 cm^3 total volume of ice that the tray can make at one time
Written in pi
64 cm^3
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Answer: Its 64[tex]\pi[/tex]!!!
Step-by-step explanation:
A company opened in 1998 and turned a profit its first year. The company's revenues increased annually thereafter. Which of the
following functions could model this situation where x represents the number of years in operation, and f(x) represents the
company's annual revenue [in millions]?
Answer:
B. f(x) = 884 • [tex]1.22^{x}[/tex]
Step-by-step explanation:
I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo
My answer:
Given that:
A company opened in 1998 and turned a profit its first year, it means that the company has initial value in its function The company's revenues increased annually thereafter => it is an exponental function with the base number is greater than 1 x represents the number of years in operation => which means x is the domain of the company revenue functionf(x) represents the company's annual revenueThe following functions could model this situation is:
B. f(x) = 884 • [tex]1.22^{x}[/tex] where:
884 is a profit its first year
1.22 growth rate in revenue
x represents the number of years in operation
Hope it will find you well.
The Hydro water department has a monthly service charge of $10.10 and a volume charge of $1.58 for every 100 cubic feet of water. The total monthly cost is equal to the service charge plus the charge for the volume used during the month. If we let x represent the number of cubic feet of water (in hundreds) and y represent the total monthly cost, then we have: total monthly cost = volume charge + service charge y = 1.58x + 10.10 If the Johnson family used 200 ft3 less water this month than last month, then they can expect A. an increase in their water bill of $3.16. B. a decrease in their water bill of $3.16. C. a decrease in their water bill of $20.20. D. an increase in their water bill of $20.20.
Answer:
B. a decrease in their water bill of $3.16.
Step-by-step explanation:
Monthly service charge =$10.10
Volume charge = $1.58 for every 100 cubic feet of water.
Total monthly cost = 1.58x + 10.10
If the Johnson family used [tex]200ft^3[/tex] less water this month than last month, then they can expect a reduction in their bill by the Volume charge for [tex]200ft^3[/tex].
Volume Charge per [tex]100ft^3[/tex] of water = $1.58
Therefore: Volume Charge for [tex]200ft^3[/tex] of water = 2 X $1.58=$3.16
Therefore, the Johnson family can expect a decrease in their water bill of $3.16.
The correct answer is B) a decrease in their water bill of $3.16.
Given the equation: y = 1.58x + 10.10
Johnson family used 200 cubic feet less water.
200 cubic feet = 2 hundreds of cubic feet.
Change in water usage: [tex]\(\Delta x = -2\)[/tex]
Calculate the change in the water bill:
[tex]\(\Delta y = 1.58 \times \Delta x\)[/tex]
[tex]\(\Delta x = -2\): \(\Delta y = 1.58 \times (-2)\)[/tex]
[tex]\(\Delta y = -3.16\).[/tex]
The water bill will decrease by $3.16.
Correct answer: B. a decrease in their water bill of $3.16.
A rectangular prism aquarium holds 64 gallons of water. A similarly shaped aquarium holds 8 gallons of water. If a 1.5 ft2 cover fits on the smaller tank, what is the area of a cover that will fit on the larger tank
Answer:
The area of a cover that will fit on the larger tank is 6 square inches
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its Volumes is equal to the scale factor cubed
Let
z ---> the scale factor
so
[tex]z^3=\frac{64}{8}=8[/tex]
[tex]z=2[/tex]
step 2
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area of a cover that will fit on the larger tank
y ---> the area of a cover that will fit on the smaller tank
so
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]z=2\\y=1.5\ ft^2[/tex]
substitute the given values
[tex]2^2=\frac{x}{1.5}[/tex]
solve for x
[tex]x=4(1.5)=6\ ft^2[/tex]
The area of the cover that will fit on the larger aquarium is approximately 12 square feet, calculated by multiplying the area of the smaller cover by the square of the scaling factor for linear dimensions (≈ 2.83) due to the difference in volume.
Explanation:Understanding Area Scaling in Rectangular PrismsTo find the area of a cover that will fit on the larger aquarium, we begin by understanding that the area scales by the square of the linear dimensions.
Since the volume of the larger aquarium is 64 gallons and the smaller one is 8 gallons, the volume scales by a factor of 64/8 = 8. Taking the square root of 8 gives us the scaling factor for the linear dimensions, which is sqrt(8) ≈ 2.83. The larger tank's cover will therefore need to increase by this scaling factor squared for its area.
To calculate the area of the larger tank's cover, we multiply the area of the smaller cover by this scaling factor squared: 1.5 ft2 * 2.832 ≈ 12 ft2. Thus, the cover for the larger tank should be approximately 12 ft2 in area. This demonstrates the concept that area is proportional to the square of the linear dimensions when scaling similar shapes.
Mikayla bought five shirts at $x three of the five came with a matching top for an additional $9 each. Write and simplify an expression that represents the total cost of her purchase
Answer:
The simplified expression that represents the cost of her purchase is "5x + 27"
Step-by-step explanation:
Since Mikayla bought five shirts each costing $x we need to multiply the number of shirts by the cost, so 5*x, but since three of these shirts came with and additional top that costs $9 we need to take those into account. So the expression that represents the cost of her purchase is:
cost of purchase = 5*x + 3*9
cost of purchase = 5x + 27
Answer:
5x + 27
Step-by-step explanation:
Since Mikayla bought five shirts each costing $x it would be 5x
->if three of the five came with a matching top for an additional $9 each, it would be 3 x 9.
therefore, the expression that represents the cost of her purchase is:
Total cost of purchase = 5x + (3 x 9)
Total cost of purchase = 5x + 27
Finding the coefficient a of the term in the expansion of the binomial.[tex](x^{2} + 3)^{12} ax^{8}[/tex]
Answer:
3,247,695
Step-by-step explanation:
We want the coefficient of the term with x^8
So Use Newton's Binomial Expansion formula
Formula is (x + y) ^n = Sum for i=0 to n (n choose i) x^(n-i)*y^i
here (x^2 + 3) ^ 12
( 12 choose i) * (x^2)^(12-i) * (3)^i
i needs to equal 8 for us to get x^8
(12 choose 8) * (x^2)^(12-8) * (3^8)
= (12 choose 8) * x^8 * (3^8)
so a = (12 choose 8) * [tex]3^{8}[/tex]
a = (12! /(8! * 4!) ) * [tex]3^{8}[/tex]
a = ( 12*11*10*9/ 4*3*2*1) * [tex]3^{8}[/tex]
a = (11*5*9) * [tex]3^{8}[/tex]
a = 11*5*9 * 6561
a = 3,247,695
Which unit of measurement can be used to express the volume of this prism
The unit of measure used to express the volume of a prism is cubic units correct option is c.
Volume refers to the amount of space occupied by a three-dimensional object. A prism, being a three-dimensional shape with length, width, and height, necessitates a measurement that encapsulates all three dimensions.
Prisms have a base shape that repeats through their height. Calculating volume involves finding the space enclosed within this repeating shape. By multiplying the area of the prism's base by its height.
Cubic units represent the volume of an object, akin to how square units represent area. They measure the number of unit cubes needed to fill the three-dimensional space within the prism. This measurement allows for precise quantification of space in a three-dimensional context.
complete the question
Which unit of measure can be used to express the volume of the prism?
a) unit squares
b) square units
c) cubic units
d) units
What is the yellow structure and what role does it play in a cell?
1) What are the zeros of f(x) = (x + 4)(x – 7)?
Choose 1 answer:
® -4 and 7
®
4 and - 7
©
(-4,0) and (7,0)
0
(4,0) and (-7,0)
The zeros of the function f(x) = (x + 4)(x – 7) are x = -4 and x = 7. These values are where the function intersects the x-axis and can be expressed as points (-4, 0) and (7, 0) on a graph.
Explanation:To find the zeros of the function f(x) = (x + 4)(x – 7), we need to determine the values of x that make f(x) equal to zero. This means each factor in the product must be set equal to zero and solved for x individually.
Setting the first factor equal to zero gives us x + 4 = 0, which simplifies to x = -4.
Similarly, setting the second factor equal to zero gives us x – 7 = 0, which simplifies to x = 7. Thus, the zeros of the function are x = -4 and x = 7.
These can be written as the ordered pairs (-4,0) and (7,0) when we consider them as points on the Cartesian plane where the function intersects te x-axis.
The correct choice from the options provided would be -4 and 7, which corresponds to the first option.
It is not necessary to provide the y-coordinates when identifying the zeros of a function, as by definition, they are points where the y-value is zero.
Circle O is shown. Line segments A O and B O are radii. The length of O B is 16 inches. Angle A O B has a measure of StartFraction pi Over 4 EndFraction In circle O, angle AOB measures radians. What is the length of arc AB? π in
Answer:
4
Step-by-step explanation:
edg
Answer:
4
Step-by-step explanation:
i just got it right
Leila has $134, and Dianne had $180. After both of them spent an equal amount of money shopping, Dianne had 3 times as much money as Leila. How much did each of them spend?
They spent $111 on shopping
Step-by-step explanation:
Let the amount they spent be 'a'
Leilas amount = $134
Diannes amount = $180
After they spent same amount on shopping dianne had 3 times as much money as Leila
180 - a = 3(134 - a)
180 - a = 402 - 3a
3a - a = 402 - 180
2a = 222
a = $111
They spent $111 on shopping
Add mix numbers Madison made a fruit salad . She used 3 1 fourth cups of straw berries and 2 1 fourths cups of blueberries. How many cups of berries did Madison use?
Answer:
1 1/4
Step-by-step explanation:
For the strawberries, we will have to multiply 3 by 1/4 to get the total amount of strawberries used.
1/4 * 3 = 3/4
For the blueberries, we will have to multiply 2 by 1/4 to get the total amount of blueberries used.
1/4 * 2 = 2/4
Simplify that to get 1/2
Now we need to add 3/4 and 1/2
3/4 + 1/2 = 5/4
Simplify that and we get our answer;
1 1/4
Explain how the exterior angle relates to the interior angles.
Answer: The exterior angle, D, is supplementary to the adjacent interior angle, C. Together, they form a straight line, measuring 180°. The measure of the remote interior angles, A and B are equal to the measure of the exterior angle D.
Step-by-step explanation: I just did the assignment.
Answer:
Sample answer: The exterior angle, D, is supplementary to the adjacent interior angle, C. Together, they form a straight line, measuring 180°. The measure of the remote interior angles, A and B are equal to the measure of the exterior angle D.
Step-by-step explanation:
The mean absolute deviation is 0.1 what conclusions can be drawn A. The data points are closer to the media. B. The data points are far from the median C. The data points are far from the mean D. The data points are close to the mean
Answer:
D. The data points are close to the mean
Step-by-step explanation:
given data
mean absolute deviation = 0.1
The mean absolute deviation is the average of the absolute deviations of the data points relative to the mean. This means that the mean absolute deviation is averaged through the data, telling how far each data point is. The small value of the mean absolute deviation indicates that the mean difference (absolute deviation) between the data points and the mean is small and therefore the data points are close to the mean. The large value of the mean absolute deviation indicates that the data points are far above the mean. so correct option is D. The data points are close to the mean
A rectangular photograph is 7 inches long and 6 inches wide. The photograph is framed using a material that is x inches wide. If the area of the frame and photograph combined is 156 square inches, what is the width of the framing material
Answer:
The width of the framing material is 3 inches
Step-by-step explanation:
we know that
The area of the frame and photograph combined is given by the expression
[tex]156=(7+2x)(6+2x)[/tex]
solve for x
Expanded the expression
[tex]156=42+14x+12x+4x^2\\4x^2+26x+42-156=0[/tex]
[tex]4x^2+26x-114=0[/tex]
solve the quadratic equation by graphing
using a graphing tool
The solution is x=3 in
see the attached figure
therefore
The width of the framing material is 3 inches
The width of the framing material is [tex]\( x = 3 \)[/tex] inches
Given:
- Length of the photograph = 7 inches
- Width of the photograph = 6 inches
- Width of framing material = x inches
- Area of frame and photograph combined = 156 square inches
The total length of the framed photograph would be [tex]\( 7 + 2x \)[/tex] inches, and the total width would be [tex]\( 6 + 2x \)[/tex] inches.
So, the area of the framed photograph is the product of its total length and total width:
[tex]\[ \text{Area of framed photograph} = (7 + 2x)(6 + 2x) \][/tex]
Given that the area of the framed photograph is 156 square inches, we set up the equation:
[tex]\[ (7 + 2x)(6 + 2x) = 156 \][/tex]
Expanding and simplifying:
[tex]\[ 42 + 14x + 12x + 4x^2 = 156 \][/tex]
[tex]\[ 4x^2 + 26x + 42 = 156 \][/tex]
[tex]\[ 4x^2 + 26x - 114 = 0 \][/tex]
Now, let's solve this quadratic equation for x . We can simplify it by dividing all terms by 2:
[tex]\[ 2x^2 + 13x - 57 = 0 \][/tex]
Using the quadratic formula:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
Where:
- a = 2
- b = 13
- c = -57
Plugging in the values:
[tex]\[ x = \frac{{-13 \pm \sqrt{{13^2 - 4(2)(-57)}}}}{{2(2)}} \][/tex]
[tex]\[ x = \frac{{-13 \pm \sqrt{{625}}}}{{4}} \][/tex]
[tex]\[ x = \frac{{-13 \pm 25}}{{4}} \][/tex]
So, we have two possible solutions for x:
[tex]\[ x_1 = \frac{{-13 + 25}}{{4}} = 3 \][/tex]
[tex]\[ x_2 = \frac{{-13 - 25}}{{4}} = -9 \][/tex]
Since the width of the framing material cannot be negative, we discard [tex]\( x_2 \).[/tex]
Therefore, the width of the framing material is [tex]\( x = 3 \)[/tex] inches.
The population of Brazil was 162,300,000 in 1995. It was growing at a rate of about 2% per decade. Predict the population, to the nearest hundred thousand, of Brazil in 2015
Answer:
The population is 168,900,000 to the nearest hundred thousand
Step-by-step explanation:
In this question, we are tasked with calculating the population of Brazil given its population in 1995 and her growth rate per decade.
Mathematically, we use an exponential function to calculate this population.
This can be written as P = I(1 + r)^n
where P is the population in 2015 which we are looking for,
I is the initial population which is 162,300,000
r is the rate of increase per decade given as 2% = 2/100 = 0.02,
n is the number of times between the years we are expecting this growth. The difference between the years 2015 and 1995 is 20 years which signifies 2 decades(1 decade is 10 years). Thus our n is 2
We plug these values into the equation above;
P = 162,300,000(1+0.02)^2
P = 162,300,000(1.02)^2
P = 168,856,920 which is 168,900,000 to the nearest hundred thousand