1930.54 can be written in standard form as 1.93054 × 10³. Option D is correct.
What is a standard form?A number can be written in standard form to make it simpler to read. It is frequently used for extremely high or extremely low figures. Mathematics and other science fields employ the use of standard form, which is similar to scientific notation.
When a decimal number is multiplied by a power of 10, it is said to be expressed in standard form.
Similar to scientific notation, standard form represents a number as a decimal number times a power of 10. (i.e a*10^b)
From the given information:
1930.54 can be written in standard form as 1.93054 × 10³
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what is the area of rectangle with length is 4/7 and width is 3/5
Answer: 12/35 units sqr
Step-by-step explanation: Multiply both values to find area and put proper units.
Answer:
Step-by-step explanation:
The area of a rectangle is given by the formula: area = length x width.
For a rectangle with length 4/7 and width 3/5, the area can be calculated as follows:
area = 4/7 x 3/5
= 12/35
So, the area of the rectangle with length 4/7 and width 3/5 is 12/35 square units.
Geometric number between 7 and 28.
Answer: 16
Step-by-step explanation:
The geometric number between 7 and 28 is 16. Geometric numbers are the numbers you get by multiplying by a factor. If we multiply by 2 for this common geometric sequence, we get 16:
1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16,16 * 2 = 32, etc.
7 < 16 < 28
Match the square root expression with it's correct simplified radical.
The square root expression with it's correct simplified radical can be matched as follow:
√45 = 3√5
√200 = 10√2
√80 = 4√5
√24 = 2√6
How to match the square root expression with it's correct simplified radical?
A simplified radical is a radical expression in which the radicand (the expression inside the square root symbol) has been simplified as much as possible. For example, the simplified form of √8 is 2√2.
√45 = √(9*5) = √9 * √5 = 3 * √5 = 3√5
√200 = √(100*2) = √100 * √2 = 10 * √2 = 10√2
√80 = √(16*5) = √16 * √5 = 4 * √5 = 4√5
√24 = √(4*6) = √4 * √6 = 2 * √6 = 2√6
Thus, match the square root expression with it's correct simplified radical accordingly.
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suppose is an matrix that can be obtained from using the row operations (in the given order) what is ?
we add row 1 to row 3 to get the final matrix = [3, 0, 3; 1, 1, 1; 0, 0, 0]. Thus, the new matrix is obtained by applying the given row operations in the given order.
Let A be a given matrix.
Row Operation 1: Exchange row 1 and row 2.
Row Operation 2: Multiply row 1 by 3.
Row Operation 3: Add row 1 to row 3.
Then,
= [ 3, 0, 3; 1, 1, 1; 0, 0, 0 ]
We can obtain the matrix by applying the row operations in the given order. First, we exchange row 1 and row 2 to obtain the matrix [1, 1, 1; 3, 0, 3; 0, 0, 0]. Then we multiply row 1 by 3 to get [3, 0, 3; 1, 1, 1; 0, 0, 0]. Finally, we add row 1 to row 3 to get the final matrix = [3, 0, 3; 1, 1, 1; 0, 0, 0]. Thus, the new matrix is obtained by applying the given row operations in the given order.
The complete question is :
Suppose [tex]$\begin{bmatrix}4 & -2 & 3 \\2 & 3 & 1 \\5 & 1 & -2\end{bmatrix}$[/tex] is an matrix that can be obtained from [tex]$\begin{bmatrix}1 & 2 & 3 \\3 & 2 & 1 \\2 & 5 & -2\end{bmatrix}$[/tex]using the row operations (in the given order) [tex]$R_1 \leftrightarrow R_2, R_2 - 3R_1, R_3 - 5R_1$[/tex]
What is [tex]$\begin{bmatrix}1 & 2 & 3 \\3 & 2 & 1 \\2 & 5 & -2\end{bmatrix}$[/tex]?
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the population of all standardized exam scores has a mean of 500 and a standard deviation of 100. twenty-five students in a professor's class take the exam, and their average score is 525. what is the z statistic that is associated with the class's average?
The z statistic that is associated with the class's average is 1.25.
In the given question the population of all standardized ex scores has a mean of 500 and a standard deviation of 100 . Twenty-five students in a professor's class take the ex , and their average score is 525.
We have to find z statistic that is associated with the class's average.
n = 25
μ = 500
σ = 100
[tex]\bar X[/tex] = 525
Then ,
z statistic = [tex]\frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt n} }[/tex]
putting the value in the formula:
z statistic = (525-500)/(100/\sqrt 25)
z statistic = (25)/(100/5)
z statistic = (25)/(20)
z statistic = 1.25
Therefore,
The z statistic that is associated with the class's average is 1.25.
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Mr. Ford wants to better understand the value of used cars over time. He reviewed some
used-car ads and recorded the relationship between age and price in a table. Finally, he
calculated a line of best fit.
Used cars
Age in years (x) 3 6 4
2
6
Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000
The equation for the line of best fit is y = -2,200x + 22,000.
Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?
Select all that apply.
They are worth roughly $2,200 less now than when they were new:
They likely had an average price around $22,000 when new.
They typically lose $2,200 of value per year.
At 5 years old, they had an average value of around $11,000.
You can estimate that the used cars Mr. Ford reviewed were worth roughly $2,200 less now than when they were new, had an average price of around $22,000 when new, and typically lose $2,200 of value per year. (option 1, 2, 3)
To calculate this, you can substitute the x-values from the table into the equation and solve for y. For example, when x is 3,
y = -2,200(3) + 22,000 = $15,000which is the price of the car when it was 3 years old. This same formula can be used to calculate the price of the car at other age values and shows that the car loses an average of $2,200 of value per year. At 5 years old, the equation would be
y = -2,200(5) + 22,000 = $11,000which is the average value of the used car at that age.
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Complete Question:
Mr. Ford wants to better understand the value of used cars over time. He reviewed some used-car ads and recorded the relationship between age and price in a table. Finally, he calculated a line of best fit. Used cars Age in years (x) 3 6 4 2 6
Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000
The equation for the line of best fit is y = -2,200x + 22,000.
Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?
Select all that apply.
They are worth roughly $2,200 less now than when they were new:They likely had an average price of around $22,000 when new.They typically lose $2,200 of value per year.At 5 years old, they had an average value of around $11,000.Find the equation of the line shown
Answer:
using the equation of the straight line we solve
Can someone please help me with this question. If you do, you’ll be rewarded with brainliest and extra points!
Answer:
EG/HJ=GF/JI or EG/HJ=FE/IH
Step-by-step explanation:
Given
AngleF=AngleI
AngleE=AngleH
Therefore triangles EGF AND HJI are similar by Angle-Angle Similarity Theorem
So
EG/HJ=GF/JI=FE/IH as they are the corresponding sides of a similar triangle
Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.
How many grams of 25% sugar syrup did Samantha use?
Pls help :D Thxs
Samantha used 120 grams of 25% sugar syrup.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.
Let Samantha used y grams of 25% sugar syrup.
Then, she used (120 - y) grams of 10% sugar syrup.
We know that the final concentration of sugar syrup is 15%, which means that 15% of the total 120 grams of the syrup is sugar.
This can be expressed as:
0.15 x (y + (120 - y)) = 0.15 x 120
Expanding and simplifying the equation, we get:
0.15y + 0.15 x 120 - 0.15y = 18
0.15 x 120 = 18
Solving for y, we get:
y = 120 x 18 / (0.15 x 120)
= 120 x 18 / 18
= 120.
Hence, Samantha used 120 grams of 25% sugar syrup.
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Answer:
work hard you can get it
Step-by-step explanation:
lol
Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of D′ if the preimage is rotated 90° counterclockwise.
D′(−2, −4)
D′(−2, 4)
D′(2, 4)
D′(4, −2)
The image vertices of D′ if the preimage is rotated 90° counterclockwise is: A. D′(−2, −4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices for D, the coordinates of the vertices of the image point D' are as follows:
(x, y) → (-y, x)
Ordered pair D = (-4, 2) → Ordered pair D' = (-2, -4)
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the sum of a five-term arithmetic sequence is 100. if all terms are positive integers, what is the smallest possible value for a term?
The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".
The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:
a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100
Simplifying the expression, we get:
5a + 10d = 100
Dividing both sides by 5, we get:
a + 2d = 20
Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:
1 + 2 * 1 = 3
Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.
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TRIG STUFF EASY WILL GIVE BRAINLIEST IF ALL ARE CORRECT
Answer:
x = 46.2 (nearest tenth)KN = 34.5 (nearest tenth)KL = 41.1 (nearest tenth)x = 15.7 (nearest tenth)Step-by-step explanation:
To find the missing side lengths in the given right triangles, use trigonometric ratios.
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.
θ = 18°O = 15A = xTherefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:
[tex]\implies \tan 18^{\circ}=\dfrac{15}{x}[/tex]
[tex]\implies x\tan 18^{\circ}=15[/tex]
[tex]\implies x=\dfrac{15}{\tan 18^{\circ}}[/tex]
[tex]\implies x=46.165253...[/tex]
[tex]\implies x=46.2\;\;\sf(nearest\;tenth)[/tex]
----------------------------------------------------------------------------------------
Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.
Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.
As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.
As KL is parallel to NM, then m∠K = 90°. Therefore, m∠KLN = 40°.
(Refer to the attached diagram).
For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:
[tex]\implies \tan 50^{\circ}=\dfrac{LN}{45}[/tex]
[tex]\implies LN=45\tan 50^{\circ}[/tex]
LN is the hypotenuse of right triangle KLN.
If we use ∠KNL as θ, then side KN is adjacent to the angle.
Therefore, to find the KN use the cosine ratio:
[tex]\implies \cos 50^{\circ}=\dfrac{KN}{LN}[/tex]
[tex]\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}[/tex]
[tex]\implies KN=45\tan 50^{\circ}\cos 50^{\circ}[/tex]
[tex]\implies KN=34.471999...[/tex]
[tex]\implies KN=34.5\;\; \sf (nearest\;tenth)[/tex]
As KL is the side opposite ∠KNL, to find KL use the sine ratio:
[tex]\implies \sin 50^{\circ}=\dfrac{KL}{LN}[/tex]
[tex]\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}[/tex]
[tex]\implies KL=45\tan 50^{\circ}\sin50^{\circ}[/tex]
[tex]\implies KL=41.0821297...[/tex]
[tex]\implies KL=41.1\;\;\sf (nearest\;tenth)[/tex]
----------------------------------------------------------------------------------------
From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.
θ = 70°A = xH = 46Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:
[tex]\implies \cos 70^{\circ}=\dfrac{x}{46}[/tex]
[tex]\implies x=46\cos 70^{\circ}[/tex]
[tex]\implies x=15.732926...[/tex]
[tex]\implies x=15.7\;\;\sf(nearest\;tenth)[/tex]
An online clothing company sells custom sweatshirts. The company charges $6.50 for each sweatshirt and a flat fee of $3.99 for shipping. describe how the linear function would change if the shipping charge applied to each sweatshirt.
The description is that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges
How to describe how the linear function would changeFrom the question, we have the following parameters that can be used in our computation:
The company charges $6.50 for each sweatshirt Flat fee of $3.99 for shippingUsing the above as a guide, we have the following:
Slope = 6.50
This means that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges
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32c as a percentage of R3. 80
Answer:
40%
Step-by-step explanation:
32 out of 80 as a percentage it is 40%
Maeve currently has $130 and plans to earn more money each of the 8 weekends this summer. She wants at least $1,250 by the end of the summer. How much does she need to earn each weekend? Assume she earns the same amount each weekend. Solve her problem, and then graph the solution on a number line.
Answer: $140 each weekend
Step-by-step explanation:
$1250 - $130 = $1,120
$1,120 divided by 8 weekends = $140
write a recursive rule for the sequence: 100,3,97,-94,191
The recursive rule for the sequence is T(n) = T(n - 2) - T(n - 1)
How to determine the recursive rule for the sequence?From the question, we have the following parameters that can be used in our computation:
100, 3 , 97 ,-94 , 191
The above definitions imply that we simply subtract the current from the previous term to get the next term
Using the above as a guide,
So, we have the following representation
T(n) = T(n - 2) - T(n - 1)
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[tex]\sqrt[4]{\frac{-15}{16} }[/tex]
Need help doing this please. I think it might be simple, just kinda unsure how to do it.
The solution to the expression ⁴√(-15/16) is (-15/16)^1/4
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
⁴√(-15/16)
The above expression means that we calculate the 4th root of -15/16
-15 and 16 do not have perfect fourth roots
This means that the expression can only be rewritten as
(-15/16)^1/4
It cannot be evaluated
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.Which is not a method by which minerals form
The option that is not a way by which minerals are being formed is decrystallization. That is option B
What are ways by which minerals are formed?Minerals are organic substances that are form through the following ways;
volcanic gases, sediment formation, oxidation, crystallization from magma, or deposition from a saline fluid,Decrystallization is not a way through which minerals are formed because it is just the break down of solid or crystal structures.
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Complete question:
Which of the following is not a method by which minerals form?. a. crystallization. b. decrystallization. c. water evaporation from a solution. d. cooling of magma or lava
if x,y,z are different and =mod x x^2 1+x^3
y y^2 1+y^3 = 0 then show than 1+xyz=0
z z^2 1+z^3
Given that x, y, z are different and satisfy the equations:
x^3 + x^2 - x = 0
y^3 + y^2 - y = 0
z^3 + z^2 - z = 0
We can multiply the first equation by y, the second by z, and the third by x to obtain:
x^3y + x^2y - xy = 0
y^3z + y^2z - yz = 0
z^3x + z^2x - zx = 0
Adding these three equations together, we get:
x^3y + x^2y - xy + y^3z + y^2z - yz + z^3x + z^2x - zx = 0
Expanding and simplifying, we find that:
x^2y + xy^2 + y^2z + yz^2 + z^2x + zx^2 - xy - yz - zx = 0
Now, we use the fact that x, y, and z are roots of the equations given above to simplify the expression further:
x^2 - x + y^2 - y + z^2 - z = 0
We can also write this as:
(x - 1)(x + 1) + (y - 1)(y + 1) + (z - 1)(z + 1) = 0
This expression can be factorized as:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
Since x, y, and z are all different, we have that:
(x - 1)(x + 1) ≠ 0
(y - 1)(y + 1) ≠ 0
(z - 1)(z + 1) ≠ 0
Therefore, we have:
(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = (x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0
So, we can conclude that:
xyz = -1
And,
1 + xyz = 0
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Look at the digram.
If AB BC and AB = 18 inches, AE = 5 inches, and CE = 6 inches, what is the length of AD?
A. 1.5 inches
B. 2.5 inches
C. 6.5 inches
D. 7.5 inches
Length of AD is, 2.5 inches
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Values are,
AB = 18 inches,
AE = 5 inches,
CE = 6 inches,
Let the length of ED = x
Now, By the figure,
⇒ ΔABD ≈ ΔECD
Hence, By definition of proportional we get;
⇒ AB / AD = EC / ED
⇒ AB / (AE + ED) = EC / ED
⇒ 18 / (5 + x) = 6 / x
⇒ 3x = 5 + x
⇒ 3x - x =5
⇒ 2x = 5
⇒ x = 2.5 inches
Thus, Length of AD is, 2.5 inches
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A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of 3% per year. The original population was 48,000. The student made an error when writing their exponential function. Find and explain the error in the student’s work below.
y=48,000(1.03)^x
The error made by the student in the exponential function, y = 48,000(1.03)^x is that the function represented an exponential growth rather than an exponential decay.
What is an exponential function?An exponential function is written in the form y = abˣ.
In the exponential function, the exponent, x is a variable.
Annual decreasing rate of the fish population = 3% or 0.03
Original population = 48,000
Let the number of years = x
Exponential function: 48,000 (1 - 0.03)^x
= 48,000(0.97)^x
Thus, to represent an exponential decay, the exponential function should have been written as y = 48,000(0.97)^x.
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PLEASE PLEASE HELP!!!
Solve √3x + 4 - 2 = 3
a. x = -1
b. x = 7
c. x ≈ 9.7
d. no solution
If the graph of f(x) = 9* is shifted 2 units to the right, then what would be the equation of the new graph?
The equation of the new graph is f(x) = 9^(x - 2)
What would be the equation of the new graph?From the question, we have the following parameters that can be used in our computation:
f(x) = 9^x
Also, we have
shifted 2 units to the right,
This is represented as
(x, y) = (x - 2, y)
Substitute the known values in the above equation, so, we have the following representation
f(x) = 9^(x - 2)
Hence, the function is f(x) = 9^(x - 2)
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Given: KLMN is a trapezoid, KL=MN,
m∠1=m∠2,
LM:KN = 8/9, PKLMN=132
Find The length of midsegment
KLMN is a trapezoid where KL=MN and m∠1=m∠2 . It is also given that LM:KN = 8/9 and PKLMN=132.The midsegment is 34 units long.
The trapezoidal shape KLMN, where KL = MN.
m∠1=m∠2
Moreover, LM/KN = 8/9
Additionally, KLMN's perimeter is 132 units.
The midsegment's size (KM).
We can see that in the above case, KM is a transversal in relation to the parallel lines LM and KN. which implies,
∠KML=∠MKN
∠1=∠2
Two base angles are clearly equal. So, KLM and KMN are isosceles triangles.
Using the side ratios of two triangles as an example,
= KL: LM: MN: KN
= 8 : 8 : 8 : 9
The ratio units add out to 8 + 8 + 8 + 9 = 33. Consequently, each ratio's value is,
=[tex]\frac{perimeter}{33} \\\\\frac{132}{33} \\\\=4[/tex]
The segment LM's length is thus,
LM=8×4=32
Additionally, section KN's length is
KN=9×4=36
Taking the average of LM and KN as, one can then determine the length of the midsegment KM.
[tex]KM=\frac{LM+KN}{2} \\\\\\KM=\frac{32+36}{2}[/tex]
KE=34
As a result, the midsegment is 34 units long.
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The bottom of a circular swimming pool with a radius of 30ft, was painted blue. How many square feet of the pool was painted blue?
Answer:
2826 sqft
Step-by-step explanation:
π r² = 900π =2826
At a university, the student body is made up of approximately 12000 students. Of that total, there are approximately 3500 graduate students and 8500 undergraduate students. Which of the following fractions represents the ratio of undergraduate students to graduate students?
Step-by-step explanation:
Seeing the question, I assume there are answer choices, but I'll give all possible answers below.
A ratio is pretty much a fraction, that's about it. It's asking the ratio of undergraduate to graduate, which creates
[tex] \frac{undergraduate}{graduate} [/tex]
Now we plug in those numbers in the correct spots
[tex] \frac{8500}{3500} [/tex]
Now to simplify. Since both of these numbers end in 0, there a little truck you can do to automatically make it smaller, and that's getting rid of all the 0s on the end. That makes it...
[tex] \frac{85}{35} [/tex]
To continue simplifying
[tex] \frac{8500}{3500} = \frac{85}{35} = \frac{17}{7} [/tex]
The parking lot at the local ice cream store has 4 cylindrical posts in front of the store. These post need to be painted bright yellow. The diameter of each post is 1 foot and each post is 3 feet high.
Use 3. 14 for pi.
Approximately how many square feet must be painted if all 4 posts are painted?
If all 4 posts are painted, 44 square feet must be painted.
We know that the formula for the surface area of the cylinder is:
A = 2πrh + 2πr²
Here, the dimensions of the each cylindrical post:
the diameter d = 1 foot and the height is 3 feet high.
So, the radius r = 0.5 ft and height h = 3 ft
Let us assume that the surface area of one post be A₁
Using above formula of surface area of cylinder,
A₁ = 2πr(h + r)
A₁ = 2 × π × 0.5 × (3 + 0.5)
A₁ = 2 × 3.14 × 0.5 × (3.5)
A₁ = 10.99
A₁ ≈ 11 sq.ft.
So, the total surface area of 4 cylindrical posts would be,
A = 4 × A₁
A = 4 × 11
A = 44 sq.ft.
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Every year, 4% of people drop out of their course at
SmartyPants University. 3,168 people made it to the end of this
year. How many people started this year?
a right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. what is the surface area in square centimeters if the height is 2 centimeters?
The surface area of the right triangular prism with legs of 5 centimeters and 12 centimeters, a hypotenuse of 13 centimeters, and a height of 2 centimeters is 108 square centimeters.
Surface area refers to the total area of the surface of a three-dimensional object. When it comes to a right triangular prism, the surface area includes the area of all six faces.
Let's call the height of the triangular prism "h" and label the legs of the triangle "a" and "b". Using these values, we can find the area of the base of the triangular prism. The area of a right triangle is equal to 1/2 times the product of the legs, so the area of the base is
=> (1/2) * a * b = (1/2) * 5 * 12 = 30 square centimeters.
Next, we need to find the surface area of each of the three lateral faces. Each of these faces is a rectangle, so we can find the area by multiplying the height of the prism by the length of one of the sides of the triangle base.
The length of one side of the triangle base is equal to the hypotenuse, which is 13 centimeters. So, the surface area of each of the three lateral faces is
=> h * 13 = 2 * 13 = 26 square centimeters.
Finally, we can find the total surface area by adding the surface area of the base and the surface area of the three lateral faces.
The surface area of the base is 30 square centimeters, and the surface area of each lateral face is 26 square centimeters, so the total surface area is
=> 30 + 3 * 26 = 30 + 78 = 108 square centimeters.
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Write an exponential decay function to model each situation. Then estimate the value of x for the given value of f(x)
initial value: 100
decay factor: .95
f(x)=60
Answer:
f(x) = 100(0.95^x)x ≈ 9.959 for f(x) = 60Step-by-step explanation:
You want the value of x that makes f(x) = 60, when f(x) is the exponential function with an initial value of 100 and a decay factor of 0.95.
Exponential functionThe form of an exponential function is ...
f(x) = (initial value) · (decay factor)^x
ApplicationFor the given initial value and decay factor, the function is ...
f(x) = 100 (0.95^x)
Solving for x, we find ...
f(x)/100 = 0.95^x
log(f(x)/100) = x·log(0.95)
x = log(f(x)/100)/log(0.95)
For f(x) = 60, the value of x is about ...
x = log(60/100)/log(0.95) ≈ 9.959
The value of x is about 9.959.